Practical Exercises

Exercise 2.1 A person is required to pay four equal annual payments of ` 4,000 each in his Deposit account that pays
10 per cent interest per year. Find out the future value of annuity at the end of 4 years.

Exercise 2.2 A company offers a Fixed deposit scheme whereby ` 10,000 matures to ` 12,625 after 2 years, on half-
yearly compounding basis. If the company wishes to amend the scheme by compounding interest every quarter,

what will be the revised maturity value?

Exercise 2.3 Ascertain the compound value and compound interest of an amount of ` 75,000 at 8 percent

compounded semi-annually for 5 years.

Exercise 2.4 Based on the credit rating of the bonds, Rakshit has decided to apply the following discount rates for

valuing bonds:

N
Credit Rating Discount Rate

N
AAA 364-day T-bill rate + 3% spread

AA AAA + 2% spread

A
A AAA + 3% spread

He is considering to invest in a AA rated, ` 1,000 face value bond currently selling at ` 1,025.86. The bond has five

M
years to maturity and the coupon rate on the bond is 15% per annum payable annually. The next interest payment

is due one year from today and the bond is redeemable at par. (Assume the 364-day T-bill rate to be 9%.)

X
You are required to: (i)Calculate the intrinsic value of the bond for Rakshit. Should he invest in the bond ?

A
(ii) Calculate the current yield (CY) and the yield to maturity (YTM) of the bond.

T
Exercise 2.5 The following data are available for a bond:

Face value ` 1,000 Redemption value ` 1,000

Coupon rate 16% Yield to maturity 17%

Years to Maturity 6

What is the current market price, duration and volatility of this bond ? Calculate the expected market price, if increase

in required yield by 75 basis points.

 Key to Practical Exercises

Exercise 2.1

[ ]
n
(1 + i) - 1
A = P
i

Where, A = Annual or future value which is the sum of the compound amounts of all payments

P = Amount of each instalment

i = Interest rate per period

n = Number of periods

[ ]
n
(1 + 0.10) - 1
A = 4,000 = 4,000 × 4.641 = ` 18,564
0.10

N
Therefore, the future value of annuity at the end of 4th year is ` 18,564.

N
Exercise 2.2

A
Computation of Rate of Interest and Revised Maturity Value

Principal = ` 10,000 Amount = ` 12,625

M
12,625
10,000 =
4
(1 + i)

X
P = A × (PVF )
n n, i

A
10,000 = 12,625 (PVF )
4, i

T
0.7921 = (PVF )
4, i

According to the Table on Present Value Factor (PVF

4 ,i
) of a lump sum of ` 1, a PVF of 0.7921 for half year at interest
(i) = 6 per cent. Therefore, the annual interest rate is 2 × 0.06 = 12 percent.

i = 6% for half year i = 12% for full year.

Therefore, rate of interest is 12% per annum.

( ) ( )
12 1 2 x 4 3 8
8
Revised maturity value = 10,000 1 + × = 10,000 1 + = 10,000 (1.03)
100 4 100

= 10,000 × 1.267 [considering (CVF ) = 1.267]

8, 3

Revised maturity value = 12,670

Exercise 2.3

Semi-annual rate of interest (i) = 8/2 = 4% n = 5 × 2 = 10 P = ` 75,000

n 10
Compound value = P(1 + i) = 75,000 (1 + 0.04) = 75,000 × 1.4802 = ` 1,11,015
Compound interest = ` 1,11,015 - ` 75,000 = ` 36,015

Exercise 2.4

AA rated face value of bond = ` 1,000 Maturity period of bond = 5 years

Current selling price = ` 1,025.86 Coupon rate on bond = 15% p.a. payable annually

Bond redeemable at par at the end of 5th year.

Net interest payment is due one year from today.

Discount rate for AA rated bond = 9% + 3% + 2% = 14%

Calculation of present values of cash inflow from bond ( ) `

Year end Cash inflow P.V. factor Present

@ 14% values

1 150 0.8772 131.58

2 150 0.7695 115.43

3 150 0.6750 101.25

4 150 0.5921 88.82

5 1,150 0.5194 597.31

Present value of total cash inflows 1,034.40

Therefore, the intrinsic value of bond is ` 1,034.40. Since the intrinsic value of bond ( ` 1,034.40) is more than its

current market value ( ` 1,025.86), it is suggested to purchase the bond.

Calculation of current yield and the yield to maturity (YTM) of the bond

$PVQPO 

N
Current yield = ×  = ×  = 14.62%
.BSLFU QSJDF  

N
Yield to Maturity (YTM)

` `

A
P = 150 × PVIFA @ 15%, for 4 years + 1,150 × PVIF at 15%, for 5 years

= (150 × 2.855) + (1,150 × 0.4972) = 428.25 + 571.78 = ` 1,000.03

` `

M
Present values found at 14% is 1,034.40 Present values found at 15% is 1,000.03

By interpolation

X
   
YTM =  + × = 14.26%

A
   

T
Exercise 2.5

(a) Calculation of Current Market Price of Bond

Discount or premium
Coupon rate +
Years outstanding
YTM =
Face value + Market value

Since, YTM (17%) is more than coupon rate (16%), the market price is expected to be less than the face value.

Let ‘x ’ be the market price

1,000 - x
160 +
6
0.17 =
1,000 + x

∴x = ` 960.26

Alternatively:

Coupon interest amount p.a. ` 160 for 6 years at a discount rate of 17%.

P.V. of interest receivable = ` 160 × 3.589 = ` 574.24

P.V. of maturity value of bond at the end of 6th year at a discount rate of 17%

= ` 1,000 × 0.390 = ` 390

Total present value (current market price) = ` 574.24 + ` 390.00 = ` 964.24

(b) Calculation of Duration of the Bond

Year Cash P.V. Present Proportion Proportion of

outflow factor value of bond value bond value

`
( ) @ 17% `
( ) × Time

1 160 0.855 136.80 0.142 0.142

2 160 0.731 116.96 0.122 0.244

3 160 0.624 99.84 0.104 0.312

4 160 0.534 85.44 0.089 0.356

5 160 0.456 72.96 0.076 0.380

6 1160 0.390 452.40 0.467 2.802

964.40 1.000 4.236

Duration of the Bond is 4.236 years.

Duration 4.236
(c) Calculation of Volatility of the Bond = = = 3.62
1 + YTM 1 + 0.17

N
(d) Calculation of Expected Market price of Bond, if increase in required yield is by 75 basis points.

N
Expected decrease in market price = ` 960.26 × 0.75 (3.62/100) = ` 26.071

Expected market price = ` 960.26 - ` 26.071 = ` 934.189

A
Alternatively:

= 964.4 × 0.75 (3.62/100) = ` 26.18

M
= ` 964.40 - ` 26.18 = ` 938.22

A X
T
 Key To Short Answer Questions

True or False Statements

1. True - The time value of money is based on the concept that there is an opportunity cost for forgoing or

sacrificing the present consumption and therefore return is payable to the all forms of investors in the

form of dividends, interest, capital appreciation etc.

2. False - Floating rate loans are raised, instead of a predetermined rate at which interest is paid, the rate of

interest will vary periodically, based on a benchmark rate. The floating rate of interest will also raise

as if there is an increase in the market rates, and falls as market rate of interest falls.

3. False - The value of the bond is the present value of the expected returns from the bond during the holding

period. If the investor’s required rate of return is greater than the annual interest on the bond, the value

of the bond is lesser than its par value.

True

N
4. - A government bond will have low risk rate and will have consistent cash flows till maturity. Therefore,

a lower discount rate will be applied to the cash flows of the government bond.

N
5. False - The risk is more in holding securities for a longer period than short period. In the long-term securities

the funds of the investors are tied up for long periods and for this the investors naturally expect for

A
higher return than the short-term securities. Therefore, whenever the required rate of return is

different from the coupon interest rate, the amount of time to maturity will affect the bond value.

M
6. True - The time value of money is an important factor to be considered in investment decisions. The value

X
of money received today is higher from the value of money received after some time in future.

7. False - The rate of interest quoted in securities are known as ‘nominal or money rate of interest’. The ‘real

A
rate of interest’ represents the rate of interest that would be required in the absence of inflation.

T
8. True - Traditionally interest is regarded as return on capital invested. Capital being a factor of production

is rewarded by way of interest. Interest rates are the measure of cost of borrowing.

9. True - Rising inflation takes away the intrinsic value of currency. To adjust or compensate for that, the

interest rates also increase.

10. True - The higher the default risk, higher will be rate of interest. The rate of interest on government securities

is lesser than rate of interest on bonds issued by the corporate, since government security is risk-free.

11. False - Not all interest payments are fixed at the time of issue at a predetermined percentage. Instead they are

pegged to a benchmark. The interest payable on such securities is floating and reset at predetermined

intervals according to the agreed benchmark, which with fluctuations.

12. True - When the interest rates fall substantially, the demand for shares increases, their prices rise too, and

so the dividend return gained from the fall in interest rates. If interest rates wentup, the shareholder

would probably want a higher return from his shares and share prices would fall.

13. True - The British Bankers Association publishes LIBOR everyday. LIBOR is based on interest rates at which

banks offer to lend unsecured funds to other banks in London wholesale inter money market.

14. False - Business firms generally prefer long-term debt because short-term debt subjects the firm to greater

dangers of having to refund debt under adverse conditions. Accordingly firms are willing to pay a

higher rate for long-term funds than for short-term funds.

15. False - The YTM is downward sloping in the long-term securities, since the funds of the investors are tied up

for long periods and for this the investors naturally expects for higher return than the short-term

securities.
16. True - The actual return on dated stocks must include the rate of interest and any capital gain which results

from differences between their cost and redemption price.

17. True - The discounting technique converts cash inflows and outflows for different years into their respective

values at the same point of time, allows for the time value of money.

18. False - The value of a bond is the present value of expected returns from the bond during the holding period.

It is necessary to discount the stream of expected returns at the expected rate of return to determine

the value of the bond.

19. False - When the market interest rate rises beyond the coupon of the bond, the price of the bond will have

to be lowered so that the income from the bond is in line with market rates.

20. True - A warrant is a long-term security usually, attached to a bond or preferred stock, that gives the holder

the right to buy a fixed number of a company’s common shares.

Choose Correct Word

1. falling

2. less

N
3. prime lending

4. less

N
5. higher

A
6. easier

7. fixed

M
8. bond

9. disappear

X
10. equity shares

A
11. warrant

12. conversion value

T
13. premium

14. conversion price

Choose Correct Answer

1. (B) wealth

2. (C) time value of money

3. (A) simple

4. (A) market

5. (B) real

6. (D) below

7. (C) term structure

8. (B) yield to maturity

9. (A) higher

10. (D) downward

11. (C) discounting

12. (D) discounting factors

13. (C) amortization

14. (A) sinking

15. (B) lower

16. (A) ` 26,295

17. (A) more than 9.50%

18. (A) increase

19. (A) call

20. (B) Effective duration

21. (C) ` 4,525

22. (D) all of the above

23. (A) increase

24. (C) stagflation

25. (B) default risk

26. (A) inflation

27. (C) London Inter Bank Offer Rate

28. (D) NSE

29. (D) all of the above

30. (C) at premium

N
31. (A) its current yield is more than its yield-to-maturity

32. (A) London Inter Bank Offer Rate

N
33. (C) the possibility to increase profits

A
34. (C) If market price > face value, their Coupon Rate > Current Yield > YTM

X M
T A
 Practical Exercises

Exercise 3-1 Following information is available in respect of the return from Reliance’s stock under different

economic conditions:

Economic condition (%) Return Probability

Good 20 0.2

Average 16 0.4

Bad 10 0.2

Poor 4 0.2

Find out the expected return of the stock and risk associated with it.

Exercise 3-2 A portfolio consists of three securities P, Q and R with the following parameters:

N
Security Correlation

coefficient
P Q R

N
Expected return (%) 25 22 20

A
Standard deviation (%) 30 26 24

Correlation coefficient:

M
PQ - 0.5

QR + 0.4

X
PR + 0.6

A
If the securities are equally weighted, how much is the risk and return of the portfolio of these three securities?

T
Exercise 3-3 Stocks A and B have the following historical returns:

Year Stock A’s return (K )

A Stock B’s return (K )
B
(%) (%)

2012 -12.24 -5.00

2013 23.67 19.55

2014 35.45 44.09

2015 5.82 1.20

2016 28.30 21.16

You are required to calculate the average rate of return for each stock during the period 2012 through 2016. Assume

that someone held a portfolio consisting 50% of stock A and 50% of stock B.

What would have been the realised rate of return on the portfolio in each year from 2012 through 2016?

What would have been the average return on the portfolio during the period?

(You may assume that the year ended on 31st March).

Exercise 3-4 Ritesh holds a well diversified portfolio of stock in XYZ Group. During the last 5 years, returns on these

stock have averaged 20% per year and had a standard deviation of 15%. He is satisfied with the yearly availability

of his portfolio and likes to reduce its risk without affecting overall returns. He approaches you for help in finding

an appropriate diversification medium.

After a lengthy review of alternatives, you conclude - (i) future average returns and volatility of returns on his current

portfolio will be the same as he has historically expected; and (ii) to provide a quarter degree of diversification in his

portfolio, investment could be made in stocks of the following groups:

Groups Expected Co-relation of returns Standard

returns with XYZ Group deviation

Rekha Ltd. 20% + 1.0 15%

Tina Ltd. 20% - 1.0 15%

Bipasha Ltd. 20% + 0.0 15%

(i) If Ritesh invests 50% of his funds in Rekha Ltd. and leaves the remainder in XYZ Group, would this affect both

his expected returns and his risk? Why?

(ii) If Ritesh invests 50% of his funds in Tina Ltd. and leaves the remainder in XYZ Group, how would this affect

both his expected return and his risk? Why?

(iii) What should Ritesh do? Indicate precise portfolio weightage.

Exercise 3-5 You are considering investment in one or both of two securities, X and Y and you are given the

following information:

Security X

N
Possible rates of return (%) 30 25 20

Possibility of occurrence 0.3 0.4 0.3

N
Security Y

Possible rates of return (%) 50 30 10

A
Possibility of occurrence 0.2 0.6 0.2

M
You are required to:

(i) Calculate the expected return for each security separately and for a portfolio comprising 60% X and 40% Y,

X
assuming positive correlation between the possible rates of return from the shares comprising the portfolio.

(ii) Calculate the expected risk of each security separately and of the portfolio as defined above. You may use

A
standard deviation as the measure of risk.

T
Exercise 3-6 Following is the data regarding six securities:

Securities U V W X Y Z

Return (%) 10 10 15 5 11 10

Risk (%) (standard deviation) 5 6 13 5 6 7

(i) Which of three securities will be selected ?

(ii) Assuming perfect correlation, analyse whether it is preferable to invest 80% in security U and 20% in security

W or to invest 100% in Y.

Exercise 3-7 Following information is available in respect of dividend, market price and market condition after one

year.

Market condition Probability Market price Dividend per share

`
( ) `
( )

Good 0.25 115 9

Normal 0.50 107 5

Bad 0.25 97 3

The existing market price of an equity share is ` 106 (F.V. ` 1), which is cum 10% bonus debenture of ` 6 each, per
share. M/s. X Finance Company Ltd,. has offered the buy-back of debentures at face value.

Find out the expected return and variability of returns of the equity shares.

And also advise whether to accept buyback offer ?

Exercise 3-8 The historical rates of return of two securities over the past ten years are given. Calculate the

Covariance and the Correlation coefficient of the two securities: (Return per cent)

Years 1 2 3 4 5 6 7 8 9 10

Security 1 12 8 7 14 16 15 18 20 16 22

Security 2 20 22 24 18 15 20 24 25 22 20

Exercise 3-9 Consider the following information on two stocks, A and B:

Year Return on A (%) Return on B (%)

2015 10 12

2016 16 18

You are required to determine:

(i) The expected return on a portfolio containing A and B in the proportion of 40% and 60% respectively.

(ii) The standard deviation of return from each of the two stocks.

N
(iii) The covariance of returns from the two stocks.

(iv) Correlation coefficient between the returns of the two stocks.

N
(v) The risk of a portfolio containing A and B in the proportion of 40% and 60%.

M A
A X
T
 Key to Practical Exercises

Exercise 3-1

2
Economic Return Probability Return × P (Return - Average)

condition (%) Probability

2
Good 20 0.2 0.040 0.2 × (0.20 - 0.132) = 0.00092

2
Average 16 0.4 0.064 0.4 × (0.16 - 0.132) = 0.00031

2
Bad 10 0.2 0.020 0.2 × (0.10 - 0.132) = 0.00020

2
Poor 4 0.2 0.008 0.2 × (0.04 - 0.132) = 0.00169

Total 1.0 0.132 0.00312

(i) Expected return = 13.2%

N
(ii) Risk associated with stock =  = 0.05586 × 100 = 5.586%

N
Exercise 3-2

A
Expected Portfolio Return = (25 × 1/3) + (22 × 1/3) + (20 × 1/3) = 22.33%

Portfolio Risk ( σ 2
) =
2
(30) (1/3)
2 2
+ (26) (1/3)
2 2
+ (24) (1/3)
2
+ 2(1/3) (1/3) (- 0.5) (30) (26)

M
P

+ 2(1/3) (1/3) (0.4) (26) (24) + 2 (1/3) (1/3) (0.6) (30) (24)

X
= 100 + 75.11 + 64 - 86.67 + 55.47 + 96 = 303.91

A
=  = 17.43%
P

T
Exercise 3-3

Calculation of Average Rate of Return on Portfolio during 2012-2016

Year Stock A’s Stock B’s

return (%) return (%)

2012 -12.24 -5.00

2013 23.67 19.55

2014 35.45 44.09

2015 5.82 1.20

2016 28.30 21.16

81.00 81.00

Average Rate of Return 81/5 years 81/5 years

= 16.20% = 16.20%

Calculation of Realised Rate of Return on Portfolio during 2012-2016 `

( )

Stock A Stock B Total

Net return
Year Proportion Return Net Proportion Return Net

Return Return

2012 0.50 -12.24 -6.12 0.50 -5.00 -2.50 -8.62

2013 0.50 23.67 11.83 0.50 19.55 9.77 21.60

2014 0.50 35.45 17.72 0.50 44.09 22.04 39.76

 `
( )

Stock A Stock B Total

Net return
Year Proportion Return Net Proportion Return Net

Return Return

2015 0.50 5.82 2.91 0.50 1.20 0.60 3.51

2016 0.50 28.30 14.15 0.50 21.16 10.58 24.73

81.00 40.49 81.00 40.49 80.98

Average Rate of Return = ` 80.98/5 = 16.20%

Exercise 3-4

As the expected return of existing portfolio as well as new securities are same, there will not be any change in the

return level. However, the portfolio risk , σ p

would be as follows:

σ p
= 8 Y σ Y + 8 Z σ Z +  8 Y 8 Z σ Y σ Z σ YZ

σ = √ (0.5)
2
(15)
2
+ (0.5)
2
(15)
2
+ 2 ( 0.5) (0.5) (15) (15) (1)

N
XR

=  +  +  =  = 15

Portfolio of XYZ and Tina

σ XT
= √ (0.5)
2
(15)
2
+ (0.5)
2
(15)
2
+ 2 ( 0.5) (0.5) (15) (15) (-1)

A N
M
=  +   = 

X
(i) Risk and return of XYZ portfolio are the same as those of Rekha portfolio and the correlation coefficient is 1.0.

A
So, there is no diversification gain.

T
(ii) Return would remain at 20% but risk would fall to zero since r = - 1.0

(iii) Invest 50/50 in XYZ Group portfolio and Group Tina Ltd. portfolio.

Exercise 3-5

Calculation of Expected Return

Security X = (30 × 0.30) + (25 × 0.40) + (20 × 0.30) = 9 + 10 + 6 = 25%

Security Y = (50 × 0.20) + (30 × 0.60) + (10 × 0.20) = 10 + 18 + 2 = 30%

Assuming a positive correlation between the two securities,

Expected return of portfolio '

= (0.6 × 0.25) + (0.4 × 0.30) = 0.15 + 0.12 = 27%

Calculation of Variance of Return

2 2 2
Security X = (30 - 25) (0.3) + (25 - 25) (0.4) + (20 - 25) (0.3)

= (25 × 0.3) + 0 + (25 × 0.3) = 7.5 + 0 + 7.5 = 15%

2 2 2
Security Y = (50 - 30) (0.2) + (30 - 30) (0.6) + (10 - 30) (0.2)

= (400 × 0.2) + 0 + (400 × 0.2) = 80 + 0 + 80 = 160%

Standard deviation = WBSJBODF

Standard deviation of security X =  = 3.87 Standard deviation of security Y =  = 12.65

Hence, the expected risk of security X is 3.87 and of security Y is 12.65.

For the portfolio, each security has three outcomes giving nine possible combinations where the return on security

X is weighted by 60% and on security Y by 40%.

 Outcomes 'J − '
 P(Fi) 'J − '
 × 1 'J

Fi(%) ' =  P(Xi) × P(Yi) (%)

30 × 0.6 + 50 × 0.4 = 38 121 0.06 7.26

30 × 0.6 + 30 × 0.4 = 30 9 0.18 1.62

30 × 0.6 + 10 × 0.4 = 22 25 0.06 1.50

25 × 0.6 + 50 × 0.4 = 35 64 0.08 5.12

25 × 0.6 + 30 × 0.4 = 27 0 0.24 0

25 × 0.6 + 10 × 0.4 = 19 64 0.08 5.12

20 × 0.6 + 50 × 0.4 = 32 25 0.06 1.50

20 × 0.6 + 30 × 0.4 = 24 9 0.18 1.62

20 × 0.6 + 10 × 0.4 = 16 121 0.06 7.26

1.00 31.00

Standard Deviation of Portfolio (F) = ∑ 'J − '

 × 1 'J
=  = 5.57

N
Hence, the expected risk of portfolio is 5.57%.

N
Exercise 3-6

A
(i) Analysis of Risk-Return of securities

¾ Security U gives a return of 10% at a risk level of 5% and security V and security Z will give the same return

M
of 10% but its risk level is 6% and 7% respectively which is higher than risk level of security U. Therefore

X
out of three securities U, V and Z, we can select security U.

¾ Since the return is lowest and its risk level is also same for security X i.e. 5%, we can ignore the security.

A
¾ Securities W and Y offer more return but it carries higher risk level.

T
¾ In view of the above observations. We can select security U, W and Y based on individual preferences.

(ii) Investment decision affirming perfect correlation exists

(a) Invest 80% in security U and 20% in security W

Return = (10% × 0.80) + (15% × 0.20)= 11%

Risk = (5% × 0.80) + (13% × 0.20) = 6.6%

(b) Invest 100% in security Y

Return 11% Risk 6%

For the same return of 11%, investment in securities U and W, at 80 : 20 proportion, carries a higher level of risk of

6.6% as compared to investment in security Y which carries the risk level of 6%. Therefore investment in security Y

is preferable.

Exercise 3-7

Existing market price of equity share = ` 106 (which is cum 10% bonus debenture of ` 6 each per share)

Ex-market price of equity share = ` 106 - ` 6 = ` 100

Total return = Market price + Dividend per share

Good = ` 115 + ` 9 = ` 124

Normal = ` 107 + ` 5 = ` 112

Bad = ` 97 + ` 3 = ` 100
Calculation of Expected Return

Market condition Probability Total return Cost Net return

( ) ` ( ) ` `
( )

Good 0.25 124 100 24

Normal 0.50 112 100 12

Bad 0.25 100 100 0

Expected Return = (24 × 0.25) + (12 × 0.50) + (0 × 0.25) = ` 12

Net return ` 12
= × 100 = × 100 = 12%
Cost ` 100

Calculation of Variability of Return

Variance = 4%

2 2 2
4% = 0.25(24 - 12) + 0.50(12 - 12) + 0.25(0 - 12)

2 2 2
= 0.25(12) + 0.50(0) + 0.25(-12)

N
= 36 + 0 + 36

N
S.D. =  = 8.485

Advise - M/s. X Finance Company Ltd. had offered the buy-back of debentures at face value, at 10% rate of interest

A
which is less than the 12% expected return of the equity. This will help in trading on equity i.e. the advantage gained

M
on lower rate of interest payable to debentureholders will increase the rate of return for the equity shareholders and

will also improve the market value of equity share. Hence, the buy-back offer can be accepted.

X
Exercise 3-8

A
Calculation of Covariance

T
– – – –
2 2
Year R R (R - R ) (R - R ) (R - R )(R - R ) R R
1 2 1 1 2 2 1 1 2 2 1 2

1 12 20 - 2.8 - 1 2.8 144 400

2 8 22 - 6.8 1 - 6.8 64 484

3 7 24 - 7.8 3 - 23.4 49 576

4 14 18 - 0.8 -3 2.4 196 324

5 16 15 1.2 - 6 - 7.2 256 225

6 15 20 0.2 -1 - 0.2 225 400

7 18 24 3.2 3 9.6 324 576

8 20 25 5.2 4 20.8 400 625

9 16 22 1.2 1 1.2 256 484

10 22 20 7.2 - 1 - 7.2 484 400

– – –
N ΣR 1
ΣR 2
Σ(R 1
- R )
1
Σ(R 2
- R )
2
Σ(R 1
- R )(R
1 2
- R )
2
ΣR 1
2
ΣR 2

= 10 = 148 = 210 = 0 = 0 = -8 = 2398 = 4494

– –
R
1
= ΣR /N 1
= 148/10 = 14.8 R
2
= ΣR /N 2
= 210/10 = 21

– –
Σ(R 1
- R )(R
1 2
- R )
2
-8
Covariance = = = -0.8
N 10
Standard Deviation of Security 1 ( σ)
1

  
/3  Σ3 
 ×  

   
= = = =  = 4.56

/  ×  

Standard Deviation of Security 2 ( σ2)

  
/3  Σ3 
 ×  

   
= = = =  = 2.90

/  ×  

Correlation Coefficient (r )
1 2

Cov -0.8 -0.8

r = = = = -0.0605
1 2
σ σ2
1
4.56 × 2.90 13.22

Exercise 3-9

(i) Expected return of the portfolio A and B

E(A) = (10 + 16)/2 = 13%

N
E(B) = (12 + 18)/2 = 15%

N
/
Rp =
∑9 3 J J = 0.4(13) + 0.6(15) = 14.2%

A
J =

(ii) Stock A

2 2

M
Variance = 0.5(10 - 13) + 0.5 (16 - 13) = 9

X
Standard deviation = = 3%

A
Stock B

2 2
Variance = 0.5(12 - 15) + 0.5(18 - 15) = 9

T
Standard deviation = 3%

(iii) Covariance of stocks A and B

Cov = 0.5(10 - 13)(12 - 15) + 0.5(16 - 13)(18 - 15) = 9

AB

(iv) Correlation coefficient

$PW "# 
r = = = 1
AB
σ"σ# × 
(v) Portfolio Risk

 
σp = 9 "σ " + 9  # σ  # +  9 " 9 # σ " σ # σ "#

 
= 

+ 
 
 +  





=  +  +  = 3%

 Key to Short Answer Questions

True or False Statements

1. True - The prime objective of Financial Management is maximize the value of the firm, which is possible only

when well balanced financial decisions are taken. The management should try to maximize the

average profit while minimizing the risk. An important financial principle is that the value of money

is time dependent. The value of money received today is different from the value of money received

after some time in the future.

2. True - The projects promising a high average profit are generally accompanied by high risk. The higher the

return, other things being equal, higher the market value and vice versa. It should be kept in mind that

risk and return go together.

3. True - When a company produce single product when the company’s profits and cash flows fluctuates

widely. This increase the risk of a firm. Diversification reduces the risk of firm. Therefore, diversifi-

N
cation is an important strategic alternative to growth.

False

N
4. - A business portfolio is the collection of strategic business units that make up a corporation. Industrial

groups will also have similar investment motives like individual investors as to risk and return on

A
investment.

5. False - Risk means possibility of a future loss which can be foreseen and can be qualified of likelihood of

M
future outcomes. In case of uncertainty, it is known exactly what will happen in future and it cannot

be quantified.

X
6. True - Business risk relates to the type of projects it undertakes, the company’s competitive position, market

A
conditions, product mix, input availability, labour supply etc. It arises due to higher amount of fixed

overheads in cost structure.

T
7. True - Investors don't like risk and greater the riskiness of returns on a project, the greater the return they

will require.

8. True - The projects promising a high average profit are generally accompanied by high risk. Managers

should accept such projects only if they will induce an increase in stock price.

9. False - Statistically the risk can be expressed in terms of variance or standard deviation.

10. False - The securities consisting in a portfolio are associated with each other. The portfolio risk also considers

the covariance between the returns of the investment. Covariance of two securities is a measure of

their co-movement, it expresses the degree to which the securities vary together.

11. True - It is an important principle of efficient capital market that investors should not hold all their eggs in

one basket, they should hold a well diversified portfolio in order to diversify risk and achieve

maximum return for a given level of risk.

Choose Correct Word

1. business

2. financial

3. business risk

4. risk-return trade off

5. lower

6. higher

7. discount
 8. negatively

9. risk averse

10. indifference

11. risk averse

12. increase

13. financial

14. high

15. minimize

16. unsystematic

17. optimal

Choose Correct Answer

1.(B) equal to

2. (A) risk-taker investor

3. (D) high

N
4. (B) market

N
5. (A) required

6. (A) sufficient

A
7. (B) equal to

8. (A) increasing

M
9. (C) risk premium

X
10. (B) equal to

A
11. (B) less than

12. (A) The portfolio’s expected return is 15%

T
13. (D) The stock is a good buy

14. (A) a higher expected return and lower standard deviation

 Key to Practical Exercises

Exercise 4-1

Absolute cash ratio indicates the position of the ready cash for meeting the current liabilities. The cash position to

total assets ratio is a measure of liquid layer of the assets deployed by business. Interval measure gives an idea about

the time length that can be covered by the available cash for meeting operating expenses. On analysis of the data given

in the question, following points can be summarized:

(a) Absolute cash ratio of MRD Ltd. is better than the industry average.

(b) Cash position to total assets ratio of MRD Ltd. is lower than that of industry.

These ratios indicate that either current liabilities of MRD Ltd. are relatively lower than that of the industry

or its total assets are relatively higher than those of the industry.

(c) Cash interval of MRD Ltd. is also lower than that of the industry.

N
Therefore, by overall assessment, it can be concluded that MRD Ltd. is maintaining low cash position as compared

to the industry.

N
Exercise 4-2

A
(a) Dividend Yield on Ordinary Shares

Dividend 0.20
= = × 100 = 5%

M
Market price per share 4

X
(b) Earnings Yield

Profit after tax - Preference dividend Nominal share value

A
= × 100 ×
Ordinary share capital Market price

T
5,42,000 - 42,000 1
= × 100 × = 7.8
16,00,000 4

(c) P/E Ratio

Market price of shares

=
EPS

Profit after tax - Preference dividend 5,42,000 - 42,000

EPS = = = 0.3125
No. of ordinary shares 16,00,000

P/E Ratio = 4/0.3125 = 12.8

(d) Priority Percentage

Priority payment ` %

Preference dividend 42,000 0 - 7.75

Ordinary dividend 3,20,000 7.75 - 66.79

Retained profit 1,80,000 66.79 - 100

5,42,000 100%

(e) Net Cash Flow ( )`

PBT 10,84,000

Less: Tax @ 50% 5,42,000

PAT 5,42,000
 `
( )

Add:Depreciation 1,20,000

6,62,000

Less: Preference dividend 42,000

Ordinary dividend 3,20,000 3,62,000

Net Cash Flow 3,00,000

Exercise 4-3

Calculation of Profit after Tax `

( )

Sales 22,50,000

Less: Direct costs 15,00,000

Gross profit 7,50,000

Less: Operating expense 2,40,000

EBIT 5,10,000

N
Less: Interest ( ` 7,50,000 × 9/100) 67,500

N
EBT 4,42,500

Less: Tax (@ 40%) 1,77,000

A
EAT 2,65,500

M
(i) Calculation of Net profit margin

&#*5  U
C     

X
Net profit margin = ×  = ×  = 13.6%
4BMFT C   

A
(ii) Calculation of Return on Assets (ROA)

T
&#*5  U
C     

ROA = × = ×  = 12.24%

5PUBM BTTFUT C   

(iii) Calculation of Asset Turnover

4BMFT C   

"TTFUT
Asset turnover = = = 0.9
C   

(iv) Calculation of Return on Equity (ROE)

1"5 C   
ROE = ×  = ×  = 15.17%
&RVJUZ C   

Exercise 4-4

Ratio Comments

(a) Current Ratio Ideal ratio is 2. The company’s position is above the normal value and the industry

standard. This may also be due to excessive stock.

(b) Debtors’ Turnover Ratio The industry standard indicates an average collection period of two months, while

for the company it is only 1½ months. The company’s position is better.

(c) Stock Turnover Ratio The stock is moving very slowly. Obviously there is excessive stock in the company.

Perhaps this has boosted up the current ratio. The sales volume has to be consider-

ably increased and stock level brought down.

(d) Net Profit Ratio Here the company’s performance is very unsatisfactory compared to the overall

position in the industry. This calls for steps to get better sales realization and

reduction of the cost of production.

 Ratio Comments

(e) Total Debt to Total Assets The percentage is disproportionately high in the company indicating a larger

proportion of debt in the capital structure. Too high a debt component means too

high a risk for equity shareholders.

Exercise 4-5

Calculation of Ratios

Current Assets 25,00,000

(1) Current Ratio = = = 2.78
Current Liabilities 9,00,000

Sales 60,00,000
(2) Sales/Debtors = = = 8.00
Debtors 7,50,000

Sales 60,00,000
(3) Sales/Stock = = = 4.80
Stock 12,50,000

Sales 60,00,000
(4) Sales/Total Assets = = = 1.5
Total Assets 40,00,000

N
Gross profit 17,00,000
(5) Gross Profit Ratio = × 100 = × 100 = 28.33%

N
Sales 60,00,000

Comparison of X Ltd.’s Ratios with Industry Norms

A
Ratio X Ltd. Industry Comment

M
(1) Current Ratio 2.78 2.50 The current ratio of the company indicates better short-term

solvency position as compared to the industry. But composition

X
of current assets have to be analyzed to ascertain any excess

investments in current assets.

A
(2) Sales/Debtors 8.00 7.5 The company’s average debtors collection period is marginally

T
less than the industry, and it indicates better management of

receivables.

(3) Sales/Stock 4.8 8.0 It indicates excess carrying of inventory as compared to industry.

The low turnover ratio may also be due to lower sales volume.

(4) Sales/Total assets 1.5 2.5 The company has either excess investments in fixed assets or

lower sales performance.

(5) Gross profit Ratio 28.33% 35% The gross profit margin is much lesser than the industry average,

it may be due high cost of production, lower selling price etc.

Exercise 4-6

(` ’000)
Current Assets

Inventory 400

Debtors 175

Marketable securities 75

Cash 50

700

Current Liabilities

Creditors 180

Bills payable 20

Other current liabilities 80

280
 `
( ’000)
Current assets 700
(1) Current Ratio = = = 2.5
Current liabilities 280

Liquid assets 300

(2) Quick Ratio = = = 1.07
Current liabilities 280

Sales 1,600
(3) Sales to Inventory = = = 4 times
Inventory 400

Debtors 175
(4) Average Collection Period = = = 40 days
Average daily sales 4.4

Debts 700
(5) Debts to Assets = × 100 = × 100 = 46.7%
Total assets 1,500

Debts 700
(6) Debt-Equity Ratio = = = 1.35
Shareholders funds 520

EBIT 250
(7) Times Interest Earned = = = 5.56
Interest charges 45

N
Net profit 123
(8) Net Profit Margin = × 100 = × 100 = 7.7%

N
Sales 1,600

Price per share 15

A
(9) Price to Earnings Ratio = = = 4.88
E.P.S. 3.075

Net profit 123

M
(10) Return to Total Assets = × 100 = × 100 = 8.2%
Total assets 1,500

X
Date : 15-06-2016

A
To

The Managing Director,

T
A.G. Limited,

New Delhi.

Dear Sir,

I have made a thorough analysis of the performance of the company by computing various important ratios and it

is compared with the industry average ratios. Details of which are given in the following table with suitable

suggestions for improvement.

Interpretation of A.G. Ltd. ratios with Industry average ratios and suggestions for improvement

Ratio Industry Company Interpretation of company ratios with

average ratios industry average ratios ratios

(1) Current Ratio 2.4 2.5 Slightly higher than the industry average and it is satisfactory. It

can be further improved either by having more current assets or

by reducing current liabilities.

(2) Quick Ratio 1.5 1.07 It is much lower than the industry average. It indicates funds are

locked-up in inventories. It is suggested to reduce the inventory

levels and use the techniques of JIT and supply chain management.

(3) Sales to Inventory 8 4 It indicates very poor performance in sales

(times) as well as inefficient management of inventory. Improve the

efficiency of marketing function and stores function and reduce

the levels of stocks.

 Ratio Industry Company Interpretation of company ratios with

average ratios industry average ratios ratios

(4) Average Collection 36 40 It indicates liberal collection policy and more

Period (days) funds are locked-up in debtors balances. It is suggested to reduce

the credit period and improve timely collection of debts.

(5) Debts to Assets 40% 46.7% Company’s assets are more financed with debt funds as compared

with industry average. It is suggested to reduce this ratio to give

more control to equity fund holders.

(6) Debt-Equity Ratio 2:1 1.35:1 The ratio is satisfactory. The company is less geared and more

relying on equity funds as compared to industry.

(7) Times Interest Earned 6 5.56 It is slightly less than the industry average. But still it is satisfactory

for debt providers.

(8) Net Profit Margin 7% 7.7% It is slightly higher than the industry average. It can be further

improved by increasing sales and reducing the operating costs

N
and finance charges.

(9) Price to Earnings Ratio 15 4.88 It indicates the company’s shares are under valued by the market.

N
It may be due to lack of poor information to investors about the

A
company’s performance. The company may launch publicity

campaign to inform the public about company’s progress.

M
(10) Return to Total Assets 11% 8.2% It indicates under utilization of company’s assets. It is suggested

to reduce unused assets and assets which does not earn. The

X
management should note that each rupee invested must earn

profit.

A
The management is suggested to take appropriate actions, keeping in view of the above analysis and suggestions, for

T
the growth, prosperity and profitability of the company.

Thanking you,

Yours faithfully,

(Anand Desai)

Financial Consultant

Exercise 4-7

Working Notes

(1) Calculation of Net worth

Net worth = Capital + Reserves

= ` 2,00,000 + ` 3,00,000 = ` 5,00,000

(2) Calculation of Current Liabilities

Total debt 1
=
Net worth 2

2 × Total debt = Net worth

2 × Total debt = ` 5,00,000

Total debt = ` 5,00,000/2 = ` 2,50,000

∴ Current liabilities = ` 2,50,000
(3) Calculation of Total Assets

Total of liabilities side = Equity share capital + Reserves and surplus + Current liabilities

= ` 2,00,000 + ` 3,00,000 + ` 2,50,000 = ` 7,50,000

Total of liabilities side = Total assets

∴ Total assets = ` 7,50,000

(4) Calculation of Sales

Sales
Total assets Turnover =
Total assets

Sales
2 =
` 7,50,000

∴ Sales = ` 15,00,000

(5) Calculation of Inventory

Gross profit is 30% sales

∴ Cost of sales is 70/100 of sales ` `

N
= 15,00,000 × 70/100 = 10,50,000

Cost of sales
Inventory turnover =

N
Inventory

` 10,50,000

A
3 =
Inventory

∴ Inventory ` ` 3,50,000

M
= 10,50,000/3 =

(6) Calculation of Debtors

X
Debtors
Average collection period = × 360 days

A
Sales

T
Debtors × 360 days
40 days =
` 15,00,000

Debtors × 360 days = ` 6,00,00,000

Debtors = ` 6,00,00,000/360 = ` 1,66,667

(7) Calculation of Current Assets

Current assets - Stock

Acid Test Ratio =
Current liabilities

3 Current assets - ` 3,50,000

=
4 ` 2,50,000

4 (Current assets - ` 3,50,000) = ` 2,50,000 × 3

4 Current assets - ` 14,00,000 = ` 7,50,000

4 Current assets = ` 7,50,000 + ` 14,00,000

Current assets = ` 21,50,000/4 = ` 5,37,500

(8) Calculation of Fixed Assets

Total assets - Current assets = Fixed assets

= ` 7,50,000 - ` 5,37,500 = ` 2,12,500

(9) Calculation of Cash in Hand and Bank

Current assets - Inventory - Debtors = Cash in hand and Bank

= ` 5,37,500 - ` 3,50,000 - ` 1,66,667 = ` 20,833

 Balance Sheet as on ......

Liabilities ` Assets `

Equity share capital 2,00,000 Plant and Machinery 2,12,500

Reserves and Surplus 3,00,000 and other fixed assets

Current liabilities 2,50,000 Current Assets:

Inventory 3,50,000

Accounts Receivable 1,66,667

Cash in hand and Bank 20,833

7,50,000 7,50,000

Exercise 4-8

(a) Calculation of Current Assets and Current Liabilities

Current ratio = 2.5

Net working capital = ` 60,000

N
$VSSFOU BTTFUT $"

= 2.5

N
$VSSFOU MJBCJMJUJF T $-

CA = 2.5 CL

A
2.5CL - CL = 60,000

M
1.5 CL = 60,000

CL = 60,000/1.5 = 40,000

X
Therefore,

` 40,000

A
Current liabilities =

Current assets = 40,000 × 2.5 = ` 1,00,000

T
(b) Calculation of Stock

Liquid ratio = 1.5

$VSSFOU BTTFUT 4UPDL

$VSSFOU MJBCJMJUJF T
= 1.5

   4UPDL
= 1.5
 

1,00,000 - Stock = 1.5 × 40,000

Stock = 1,00,000 - 60,000 = ` 40,000

(c) Calculation of Cost of Sales

Stock turnover ratio = 6 times

$PTU PG TBMFT
$MPTJOH TUPDL
= 6 times

$PTU PG TBMFT

= 6
 

Cost of sales = 6 × 40,000 = ` 2,40,000

(d) Calculation of Gross Profit

Gross profit ratio = 20%

Cost of sales = 80%

Sales = 2,40,000 × 100/80 = ` 3,00,000

 (e) Calculation of Fixed Assets

Fixed assets turnover ratio = 2

$PTU PG TBMFT
'JYFE BTTFUT
= 2

  
= 2
'JYFE BTTFUT

Fixed assets × 2 = 2,40,000

Fixed assets = 2,40,000/2 = ` 1,20,000

(f) Calculation of Debtors

Average collection period = 2 months

%FCUPST × 
= 2 months
4BMFT
%FCUPST × 
= 2
  

N
Debtors × 12 = 2 × 3,00,000

N
Debtors = 6,00,000/12 = ` 50,000

A
(g) Calculation of Shareholders Net worth

Fixed assets to Shareholders net worth = 0.8

'JYFE BTTFUT

M
= 0.8
/FU XPSUI

X
  
= 0.8

A
/FU XPSUI

` 1,50,000

T
Net worth = 1,20,000/0.8 =

(h) Calculation of Reserves and Share capital

Reserve and surplus to Capital = 0.5

Share capital = 1,50,000 × 2/3 = ` 1,00,000

Reserves and surplus = 1,50,000 × 1/3 = ` 50,000

Balance Sheet of Big Brothers Ltd. as on .....

Liabilities ` Assets `

Share capital 1,00,000 Fixed assets 1,20,000

Reserves and surplus 50,000 Current assets:

Long-term loan 30,000 Stock 40,000

Current liabilities 40,000 Debtors 50,000

Cash (balancing figure) 10,000 1,00,000

2,20,000 2,20,000

Exercise 4-9

Working Notes

(a) Calculation of Sales and Cost of sales

Gross profit = 25% of sales (given)

Sales = ` 6,00,000 × 100/25 = ` 24,00,000

Cost of sales = Sales - Gross profit

= ` 24,00,000 - ` 6,00,000 = ` 18,00,000

(b) Calculation of Materials, Labour and Overheads

Material used = 40% of cost of sales (given)

= ` 18,00,000 × 40/100 = ` 7,20,000

Wages and overheads = ` 18,00,000 - ` 7,20,000 = ` 10,80,000

(c) Calculation of Stock and Debtors

Stock turnover ratio = 5 times (given)

$PTU PG TBMFT
4UPDL
5 =

C   
5 =
4UPDL

5 × Stock = ` 18,00,000
Stock = ` 18,00,000/5 = ` 3,60,000

Average debt collection period = 2 months

%FCUPST
× 

N
2 =
4BMFT

N
%FCUPST
2 = × 
C   

A
2 × ` 24,00,000 = Debtors × 12

Debtors = ` 48,00,000/12 = ` 4,00,000

M
(d) Calculation of Current assets and Current liabilities

X
Current ratio = 2 (given)

$VSSFOU BTTFUT

A
= 2
$VSSFOU MJBCJMJUJFT

T
Current assets = 2 Current liabilities

Current assets = ` 3,60,000 + ` 4,00,000

= ` 7,60,000
Current liabilities = ` 7,60,000 × ½ = ` 3,80,000

(e) Calculation of Trade creditors and Bank overdraft

Trade creditors = 3 months of material consumed

= ` 7,20,000 × 3/12 = ` 1,80,000

Bank overdraft = ` 3,80,000 - ` 1,80,000 = ` 2,00,000

(f) Calculation of Fixed assets

Proprietary ratio = 80% (given)

'JYFE BTTFUT
$BQJUBM FNQMPZFE
= 0.80

8PSLJOH DBQJUBM
$BQJUBM FNQMPZFE
= 0.20

Working capital = Current assets - Current liabilities = ` 7,60,000 - ` 3,80,000 = ` 3,80,000

Fixed assets = ` 3,80,000 × 80/20 = ` 15,20,000
Capital employed = Fixed assets + Working capital = ` 15,20,000 + ` 3,80,000 = ` 19,00,000
∴ Long-term funds = ` 19,00,000
 (g) Calculation of Debentures, Preference share capital and Equity share capital

Capital gearing ratio = 30% (given)

1SFG TIBSF DBQJUBM + %FCFOUVSFT

= 30%
5PUBM MPOH UFSN GVOET

Pref. share capital + Debentures = ` 19,00,000 × 30/100 = ` 5,70,000

Preference share capital = ` 5,70,000 × 2/3 = ` 3,80,000
Debentures = ` 5,70,000 × 1/3 = ` 1,90,000
Equity shareholders’ Fund = Total long-term funds - (Preference share capital + Debentures)

= ` 19,00,000 - ` 5,70,000 = ` 13,30,000

General reserve and P&L account = 20% of Equity shareholders’ fund

= ` 13,30,000 × 20/100 = ` 2,66,000

Equity share capital = ` 13,30,000 - ` 2,66,000 = ` 10,64,000
Net profit = 10% of Equity share capital

= ` 10,64,000 × 10/100 = ` 1,06,400

N
General reserve = ` 2,66,000 - ` 1,06,400 = ` 1,59,600

N
Projected Trading and Profit and Loss Account for the year ending March 31, 2017

` `

A
Particulars ( ) Particulars ( )

To Material used 7,20,000 By Sales 24,00,000

M
To Wages and overheads 10,80,000

To Gross profit c/d 6,00,000

X
24,00,000 24,00,000

A
To Expenses (balancing figure) 4,93,600 By Gross profit b/d 6,00,000

T
To Net profit 1,06,400

6,00,000 6,00,000

Projected Balance Sheet as on March 31, 2017

Liabilities `
( ) Assets `
( )

Share capital Fixed assets 15,20,000

Equity share capital 10,64,000 Current assets

Preference share capital 3,80,000 Stock 3,60,000

Reserves and surplus Debtors 4,00,000

General reserves 1,59,600

Profit & Loss account 1,06,400

Secured loans

Debentures 1,90,000

Current liabilities

Trade creditors 1,80,000

Bank overdraft 2,00,000

22,80,000 22,80,000
 Practical Exercises

Exercise 4-1 Given below are cash position ratios of MRD Ltd. and the Industry Average. Industry Average is

arrived at by taking average position of 25 companies of the similar trade:

Absolute cash ratio Cash position to Cash interval

total assets ratios

MRD Ltd. 0.36 12.50% 25 days

Industry average 0.30 15% 33 days

How do you feel about the cash position of MRD Ltd. ?

Exercise 4-2 A company is capitalised as follows: `

( )

7% Preference shares, ` 1 each 6,00,000

N
Ordinary shares, ` 1 each 16,00,000

22,00,000

N
The following information is relevant as to its financial year just ended:

A
Profit after taxation at 50% ` 5,42,000

Capital commitments ` 2,40,000

M
Market price of ordinary shares ` 4

X
Ordinary dividend paid 20%

Depreciation ` 1,20,000

A
You are required to state the following showing the necessary workings - (a) Dividend yield on ordinary shares

T
(b) Earnings yield (c) Price-earnings (P/E) ratio (d) Priority percentages (e) Net cash flow.

Exercise 4-3 MNP Limited has made plans for the next year 2015-16. It is estimated that the company will employ

total assets of ` 25,00,000; 30% of assets being financed by debt at an interest cost of 9% p.a. The direct costs for the
year are estimated at ` 15,00,000 and all other operating expenses are estimated at ` 2,40,000. The sales revenue are
estimated at ` 22,50,000. Tax rate is assumed to be 40%.
Required to calculate: (i) Net profit margin (ii) Return on assets (iii) Asset turnover (iv) Return on equity.

Exercise 4-4 The actual ratios of a company compared to the industry standard are given below. Comment on each

ratio and indicate in one or two sentences the nature of action to be taken by the company.

Ratio Industry Actual for

standard the company

Current ratio 2.2 2.7

Debtors’ turnover ratio 6 8

Stock turnover ratio 10 3

Net profit ratio 5% 2.4%

Total debt to total assets 7.5% 40%

Exercise 4-5 Given below are some information regarding X Ltd. You are also provided with some key ratios for

the particular industry to which X Ltd. belongs. You are required to calculate the relevant ratios for X Ltd., compare

them with the industry norms and give your comments on the performance of the company.
 Balance Sheet of X Ltd. as at 31-3-2016

Liabilities ` Assets `
Equity share capital 25,00,000 Net fixed assets 15,00,000

10% Debentures 6,00,000 Cash 5,00,000

Sundry creditors 4,00,000 Sundry debtors 7,50,000

Bills payable 3,50,000 Stocks 12,50,000

Other current liabilities 1,50,000

40,00,000 40,00,000

The sales for the company for the year ending 31-3-2016 amounted to ` 60,00,000 and the gross profit was

` 17,00,000.

Industry Norms Ratios considered

Current ratio 2.5

Sales/Debtors 7.5

Sales/Stock 8.0

N
Sales/Total assets 2.5

N
Gross Profit ratio 35%

A
Exercise 4-6 Summarized Balance Sheet and Income Statement of AG Ltd. for the year ended 31st March, 2016 are

as under:

M
Income Statement for the year ended 31st March, 2016 ( ` ’000)

X
Sales 1,600

Less: Cost of goods sold 1,310

A
Gross margin 290

T
Less: Selling and administrative expenses 40

EBIT 250

Less: Interest expenses 45

Earnings before tax 205

Less: Tax 82

Net profit 123

Balance Sheet as on 31st March, 2016 ( ` ’000)

Liabilities

Paid-up capital (40,000 equity shares of `10 each, fully paid-up) 400

Retained earnings 120

Debentures 700

Creditors 180

Bills payable 20

Other current liabilities 80

1,500

Assets

Net fixed assets 800

Inventory 400

Debtors 175
Balance Sheet as on 31st March, 2016 ( ` ’000)

Marketable securities 75

Cash 50

1,500

Price per share: ` 15. Industry’s average ratios are:

Current ratio 2.4 Debt equity ratio 2 : 1

Quick ratio 1.5 Times interest earned 6

Sales to inventory 8.0 times Net profit margin 7%

Average collection period 36 days Price to earnings ratio 15

Debt to assets 40% Return to total assets 11%

From the above facts and figures, you are required to - (i) Calculate the relevant ratios and interpret them to identify

the problems areas. (ii) Based on the ratio analysis, as a Financial Consultant, prepare a report for consideration of

your Board of Directors clearly bringing out the reasons in respect of identified problem areas and giving suggestions

N
to solve them.

Exercise 4-7

N
Using the following information complete the Balance Sheet given below: Available information:

(a) Total Debt to Net worth 1 : 2

A
(b) Total Asset Turnover 2

(c) Gross Profit 30%

M
(d) Average Collection Period (taking one year as 360 days) 40 days

X
(e) Inventory Turnover based on cost of sales and year end inventory 3

(f) Acid Test Ratio 3 : 4

A
Balance Sheet as on .......

T
Liabilities ` Assets `

Equity Share Capital 2,00,000 Plant and Machinery and other

Reserves and Surplus 3,00,000 fixed assets ?

Current Assets:

Inventory ?

Accounts Receivable ?

Cash in hand and Bank ?

? ?

Exercise 4-8 From the following information provided by Big Brothers Ltd. draw up its balance sheet:

Current ratio 2.5 Fixed assets turnover ratio (on cost of sales) 2 times

Liquid ratio 1.5 Average collection period 2 months

Net working capital ` 60,000 Fixed assets to Shareholders net worth 0.8

Stock turnover ratio (Cost of sales/ Closing stock) 6 times Reserve and surplus to Capital 0.5

Gross profit ratio 20% Long-term loans ` 30,000

Exercise 4-9 From the following information, prepare the projected Trading and Profit and Loss account for the

next financial year ending 31st March, 2017 and the projected balance sheet as on that date:
Gross profit ratio 25%

Net profit to equity capital 10%

Stock turnover ratio 5 times

Average debt collection period 2 months

Creditors velocity 3 months

Current ratio 2

Proprietary ratio (fixed assets to capital employed) 80%

Capital gearing ratio (preference shares and debentures to total long-term funds) 30%

General reserve and profit and loss to equity shareholders’ fund 20%

Preference share capital to debentures 2

Cost of sales consists of 40% for materials and balance for wages and overheads. Gross profit is ` 6,00,000.

N N
M A
A X
T
 Key to Short Answer Questions

True or False Statements

1. True - The accounting ratio means significant relationships which exist between figures shown in the

financial statements. The ratios will be effective only when they are compared with ratios of base period or

with standards or with the industry ratios. Therefore, ratio analysis provides basis for interfirm, as well as,

intra-firm comparison.

2. True - Ratio analysis is a process of comparison of one figure against another, which make a ratio. A ratio

is a quotient of two numbers and the relation expressed between two accounting figures is known as

‘accounting ratio’.

3. True - Interpretation of ratios is a highly technical job for a Financial analyst. Ratio analysis is only a

technique, for making judgements and not a substitute for judgements. The calculation of ratios is a

relatively easy and simple task but the proper analysis and interpretation of ratios can be made only by a

N
skilled analyst.

4. True - For computation of capital gearing ratio, the fixed interest bearing funds include debentures, long-

N
term loans and preference share capital. It indicates the changes in benefits accruing to equity shareholders

A
by changing the levels of fixed interest bearing funds in the organization.

5. True - The fixed assets to long-term funds ratio indicates the proportion of long-term funds deployed in

M
fixed assets. The higher the ratio indicates the safer the funds available in case of liquidation.

6. True - The sales to capital employed ratio is ascertained by dividing sales with capital employed. This ratio

X
indicates, efficiency utilization of capital employed in generating revenue.

A
7. True - The P/E ratio indicates the market price of an equity share to the EPS. It measures the number of

times the earnings per share discounts the market price of an equity share. The ratio indicates how much

T
an investor is prepared to pay per rupee of earnings. Therefore, when the riskiness of a firm decreases, its

P/E ratio becomes higher.

8. False - The market price to Book value ratio (P/BV ratio) measures the relationship between the accounting

value of the firm’s assets and the market price of its stock. Generally, the higher rate of return a firm is

earning on its common equity the higher will be the P/BV ratio.

9. True - The firms with high turnover and with low margin are not attractive to the investors and therefore,

their share prices will be quoted less in the stock market.

10. True - The price to book value ratio is calculated by dividing the stock price per share by the book value per

share. Generally, the higher the rate of return a firm is earning on its common equity, the higher will be the

P/BV ratio.

11. True - The trend ratios of select major financial items are computed and analyzed to arrive at the

conclusions for important changes in the trend. It is important to cross-check the financial statement

information by studying financial statement information by studying financial ratio changes during the

forecast period.

Choose Correct Word

1. gross

2. networth

3. capital

4. index numbers

5. forecasting
 6. book

7. 1 : 2

8. current liabilities

9. 2 : 1

10. sales

11. zero

12. long-term funds

13. EPS

14. cash EPS

15. capital employed

16. income

17. profitability

N
18. financial

N
19. comparative

A
20. Ratio analysis

21. positively

M
22. positively

X
Choose Correct Answer

A
1. (D) balance sheet

T
2. (C) annual report

3. (A) solvency

4. (D) P/BV ratio

5. (C) investment

6. (B) standards

7. (C) price-earning ratio

8. (B) third dimensional

9. (C) schedules

10. (D) comparative

11. (B) 100

12. (C) index numbers

13. (B) trend

14. (A) most recent four quarters’ EPS

15. (A) companies

16. (C) profitability

17. (A) liquidity

18. (A) 2 : 1
19. (B) 1 : 1

20. (B) cyclical

21. (C) absolute

22. (B) cash operating

23. (B) super quick

24. (C) defensive interval

25. (B) 3 : 1

26. (A) listed companies

27. (A) depreciation

28. (B) vertical analysis

29. (C) Profit and loss appropriation A/c

30. (C) profitability

N
31. (A) gross profit

N
32. (D) return on investment

A
33. (B) operating

34. (C) cash EPS

M
35. (C) common size statements

X
36. (C) sales or cash

A
37. (D) debt service coverage ratio

T
38. (A) inflation

39. (C) market based

40. (C) ratio analysis

41. (C) commercial life of asset

42. (D) manufacturing concern

43. (B) have adverse impact on profitability

44. (A) horizontal consistency

45. (C) short-term liquidity

46. (D) short-term analysis

47. (C) return on investment

48. (B) interfirm comparison

49. (B) long-term investments

50. (B) cash

51. (B) proprietary

52. (C) fixed assets to long-term funds

53. (D) sales to capital employed

54. (D) Fixed assets/Long-term funds

55. (C) industry norm

56. (C) bills receivable

57. (B) ` 40,000

58. (B) 4

59. (C) 10

60. (A) ` 150

61. (A) 1.56

62. (D) all of the above

63. (C) Quick Assets/Current Liabilities

64. (B) Net profit + Depreciation

65. (C) as given in (A) and (B)

66. (A) AB Ltd. has 1 lakh ` 10 ordinary shares in issue

N
67. (D) all of the above

N
68. (D) Discount rate falls and reinvestment rate rises

A
69. (A) has a higher level of short-term liabilities than the industry

70. (D) all of the above

M
71. (C) making cash payment to creditors

X
72. (B) the firm’s equity is currently valued at more than what the stockholders invested in the firm

A
73. (D) earnings before interest, tax, depreciation and amortisation

T
74. (C) cash available for meeting financial flows like debt servicing, dividend payments etc.

75. (D) all of the above

76. (C) current ratio = 1.2 and quick ratio = 0.6

77. (A) F’s share price must be, twice that of G

 Practical Exercises

Exercise 5-1 The comparative Balance sheets of Beta Ltd. are indicated in condensed form as under: `
( )

Particulars 31-12-2016 31-12-2015

Fixed assets 5,20,000 4,80,000

Less: Depreciation 1,40,000 1,08,000

3,80,000 3,72,000

Investment at cost 50,000 1,00,000

Stocks 90,500 55,600

Sundry debtors 1,67,800 1,18,300

Cash and bank balance 47,500 49,800

Preliminary expenses - 7,200

N
7,35,800 7,02,900

N
Share capital

A
Ordinary shares of ` 100 each issued for cash 4,00,000 3,60,000

General reserve 60,000 1,10,000

M
Surplus in Profit and Loss A/c 33,450 20,450

Sundry creditors 1,95,350 1,33,650

X
Proposed dividend 15,000 28,800

A
Provision for taxation 32,000 50,000

7,35,800 7,02,900

T
The net profit for the year (after providing for depreciation ` 40,000, writing off preliminary expenses ` 7,200 and
making provision for taxation ` 32,000) amounted to ` 38,000. The company sold during the year old machinery

costing ` 9,000 for `3,000. The accumulated depreciation on the said machinery was ` 8,000. A portion of the

company’s investment became worthless and was written off to general reserve. The cost of such investment was

` 50,000. During the year the company paid an interim dividend of ` 10,000 and directors have recommended a final
dividend of ` 15,000 for the year 2015.

Prepare: (a) Statement of Sources and Applications of Funds for the year ended 31st December, 2016 and

(b) Schedule of Working Capital Changes.

Exercise 5-2 Following are the summarized balance sheets of ABC Ltd. as on 31st December, 2015 and 2016: ( `)

Particulars 2015 2016

Liabilities

Creditors 39,500 41,135

Bills payable 33,780 11,525

Bank overdraft 59,510 -

Provision for taxation 40,000 50,000

Reserves 50,000 50,000

Profit and loss account 39,690 41,220

Share capital 2,00,000 2,60,000

4,62,480 4,53,880
Particulars 2015 2016

Assets

Cash at bank 2,500 2,700

Debtors 87,490 73,360

Stock 1,11,040 97,370

Land and buildings 1,48,500 1,44,250

Plant and machinery 1,12,950 1,16,200

Goodwill - 20,000

4,62,480 4,53,880

Additional Information:

(a) During the year 2016, an interim dividend of ` 26,000 was paid.

(b) The assets of another company were purchased for ` 60,000 payable in fully paid shares of the company. These
assets consisted of Stock - ` 22,000; Machinery - ` 18,000 and Goodwill - ` 20,000.

(c) Sundry purchases of plant were made totalling ` 5,600.

N
(d) Income-tax paid during 2016 amounted to ` 25,000.

N
(e) The net profit for 2016 before tax was 62,530.

You are required to prepare a funds flow statement for the year 2016 and a schedule setting out changes in working

A
capital.

Exercise 5-3 From the following balance sheets and information of Everest Ltd. for 2015 and 2016 draw out a funds

M
flow statement and statement of changes in working capital for 2016.

X
Balance Sheets of Everest Ltd. ( )`

A
Particulars 2015 2016

T
Liabilities

Equity share capital 2,00,000 3,00,000

8% Preference share capital (redeemable) 1,00,000 50,000

General reserve 20,000 30,000

Capital reserve - 25,000

Profit and loss account 18,000 27,000

Proposed dividend 28,000 39,000

Sundry creditors 25,000 47,000

Bills payable 10,000 6,000

Liabilities for expenses 8,000 6,000

Provision for taxation 28,000 32,000

4,37,000 5,62,000

Assets

Goodwill 50,000 40,000

Land and building 1,00,000 75,000

Plant 90,000 1,91,000

Trade investment 10,000 35,000

Sundry debtors 60,000 90,000

Stock 85,000 78,000

Particulars 2015 2016

Bills receivable 15,000 18,000

Cash in hand 7,000 6,000

Cash at bank 10,000 22,000

Preliminary expenses 10,000 7,000

4,37,000 5,62,000

(i) In 2016 ` 18,000 depreciation has been written off from plant account and no depreciation has been charged
on land and building.

(ii) A piece of land has been sold out and the balance has been revalued. Profits on revaluation and sales being

transferred to capital reserve. There is no other entry in capital reserve account.

(iii) A plant was sold for ` 12,000 (w.d.v. ` 15,000).

(iv) ` 2,100 dividend has been received, but it includes ` 600 pre-acquisition dividend.

N
(v) An interim dividend of 10,000 has been paid in 2016.

Exercise 5-4 From the figures given below, prepare a statement showing the application and sources of funds

N
during the year 2015-16.

A
( )`

31.03.2015 31.03.2016

M
Assets

X
Fixed assets (net) 5,10,000 6,20,000

Investments 30,000 80,000

A
Current assets 2,40,000 3,75,000

T
Discount on debentures 10,000 5,000

7,90,000 10,80,000

Liabilities

Share capital (equity) 3,00,000 3,50,000

Share capital (preference) 2,00,000 1,00,000

Debentures 1,00,000 2,00,000

Reserves 1,10,000 2,70,000

Provision for doubtful debts 10,000 15,000

Current liabilities 70,000 1,45,000

7,90,000 10,80,000

You are informed that during the year:

(i) A machine costing ` 70,000 (book value ` 40,000) was disposed of for ` 25,000.

(ii) Preference share redemption was carried out at a premium of 5%.

(iii) Dividend at 15% was paid on equity shares for the year 2015.

Further:

(a) The provision for depreciation stood at ` 1,50,000 on 31-3-2015 and at `1,90,000 on 31-3-2016.
(b) Stock which was valued at ` 90,000 as on 31-3-2015 was written up to its cost ` 1,00,000 for preparing the Profit
and Loss account for 2016.
Exercise 5-5 The following Balance Sheets of Chandan Products Ltd. for the years 2015 and 2016 are available:

( ) `

Particulars 2015 2016

Liabilities

Share capital 6,00,000 7,00,000

General reserve 2,00,000 2,50,000

Capital reserve (Profit on sale of investments) - 10,000

Profit and loss account 1,00,000 2,00,000

7% debentures 3,00,000 2,00,000

Creditors for expenses 10,000 12,000

Creditors for supply of goods 1,60,000 2,50,000

Proposed dividend 30,000 35,000

Provision for taxation 70,000 75,000

N
14,70,000 17,32,000

N
Assets

Fixed assets 10,00,000 12,00,000

A
Less: Accumulated depreciation 2,00,000 2,50,000

8,00,000 9,50,000

M
Investments (at cost) 1,80,000 1,80,000

X
Stock (at cost) 2,00,000 2,70,000

Sundry debtors

A
( less Provision for ` 20,000 and ` 25,000 respectively) 2,25,000 2,45,000

T
Bills receivable 40,000 65,000

Prepayment of expenses 10,000 12,000

Miscellaneous expenditure 15,000 10,000

14,70,000 17,32,000

Other Information:

(i) During the year 2016 fixed assets (WDV ` 10,000, depreciation written off ` 30,000) was sold for ` 8,000.

(ii) The proposed dividend of last year was paid in 2016.

(iii) During the year 2016 investments costing ` 80,000 were sold and later in the year investments of the same cost
were purchased.

(iv) Debentures were redeemed at a premium of 10% in 2016.

(v) Liability for taxation for 2015 came to ` 55,000.

(vi) During the year 2016 bad debts written off were ` 15,000 against the provision account.

Prepare a Funds Flow Statement.

 Key to Practical Exercises

Exercise 5-1

Working Notes

Calculation of Funds from Operations `

( )

Net Profit for the year 38,000

Add: Provision for depreciation 40,000

Preliminary expenses written off 7,200 47,200

85,200

Less: Profit on sale of machinery 2,000

Proposed dividend 15,000 17,000

Funds from Operations 68,200

N
Fixed Assets A/c `
( )

N
ToBalance b/d 4,80,000 By Bank (sale of machinery) 9,000

ToBank (purchase of assets) 49,000 By Balance c/d 5,20,000

A
5,29,000 5,29,000

M
Statement of Sources and Application of Funds for the Year ended 31st December, 2016 ( )

Sources of Funds

X
Funds from operation 68,200

A
Issue of capital 40,000

T
Sale of machinery 3,000

1,11,200

Application of Funds

Interim dividend 10,000

Purchase of fixed assets 49,000

Increase in working capital (balancing figure) 52,200

1,11,200

Schedule of Working Capital Change `

( )

Particulars 2015 2016 Increase Decrease

Current Assets

Cash and bank 49,800 47,500 - 2,300

Sundry debtors 1,18,300 1,67,800 49,500 -

Stocks 55,600 90,500 34,900 -

(a) 2,23,700 3,05,800

Current Liabilities

Sundry creditors 1,33,650 1,95,350 - 61,700

Provision for taxation 50,000 32,000 18,000 -

Proposed dividend 28,800 15,000 13,800 -

 `
( )

Particulars 2015 2016 Increase Decrease

(b) 2,12,450 2,42,350

Net Working Capital (a) - (b) 11,250 63,450

Increase in Working Capital 52,200 - - 52,200

63,450 63,450 1,16,200 1,16,200

Exercise 5-2

Provision for Taxation A/c `

( )

ToBank (Income tax paid) 25,000 By Balance b/d 40,000

ToBalance c/d 50,000 By Profit and Loss A/c 35,000

- Provision (bal. figure)

75,000 75,000

N
Plant and Machinery A/c

To Balance b/d 1,12,950 By Depreciation 20,350

N
To Share Capital A/c - purchase 18,000 By Balance c/d (balancing figure) 1,16,200

A
To Bank - purchase 5,600

1,36,550 1,36,550

M
Issue of Share Capital

X
(a) Issue of share capital for ` 38,000 (i.e. for machinery ` 18,000 and goodwill ` 20,000) will not affect the funds

flow and hence need not be shown in funds flow statement.

A
(b) Issue of Share Capital for ` 22,000 will affect the funds and it should be shown in the funds flow statement.

T
Income-tax

(a) Income-tax ` 25,000 paid in the year 2016 is shown in the working capital statement and it need not be shown

in the Funds flow statement.

(b) Provision for taxation is considered as current liability, accordingly funds flow statement is prepared.

Calculation of Funds from Operations `

( )

Net profit before tax 62,530

Less: Provision for tax 35,000

Profit after Tax 27,530

Add: Depreciation on plant and machinery 20,350

Depreciation on land and buildings 4,250 24,600

Funds from Operations 52,130

Funds Flow Statement for the Year 2016 `

( )

Sources of Funds

Funds from operations 52,130

Issue of capital 22,000

74,130

Application of Funds

Purchase of plant 5,600

Interim dividend paid 26,000

Increase in working capital (balancing figure) 42,530

74,130
Statement of Changes in Working Capital `
( )

Particulars As on As on Working capital

31-12-2015 31-12-2016 Increase Decrease

Current Assets

Cash at bank 2,500 2,700 200 -

Debtors 87,490 73,360 - 14,130

Stock 1,11,040 97,370 - 13,670

(a) 2,01,030 1,73,430

Current Liabilities

Creditors 39,500 41,135 - 1,635

Bills payable 33,780 11,525 22,255 -

Bank overdraft 59,510 - 59,510 -

Provision for tax 40,000 50,000 - 10,000

(b) 1,72,790 1,02,660

N
Net Working Capital (a) - (b) 28,240 70,770

Increase in Working Capital 42,530 - - 42,530

N
70,770 70,770 81,965 81,965

A
Exercise 5-3

M
Working Notes ( )

Land and Building A/c

X
To Balance b/d 1,00,000 By Bank (Sale) (balancing figure) 50,000

A
To Capital reserve 25,000 By Balance c/d 75,000

(profit on revaluation and sale)

T
1,25,000 1,25,000

Plant A/c

To Balance b/d 90,000 By Depreciation 18,000

To Bank - purchases 1,34,000 By Bank 12,000

(balancing figure) By Loss on sale of plant 3,000

By Balance c/d 1,91,000

2,24,000 2,24,000

Investment A/c

To Balance b/d 10,000 By Dividend received (pre-acquisition) 600

To Bank (balancing figure) 25,600 By Balance c/d 35,000

35,600 35,600

Adjusted Profit and Loss A/c

To Loss on sale of machinery 3,000 By Balance b/d 18,000

To Depreciation 18,000 By Dividend (2,100 - 600) 1,500

To Appropriations: By Income from operations 1,00,500*

General reserve 10,000 (Less: Taxation)

Proposed dividend 39,000

Interim dividend 10,000

To Goodwill written off 10,000

To Preliminary expenses 3,000

To Balance c/d 27,000

1,20,000 1,20,000

*Balancing figure.

Funds flow Statement of Everest Ltd. for the year 2016 `

( )

Sources of Funds

Issue of equity capital 1,00,000

Sale of land 50,000

Sale of plant 12,000

Dividend received 2,100

Income from operations 1,00,500

2,64,600

Application of Funds

N
Redemption of preference shares 50,000

N
Purchase of plant 1,34,000

Purchase of Investments 25,600

A
Dividend for 2015 28,000

Interim dividend 10,000

M
Increase in working capital (balancing figure) 17,000

X
2,64,600

A
Statement of Changes in Working Capital ( )

T
Particulars 2015 2016 Increase Decrease

Current Assets

Sundry debtors 60,000 90,000 30,000 -

Stock 85,000 78,000 - 7,000

Bills receivable 15,000 18,000 3,000 -

Cash in hand 7,000 6,000 - 1,000

Cash at bank 10,000 22,000 12,000 -

(a) 1,77,000 2,14,000

Current Liabilities

Sundry creditors 25,000 47,000 - 22,000

Provisions for taxation 28,000 32,000 - 4,000

Liabilities for expenses 8,000 6,000 2,000 -

Bills payable 10,000 6,000 4,000 -

(b) 71,000 91,000

Net Working Capital (a) - (b) 1,06,000 1,23,000

Increase in Working Capital 17,000 - - 17,000

1,23,000 1,23,000 51,000 51,000

Exercise 5-4

Fixed Assets A/c `

( )

To Balance b/d (5,10,000 + 1,50,000) 6,60,000 By Bank A/c 25,000

To Bank A/c -purchase 2,20,000 By Provision for depreciation A/c 30,000

(bal. figure) By Loss on sale of assets A/c 15,000

By Balance c/d (6,20,000 + 1,90,000) 8,10,000

8,80,000 8,80,000

Provision for Depreciation on Fixed Assets A/c

To Fixed assets A/c 30,000 By Balance b/d 1,50,000

To Balance c/d 1,90,000 By Profit & Loss A/c 70,000

2,20,000 2,20,000

Preference Share Capital A/c

To Bank A/c 1,05,000 By Balance b/d 2,00,000

N
To Balance c/d 1,00,000 By Share premium on redemption A/c 5,000

2,05,000 2,05,000

N
Profit and Loss Adjustment A/c

A
To Loss on sale of fixed assets 15,000 By Balance b/d 1,10,000

To Provision for depreciation 70,000 By Op. stock written up during 2009-10 10,000

M
To Dividend 45,000 By Funds from operations 2,90,000

X
To Discount on debentures 5,000

To Share premium on redemption A/c 5,000

A
To Balance c/d 2,70,000

T
4,10,000 4,10,000

Statement of Sources and Application of Funds for the Year ended 31-3-2016 `
( )

Sources of Funds

Issue of equity share capital 50,000

Issue of debentures 1,00,000

Sale of machine 25,000

Funds from operations 2,90,000

4,65,000

Application of Funds

Purchase of investments 50,000

Redemption of preference capital 1,05,000

Purchase of fixed assets 2,20,000

Payment of dividend 45,000

Increase in working capital (bal. figure) 45,000

4,65,000

Statement of Changes in Working Capital `

( )

Particulars 2015 2016 Increase Decrease

Current Assets (a) 2,50,000* 3,75,000 1,25,000 -

Current Liabilities 70,000 1,45,000 - 75,000

 `
( )

Particulars 2015 2016 Increase Decrease

Provision for doubtful debts 10,000 15,000 - 5,000

(b) 80,000 1,60,000

Working Capital (a) - (b) 1,70,000 2,15,000

Increase in Working Capital 45,000 - - 45,000

2,15,000 2,15,000 1,25,000 1,25,000

*` 2,40,000 + ` 10,000 = ` 2,50,000

Exercise 5-5

Working Notes `
( )

Fixed Assets A/c

To Balance b/d 10,00,000 By Scrapped Assets A/c 40,000

To Bank - Purchase (bal. figure) 2,40,000 By Balance c/d 12,00,000

N
12,40,000 12,40,000

N
Accumulated Depreciation A/c

A
To Scrapped Assets A/c 30,000 By Balance c/d 2,00,000

To Balance b/d 2,50,000 By Profit and Loss A/c 80,000

M
- Dep. for the year (bal. figure)

2,80,000 2,80,000

X
Scrapped Assets A/c

A
To Fixed Assets A/c 40,000 By Accumulated Depreciation A/c 30,000

T
By Bank - Sale proceeds 8,000

By Profit and Loss A/c 2,000

- Loss on sale of assets (bal. figure)

40,000 40,000

Investment A/c

To Balance b/d 1,80,000 By Bank - Sale 90,000

To Bank - Purchase 80,000 By Balance c/d 1,80,000

To Capital reserve 10,000

- Profit on sale of Investment

2,70,000 2,70,000

Calculation of Funds from Operations `

( )

Profit and Loss A/c balance as on 31-12-2016 2,00,000

Add:

Depreciation written off 80,000

Loss on Sale of scrapped Assets 2,000

Miscellaneous expenditure written off 5,000

Appropriation to general reserve 50,000

Provision for premium on redemption of debentures 10,000

Proposed dividend 35,000

Provision for taxation [75,000 - (70,000 - 55,000)] 60,000 2,42,000

Calculation of Funds from Operations `
( )

4,42,000

Less: Balance as on 1-1-2016 1,00,000

Funds from Operations 3,42,000

Funds Flow Statement of Chandan Products Ltd. for the Year ended 31st December, 2016 `
( )

Sources of Funds

Issue of share capital 1,00,000

Sale of Investments 90,000

Sale of scrapped assets 8,000

Funds from operations 3,42,000

5,40,000

Application of Funds

Purchase of fixed assets 2,40,000

Purchase of Investments 80,000

N
Redemption of debentures 1,00,000

Premium on redemption 10,000

N
Payment of dividend 30,000

A
Payment of taxes 55,000

Increase in working capital (balancing figure) 25,000

M
5,40,000

Schedule of Change in Working Capital `

( )

X
Particulars 2015 2016 Increase Decrease

A
Current Assets

T
Sundry Debtors (net) 2,25,000 2,45,000 20,000 -

Stock 2,00,000 2,70,000 70,000 -

Bills receivables 40,000 65,000 25,000 -

Expenses prepaid 10,000 12,000 2,000 -

(a) 4,75,000 5,92,000

Current Liabilities

Creditors for expenses 10,000 12,000 - 2,000

Creditors for supply of goods 1,60,000 2,50,000 - 90,000

(b) 1,70,000 2,62,000

Working Capital (a) - (b) 3,05,000 3,30,000

Increase in Working Capital 25,000 - - 25,000

3,30,000 3,30,000 1,17,000 1,17,000

 Key to Short Answer Questions

True or False Statements

1. True - In funds flow analysis, the details of financial resources availed and the ways in which such resources

are used during a particular accounting period. The cash flow analysis is a narrow concept which considers

the movement of cash and cash equivalents during the period of analysis.

2. False - A funds flow statement analyses the changes which have taken place in the assets and liabilities
during certain period as disclosed by a comparison of the opening and closing balance sheets.

3. True - The excess of funds generated over funds outgo from non-current assets and non-current liabilities

will lead to increase or decrease in working capital.

4. False - The amount of depreciation debited to profit and loss account is to be added back to arrive at the
funds generated from operations.

N
5. False - Any profit or loss on sale of non-current assets (fixed assets and long-term investments) is adjusted
to arrive at the true funds from operations.

N
6. True - Issue of equity shares and purchase of machinery are non-current items, any changes between them

A
will not have affect on the funds flow.

7. False - Increase in sundry debtors balance, means there is an application of fund. Decrease in current assets

M
means the fund has generated.

False - The main objective of income statement is to ascertain the net profit earned or loss incurred by the

X
8.

company out of business operations at the end of particular period. The main objective of funds flow

A
statement is to ascertain the funds generated from operations.

False - A funds flow statement need not be included in the annual report sent for shareholders.

T
9.

10. True - The primary purpose funds flow analysis is to explain the net changes in working capital. When

‘fund’ means working capital, flow of funds refers to movement of funds which cause a change in working

capital of the organization.

Choose Correct Word

1. working capital

2. decrease

3. funds flow

4. decrease

5. balance sheet

6. decrease

7. accrual

8. current

9. single

10. appropriation

11. current

12. deducted

13. added back

Choose Correct Answer

1. (D) all of the above

2. (B) noncurrent liabilities

3. (C) application of fund

4. (C) use up the funds

5. (B) statutory requirements

6. (C) a fixed liability and a current liability

7. (D) all of the above

8. (B) funds flow

9. (A) working capital

10. (C) source

11. (B) decrease

N
12. (A) working capital

N
13. (A) depreciation

A
14. (B) statement of sources and application of funds

15. (D) all of the above

M
16. (A) added back to the reported profit

X
17. (A) X Ltd. has 1 lakh ` 10 ordinary shares issued

T A
 Practical Exercises

Exercise 6-1 From the following balance sheets of Winners Ltd. for years ended 31 st March, 2015 and 2016, prepare

a cash flow statement. `

( )

31.3.2015 31.3.2016

Liabilities

Equity shares of ` 100 each 9,00,000 12,00,000

Securities premium - 90,000

Profit and loss appropriation account 3,00,000 3,00,000

Profit for the year 50,000 6,00,000

9% Debentures 4,00,000 3,00,000

Sundry creditors 4,05,000 2,30,000

N
Provision for taxation 1,50,000 3,00,000

N
Proposed dividend 45,000 1,00,000

22,50,000 31,20,000

A
Assets:

Land 6,00,000 7,50,000

M
Plant and machinery 12,00,000 13,50,000

X
Less: Depreciation 4,20,000 7,80,000 4,50,000 9,00,000

Loans to subsidiary company 50,000 -

A
Share in subsidiary company 60,000 60,000

T
Stock in trade 3,70,000 4,50,000

Debtors 3,00,000 4,00,000

Bank 90,000 5,60,000

22,50,000 31,20,000

The following additional information are available:

(i) A plant costing ` 1,50,000 was sold during the year for ` 60,000. Accumulated depreciation on this plant was
` 1,00,000 and profit/loss; If any, arising out of this sale was transferred to Profit and loss account.

(ii) During the year, the company paid income-tax amounting to ` 1,80,000.

Exercise 6-2 From the following information as contained in income statement and balance sheets of Ril Ltd., you

are required to prepare a Cash flow statement using (i) Direct method, and (ii) Indirect method:

Income Statement for the year ended 31st March, 2016 ( ` crores)

Net sales 20,301

Less: Cost of sales 15,984

Depreciation 2,534

Salaries and wages 375

Operating expenses 891

Provision for tax 57 19,841

Net operating profit 460

Add: Other income 645

 Profit on sale of asset 42 687

Profit for the year 1,147

Add: Balance of Profit and Loss Account b/f 11,183

12,330

Less: Dividend declared 420

Tax on dividend 46 466

11,864

Add: Share Premium Account 772

Profit and Loss Account as on 31st March, 2016 12,636

Comparative Balance Sheets ( ` crores)

Particulars As on 31-3-2016 As on 31-3-2015

Assets:

Fixed Assets:

N
Land 1,029 901

Building and equipment 23,634 21,187

N
Gross block 24,663 22,088

A
Less: Accumulated depreciation 9,214 6,692

Net block 15,449 15,396

M
Investments 6,067 4,295

Current Assets:

X
Cash 1,082 4,898

A
Debtors 842 457

Stock 1,823 1,409

T
Advances 4,059 1,676

Other current assets 48 7,854 25 8,465

29,370 28,156

Liabilities:

Equity capital 1,053 933

Preference capital 293 253

Reserves and surplus 12,636 11,183

Loans 11,520 11,650

Sundry creditors 2,959 3,345

Provision for tax 266 544

Other liabilities 643 248

29,370 28,156

Cost of equipment sold was ` 40 crore.

Exercise 6-3 From the following Balance Sheet and information, prepare Cash flow Statement of Ryan Ltd. for the

year ended 31st March, 2016

Balance Sheet `
( )

31st March, 2016 31st March, 2015

Liabilities

Equity share capital 6,00,000 5,00,000

10% Redeemable preference capital - 2,00,000

Capital redemption reserve 1,00,000 -

Capital reserve 1,00,000 -

General reserve 1,00,000 2,50,000

Profit and Loss account 70,000 50,000

9% Debentures 2,00,000 -

Sundry creditors 95,000 80,000

Bills payable 20,000 30,000

Liabilities for expenses 30,000 20,000

Provision for taxation 95,000 60,000

N
Proposed dividend 90,000 60,000

N
15,00,000 12,50,000

Assets

A
Land and Building 1,50,000 2,00,000

Plant and Machinery 7,65,000 5,00,000

M
Investments 50,000 80,000

X
Inventory 95,000 90,000

Bills receivable 65,000 70,000

A
Sundry Debtors 1,75,000 1,30,000

T
Cash and Bank 65,000 90,000

Preliminary expenses 10,000 25,000

Voluntary separation payments 1,25,000 65,000

15,00,000 12,50,000

Additional information:

(i) A piece of land has been sold out for ` 1,50,000 (cost ` 1,20,000) and the balance land was revalued. Capital

reserve consisted of profit on sale and profit on revaluation.

(ii) On 1st April, 2015 a plant was sold for ` 90,000 (original cost ` 70,000 and WDV ` 50,000) and Debentures

worth ` 1 lakh was issued at par as part consideration for plant of ` 4.5 lakhs acquired.

(iii) Part of the investments (cost ` 50,000) was sold for ` 70,000.

(iv) Pre-acquisition dividend received ` 5,000 was adjusted against cost of investment.

(v) Directors have proposed 15% dividend for the current year.

(vi) Voluntary separation cost of ` 50,000 was adjusted against General Reserve.

(vii) Income-tax liability for the current year was estimated at ` 1,35,000.

(viii) Depreciation @ 15% has been written off from Plant account but no depreciation has been charged on Land

and Building.
Exercise 6-4 The Balance Sheet of New Light Ltd. for the years ended 31st March, 2015 and 2016 are as follows:

`
( )

Liabilities 31.3.2015 31.3.2016 Assets 31.3.2015 31.3.2016

Equity share capital 12,00,000 16,00,000 Fixed assets 32,00,000 38,00,000

10% Preference share capital 4,00,000 2,80,000 Less: Depreciation 9,20,000 11,60,000

Capital reserve - 40,000 22,80,000 26,40,000

General reserve 6,80,000 8,00,000 Investment 4,00,000 3,20,000

Profit and Loss A/c 2,40,000 3,00,000 Cash 10,000 10,000

9% Debentures 4,00,000 2,80,000 Other current assets 11,10,000 13,10,000

Current liabilities 4,80,000 5,20,000 Preliminary expenses 80,000 40,000

Proposed dividend 1,20,000 1,44,000

Provision for tax 3,60,000 3,40,000

Unpaid dividend - 16,000

38,80,000 43,20,000 38,80,000 43,20,000

N
Additional information:

N
(i) The company sold one fixed asset for ` 1,00,000, the cost of which was ` 2,00,000 and the depreciation provided
on it was ` 80,000.

A
(ii) The company also decided to write off another fixed asset costing ` 56,000 on which depreciation amounting
to ` 40,000 has been provided.

M
(iii) Depreciation on fixed assets provided ` 3,60,000.

X
(iv) Company sold some investment at a profit of 40,000, which was credited to capital reserve.

(v) Debentures and preference share capital redeemed at 5% premium.

A
(vi) Company decided to value stock at cost, whereas previously the practice was to value stock at cost less 10%. The

` 2,16,000. The stock on 31.3.2016 was correctly valued at ` 3,00,000.

T
stock according to books on 31.3.2015 was

Prepare Cash flow Statement as per revised Accounting Standard-3 by Indirect Method.

Exercise 6-5 The Balance Sheet of JK Limited as on 31st March, 2015 and 31st March, 2016 are given below:

Balance Sheet as on ( ` 000)

Liabilities 31-03-15 31-03-16 Assets 31-03-15 31-03-16

Share capital 1,440 1,920 Fixed assets 3,840 4,560

Capital reserve - 48 Less: Depreciation 1,104 1,392

General reserve 816 960 2,736 3,168

Profit and loss account 288 360 Investment 480 384

9% Debentures 960 672 Cash 210 312

Current liabilities 576 624 Other current assets

(including stock) 1,134 1,272

Proposed dividend 144 174

Provision for tax 432 408 Preliminary expenses 96 48

Unpaid dividend - 18

4,656 5,184 4,656 5,184

Additional Information:

(i) During the year 2015-16, fixed assets with a book value of ` 2,40,000 (accumulated depreciation ` 84,000) was
sold for ` 1,20,000.
(ii) Provided ` 4,20,000 as depreciation.
(iii) Some investments are sold at a profit of ` 48,000 and profit was credited to capital reserve.

(iv) It decided that stocks be valued at cost, whereas previously the practice was to value stock at cost less 10 per

cent. The stock was ` 2,59,200 as on 31-03-2015. The stock as on 31-03-2016 was correctly valued at ` 3,60,000.
(v) It decided to write off fixed assets costing ` 60,000 on which depreciation amounting to ` 48,000 has been provided.
(vi) Debentures are redeemed at ` 105.

Required: Prepare a cash flow statement.

Exercise 6-6 Balance sheets of a company as on 31st March, 2015 and 2016 were as follows: `
( )

Liabilities 31-3-2015 31-3-2016 Assets 31-3-2015 31-3-2016

Equity share capital 10,00,000 10,00,000 Goodwill 1,00,000 80,000

8% Preference share capital 2,00,000 3,00,000 Land and buildings 7,00,000 6,50,000

General reserve 1,20,000 1,45,000 Plant and machinery 6,00,000 6,60,000

Securities premium - 25,000 Investments (non-trading) 2,40,000 2,20,000

Profit and loss A/c 2,10,000 3,00,000 Stock 4,00,000 3,85,000

11% Debentures 5,00,000 3,00,000 Debtors 2,88,000 4,15,000

N
Creditors 1,85,000 2,15,000 Cash and bank 88,000 93,000

Provision for tax 80,000 1,05,000 Prepaid expenses

N
15,000 11,000

Proposed dividend 1,36,000 1,44,000 Premium on redemption

A
of Debentures - 20,000

24,31,000 25,34,000 24,31,000 25,34,000

M
Additional information:

(1) Investments were sold during the year at a profit of ` 15,000.

X
(2) During the year an old machine costing ` 80,000 was sold for ` 36,000. Its written down value was ` 45,000.

A
(3) Depreciation charged on plant and machinery @ 20 per cent on the opening balance.

(4) There was no purchase or sale of land and buildings.

T
(5) Provision for tax made during the year was ` 96,000.

(6) Preference shares were issued for consideration of cash during the year.

You are required to prepare: (i) Cash flow statement as per IAS-3, (ii) Schedule of Changes in working capital.
 Key to Practical Exercises

Exercise 6-1

Working Notes

Land A/c

` `
To Balance b/d 6,00,000 By Balance c/d 7,50,000

To Bank A/c (purchases) (bal. figure) 1,50,000

7,50,000 7,50,000

Plant and Machinery A/c

To Balance b/d 12,00,000 By Bank A/c (plant sold) 60,000

N
To Profit on plant sold 10,000 By Acc. depreciation A/c (on plant sold) 1,00,000

To Bank A/c (purchases) (bal. figure) 3,00,000 By Balance c/d 13,50,000

N
15,10,000 15,10,000

A
Accumulated Depreciation A/c

M
To Plant & machinery A/c (on plant sold) 1,00,000 By Balance b/d 4,20,000

To Balance c/d 4,50,000 By Depreciation A/c (bal. figure) 1,30,000

X
5,50,000 5,50,000

A
Loans to Subsidiary A/c

T
To Balance b/d 50,000 By Bank A/c (bal. figure) 50,000

50,000 50,000

Equity Share Capital A/c

To Balance c/d 12,00,000 By Balance b/d 9,00,000

By Bank A/c (bal. figure) 3,00,000

12,00,000 12,00,000

Securities Premium A/c

To Balance c/d 90,000 By Bank A/c (bal. figure) 90,000

90,000 90,000

9% Debentures A/c

To Bank A/c (bal. figure) 1,00,000 By Balance b/d 4,00,000

To Balance c/d 3,00,000

4,00,000 4,00,000

Provision for Taxation A/c

To Bank A/c (tax paid) 1,80,000 By Balance b/d 1,50,000

To Balance c/d 3,00,000 By Transfer from P & L A/c 3,30,000

4,80,000 4,80,000
 Proposed Dividend A/c

To Bank A/c (dividend paid) 45,000 By Balance b/d 45,000

To Balance c/d 1,00,000 By Transfer from P & L A/c 1,00,000

1,45,000 1,45,000

Cash flow Statement of Winners Limited for the year ended 31.3.2016 `
( )

(A) Cash flows from Operating Activities

Net profit before tax and extraordinary items 5,50,000

Adjustments for:

Depreciation 1,30,000

Provision for taxation 3,30,000

Proposed dividend 1,00,000

Profit on sale of plant (10,000)

Operating profit before working capital changes 11,00,000

N
Adjustment for:

Increase in debtors (1,00,000)

N
Increase in stock-in-trade (80,000)

A
Decrease in creditors (1,75,000)

Cash generated from operations 7,45,000

M
Tax paid (1,80,000)

X
Net cash from Operating Activities 5,65,000

(B) Cash flows from Investing Activities

A
Purchase of land (1,50,000)

T
Sale of plant 60,000

Purchase of plant and machinery (3,00,000)

Refund of loans from subsidiary 50,000

Net cash used in Investing Activities (3,40,000)

(C) Cash flows from Financing Activities

Issue of equity shares at premium 3,90,000

Redemption of debentures (1,00,000)

Dividends paid (45,000)

Net cash from Financing Activities 2,45,000

Net increase in cash and cash equivalents (A) + (B) + (C) 4,70,000

Cash and cash equivalents at the beginning of the year 90,000

Cash and cash equivalents at the end of the year 5,60,000

Exercise 6-2

Debtors A/c ( ` crores)

To Balance b/d 457 By Bank A/c (collection) (bal. figure) 19,916

To Sales A/c 20,301 By Balance c/d 842

20,758 20,758
 Provision for Taxation A/c

To Income-tax A/c (tax paid) (bal. figure) 335 By Balance b/d 544

To Balance c/d 266 By Profit and Loss A/c 57

601 601

Building and Equipment A/c

To Balance b/d 21,187 By Accumulated Depreciation A/c 12

To Profit & Loss A/c 42 By Bank A/c (equipment sold) 70

To Bank A/c (purchase) (bal. figure) 2,487 By Balance c/d 23,634

23,716 23,716

Accumulated Depreciation A/c

To Building and Equip. A/c (bal. figure) 12 By Balance b/d 6,692

To Balance c/d 9,214 By P & L A/c (current year provision) 2,534

9,226 9,226

N
Calculation of Sale Proceeds of Asset ( ` crores)

N
Original cost of purchase 40

Less: Depreciation provided till date 12

A
W.D.V. as on date 28

Add: Profit on sale as per Income statement 42

M
Sale proceeds of asset 70

X
Calculation of Cash paid to Suppliers and Employees ( ` crores)

A
Cost of Goods Sold 15,984

T
Add: Operating expenses 891

Salaries and wages 375

17,250

Add: Other liabilities at the beginning 248

Creditors at the beginning 3,345

Stock at the end 1,823

Advances at the end 4,059

Other current assets at the end 48 9,523

26,773

Less: Creditors at the end 2,959

Other liabilities at the end 643

Stock at the beginning 1,409

Advance at the beginning 1,676

Other current assets at the beginning 25 6,712

Cash paid to Suppliers and Employees 20,061

Cash flow Statement of RIL Ltd. for the year ended 31-3-2016 (Direct Method) ( ` crores)

Cash flow from Operating Activities:

Cash receipts from customers 19,916

Cash paid to suppliers and employees (20,061)

Cash generated from operations (145)

Income-tax paid (335)

 ( ` crores)

Other income 645

Net Cash Inflow from Operating Activities (a) 165

Cash flow from Investing Activities:

Purchase of land (128)

Purchase of building and equipment (2,487)

Sale of equipment 70

Purchase of investments (1,772)

Net Cash Outflow in Investing Activities (b) (4,317)

Cash flow from Financing Activities:

Issue of equity shares 120

Issue of preference shares 40

Share premium 772

Loans repaid (130)

N
Dividend (420)

Tax on dividend (46)

N
Net Cash Inflow from Financing Activities (c) 336

A
Net decrease in Cash and Cash equivalents during the period (a + b + c) (3,816)

Cash and Cash equivalents at the beginning 4,898

M
Cash and Cash equivalents at the end 1,082

X
Cash flow Statement of RIL Ltd. for the year ended 31-3-2016 (Indirect Method) ( ` crores)

Cash flow from Operating Activities

A
Net profit before taxation and extraordinary item (1,147 + 57 - 42) 1,162

T
Adjustments for depreciation 2,534

Operating profit before working capital changes 3,696

Increase in debtors (385)

Increase in stock (414)

Increase in advances (2,383)

Increase in other current assets (23)

Decrease in creditors (386)

Increase in other liabilities 395

Income-tax paid (335)

Net Cash Inflow from Operating Activities (a) 165

Cash flow from Investing Activities:

Purchase of land (128)

Purchase of building and equipment (2,487)

Sale of equipment 70

Purchase of investments (1,772)

Net Cash Outflow in Investing Activities (b) (4,317)

Cash flow from Financing Activities:

Issue of equity shares 120

Issue of preference shares 40

Share premium 772

Loans repaid (130)

 ( ` crores)

Dividend (420)

Tax on dividend (46)

Net Cash Inflow from Financing Activities (c) 336

Net Increase in Cash and Cash equivalents during the period (a) + (b) + (c) (3,816)

Cash and Cash equivalents at the beginning 4,898

Cash and Cash equivalents at the end 1,082

Note - Since tax on dividend (corporate dividend tax) is paid on declaration/payment of dividend, it is treated as a

cash outflow from financing activities.

Exercise 6-3

Working Notes `
( )

Retained profit 70,000

Less: Balance as on 31.3.2015 (50,000)

N
20,000

N
Provision for taxation 1,35,000

Proposed dividend 90,000

A
Net profit before taxation 2,45,000

M
Land and Building A/c

` `

X
To Balance b/d 2,00,000 By Cash A/c (sale) 1,50,000

A
To Capital reserve A/c (profit on sale) 30,000 By Balance c/d 1,50,000

T
To Capital reserve A/c (revaluation profit) 70,000

3,00,000 3,00,000

Plant and Machinery A/c

To Balance b/d 5,00,000 By Cash A/c (sale) 90,000

To Profit and loss A/c 40,000 By Depreciation A/c 1,35,000

To Debentures A/c 1,00,000 By Balance c/d 7,65,000

To Bank A/c 3,50,000

9,90,000 9,90,000

Investments A/c

To Balance b/d 80,000 By Cash (sale) 70,000

To Profit and loss account 20,000 By Dividend (pre-acquisition) 5,000

To Bank (bal. figure) 25,000 By Balance c/d 50,000

1,25,000 1,25,000

Capital Reserve A/c

To Balance c/d 1,00,000 By Profit on sale of land 30,000

By Profit on revaluation of land 70,000

1,00,000 1,00,000
 General Reserve A/c

To Voluntary separation cost 50,000 By Balance b/d 2,50,000

To Capital redemption reserve A/c 1,00,000

To Balance c/d 1,00,000

2,50,000 2,50,000

Proposed Dividend A/c

To Bank (bal. figure) 60,000 By Balance b/d 60,000

To Balance c/d 90,000 By Profit and loss A/c 90,000

1,50,000 1,50,000

Provision for Taxation A/c

To Bank (bal. figure) 1,00,000 By Balance b/d 60,000

To Balance c/d 95,000 By Profit and loss A/c 1,35,000

N
1,95,000 1,95,000

N
Voluntary Separation Payments A/c

To Balance b/d 65,000 By General reserve 50,000

A
To Bank (bal. figure) 1,10,000 By Balance c/d 1,25,000

1,75,000 1,75,000

M
`

X
Cash flow Statement of Ryan Limited for the year ended 31st March, 2016 (Indirect Method) ( )

Cash flow from Operating Activities

A
Net profit before taxation 2,45,000

T
Adjustment for:

Depreciation 1,35,000

Preliminary expenses 15,000

Profit on sale of plant (40,000)

Profit on sale of investments (20,000)

Interest on debentures 18,000

Operating profit before working capital changes 3,53,000

Increase in inventory (5,000)

Decrease in bills receivable 5,000

Increase in debtors (45,000)

Increase in creditors 15,000

Decrease in bills payable (10,000)

Increase in accrued liabilities 10,000

Cash generated from operations 3,23,000

Income taxes paid (1,00,000)

2,23,000

Voluntary separation payments (1,10,000)

Net cash from operating activities (A) 1,13,000

 `
( )

Cash flow from Investing Activities

Proceeds from sale of land 1,50,000

Proceeds from sale of plant 90,000

Proceeds from sale of investments 70,000

Purchase of plant (3,50,000)

Purchase of investments (25,000)

Pre-acquisition dividend received 5,000

Net cash used in Investing Activities (B) (60,000)

Cash flow from Financing Activities

Proceeds from issue of equity shares 1,00,000

Proceeds from issue of debentures 1,00,000

Redemption of preference shares (2,00,000)

Dividends paid (60,000)

N
Interest paid on debentures (18,000)

N
Net cash used in Financing Activities (C) (78,000)

Net decrease in cash and cash equivalents during the year (A) + (B) + (C) (25,000)

A
Cash and cash equivalents at the beginning of the year 90,000

Cash and cash equivalents at the end of the year 65,000

Exercise 6-4

Working Notes

X M
A
  
Increase in opening stock due to revaluation = ×  = ` 24,000

T


Opening balance of other current assets = 11,10,000 + 24,000 = ` 11,34,000

Due to under valuation of stock, the opening balance of Profit and Loss Account be increased by ` 24,000.

Opening balance of P&L A/c after revaluation of stock = 2,40,000 + 24,000 = ` 2,64,000

Investment A/c

` `
To Balance b/d 4,00,000 By Bank A/c (sale) (bal. figure) 1,20,000

To Capital reserve A/c By Balance c/d 3,20,000

(profit on sale of investment) 40,000

4,40,000 4,40,000

Fixed Assets A/c

ToBalance b/d 32,00,000 By Bank A/c (sale of assets) 1,00,000

ToBank A/c (purchase)(bal. figure) 8,56,000 By Accumulated

depreciation A/c 80,000

By Profit and loss A/c

(loss on sale of assets) 20,000 2,00,000

By Accumulated

depreciation A/c 40,000

 ` `

By Profit and loss A/c

(assets written off) 16,000 56,000

By Balance c/d 38,00,000

40,56,000 40,56,000

Accumulated Depreciation A/c

To Fixed assets A/c 80,000 By Balance b/d 9,20,000

To Fixed assets A/c 40,000 By Profit and loss A/c

(depreciation for the period)

To Balance c/d 11,60,000 3,60,000

12,80,000 12,80,000

Unpaid dividend is taken as non-current item and dividend paid is shown at ` 1,04,000 (1,20,000 - 16,000).

Note: Alternatively, unpaid dividend can be assumed as current liability and hence, dividend paid can be shown at

` 1,20,000. Dut to this assumption cash flow from operating activities would be affected. The cash flow from

N
operating activities will increase by `16,000 to ` 6,08,000 and cashflow from financing activities will get reduced by
` 16,000 to ` 28,000.

N
Cash flow Statement of New Light Ltd. for the year ended 31st March, 2016 `
( )

A
Cash flow from Operating Activities

Profit after appropriation

M
Increase in Profit and loss A/c after inventory adjustment

[3,00,000 - (2,40,000 + 24,000)] 36,000

X
Transfer to General reserve 1,20,000

A
Proposed Dividend 1,44,000

T
Provision for tax 3,40,000

Net profit before taxation and extraordinary item 6,40,000

Adjustments for:

Preliminary expenses written off 40,000

Depreciation 3,60,000

Loss on sale of fixed assets 20,000

Decrease in value of fixed assets 16,000

Premium on redemption of preference share capital 6,000

Premium on redemption of debentures 6,000

Operating profit before working capital changes 10,88,000

Increase in current liabilities (5,20,000 - ` 4,80,000) 40,000

Increase in other current assets [13,10,000 - (11,10,000 + 24,000)] (1,76,000)

Cash generated from operations 9,52,000

Income taxes paid (3,60,000)

Net cash from Operating Activities 5,92,000

Cash flow from Investing Activities

Purchase of fixed assets (8,56,000)

Proceeds from sale of fixed assets 1,00,000

Proceeds from sale of investments 1,20,000

Net cash used in Investing Activities (B) (6,36,000)

 `
( )

Cash flow from Financing Activities

Proceeds from issuance of share capital 4,00,000

Redemption of preference share capital (1,20,000 + 6,000) (1,26,000)

Redemption of debentures (1,20,000 + 6,000) (1,26,000)

Dividend paid (1,04,000)

Net cash from Financing Activities (C) 44,000

Net increase in cash and cash equivalent during the year (A) + (B) + (C) Nil

Cash and cash equivalent at the beginning of the year 10,000

Cash and cash equivalent at the end of the year 10,000

Exercise 6-5

Fixed Assets A/c

Particulars ` Particulars `

N
To Balance b/d 38,40,000 By Depreciation provision A/c 84,000

To Cash A/c (bal. figure) 10,20,000 (Tr. of depreciation on fixed assets sold)

N
(purchase of fixed assets) By Cash A/c 1,20,000

(Fixed assets sold)

A
By Profit and Loss A/c 36,000

(Loss on assets sold)

M
By Depreciation provision A/c 48,000

X
((Tr. of depreciation on fixed assets

written off)

A
By Profit and Loss A/c 12,000

T
(Fixed assets written off)

By Balance c/d 45,60,000

48,60,000 48,60,000

Depreciation Provision A/c

To Fixed assets A/c 84,000 By Balance b/d 11,04,000

(on fixed assets sold)

By Profit and loss A/c 4,20,000

(Depreciation provided during the year)

To Fixed assets A/c 48,000

(on fixed assets written off)

To Balance c/d 13,92,000

15,24,000 15,24,000

Investments A/c

To Balance b/d 4,80,000 By Cash A/c (sale of investments) 1,44,000

To Capital reserve A/c 48,000 By Balance c/d 3,84,000

5,28,000 5,28,000

Capital Reserve A/c

By Balance b/d Nil

To Balance c/d 48,000 By Investments A/c 48,000

48,000 48,000
 General Reserve A/c

By Balance b/d 8,16,000

To Balance c/d 9,60,000 By Profit and loss A/c 1,44,000

9,60,000 9,60,000

Proposed Dividend A/c

To Cash A/c 1,26,000 By Balance b/d 1,44,000

To Unpaid dividend A/c 18,000 By Profit and loss A/c 1,74,000

To Balance c/d 1,74,000

3,18,000 3,18,000

Provision for Tax A/c

To Cash A/c 4,32,000 By Balance b/d 4,32,000

To Balance c/d 4,08,000 By Profit and loss A/c 4,08,000

8,40,000 8,40,000

N
Profit and Loss A/c

N
To Depreciation provision A/c 4,20,000 By Balance b/d 2,88,000

(transfer)

A
By Under valuation of Opening stock 28,800

To Fixed assets A/c 36,000 By Funds from Operation 12,99,600

(loss on fixed assets sold)

M
To Fixed assets A/c 12,000

X
(fixed assets written off)

To General reserve A/c (transfer) 1,44,000

A
To Proposed dividend A/c 1,74,000

T
To Provision for tax A/c 4,08,000

To Preliminary expenses written off 48,000

To Premium on redemption

of debentures 14,400

To Balance c/d 3,60,000

16,16,400 16,16,400

Cash Flow Statement for the year ended 31st March, 2016 `
( )

(A) Cash flow from Operating Activities

Profit and Loss A/c [3,60,000 - (2,88,000 + 28,800)] 43,200

Adjustments:

Increase in general reserve 1,44,000

Depreciation 4,20,000

Provision for tax 4,08,000

Loss on sale of machine 36,000

Premium on redemption of debentures 14,400

Proposed dividend 1,74,000

Preliminary expenses written off 48,000

Fixed assets written off 12,000 12,56,400

Funds from Operation 12,99,600

 `
( )

Increase in sundry current liabilities 48,000

Increase in current assets [12,72,000 - (11,34,000 + 28,800)] (1,09,200)

Cash before tax 12,38,400

Tax paid 4,32,000

Cash from Operating Activities 8,06,400

(B) Cash from Investing Activities:

Purchase of fixed assets (10,20,000)

Sale of investment 1,44,000

Sale of fixed assets 1,20,000 (7,56,000)

(C) Cash from Financing Activities:

Issue of share capital 4,80,000

Redemption of debentures (3,02,400)

N
Dividend paid (1,26,000) 51,600

Net increase in cash and cash equivalents (A) + (C) - (B) 1,02,000

N
Opening cash and cash equivalents 2,10,000

A
Closing cash and cash equivalents 3,12,000

M
Exercise 6-6

Working Notes

X
Provision for Tax A/c

` `

A
To Bank (paid) 71,000 By Balance b/d 80,000

T
To Balance c/d 1,05,000 By Profit and loss A/c 96,000

1,76,000 1,76,000

Investment A/c

To Balance b/d 2,40,000 By Bank A/c 35,000

To Profit and loss A/c (profit on sale) 15,000 By Balance c/d 2,20,000

2,55,000 2,55,000

Plant and Machinery A/c

To Balance b/d 6,00,000 By Bank (sale) 36,000

To Bank A/c (purchase) 2,25,000 By Profit and loss A/c (loss on sale) 9,000

By Depreciation 1,20,000

By Balance c/d 6,60,000

8,25,000 8,25,000

Note - Since the date of redemption of debentures is not mentioned in the question, it is assumed that the debentures

are redeemed at the beginning of the year.

Cash Flow Statement for the year ending 31st March, 2016 `
( )

(A) Cash flow from Operating Activities

Profit and Loss A/c as on 31-3-2016 3,00,000

Less: Profit and Loss as on 31-3-2015 2,10,000

90,000
 `
( )

Add: Transfer to General reserve 25,000

Provision for tax 96,000

Proposed dividend 1,44,000 2,65,000

Profit before tax 3,55,000

Adjustment for Depreciation:

Land and buildings 50,000

Plant and machinery 1,20,000 1,70,000

Profit on sale of investments (15,000)

Loss on sale of plant and machinery 9,000

Goodwill written off 20,000

Interest expenses 33,000

Operating profit before working capital changes 5,72,000

N
Adjustment for Working capital changes:

Decrease in Prepaid expenses 4,000

N
Decrease in Stock 15,000

A
Increase in Debtors (1,27,000)

Increase in Creditors 30,000

M
Cash generated from operations 4,94,000

X
Income tax paid (71,000)

Net Cash Inflow from Operating Activities (a) 4,23,000

A
(B) Cash Flow from Investing Activities

T
Sale of investment 35,000

Sale of Plant and machinery 36,000

Purchase of Plant and machinery (2,25,000)

Net Cash Outflow from Investing Activities (b) (1,54,000)

(C ) Cash Flow from Financing Activities

Issue of Preference shares 1,00,000

Premium received on issue of securities 25,000

Redemption of Debentures at premium (2,20,000)

Dividend paid (1,36,000)

Interest paid to Debenture holders (33,000)

Net Cash Outflow from Financing Activities (c) (2,64,000)

Net increase in Cash and Cash Equivalents during the year (a) + (b) + (c) 5,000

Cash and Cash Equivalents at the beginning of the year 88,000

Cash and Cash Equivalents at the end of the year 93,000

Schedule of Changes in Working Capital `
( )

Particulars 31st March Change in working capital

2015 2016 Increase Decrease

Current Assets:

Stock 4,00,000 3,85,000 - 15,000

Debtors 2,88,000 4,15,000 1,27,000 -

Prepaid expenses 15,000 11,000 - 4,000

Cash and bank 88,000 93,000 5,000 -

7,91,000 9,04,000

Current Liabilities:

Creditors 1,85,000 2,15,000 - 30,000

1,85,000 2,15,000

Working Capital 6,06,000 6,89,000

N
Increase in Working capital 83,000 - - 83,000

6,89,000 6,89,000 1,32,000 1,32,000

A N
X M
T A
 Key to Short Answer Questions

True or False Statements

1. False - The information about the cash flows of a firm is useful in providing users of financial statements
with a basis to assess the ability of the enterprise to generate cash and cash equivalents to generate cash and

cash equivalents and need of the enterprise to utilize these cash flows.

2. False - Accounting Standard-3 (revised) made it mandatory for all listed companies and companies whose
turnover during the accounting period exceeds ` 50 crores.

3. False - Cash equivalents are short-term, highly liquid investments that are readily convertible into known
amounts of cash and which are subject to an insignificant risk of changes in value. E.g. treasury bills,

commercial paper etc.

4. False - The difference between the cash inflows and outflows is known as ‘net cash flow’ which can be either

N
net cash inflow or net cash outflow.

5. True - The comparison of actual and budgeted cash flow statement will disclose the failure or success of

N
management in managing cash resources and necessary remedial measures can be taken in case of

deviations.

A
6. False - A cash budget is different from a cash flow statement. The cash budget is prepared for the

forthcoming period as a planning exercise.

M
7. False - Cash advances and loans made to third party is considered as investment activity.

X
8. True - The difference amount arise due to changes in exchange rates, should not be included in operating,

A
investing and financing activities. This shall be shown separately in the reconciliation statement.

True

T
9. - Such transactions should be disclosed elsewhere in the financial statements. Example of such

transaction is issue of shares for acquisition of plant and machinery.

10. False - Such receipts should be considered as cash inflow from investing activities. In case of financial

enterprises, the interest and dividends received are classified as cash inflows from operating activities.

11. False - It is a non-cash transaction, which cannot be taken into cash flow statement.
12. True - For preparation of cash flow statement, balance sheets at the beginning and at the end of the

accounting period is required to identify the changes that have taken place in assets, liabilities and capital.

13. True - Under direct method, items like depreciation, amortization of intangible assets, preliminary

expenses, discount on issue or redemption of debentures etc. are ignored from cash flow statement since

the direct method includes only cash transactions and non-cash items are omitted.

Choose Correct Word

1. operating

2. indirect

3. exchange rate

4. investing

5. AS-3 Revised

6. financing

7. operating

8. reduce
 9. postmortem

10. direct

11. reduce

12. investing

Choose Correct Answer

1. (D) all of the above

2. (B) public deposit

3. (C) not treated as cash flows

4. (A) at the reporting date of cash flow statement

5. (C) investing activities

6. (C) cash inflows from investing activities

7. (C) financing activities

N
8. (C) ` 120 lakhs

N
9. (C) as given (A) and (B)

10. (B) adjustment of bonus towards call money

A
11. (A) supplements the profit and loss account and balance sheet

X M
T A
 Practical Exercises

Exercise 7-1 X Ltd. earned ` 1.6 million on net assets of ` 20 million. The cost of capital is 11.5%. Calculate the net
percentage return on investment and EVA.

Exercise 7-2 Calculate Economic Value Added (EVA) with the help of following information of Hypothetical Ltd.:

Financial leverage : 1.4 times Cost of Equity : 17.5% Income Tax Rate: 30%

Capital structure : Equity capital ` 170 lakhs; Reserves & surplus ` 130 lakhs; 10% Debentures ` 400 lakhs

Exercise 7-3 Tender Ltd. has earned a net profit of ` 15 lakhs after tax at 30%. Interest cost charged by financial
institution was ` 10 lakhs. The invested capital is ` 95 lakhs of which 55% is debt. The company maintains a weighted
average cost of capital of 13%. Required:

(a) Compute the operating income

N
(b) Compute the Economic value added (EVA)

(c) Tender Ltd. has 6 lac equity shares outstanding. How much dividend can the company pay before the value

N
of the entity starts declining?

Exercise 7-4 `

A
Calculate EVA from the following data for the year ended 31st March, 2016 ( crores)

Average debt 50

M
Average equity 2766

Profit after tax, before exceptional item 15.41

X
Interest after taxes 5

A
Cost of debt (post tax) 7.72% Cost of equity 16.7% Weighted average cost of capital 16.54%

T
Exercise 7-5 From the following information concerning Nebula Ltd., prepare a statement showing computation

of EVA for the year ended 31st March, 2015:

Summarized Profit and Loss Account for the year ended 31st March, 2016 `
( )

Sales 20,00,000

Cost of goods sold 12,00,000

Gross profit 8,00,000

Expenses: General 2,00,000

Office and administration 2,50,000

Selling and distribution 64,000 5,14,000

Profit before interest and tax (PBIT) 2,86,000

Interest 36,000

Profit before tax (PBT) 2,50,000

Tax 40% 1,00,000

Profit after tax 1,50,000

 Summarized Balance Sheet as on 31st March, 2016

Liabilities ` Assets `
Equity shares 2,40,000 Fixed assets (net) 6,00,000

Reserves 1,60,000 Current Assets:

Term loan 2,40,000 Stock 1,20,000

Current liabilities 1,60,000 Debtors 60,000

Bank 20,000

8,00,000 8,00,000

Other particulars:

(1) General expenses include R&D expenses of ` 80,000. For EVA computation R&D expenses are to be considered
as an investment.

(2) Cost of goods sold include depreciation expense of ` 60,000.

(3) The expectation return of shareholders is 12%.

N
Exercise 7-6 Delta Ltd.’s current financial year’s income statement reports its net income as ` 15,00,000. Delta’s
marginal tax rate is 40% and its interest expense for the year was ` 15,00,000. The company has ` 1,00,00,000 of

N
invested capital, of which 60% is debt. In addition, Delta Ltd. tries to maintain a WACC of 12.6%.

(i) Compute the operating income or EBIT earned by Delta Ltd. in the current year.

A
(ii) What is Delta Ltd.’s EVA for the current year ?

(iii) Delta Ltd. has 2,50,000 equity shares outstanding. According to the EVA you computed in (ii), how much can

M
Delta pay in dividend per share before the value of the company would start to decrease? If Delta does not pay

X
any dividends, what would you expect to happen to the value of the company ?

A
Exercise 7-7 The Accounts of Siteraze Ltd. (SL), engaged in manufacturing business are summarized below :

T
Income Statement for the year ended March 31, 2016 ( million)

Sales revenue 95.00

Less: Cost of goods sold 59.10

General expenses 6.80

Administrative expenses 7.80

Selling and distribution expenses 2.90

Interest on loan 1.80 78.40

Earnings before tax (EBT) 16.60

Less: Corporate taxes (0.35) 5.81

Earnings after taxes (EAT) 10.79

Balance Sheet as on March 31, 2016

Liabilities ` million Assets ` million

Equity share capital 10.00 Freehold land and buildings (net) 20.00

(10 lakh shares of ` 10 each) Plant and machinery (net) 28.50

Reserves and surplus 31.50 Current Assets:

10% Loan 18.00 Stock 10.00

Creditors and other liabilities 18.00 Debtors 15.00

Bank and cash balances 4.00

77.50 77.50
Additional information:

(1) The risk free rate of return in the economy is 8% and the premium expected from business in general is 5%.

The beta of Siteraze Ltd. shares is currently 1.27.

(2) The equity shares of this company (SL) quoted in the market as on 31.3.2016 are ` 50 per share.

(3) General expenses include R & D expenses of ` 0.50 million.

Note: For EVA computation R&D expenses are to be considered as an investment.

Requirements:

(i) Determine the Economic Value Added (EVA) for the year ended March 31, 2016 and

(ii) Determine the amount of Market Value Added (MVA) of the year ended March 31, 2016.

Exercise 7-8 ABC Co. is considering a new sales strategy that will be valid for the next 4 years. They want to know

the value of new strategy. Following information relating to the year which has just ended, is available:

Income Statement `
( )

Sales 20,000

N
Gross margin (20%) 4,000

Administration, Selling & Distribution Expense (10%) 2,000

N
PBT 2,000

Tax (30%) 600

A
PAT 1,400

M
Balance Sheet Information `
( )

Fixed assets 8,000

X
Current assets 4,000

A
Equity 12,000

T
If it adopts the new strategy, sales will grow at the rate of 20% per year for three years. The gross margin ratio, assets

turnover ratio, the capital structure and income-tax rate will remain unchanged.

Depreciation would be at 10% of net fixed assets at the beginning of the year.

The Company’s target rate of return is 15%.

Determine the incremental value due to adoption of the strategy.

 Key to Practical Exercises

Exercise 7-1

Earnings = ` 1.6 million Capital employed = ` 20 million Cost of capital = 11.5%

C  NJMMJPO
Return on Investment = ×  = 8%
C  NJMMJPO
Economic Value Added = ` 1.6 million - ( ` 20 million × 11.5/100)

= ` 1.6 million - ` 2.3 million = (-) ` 0.7 million (negative EVA)

Exercise 7-2

EBIT
Financial Leverage =
EBT

N
Financial Leverage = 1.4 times (given)

Then,

N
EBIT
1.4 =
EBT

A
EBIT
1.4 =
EBIT - 40

M
1.4 (EBIT - 40) = EBIT

1.4 EBIT - 56 = EBIT

X
1.4 EBIT - EBIT = 56

A
0.4 EBIT = 56

T
EBIT = 56/0.4 = 140

∴ Earnings Before Interest and Tax = ` 140 lakh

NOPAT = EBIT - Tax = ` 140 lakhs (1- 0.30)

= ` 98 lakhs

WACC = (K × % of equity) + (K × % of debt)

e d

= (17.5% × 300/700) + (10% (1- 0.30) × 400/700)

= 7.5% + 4% = 11.5%

EVA = NOPAT - (WACC × Total capital)

= ` 98 lakh - (0.115 × ` 700 lakhs) = ` 17.50 lakhs

Exercise 7-3

C   
Taxable income = = ` 21,42,857
 

Operating income = Taxable income + Interest

= ` 21,42,857 + ` 10,00,000 = ` 31,42,857

Economic Value Added = [EBIT (1 - t)] - [WACC × Invested capital]

= [ ` 31,42,857 (1 - 0.30)] - [0.13 × ` 95,00,000]

= ` 22,00,000 - ` 12,35,000 = ` 9,65,000
Dividend that can pay before the value of the entity starts declining

= ` 9,65,000/6,00,000 shares = ` 1.6083

Exercise 7-4

Source Amount Proportion Cost of capital Weighted cost

( ` crores) (%) of capital (%)

Equity 2,766 0.982 16.70 16.40

Debt 50 0.018 7.72 0.14

2,816 1.000 WACC = 16.54

Cost of Capital Employed (COCE) = 2,816 × 16.54/100 = ` 465.77 crores

( ` crores)

Profit after tax, before exceptional items 1,541

Add: Interest after taxes 5

Net Operating Profit After Tax (NOPAT) 1,546

N
EVA = NOPAT - COCE

N
= 1,546 - 465.77 = 1,080.23 crores

A
Exercise 7-5

Calculation of NOPAT `
( )

M
Net profit after tax and interest 1,50,000

` 36,000 × (1 - 0.4)]

X
Add: Tax adjusted interest [ 21,600

Profit after tax, but before interest 1,71,600

A
R & D expenses, reintegrated 80,000

T
Net operating profit after tax (NOPAT) 2,51,600

Calculation of Capital Employed `

( )

Share capital 2,40,000

Reserves 1,60,000

Adjustment for R & D 80,000

Equity funds 4,80,000

Add: Long-term debt 2,40,000

Capital employed 7,20,000

 , + &  +  ,  − U
× % 
WACC =  F   E 
 %+&   %+& 

  ×   +    − 

 
=
   
     

= 0.08 + 0.03 = 0.11 or 11%

Cost of Capital Employed = Capital employed × WACC = ` 7,20,000 × 11/100 = ` 79,200

Economic Value Added = NOPAT - Cost of capital employed = ` 2,51,600 - ` 79,200 = ` 1,72,400
Exercise 7-6

Reported Net Income = ` 15,00,000 Capital invested = ` 1,00,00,000

Marginal tax rate = 40% Debt = ` 60,00,000

Interest expense for the year = ` 15,00,000 Expected WACC = 12.6%

(i) Computation of Operating Income or EBIT for the current year

/FU JODPNF C   

Taxable income = = = ` 25,00,000
 − 


Again, Taxable income = EBIT - Interest

EBIT = Taxable income + Interest = ` 25,00,000 + ` 15,00,000 = ` 40,00,000

(ii) Computation of Economic Value Added (EVA) for the current year

EVA = EBIT(1 - T) - (Capital invested × WACC)

= [ ` 40,00,000 (1 - 0.40)] - [` 1,00,00,000 × 0.126]

= ` 24,00,000 - ` 12,60,000 = ` 11,40,000

N
(iii) Analysis

C   
EVA dividend = = ` 4.56

N
   TIBSFT

A
In case, if dividend is skipped off, the value of Delta Ltd. would increase due to its expected higher growth and higher

level of EBIT.

M
Exercise 7-7

X
Calculation of NOPAT ( ` million)

Net profit after tax and interest

A
10.79

Add: Tax adjusted interest [1.80 (1 - 0.35)] 1.17

T
Profit after tax before interest 11.96

R & D expenses reintegrated 0.50

Net operating profit after taxes (NOPAT) 12.46

Calculation of Capital Employed ( ` million)

Share capital 10.00

Reserves and surplus 31.50

Adjustment for R & D 0.50

Equity 42.00

10% Loan 18.00

Capital employed 60.00

Calculation of WACC

Cost of Equity = 8% + 1.27 (5%) = 14.35%

Cost of Debt = 10%

WACC = (14.35 × 0.70) + [10(1 - 0.35) × 0.30] = 10.045 + 1.95 = 11.995% say 12%

Calculation of Economic Value Added (EVA) ( ` million)

Net operating profit after tax (NOPAT) 12.46

Less: Cost of capital employed ( ` 60 million × 0.12) 7.20

Economic Value Added (EVA) 5.26

Calculation of Market Value Added (MVA) for the year ended 31st March, 2016

Market value per Equity share = ` 50

No. of equity shares outstanding = 10,00,000

(` million)

Total market value (10,00,000 shares × ` 50) 50.00

Less: Value of equity funds:

Share capital 10.00

Reserves and Surplus 31.50

R & D adjustment 0.50 42.00

Market Value Added (MVA) 8.00

Exercise 7-8

Projected Cash Flow Statement `

( )

Particulars Year 1 Year 2 Year 3 Year 4

N
Sales (growth rate at 20% p.a. for 3 years) 24,000 28,800 34,560 34,560

PBT (10% of sales) 2,400 2,880 3,456 3,456

N
PAT (70% of PBT) 1,680 2,016 2,419.2 2,419.2

Depreciation (10% of net fixed assets) 800 960 1,152 1,382

A
(a) 2,480 2,976 3,571.2 3,801.2

M
Addition to fixed assets 2,400 2,880 3,456 1,382

Increase in current assets 800 960 1,152 -

X
(b) 3,200 3,840 4,608 1,382

A
Operating cash flow (a) - (b) (720) (864) (1,036.8) 2,419.2

T
Projected Balance Sheet `
( )

Particulars Year 1 Year 2 Year 3 Year 4

Fixed assets (40% of sales) 9,600 11,520 13,824 13,824

Current assets (20% of sales) 4,800 5,760 6,912 6,912

Total assets 14,400 17,280 20,736 20,736

Equity 14,400 17,280 20,736 20,736

Calculation of Present Value of Projected Cash flow `

( )

Year Cash flow P.V. @ 15% Present values

1 - 720 0.870 - 626.40

2 - 864 0.756 - 653.18

3 - 1,036.8 0.658 - 682.21

- 1,961.79

Residual value = 2,419.20/0.15 = ` 16,128

16,128 16,128
P.V. of residual value =
3
= = ` 10,603.55
(1.15) 1.521

Total shareholders value = 10,603.55 - 1,961.79 = ` 8,641.76

Pre-strategy value = 1,400/0.15 = ` 9,333.33

Value of strategy = 8,641.76 - 9,333.33 = (-) ` 691.57

Analysis - There is a negative incremental value due to adoption of the strategy and hence it is not financially viable.
 Key to Short Answer Questions

True or False Statements

1. False - Economic Value Added (EVA) is most directly linked to the creation of shareholder’s wealth over

time.

2. True - Value drivers for a business concern are its drivers for cash flow, profitability and its sustainability.

3. True - The company creates shareholder value only if it generates returns in excess of its cost of capital. The

excess of returns over cost of capital is simply termed as EVA. If a company’s EVA is negative, the firm

is destroying shareholders wealth even though it may be reporting positive and growing EPS or return

on capital employed.

4. False - EVA is a better system, than ROI, to encourage growth in new products, new equipment, and new

manufacturing facilities.

N
5. False - EVA is the excess of returns over cost of capital. MVA is excess of market value of capital employed

in the firm over its book value of capital employed.

N
6. False - EVA measures the absolute rupee value of wealth created.

A
7. False - Under EVA, the cost of equity is measured on the basis of capital asset pricing model (CAPM).

True

M
8. - An EVA based incentive system encourages managers to operate in a such a way as to maximize the

EVA, not just of the operations they oversee but of the company as a whole.

X
9. True - In the short-term, EVA can be improved by reducing assets faster than the earnings and if this is

A
pursued for long it can lead to problems in the longer run when new improvements to the asset base

are made.

T
10. True - The value created by a particular business unit for its brand could be equated with the value of wealth

that the brand has generated over a period of time.

11. True - MVA measures how much a company’s stock has added and compares it with the capital those same

investors put into the firm. Continuous improvements in EVA year after year will lead to increase

MVA.

12. True - SVA insists the managers to take decisions which can create value for the shareholders and at the same

time, benefit other stakeholders.

13. True - VBM aim to provide consistency of the firm’s strategy, mission, governance, culture, communication,

organization of the corporation, decision processes, reward processes and systems etc.

Choose Correct Word

1. wealth

2. bonus

3. value drivers

4. economic

5. NOPAT

6. non-operating

7. residual income

8. shareholder
 9. SVA

10. less

11. MVA

12. directly

Choose Correct Answer

1. (D) all of the above

2. (A) EVA will increase

3. (C) increase

4. (B) destroying

5. (A) EVA

6. (B) if the returns exceed the WACC

7. (C) current market value of assets and liabilities

N
8. (A) EVA is a measure to determine whether an investment contributes positively to owner’s wealth

A N
X M
T A
 Practical Exercises

Exercise 8-1 You are a Finance Manager in Big Pen Ltd. The degree of operating leverage of your company is 5.0.

The degree of financial leverage of your company is 3.0.

Your Managing Director has found that the degree of operating leverage and the degree of financial leverage of your

nearest competitor Small Pen Ltd. are 6.0 and 4.0 respectively. In his opinion, the Small Pen Ltd. is better than that

of Big Pen Ltd. because of higher value of degree of leverages.

Do you agree with the opinion of your Managing Director? Give reasons.

Exercise 8-2 Consider the figures available for Bison Panels Ltd.

Net sales ` 16 crores Capital employed:

EBIT as a percentage of sales 10% Equity share capital ( ` 10 each) ` 4 crores

Corporate tax rate 40% 10% Preference shares of ` 100 each ` 3 crores

N
12% Secured debentures ` 2 crores

N
You are required to calculate: (a) EPS and (b) The percentage change in EPS if EBIT increases by 10%.

A
Exercise 8-3 A simplified income statement of Abhilash Ltd. for the year ended is given below. Calculate and

interpret its degree of operating leverage, degree of financial leverage and degree of combined leverage.

M
Particulars of income of Abhilash Ltd. for the year ended on 31st March, 2016 are as follows: `
( )

X
Sales 1,05,00,000

Variable cost 76,70,000

A
Fixed cost 7,50,000

T
EBIT 20,80,000

Interest 11,00,000

Taxes (30%) 2,94,000

Net income 6,86,000

Exercise 8-4 The share capital of a company is ` 10,00,000 with shares of face value of ` 10. The company has debt
capital of` 6,00,000 at 10% rate of interest. The sales of the firm are 3,00,000 units per annum at a selling price of
` 5 per unit and the variable cost is ` 3 per unit. The fixed cost amounts to ` 2,00,000. The company pays tax at 35%.
If the sales increase by 10%, calculate:

(i) Percentage increase in EPS,

(ii) Degree of operating leverage at the two levels, and

(iii) Degree of financial leverage at the two levels.

Exercise 8-5 DIGI Computers Ltd. is a manufacturer of computer systems. The company is marketing its products

in domestic as well as global markets. It has a total sales of ` 1 crore. Its variable and fixed costs amount to ` 60 lakh
and ` 10 lakh respectively. It has borrowed ` 60 lakh @ 10% per annum and has an equity capital of `75 lakh.
(i) What is company’s return on investment ?

(ii) Does it have favourable financial leverage ?

(iii) If the firm belongs to an industry whose asset turnover is 1, does it have a high or low asset leverage?

(iv) What are the operating, financial and combined leverages of the firm ?

(v) If sales drop to ` 50 lakh, what will be the new EBIT ?

Exercise 8-6 The Balance Sheet of Alpha Numeric Company is given below:

Liabilities ` Assets `

`
Equity capital ( 10 per share) 90,000 Net fixed assets 2,25,000

10% Long-term debt 1,20,000 Current assets 75,000

Retained earnings 30,000

Current liabilities 60,000

3,00,000 3,00,000

The company’s total assets turnover ratio is 3, its fixed operating cost is ` 1,50,000 and its variable operating cost ratio
is 50%. The income-tax rate is 50%.

You are required to:

(i) Calculate the different type of leverages for the company.

(ii) Determine the likely level of EBIT if EPS is: (a) ` 1 (b) ` 2 (c) ` 0

N N
M A
A X
T
 Key to Practical Exercises

Exercise 8-1

Particulars Big pen Ltd. Small pen Ltd.

Contribution
(1) Operating Leverage = 5 6
EBIT

EBIT
(2) Financial Leverage = 3 4
EBT

Contribution
(3) Combined Leverage = 15 24
EBT

(a) The operating leverage of Big pen Ltd. is 5 and of Small pen Ltd. is 6. It means change in the level of sales will

N
have more impact on EBIT of Small pen Ltd. than that of Big pen Ltd. The volume of fixed cost may be higher

in case of Small pen Ltd. than that of Big pen Ltd. The business risk of Small pen Ltd. is also more as compared

N
to Big pen Ltd.

(b) The financial leverage of Big pen Ltd. is 3, and of Small pen Ltd. is 4. It means the interest burden of Small pen

A
Ltd. is higher than Big pen Ltd. Financial risk of Small pen Ltd. is higher as compared to Big pen Ltd.

(c) The degree of combined leverage of Big pen Ltd. is 15 and that of Small pen Ltd. is 24. It means any change in

M
sales will show more impact on EPS in case of Small pen Ltd.

X
In view of the above, The Managing Directors’ opinion about Small pen Ltd. is wrong. Therefore, Big pen Ltd. carries

less business risk and financial risk as compared to Small pen Ltd.

T A
Exercise 8-2

EBIT = ` 16 crores × 10/100 = `1.6 crores Interest on debentures = ` 0.24 crores

Preference dividend = ` 0.30 crores Number of equity shares = 40,00,000

(a) Calculation of EPS

(EBIT - I) (1 - t) - D [(1.6 - 0.24) (1 - 0.40)] - 0.30 0.516

P
EPS = = = = ` 1.29
N 0.40 0.40

(b) Calculation of percentage change in EPS if EBIT increases by 10%.

Current EPS = ` 1.29

[(1.76 - 0.24) (1 - 0.40)] - 0.30 0.612
Revised EPS = = = ` 1.53
0.40 0.40

Increase in EPS = ` 1.53 - ` 1.29 = ` 0.24

0.24
Percentage change in EPS = × 100 = 18.6%
1.29

A 10% change in EBIT has caused 18.6% change in EPS.

Verification:

1.60 1.60
DFL = = = 1.86

1.60 - 0.24 - ( 0.30

1 - 0.40
) 0.86

A 10% change in EBIT would cause 18.6% ( i.e. 1.86 × 10%) change in EPS.
Exercise 8-3

Profitability Statement `
( )

Sales 1,05,00,000

Less: Variable cost 76,70,000

Contribution 28,30,000

Less: Fixed cost 7,50,000

EBIT 20,80,000

Less: Interest 11,00,000

EBT 9,80,000

Less: Tax @ 30% 2,94,000

EAT 6,86,000

Contribution ` 28,30,000
(i) Operating Leverage = = = 1.36

EBIT ` 20,80,000

N
It indicates that 1% change in sales is expected to result in a 1.36% change in EBIT.

EBIT ` 20,80,000

N
(ii) Financial Leverage = = = 2.12

EBT ` 9,80,000

A
It represents that 1% change in EBIT is expected to result in 2.12% change in net income.

(iii) Combined Leverage = Operating leverage × Financial leverage = 1.36 × 2.12 = 2.88

M
This means that a 1% change in sales is expected to change net income by 2.88%.

X
Exercise 8-4
`

A
( )

Particulars Existing Revised

T
Sales (units) 3,00,000 3,30,000

Sales (@ ` 5) 15,00,000 16,50,000

Less: Variable cost (@ ` 3) 9,00,000 9,90,000

Contribution 6,00,000 6,60,000

Less: Fixed cost 2,00,000 2,00,000

EBIT 4,00,000 4,60,000

Less: Interest 60,000 60,000

3,40,000 4,00,000

Less: Tax @ 35% 1,19,000 1,40,000

EAT 2,21,000 2,60,000

EAT
(i) EPS =
No. of shares

` 2,21,000 ` 2,60,000
Existing = = ` 2.21 Revised = = ` 2.60
1,00,000 shares 1,00,000 shares

0.39
Percentage increase in EPS = × 100 = 17.65%
2.21

Contribution
(ii) Degree of Operating Leverage =
EBIT

6,00,000 6,60,000
Existing = = 1.5 Revised = = 1.43
4,00,000 4,60,000
 EBIT
(iii) Degree of Financial Leverage =
EBT

4,00,000 4,60,000
Existing = = 1.176 Revised = = 1.150
3,40,000 4,00,000

Exercise 8-5

(i) Calculation of Company’s Return on Investment

Calculation of EBIT `
( )

Sales 1,00,00,000

Less: Variable cost 60,00,000

Contribution 40,00,000

Less: Fixed cost 10,00,000

EBIT 30,00,000

Calculation of Investment `
( )

Equity share capital 75,00,000

N
10% Loan 60,00,000

N
Total investment 1,35,00,000

` 30,00,000

A
EBIT
Return on Investment = × 100 = × 100 = 22.22%
Investment ` 1,35,00,000

M
(ii) Determination of Financial Leverage

X
Return on investment = 22.22% Rate of interest on loan = 10%

The interest payable on loan funds is lesser than ROI, which will cause to have favourable financial leverage.

A
(iii) Firm’s leverage if the industry asset turnover is 1:

T
Sales ` 1,00,00,000
Asset turnover ratio = = = 0.74 Industry asset turnover = 1.00
Total assets ` 1,35,00,000
The company has lower asset leverage, which means less profitable than the industry.

(iv) Calculation of Operating, Financial and Combined Leverages

Contribution ` 40,00,000
Operating leverage = = = 1.33
EBIT ` 30,00,000
EBIT ` 30,00,000
Financial leverage = = = 1.25
EBIT - Interest ` 30,00,000 - ` 6,00,000

Contribution ` 40,00,000
Combined leverage = = = 1.667
EBT ` 24,00,000

(v) Calculation of EBIT if sales drop to ` 50 lakhs `

( )

Sales 50,00,000

Less: Variable cost ( ` 50,00,000 × 60/100) 30,00,000

Contribution 20,00,000

Less: Fixed cost 10,00,000

EBIT 10,00,000
Exercise 8-6

Sales
= Sales Turnover Ratio ∴ Sales = 3 × 3,00,000 = ` 9,00,000
Total assets

(i) Calculation of Leverages

Income Statement for the year ended..... `

( )

Sales 9,00,000

Less: Variable cost (50% of sales) 4,50,000

Contribution 4,50,000

Less: Fixed operating cost 1,50,000

EBIT 3,00,000

Less: Interest (1,20,000 × 10/100) 12,000

EBT 2,88,000

Less: Tax (@50%) 1,44,000

EAT 1,44,000

N
Contribution 4,50,000
(a) Operating Leverage = = = 1.50
EBIT 3,00,000

N
EBIT 3,00,000
(b) Financial Leverage = = = 1.04

A
EBT 2,88,000

(c) Combined Leverage = Operating Leverage × Financial Leverage = 1.50 × 1.04 = 1.56

M
(ii) Calculation of likely levels of EBIT at different levels of EPS

X
(EBIT - I) (1 - t)
EPS =
N

A
Where, EPS = Earnings per share

T
EBIT = Earnings before interest and tax

I = Interest

t = Tax rate

N = Number of equity shares

(a) Level of EBIT, if EPS is ` 1

(EBIT - 12,000) (1 - 0.50)

1 =
9,000

9,000 = (EBIT - 12,000) (0.50)

9,000 = 0.50 EBIT - 6,000

0.50 EBIT = 9,000 + 6,000

∴ EBIT = 15,000/0.50 = ` 30,000

(b) Level of EBIT, if EPS is ` 2

(EBIT - 12,000) ( 1 - 0.50)

2 =
9000

9,000 × 2 = (EBIT - 12,000) (0.50)

18,000 = 0.50 EBIT - 6,000

0.50 EBIT = 18,000 + 6,000

∴ EBIT = 24,000/0.50 = ` 48,000

(c) Level of EBIT, if EPS is ` 0

(EBIT - 12,000) (1 - 0.50)

0 =
9,000

9,000 × 0 = (EBIT - 12,000) (0.50)

0.50 EBIT - 6,000 = 0

0.50 EBIT = 6,000

∴ EBIT = 6,000/0.50 = ` 12,000

N N
M A
A X
T
 Key to Short Answer Questions

True or False Statements

1. False - Low financial leverage indicates less risky situation, low operating leverage combined with low

financial leverage will constitute an ideal situation.

2. False - The debentureholders are paid interest which is charge against profit. Whether the company earns

profit or not, it must pay an agreed rate of interest on debentures. The company should pay preference

dividend in priority to pay any equity dividend. Therefore, there is an uncertainty of estimates of

amount and timing of cash flows expected by equity shareholders as compared to debenture holders

and preference shareholders.

3. True - Leverage is the employment of fixed assets or funds for which a firm has to meet fixed costs or fixed

rate of interest obligation irrespective of the level of activities attained or the level of operating profit

earned.

N
4. False - A firm’s operating leverage would be higher if the firm has high quantum of fixed cost and low variable

N
cost.

5. False - If the operating leverage of the firm is higher, the more its profits will vary with a given percentage in

A
sales.

6. False - The operating leverage is an attribute of the firm’s business risk.

M
7. False - The DOL measures the responsiveness of EBIT to change in level of output.

X
8. True - A low ratio of EBIT/EBT indicates a low interest outflow and consequently lower borrowings.

A
9. True - The financial leverage is an indicator of responsiveness of firm’s EPS to the changes in its profit before

T
interest and tax. It indicates the use of earnings in making payments for fixed interest and fixed

dividend bearing securities.

10. False - A firm is said to be highly levered if the proportion of long-term debt and preferential share capital

is high in relation to the equity share capital.

11. False - A low operating leverage accompanied by a low financial leverage is a situation in which management

should be over cautious.

12. True - A high debt-equity ratio indicates large outside borrowings and consequently a larger outside stake

in the business which is more risky.

13. True - The interest cover is expressed as number of times interest earned. It is measured as a ratio of profit

before interest and tax to interest charges.

14. True - It refers to the practice of using borrowed funds and preference capital carrying a fixed charge in

expectation of obtaining a higher return to the equity shareholders.

Choose Correct Word

1. trading on equity

2. highly

3. low

4. under capitalization

5. EPS

6. financial

7. higher
 8. EPS

9. combined

10. financial

11. more

12. tax shield

13. debt

14. leverage

15. equity capital

16. gearing

17. ROE

18. debt

19. financial

20. trading on equity

N
21. EBIT

22. equity

N
23. falls

A
24. high

25. financial

M
Choose Correct Answer

X
1. (B) charge

A
2. (D) bank cash credit

T
3. (A) financial risk

4. (C) gearing

5. (A) financial

6. (A) financial risk

7. (B) low level of gearing

8. (A) overtrading

9. (B) financial risk

10. (B) increase

11. (A) Earnings before interest and taxes

12. (C) overtrading

13. (A) diminishes

14. (A) equity shareholders

15. (D) proportion of loan funds to networth is high

 Practical Exercises

Exercise 9-1 From the following particulars, estimate those ratios and comment on their significance:

Balance Sheet

Liabilities ` lakhs Assets ` lakhs

Equity 120 Net block 500

Secured loans 240 Stocks 80

Sundry creditors 150 Debtors 220

Bank overdraft 250

Taxes collected but not remitted 40

800 800

N
Sales ` 500 lakhs, purchases ` 350 lakhs.

N
Exercise 9-2 ABC Distributors has the following Balance Sheet and Income Statement.

A
Balance Sheet

Liabilities ` Assets `

M
Accounts payable 80,000 Cash 25,000

X
Other current liabilities 20,000 Accounts receivables 60,000

Long-term debt 1,00,000 Inventory 65,000

A
Shareholders equity (50,000) shares 3,00,000 Long-term assets 3,50,000

T
5,00,000 5,00,000

Income Statement `
( )

Sales 9,00,000

Cost of goods sold 4,00,000

General, administrative and selling expenses 1,00,000

All other expenses 2,50,000

Net Income (EAT) 1,50,000

You are required to:

(a) Determine ABC Distributor’s liquidity position by calculating the current ratio, working capital, the ratio of

current assets to total assets, the ratio of current liabilities to total assets and the cash conversion cycle.

(b) Calculate the current market price per share of ABC’s Stock if its P/E ratio is eight times earnings.

Exercise 9-3 Following information are available from recent accounts of M Ltd.:

Sales for the year ` 10,00,000

Gross profit rate 30%

Stock turnover ratio 5

Collection period for debts 30 days

It is proposed to enter an entirely new market with a product which has not been handled before. This will lead to

an additional annual sales of ` 2,00,000 having a gross profit rate of 20%. Customers will expect 60 days as credit and
additional stock of raw materials equal to three months’ usage will be needed. Raw material costs, on existing

products as with the new product, account for 75% of cost of sales.

If the proposal is implemented, how will it affect company’s key ratios (Stock turnover ratio and Debt collection

period)?

Exercise 9-4 Ramesh & Co. Ltd. manufactures water filters. The current ratio at the end of the last year was 3 : 1

which appeared to be comfortable. However, the cash flow position, in reality, is rather weak and the company finds

it difficult to effect payments to the suppliers and workers on time. The composition of working capital as per the

last balance sheet is provided here: `

( )

Current Assets:

Inventories 18,00,000

Receivables 12,00,000

Cash and bank balances 1,00,000

Loans and advances 20,00,000

51,00,000

N
Current Liabilities 17,00,000

N
Mention specific possibilities of what might be causing cash flow difficulties in this context. Suggest any better ratios

which the company might use to gauge its liquidity in future.

A
Exercise 9-5 The Hyundai Instrument Corporation is trying to determine the effect of its Inventory Turnover Ratio

M
and Days Sales Outstanding (DSO) on its cash-flow cycle. The Hyundai Corporation’s sales last year (all on credit)

were ` 1,50,000 and it earned a net profit of 6%. Its Inventory Turnover Ratio was 5 and DSO was 36.5 days. The firm

X
had fixed assets totalling ` 35,000. Hyundai had fixed assets totalling ` 35,000 and its payable deferral period is 40
days. Calculate Hyundai Instrument Corporation’s:

A
(i) Cash conversion cycle.

T
(ii) Total asset turnover and ROA, if it holds negligible amounts of cash and marketable securities.

(iii) Cash conversion cycle, Total asset turnover and Return on assets, if its Inventory turnover can be raised to 7.3.

Exercise 9-6 The Trading and Profit & Loss Account of Beta Ltd. for the year ended 31st March, 2016 is given below:

Particulars Amount Particulars Amount

`
( ) `
( )

To Opening stock: By Sales (credit) 20,00,000

Raw materials 1,80,000 By Closing stock:

Work-in-progress 60,000 Raw materials 2,00,000

Finished goods 2,60,000 5,00,000 Work-in-progress 1,00,000

To Purchases (credit) 11,00,000 Finished goods 3,00,000 6,00,000

To Wages 3,00,000

To Production expenses 2,00,000

To Gross profit c/d 5,00,000

26,00,000 26,00,000

To Administration expenses 1,75,000 By Gross profit b/f 5,00,000

To Selling expenses 75,000

To Net profit 2,50,000

5,00,000 5,00,000
The opening and closing balances of debtors were ` 1,50,000 and ` 2,00,000 respectively whereas opening and closing
creditors were ` 2,00,000 and ` 2,40,000 respectively.

You are required to ascertain the working capital requirement by operating cycle method.

Exercise 9-7 A company is considering its working capital investment and financial policies for the next year.

Estimated fixed assets and current liabilities for the next year are ` 2.60 crore and ` 2.34 crore respectively. Estimated
sales and EBIT depend on current assets investment, particularly inventories and book-debts. The Financial

Controller of the company is examining the following alternative working capital policies: ( ` crores)

Working capital policy Investment in Estimated EBIT

current assets sales

Conservative 4.50 12.30 1.23

Moderate 3.90 11.50 1.15

Aggressive 2.60 10.00 1.00

After evaluating the working capital policy, the Financial Controller has advised the adoption of the moderate

N
working capital policy. The company is now examining the use of long-term and short-term borrowings for

financing its assets. The company will use ` 2.50 crore of the equity funds. The corporate tax rate is 35%. The

N
company is considering the following debt alternatives: ( crores)

Financing policy Short-term debt Long-term debt

A
Conservative 0.54 1.12

M
Moderate 1.00 0.66

Aggressive 1.50 0.16

X
Interest rate-average 12% 16%

A
You are required to calculate the following:

T
(1) Working capital investment for each policy: (a) Net working capital position, (b) Rate of return, (c) Current

ratio.

(2) Financing for each policy: (a) Net working capital position, (b) Rate of return on shareholders equity

(c) Current ratio.

 Key to Practical Exercises

Exercise 9-1

Calculation of Working Capital Ratios

(1) Current Ratio

Current assets 300

= = 0.68
Current liabilities 440

The normal current ratio should be 2 and the company’s, current ratio is not satisfactory, since major amounts

are locked up in debtors balances.

(2) Liquid Ratio

Current assets - Stock 300 - 80

= = 1.16
Current liabilities - Bank overdraft 440 - 250

N
As the stock is secured for the bank overdraft, the company is in a position to meet its immediate liabilities.

N
But the steps should be taken to improve the liquidity position of the company.

(3) Inventory Turnover Ratio

A
Sales 500
= = 6.25
Inventory 80

M
The company has achieved higher inventory turnover ratio

X
(4) Debtors Turnover Ratio

A
Sales 500
= = 2.27
Debtors 220

T
The debtors turnover ratio is not impressive and more funds are locked up in debtors balances. This shows the

inefficiency in management of working capital.

Exercise 9-2

Working Notes `
( )

Current Assets

Cash 25,000

Accounts receivables 60,000

Inventory 65,000

(a) 1,50,000

Current Liabilities

Accounts payable 80,000

Other current liabilities 20,000

(b) 1,00,000

Working Capital (a) - (b) 50,000

Current assets 1,50,000

(1) Current ratio = = = 1.5
Current liabilities 1,00,000

Current assets 1,50,000

(2) Current assets to Total assets = = = 0.30
Total assets 5,00,000
 Current liabilities 1,00,000
(3) Current liabilities to Total assets = = = 0.20
Total assets 5,00,000

(4) Calculation of Cash Conversion Cycle

365 365
(a) Receivables collection period = = = 24.33 days
(9,00,000/60,000) 15

365 365
(b) Inventory conversion period = = = 59.35 days
(4,00,000/65,000) 6.15

365 365
(c) Payable deferral period = = = 58.4 days
(5,00,000/80,000) 6.25

Cash Conversion Cycle = (a) + (b) - (c) = 24.33 + 59.35 - 58.4 = 25.28 days

(d) Calculation of Market Price of Share of ABC Distributors

Earnings after tax ` 1,50,000

EPS = = = ` 3
No. of equity shares 50,000 equity shares

` `

N
Market price = Eight times of earnings = 8 times × 3 = 24

Exercise 9-3

N
Profitability Statement if Proposal is Implemented `
( )

A
Particulars Current Additional Projected

Sales 10,00,000 2,00,000 12,00,000

M
Less: Cost of sales 7,00,000 1,60,000 8,60,000

X
Gross profit 3,00,000 40,000 3,40,000

A
Gross profit ratio 30% 20% 28.33%

T
Calculation of Projected Stock `
( )

Existing stock ( ` 7,00,000 × 75/100 × 1/5) 1,05,000

Add: Additions ( ` 1,60,000 × 75/100 × 1/4) 30,000

Projected stock 1,35,000

` 8,60,000 × 75/100 ` 6,45,000

Projected Stock Turnover Ratio = = = 4.78
` 1,35,000 ` 1,35,000

Calculation of Projected Debtors `

( )

Existing debtors ( ` 10,00,000/12) 83,333

Add: Additions ( ` 2,00,000/12) × 2 33,333

Projected debtors 1,16,666

Projected debtors ` 1,16,666

Debt Collection Period = × 365 days = × 365 days = 35 days
Sales ` 12,00,000

Exercise 9-4

`
( )

Current Assets:

Inventories 18,00,000

Receivables 12,00,000

Cash and bank balances 1,00,000

Loans and advances 20,00,000

 `
( )

(a) 51,00,000

Current Liabilities (b) 17,00,000

Working Capital (a) - (b) 34,00,000

Analysis

(1) Current Ratio

Current assets, loans and advances 51,00,000

= = 3 : 1
Current liabilities 17,00,000

The current ratio is satisfactory, since it is above the ideal current ratio of 2 : 1.

(2) Quick Ratio

Current assets, loans and advances - Stock 51,00,000 - 18,00,000

= = 1.94 : 1
Current liabilities 17,00,000

The quick ratio is also satisfactory, since the desired quick ratio is 1 : 1 but the actual quick ratio is 1.94 : 1. The

N
company is in a position to meet its short-term financial obligations.

(3) Super Quick Ratio

N
Cash and marketable securities 1,00,000
= = 0.06 : 1

A
Current liabilities 17,00,000

The company’s cash and bank balances are grossly insufficient to meet the day to day financial needs, and

M
contingencies.

X
(4) Composition of Current Assets

Current Assets ` Proportion (%)

A
Inventories 18,00,000 35.29

T
Receivables 12,00,000 23.53

Cash and bank 1,00,000 1.96

Loans and advances 20,00,000 39.22

51,00,000 100%

The analysis of composition of current assets indicate the following:

n Excess investments in inventories could be held. Dormant and non-moving stock may also include in

inventories.

n The receivables should be further classified into good, doubtful and bad amounts.

n Cash and bank balances may not be sufficient to meet the day to day obligations.

n Substantial amount of working capital is locked up in loans and advances, which may not relate to the

business.

(5) Stock turnover ratio, Receivables turnover ratio, Debtors collection period, Creditors payment period,

Working capital turnover ratio, Current assets to total assets ratio should also be calculated for the

ascertainment of efficiency in working capital management.

Exercise 9-5

Working Notes

Inventory = ` 1,50,000/5 = ` 30,000

Receivables = ` 1,50,000 × 36.5/365 = ` 15,000
  
Inventory conversion period = = = 73 days
*OWFOUPSZ UVSOPWFS SBUJP 
Receivable collection period (DSO) = 36.5 days

(i) Calculation of Cash Conversion Cycle

Cash conversion cycle = Inventory conversion period + Receivables collection period +

Payable deferral period

= 73 + 36.5 - 40 = 69.5 days

(ii) Calculation of Total Assets Turnover and ROA

Total assets = Inventory + Receivables + Fixed assets

= ` 30,000 + ` 15,000 + ` 35,000 = ` 80,000

4BMFT C   
Total assets turnover = = = 1.875
5PUBM BTTFUT C 
Return on Assets (ROA) = Profit margin × Total assets turnover

N
= 0.06 × 1.875 = 0.1125 = 11.25%

(iii) Calculation of Cash Conversion Cycle, Total Assets Turnover and Return on Assets, if its inventory turnover

N
can be raised to 7.3.

Inventory conversion period = 365/7.3 = 50 days

A
Cash conversion cycle = 50 + 36.5 - 40 = 46.5 days

` 1,50,000/7.3 ` 20,548

M
Inventory = =

Total assets = Inventory + Receivables + Fixed assets

X
= ` 20,548 + ` 15,000 + ` 35,000 = ` 70,548
` 1,50,000/70,548

A
Total assets turnover = = 2.1262

T
C  
Return on Assets (ROA) = ×  = 12.76%
C  

Exercise 9-6

Working Notes

1,80,000 + 2,00,000
Average raw material stock = = ` 1,90,000
2

60,000 + 1,00,000
Average WIP stock = = ` 80,000
2

2,60,000 + 3,00,000
Average finished goods stock = = ` 2,80,000
2

1,50,000 + 2,00,000
Average debtors = = ` 1,75,000
2

2,00,000 + 2,40,000
Average creditors = = ` 2,20,000
2

Raw material consumed = Opening stock + Purchases - Closing stock

= 1,80,000 + 11,00,000 - 2,00,000 = ` 10,80,000

Daily average consumption of raw material

= ` 10,80,000/360 days = ` 3,000

Daily average sales = ` 20,00,000/360 days = ` 5,555.55
Daily average purchases = ` 11,00,000/360 days = ` 3,055.55
Calculation of Cost of goods sold `
( )

Raw material consumed 10,80,000

Wages 3,00,000

Prime cost 13,80,000

Add: Production expenses 2,00,000

15,80,000

Add: Opening stock of WIP 60,000

16,40,000

Less: Closing stock of WIP 1,00,000

Cost of production 15,40,000

Add: Opening stock of finished goods 2,60,000

18,00,000

Less: Closing stock of finished goods 3,00,000

Cost of goods sold 15,00,000

N
Daily average production cost = ` 15,40,000/360 days = ` 4,277.78

N
Daily average cost of goods sold = ` 15,00,000/360 days = ` 4,166.67

A
Computation of Operating cycle

(a) Raw material storage period

M
Average stock of raw material ` 1,90,000
= = 63.33 days
Daily average raw material consumption ` 3,000

X
(b) Conversion/Work-in-process period

A
Average stock of WIP ` 80,000
= = 18.70 days

T
Daily average production cost ` 4,277.78

(c) Finished goods storage period

Average stock of finished goods ` 2,80,000

= = 67.20 days
Daily average cost of goods sold ` 4,166.67

(d) Debtors collection period

Average debtors ` 1,75,000

= = 31.50 days
Daily average sales ` 5,555.55

(e) Creditors payment period

Average creditors ` 2,20,000

= = 72 days
Daily average purchases ` 3,055.55

Duration of operating cycle = 63.33 + 18.70 + 67.20 + 31.50 - 72 = 108.73 days

Number of operating cycles per year

360 360
= = = 3.311
Duration of operating cycle 108.73

Calculation of total operating expenses `

( )

Total cost of production 15,00,000

Add: Administration expenses 1,75,000

Selling expenses 75,000

Total operating expenses 17,50,000

Working capital required

Total operating expenses ` 17,50,000

= = = ` 5,28,541
No. of operating cycles per year 3.311

Assumption - The total number of days in a year is assumed to be 360 days.

Exercise 9-7

Statement Showing Working Capital Investment of each Policy ( ` crores)

Particulars Working capital policy

Conservative Moderate Aggressive

Fixed assets 2.60 2.60 2.60

Current assets 4.50 3.90 2.60

7.10 6.50 5.20

Less: Current liabilities 2.34 2.34 2.34

Net worth 4.76 4.16 2.86

N
Estimated sales 12.30 11.50 10.00

N
EBIT 1.23 1.15 1.00

(a) Net working capital position

A
(Current assets - Current liabilities) 2.16 1.56 0.26

(b) Rate of return (EBIT/Total assets) × 100 17.3% 17.7% 19.2%

M
(c) Current Ratio (Current assets/Current liabilities) 1.92 1.67 1.11

X
Evaluation of Alternative Working Capital Financing Policies ( ` crores)

A
Particulars Financing policy

T
Conservative Moderate Aggressive

Fixed assets 2.60 2.60 2.60

Current assets 3.90 3.90 3.90

Total assets 6.50 6.50 6.50

Current liabilities 2.34 2.34 2.34

Short-term debt 0.54 1.00 1.50

Long-term debt 1.12 0.66 0.16

Equity capital 2.50 2.50 2.50

Total liabilities 6.50 6.50 6.50

Budgeted sales 11.50 11.50 11.50

EBIT 1.15 1.15 1.15

Less: Interest on short-term debt @ 12% 0.06 0.12 0.18

Interest on long-term debt @ 16% 0.18 0.11 0.03

EBT 0.91 0.92 0.94

Less: Tax @ 35% 0.32 0.32 0.33

EAT 0.59 0.60 0.61

(a) Net working capital position

(Current assets - Current liabilities) 1.02 0.56 0.06

(b) Rate of return on shareholders Equity Capital

(EAT/Equity share capital) × 100 23.6% 24% 24.4%

(c) Current ratio (Current assets/Current liabilities) 1.35 1.17 1.02

 Key to Short Answer Questions

True or False Statements

1. False - The excess working capital situation is referred to as ‘over capitalization’. It is a situation where

excessive investments are made in current assets than required, leads to inefficiency in working capital

management. The excessive working capital will not result in production interruptions.

2. False - Efficient and effective utilization of working capital leads to earn higher rate of return on capital

employed and improves firm’s profitability.

3. True - If the funds are tied-up in idle current assets represent poor and inefficient working capital

managements which affects the firm’s liquidity as well as profitability.

4. False - Such assets are called core current assets, which are required by the firm to ensure the continuity of

operations which represents the minimum levels of various items of current assets.

N
5. False - The extra working capital needed to support the changing business activities should be financed

N
through short-term debt financing.

6. False - It is called operating cycle. The length of operating cycle is the indicator of efficiency in management

A
of short-term funds and working capital.

7. True - The quicker the operating cycle less investment in working capital is needed and it improves the

M
profitability.

X
8. True - Sound credit and collection policies enable to minimize investment in receivables and reduces the

length of operating cycle.

A
9. True - The higher level of investment in current assets reduces the firm’s profitability, but at the same time

T
the risk level is less.

10. False - In aggressive policy, part of permanent current assets plus total temporary current assets are financed

by short-term funds, and part of permanent current assets are financed by long-term funds.

11. False - The zero working capital strategy suggests that investment in total current assets should equal to total

current liabilities and ultimately the working capital becomes zero.

12. False - Overtrading is a situation where a firm attempts to increase its sales level without having a support

of adequate working capital.

Choose Correct Word

1. short-term

2. capital employed

3. current

4. shareholders

5. cash

6. hedging

7. short-term

8. working capital

9. short-term

10. zero

11. finished goods

12. negative

13. operating

14. within

Choose Correct Answer

1. (D) all of the above

2. (A) operating cycle

3. (B) twelve months

4. (C) core current assets

5. (B) manufacturing cycle

6. (A) current assets

7. (C) current assets

8. (B) relaxed policy

9. (D) improves profitability

N
10. (A) long-term funds

N
11. (C) hedging approach

12. (C) holding of excess balances in cash and bank

M A
A X
T
 Practical Exercises

Exercise 10-1 Prepare working capital forecast and projected profit and loss account and balance sheet from the

following information: `
( )

Issued equity share capital 50,00,000

Preference share capital 15,00,000

Fixed assets 30,66,667

Production during the previous year was 10,00,000 units which is expected to be maintained during the current year.

The expected ratios of cost to selling price are ?

Raw material 40% Direct wages 20% Overheads 20%

Raw material ordinarily remains in stock for 3 months before production. Every unit of production remains in

process for 2 months. Finished goods remain in stock for 3 months. Creditors allow 3 months for payment and

N
debtors are allowed 4 months credit. Estimated minimum cash to be held will be ` 2,00,000. Lag in payment of wages
and overheads is expected to be half a month. The selling price will be ` 8 per unit. The production is in continuous

N
process and sales are in regular cycle.

A
Exercise 10-2 On 1st April, 2016 the Board of directors of Dowell Co. Ltd. wishes to know the amount of working

capital that will be required to meet the program of activity they have planned for the year. The following

informations are available:

M
(a) Issued and paid-up capital ` 2,00,000.

X
(b) 5% Debentures (secured on assets) ` 50,000.

(c) Fixed assets valued at ` 1,25,000 on 31-3-2016.

A
(d) Production during the previous year was 60,000 units, it is planned that this level of activity should be

T
maintained during the present year.

(e) The expected ratios of cost to selling price are - Raw materials 60%, Direct wages 10%, and Overheads 20%.

(f) Raw materials are expected to remain in stores for an average of two months before these are issued for

production.

(g) Each unit of production is expected to be in process for one month.

(h) Finished goods will stay in warehouse for approximately three months.

(i) Creditors allow credit for 2 months from the date of delivery of raw materials.

(j) Credit allowed to debtors is 3 months from the date of despatch.

(k) Selling price per unit is ` 5.

(l) There is a regular production and sales cycle.

Prepare: (i) Working capital requirement forecast; and (ii) An estimated profit and loss account and balance sheet

at the end of the year.

Exercise 10-3 Estalla Garment Co. Ltd. is a famous manufacturer and exporter of garments to the European

countries. The Finance Manager of the company is preparing its working capital forecast for the next year. After

carefully screening all the documents, and collected the following information:

Production during the previous year was 15,00,000 units. The same level of activity is intended to be maintained

during the current year. The expected ratios of cost to selling price are:

Raw materials 40% Direct wages 20% Overheads 20%

The raw materials ordinarily remain in stores for 3 months before production. Every unit of production remains in

the process for 2 months and is assumed to be consisting of 100% raw material, wages and overheads. Finished goods
remain in warehouse for 3 months. Credit allowed by the creditors is 4 months from the date of the delivery of raw

material and credit given to debtors is 3 months from the date of dispatch.

Estimated balance of cash to be held ` 2,00,000 Lag in payment of expenses ½ month

Lag in payment of wages ½ month

Selling price is ` 10 per unit. Both production and sales are in a regular cycle. You are required to make a provision
of 10% for contingency (except cash). Relevant assumptions may be made. You have recently joined the company

as an Assistant Finance Manager. The job of preparing the forecast statement has been given to you. You are required

to prepare the forecast statement. The Finance Manager is particularly interested in applying the quantitative

techniques for forecasting the working capital needs of the company. You are also required to explain the approach

in the brief note to be prepared by you.

Exercise 10-4 Strong Cement Company Ltd. has an installed capacity of producing 1.25 lakh tons of cement per

annum, its present capacity utilization is 80%. The major raw material to manufacture cement is limestone which

is obtained on cash basis from a company located near the plant. The company produces cement in 200 kgs. drum.

From the information given below, determine the net working capital (NWC) requirement of the company for the

current year cost structure per drum of cement (estimated) is as under: `

( )

N
Gypsum 25

Limestone 15

N
Coal 30

Packaging material 10

A
Direct labour 50

Factory overheads (including depreciation of ` 10) 30

M
Administrative overheads 20

X
Selling overheads 25

Total cost 205

A
Profit margin 45

T
Selling price 250

Add: Sales tax (10% of selling price) 25

Invoice price to consumer 275

Additional information:

(a) Desired holding period of raw material:

Gypsum 3 months Coal 2.5 months

Limestone 1 month Packing material 1.5 months

(b) The product is in process for a period of ½ month (Assume full units of materials, namely - gypsum, limestone

and coal are required in the beginning; other conversion costs are to be taken at 50%).

(c) Finished goods are in stock for a period of 1 month before they are sold.

(d) Debtors are extended credit for a period of 3 months.

(e) Average time lag in payment of wages is approximately ½ month and of overheads: 1 month.

(f) Average time lag in payment of sales tax is 1½ months.

(g) The credit period extended by various suppliers are:

Gypsum 2 months Coal 1 month Packing material ½ month

(h) Minimum desired cash balance is ` 25 lakh. You may state your assumptions, if any.
 Key to Practical Exercises

Exercise 10-1

Projected Profit and Loss Account `

( )

Particulars 10,00,000 Per unit

units ( )` `
( )

Sales (a) 80,00,000 8.00

Costs:

Raw material (40%) 32,00,000 3.20

Direct wages (20%) 16,00,000 1.60

Overheads (20%) 16,00,000 1.60

N
(b) 64,00,000 6.40

Profit 16,00,000 1.60

N
Statement Showing Working Capital Forecast `
( )

A
Current Assets:

Stock of raw materials (10,00,000 × 3.20 × 3/12) 8,00,000

M
Work-in-progress:

X
Raw materials (10,00,000 × 3.20 × 2/12) 5,33,334

Wages (10,00,000 × 1.60 × 2/12 × 50/100) 1,33,333

A
Overheads (10,00,000 × 1.60 × 2/12 × 50/100) 1,33,333 8,00,000

T
Stock of finished goods (10,00,000 × 6.40 × 3/12) 16,00,000

Debtors (10,00,000 × 8 × 4/12) 26,66,667

Cash balance 2,00,000

(a) 60,66,667

Current Liabilities:

Creditors for raw material (10,00,000 × 3.20 × 3/12) 8,00,000

Creditors for wages (10,00,000 × 1.60 × 1/24) 66,667

Creditors for overheads (10,00,000 × 1.60 × 1/24) 66,667

(b) 9,33,334

Working capital required (a) - (b) 51,33,333

Projected Balance Sheet

Liabilities ` Assets `

Issued and Subscribed Capital Fixed assets 30,66,667

Equity share capital 50,00,000 Current assets:

Preference share capital 15,00,000 Raw material stock 8,00,000

Reserves (balancing figure) 17,00,000 Work-in-progress 8,00,000

Creditors for raw material 8,00,000 Finished goods stock 16,00,000

Wages payable 66,667 Debtors 26,66,667

Overheads payable 66,667 Cash 2,00,000

91,33,334 91,33,334

Note - Reserves include current year profit of ` 16,00,000 and previous year’s profit of ` 1,00,000.
Exercise 10-2

Calculation of Cost and Sales `

( )

Particulars 60,000 units Per unit

Raw materials 1,80,000 3.00

Direct wages 30,000 0.50

Overheads 60,000 1.00

Cost of sales 2,70,000 4.50

Profit (balancing figure) 30,000 0.50

Sales 3,00,000 5.00

Statement of Working Capital Requirement Forecast `

( )

Current Assets:

Raw materials stock ( ` 1,80,000 × 2/12) 30,000

Work-in-progress [ ` 1,80,000 + (` 30,000 × 50/100)]

N
+ ( ` 60,000 × 50/100) × 1/12 18,750

` 2,70,000 × 3/12)

N
Finished goods stock ( 67,500

Debtors ( ` 2,70,000 × 3/12) 67,500

A
(a) 1,83,750

Current Liabilities:

M
Creditors for raw materials ( ` 1,80,000 × 2/12) (b) 30,000

X
Working Capital (a) - (b) 1,53,750

A
Estimated Profit and Loss A/c of Dowell Company Ltd. for the year ending 31-3-2016 `
( )

T
Sales (60,000 units × ` 5) (a) 3,00,000

Cost of Sales:

Raw material ( ` 3,00,000 × 60/100) 1,80,000

Direct wages ( ` 3,00,000 × 10/100) 30,000

Overheads ( ` 3,00,000 × 20/100) 60,000

(b) 2,70,000

Gross profit (a) - (b) 30,000

Less: Debenture interest ( ` 50,000 × 5/100) 2,500

Net profit 27,500

Estimated Balance sheet of Dowell Company Ltd. as at 31st March, 2016

Liabilities ` Assets `

Share capital 2,00,000 Fixed assets 1,25,000

Profit and loss A/c (balancing figure) 8,750 Current assets

Profit for the year 27,500 Raw material 30,000

5% Debentures 50,000 Work-in-progress 18,750

Creditors 30,000 Finished goods 67,500

Debtors (3 months sales) 75,000

3,16,250 3,16,250
Exercise 10-3

Calculation of Profit Margin

Particulars % `

Raw materials 40 4

Direct wages 20 2

Overheads 20 2

Total cost 80 8

Add: Profit 20 2

Selling price 100 10

Estimation of Working Capital `

( )

Current Assets

Raw materials stock (15,00,000 units × ` 4 × 3/12) 15,00,000

Work-in-process (15,00,000 units × ` 8 × 2/12) 20,00,000

N
Finished goods stock (15,00,000 units × ` 8 × 3/12) 30,00,000

Debtors (15,00,000 units × ` 8 × 3/12) 30,00,000

N
(a) 95,00,000

A
Current Liabilities

Creditors for raw-material (15,00,000 units × ` 4 × 4/12) 20,00,000

M
Wages outstanding (15,00,000 units × ` 2 × 1/24) 1,25,000

` 2 × 1/24)

X
Outstanding expenses (15,00,000 units × 1,25,000

(b) 22,50,000

A
Current assets less current liabilities (a) - (b) 72,50,000

T
Add: Contingency (10% of ` 72,50,000) 7,25,000

79,75,000

Add: Desired cash balance 2,00,000

Estimated Working Capital 81,75,000

Exercise 10-4

1,25,000 tons × 0.80

(1) No. of Drums Manufactured = = 5,00,000 drums
200 kgs.

(2) Calculation of Work-in-progress `

( )

Raw material (100%)

Gypsum 25

Lime stone 15

Coal 30 70

Labour (50%) 25

Factory overheads (50%) (cash) 10

Administrative overheads (50%) 10

Cost of work-in-progress 115

 (3) Cost of Finished Goods (cash cost basis) `
( )

Total cost 205

Less: Depreciation 10

Selling overheads 25 35

Cost of Finished Goods 170

(4) Cash Cost of Debtors `

( )

Total cost 205

Less: Depreciation 10

Add: Sales tax 25

Cash Cost of Debtors 220

(5) Cash Overheads = 0 - 10 + 20 + 25 = ` 65

Calculation of Working Capital Requirement (on cash cost basis) `

( )

Current Assets:

N
Minimum desired cash balance 25,00,000

N
Raw materials:

Gypsum (5,00,000 units × ` 25 × 3/12) 31,25,000

A
Limestone (5,00,000 units × ` 15 × 1/12) 6,25,000

Coal (5,00,000 units × ` 30 × 2.5/12) 31,25,000

M
Packing material (5,00,000 units × ` 10 × 1.5/12) 6,25,000

` 115 × 1/24)

X
Work-in-progress (5,00,000 units × 23,95,833

Finished goods (5,00,000 units × ` 170 × 1/12) 70,83,333

A
Debtors (5,00,000 units × ` 220 × 3/12) 2,75,00,000

T
(a) 4,69,79,166

Current Liabilities:

Creditors:

Gypsum (5,00,000 units × ` 25 × 2/12) 20,83,333

Coal (5,00,000 units × ` 30 × 1/12) 12,50,000

Packing material (5,00,000 units × ` 10 × 1/24) 2,08,333

Wages (5,00,000 units × ` 50 × 1/24) 10,41,667

Overheads (5,00,000 units × ` 65 × 1/12) 27,08,333

Sales tax (5,00,000 units × ` 25 × 1.5/12) 15,62,500

(b) 88,54,166

Net Working Capital (a) - (b) 3,81,25,000

Note - While valuation of work-in-progress and finished goods, administrative overhead is excluded.
 Key to Short Answer Questions

True or False Statements

1. True - The time span required for conversion of raw materials into finished goods will determine the

quantum of working capital required.

2. False - The pace of sales turnover will be one of the factors in determination of capital. Quick turnover calls

for lesser investment in inventory, while low turnover rate necessitates larger investment.

3. False - Linear regression model helps in making working capital requirement projections after establishing

the average relationship between sales and working capital and its various components in the past

years.

4. True - The length of operating cycle is the major determinant of working capital requirement of a

manufacturing concern.

N
5. True - Under individual components method, the various items of current assets and current liabilities

needed in working capital are identified and estimated individually and grossed up together to arrive

N
at the working capital requirement i.e. current assets minus current liabilities.

A
6. False - Under cash cost approach the working capital is estimated on the basis of cash costs. Depreciation,

and profit margin on debtors balances are ignored in computation of cash costs.

M
7. True - During the season the plant will work at full capacity under triple shift basis, therefore working capital

requirement will also be at peak level during season. E.g. sugar industry.

X
8. False - During the period of inflation, the requirement for working capital will also be higher and vice versa,

A
due to increase in material and labour rates, increase in costs etc.

T
9. False - Working capital leverage measures the responsiveness ROCE for changes in current assets. The

working capital leverage reflects the sensitivity of the return on capital employed to the changes in

level of current assets.

10. True - Under percentage sales method, the level of current assets and current liabilities are determined by

establishing its past trend in relation to sales.

Choose Correct Word

1. percentage of sales

2. high

3. working capital

4. more

5. multiple regression

6. percentage of sales

7. depreciation

8. higher

9. high

10. high

11. low
Choose Correct Answer

1. (A) day sales method

2. (D) aggressive approach

3. (B) working capital leverage

4. (A) more

5. (C) independent variable

6. (B) long-term financing

7. (C) more

8. (D) trade credit

9. (C) cost of goods sold

10. (A) net current assets

N N
M A
A X
T
 Practical Exercises

Exercise 11-1 Tulip Ltd. produces a product which has a monthly demand of 4,000 units. The product requires a

component A which is purchased at ` 20. For every finished product one unit of component A is required. The

ordering cost is ` 120 per order and the holding cost is 10% per annum.

You are required to calculate - (i) Economic order quantity, and (ii) If the minimum lot size is 4,000 units, what is

the extra cost Tulip Ltd. has to incur ?

Exercise 11-2 P Ltd. uses three types of materials A, B and C for production of X, the final product. The relevant

monthly data for the components are as given below: (Units)

Materials A B C

Normal usage 200 150 180

Minimum usage 100 100 90

N
Maximum usage 300 250 270

Reorder quantity 750 900 720

N
Reorder period (months) 2 to 3 3 to 4 2 to 3

A
Calculate for each component: (i) Reorder level (ii) Maximum level (iii) Minimum level, (iv) Average stock level.

` 6 and inventory carrying cost per

M
Exercise 11-3 The annual demand for a product is 6,400 units. The unit cost is

unit per annum is 25% of the average inventory cost. If the cost of procurement is ` 75, determine: (i) Economic order

X
quantity (EOQ), (ii) Number of orders per annum, and (iii) Time between two consecutive orders.

A
Exercise 11-4 G. Ltd. produces a product which has a monthly demand of 4,000 units. The product requires a

component X which is purchased at ` 20. For every finished product, one unit of component is required. The

T
ordering cost is ` 120 per order and the holding cost is 10% p.a.

You are required to calculate -

(i) Economic order quantity,

(ii) If the minimum lot size to be supplied is 4,000 units, what is the extra cost, the company has to incur ?

(iii) What is the minimum carrying cost, the company has to incur ?

Exercise 11-5 ABC Company buys in lot of 125 boxes which is a three months supply. The cost per box is ` 125 and
the ordering cost is ` 250 per order. The inventory carrying cost is estimated at 20% of unit value per annum.

You are required to ascertain -

(i) What is the total annual cost of the existing inventory policy?

(ii) How much money would be saved by employing the economic order quantity (EOQ)?

Exercise 11-6 Your factory buys and uses a component for production at ` 10 per unit. Annual requirement is
20,000 units. The carrying cost of inventory is 10% per annum and ordering cost is ` 40 per order. The purchase

manager argues that as the ordering cost is very high, it is advantageous to place a single order for the entire annual

requirement. He also says that if we order 20,000 units at a time, we can get a 3% discount from the supplier. You

are required to evaluate this proposal and make your recommendations.

Exercise 11-7 A factory requires 1,500 units of an item per month. The cost of each unit is ` 27. The cost per order
is ` 150 and inventory carrying charges works out to 20% of the average inventory. Find out the economic order
quantity (EOQ) and ascertain the number of orders to be placed per year. Would you accept a 2% price discount on

a minimum supply of 1,200 units ?

Exercise 11-8 Economic Enterprises require 90,000 units of a certain item annually. The cost per unit is ` 3, the cost
per purchase order ` 300 and the inventory carrying cost ` 6 per unit per year.

(i) What is the economic order quantity

(ii) What should the firm do if the supplier offers discounts as below:

Order quantity Discount

4,500 - 5,999 2%

6,000 and above 3%

Exercise 11-9 Ten items kept in inventory by the School of Management Studies at State University are listed below.

Which items should be classified as ‘A’ items, ‘B’ items and ‘C’ items ? What percentage of items is in each class? What

percentage of total annual value is in each class ?

N
Item Annual usage Value per unit ( )

1 200 40.00

N
2 100 360.00

3 2,000 0.20

A
4 400 20.00

5 6,000 0.04

M
6 1,200 0.80

X
7 120 100.00

8 2,000 0.70

A
9 1,000 1.00

10 80 400.00

Exercise 11-10

Particulars

GP ratio

Stock turnover
T
Some selected financial figures for the last three years are given for a company as under:

Year 1

40%

20 times
Year 2

30%

25 times
Year 3

20%

20 times

Opening stock ( ) ` 90,000 1,10,000 1,30,000

Closing stock ( )` 1,10,000 1,30,000 1,70,000

Administrative expenses every year amounted to 10% of sales. The income tax rate is 40%.

You are required to prepare a comparative statement of profit for the three years and give your comments for

variations in profitability.

Exercise 11-11 A Ltd. uses inventory turnover as one performance measure to evaluate its Production manager.

Currently, its inventory turnover (based on cost of goods sold/inventory) is 10 times p.a., as compared with industry

average of 4. Average sales are ` 4,50,000 p.a. variable costs of inventory have consistently remained at 70% of sales
with fixed costs of ` 10,000. Carrying costs of inventory (excluding financing costs) are 5% p.a. Sales force

complained that low inventory levels are resulting in lost-sales due to stock-outs. Sales manager has made an

estimate based on stock-out reports as under:

Inventory policy Inventory turnover `
Sales ( )

Current 10 4,50,000

A 8 5,00,000

B 6 5,40,000

C 4 5,65,000

On the basis of above estimates, assuming a 40% tax rate and an after tax required return of 20% on investment in

inventory, which policy would you recommend ?

N N
M A
A X
T
 Key to Practical Exercises

Exercise 11-1

 "#  ×   × 

(i) EOQ = = = 2,400 units
$4 

(ii) Calculation of Extra Cost if Minimum Lot Size is 4,000 units `

( )

Ordering cost (12 orders × ` 120) 1,440

Carrying cost (4,000 units × ½ × ` 20 × 10/100) 4,000

Total cost 5,440

Cost at EOQ `
( )

` 120)

N
Ordering cost (20 orders × 2,400

Carrying cost (2,400 units × ½ × ` 20 × 10/100) 2,400

N
Total cost 4,800

A
Extra Cost = 5,440 - 4,800 = ` 640

M
Exercise 11-2

(i) Reorder Level = Maximum reorder period × Maximum usage

X
A = 3 × 300 = 900 B = 4 × 250 = 1,000 C = 3 × 270 = 810

A
(ii) Maximum Level = Reorder level + Reorder quantity - (Minimum consumption × Minimum reorder period)

T
A = 900 + 750 - (100 × 2) = 1,450 B = 1,000 + 900 - (100 × 3) = 1,600 C = 810 + 720 - (90 × 2) = 1,350

(iii) Minimum Level = Reorder level - (Normal usage × Average delivery time)

A = 900 - (200 × 2.5) = 400 B = 1,000 - (150 × 3.5) = 475 C = 810 - (180 × 2.5) = 360

(iv) Average Stock Level = (Maximum level + Minimum level)/2

A = (1,450 + 400)/2 = 925 B = (1,600 + 475)/2 = 1,038 C = (1,350 + 360)/2 = 855

Alternatively, Average Stock Level can also be calculated as under:

Average stock level = Minimum level + ½ Reorder quantity

A = 400 + (750/2) = 775 B = 475 + (900/2) = 925 C = 360 + (720/2) = 720

Exercise 11-3

 "#  ×   × 
(i) EOQ = = = 800 units
$4  × 

(ii) Number of Orders per annum = 6,400 units/800 units = 8 orders

(iii) Time between two orders = 12 months/8 orders = 1.5 months

Exercise 11-4

 "#  ×   × 

(i) EOQ = = =    = 2,400 components
$4  × 
 (ii) Statement Showing Inventory Carrying Cost if the minimum lot size is 4,000 Components `
( )

Ordering cost (48,000 units/4,000 units × ` 120) 1,440

Carrying cost (½ × 4,000 units × ` 20 × 10/100) 4,000

5,440

Statement Showing Inventory Carrying Cost if the minimum lot size is 2,400 components `
( )

Ordering cost (48,000 units/2,400 units× ` 120) 2,400

Carrying cost (½ × 2,400 units × ` 20 × 10/100) 2,400

4,800

Extra Cost = ` 5,440 - ` 4,800 = ` 640

(iii) Calculation of Minimum Carrying Cost if EOQ is not adopted

Monthly demand = 4,000 components

Minimum carrying cost = ½ × 4,000 units × ` 20 × 10/100 = ` 4,000

Exercise 11-5

N
(i) Total Present Annual Cost `
( )

N
Buying cost (125 units × 4 orders × ` 125) 62,500

A
Ordering cost (4 orders × 250) 1,000

Carrying cost (½ × 125 units × ` 125 × 20/100) 1,562

M
65,062

X
 "#  ×  × 
× 
EOQ = = =   = 100 units
$4  ×  

A
`
( )

T
Cost of purchase (500 boxes p.a. @ ` 125) 62,500

Ordering cost (5 orders × ` 250) 1,250

Carrying cost (½ × 100 units × ` 125 × 20/100) 1,250

65,000

∴ Saving by adopting EOQ = 65,062 - 65,000 = ` 62

Exercise 11-6

 "#  ×   × C    

Calculation of EOQ = = = = 1,265 units
$4 C  ×  

No. of orders to be placed in a year = 20,000 units/1,265 units = 15.8 say 16 orders

Calculation of Total cost under EOQ system `

( )

Ordering cost (16 × ` 40) 640

Carrying cost (1,265 × ½ × ` 10 × 10/100) 632

Buying cost (20,000 × ` 10) 2,00,000

Total cost 2,01,272

Calculation of Total cost of buying 20,000 units in one lot availing 3% discount ( ) `
Ordering cost 40

Carrying cost (20,000 × ½ × ` 9.70 × 10/100) 9,700

Buying cost (20,000 × ` 9.70) 1,94,000

Total cost 2,03,740

Analysis - The total cost of acquiring 20,000 units is lowest under EOQ ordering system. Therefore, the Purchase

Manager’s view is incorrect.

Exercise 11-7

 ×   × C    

Calculation of EOQ = = = 1,000 units
C  ×  

No. of orders per year = 18,000/1,000 = 18 orders

Calculation of Total cost under EOQ ordering ( ) `

` 150)

N
Ordering cost (18 × 2,700

Carrying cost (1,000 × ½ × ` 27 × 20/100) 2,700

N
Purchase cost (18,000 × ` 27) 4,86,000

Total cost 4,91,400

A
Price after 3% discount = ` 27 - 2% of ` 27 = ` 26.46 No. of orders = 18,000/1,200 = 15 orders

M
Calculation of Total cost after availing discount ( ) `
` 150)

X
Ordering cost (15 × 2,250

Carrying cost (1,200 × ½ × ` 26.46 × 20/100) 3,175

A
Purchase cost (18,000 × ` 26.46) 4,76,280

T
Total cost 4,81,705

Analysis - Since the total cost is less when 2% price discount is availed on a minimum supply of 1,200 units, it is

suggested to place 15 orders in a year with 1,200 units for each order.

Exercise 11-8

 "#  ×   × 

EOQ = = = 3,000 units
$4 

Evaluation of Purchase Decision if Supplier Offers Discounts to the Firm

Particulars Option 1 Option 2 Option 3

Annual usage (units) 90,000 90,000 90,000

Order quantity (units) 3,000 4,500 6,000

Average inventory (units) (Order quantity/2) 1,500 2,250 3,000

Number of orders (Annual usage/Order quantity) 30 20 15

Price per unit `

( ) 3.00 2.94 2.91

Cost of purchase (Annual usage × Price p.u.) 2,70,000 2,64,600 2,61,900

Carrying cost (Average inventory × ` 6 p.u.) 9,000 13,500 18,000

Ordering cost (No. of orders × ` 300) 9,000 6,000 4,500

Total cost `
( ) 2,88,000 2,84,100 2,84,400

Suggestion - From the analysis of the above it is observed that the total cost of inventory is minimum at 4,500 units

per order i.e., ` 2,84,100 per year. Hence, ordering quantity for 4,500 units each time is suggested by availing 2%

discount on purchase price of ` 3.

Exercise 11-9

Item No. Annual usage Value p.u. Annual usage value Ranking

(units) `
( ) `
( )

1 200 40.00 8,000 IV

2 100 360.00 36,000 I

3 2,000 0.20 400 IX

4 400 20.00 8,000 V

5 6,000 0.04 240 X

6 1,200 0.80 960 VIII

7 120 100.00 12,000 III

8 2,000 0.70 1,400 VI

9 1,000 1.00 1,000 VII

10 80 400.00 32,000 II

1,00,000

N
Category ‘A’ Category ‘B’ Category ‘C’

N
Item Nos. Rank Annual Item Nos. Rank Annual Item Nos. Rank Annual

usage( `) usage ( `) usage ( `)

A
2 I 36,000 7 III 12,000 8 VI 1,400

10 II 32,000 1 IV 8,000 9 VII 1,000

M
4 V 8,000 6 VIII 960

X
3 IX 400

A
5 X 240

2 - 68,000 3 - 28,000 5 - 4,000

T
20% - 68% 30% - 28% 50% - 4%

Analysis - The ten items in the total inventory are classified into ‘A’ category, ‘B’ category and ‘C’ category items. ‘A’

category consists of 2 items which represents 20% of total items, but its value of annual usage is 68%. ‘B’ category

consists of 3 items (30%) whose annual usage value represents 28%. The rest of the 5 items (50%) included in ‘C’

category whose annual usage is only ` 4,000 representing 4% of total annual usage. The management should exercise
strict control over ‘A’ category items, moderate control over ‘B’ category items. ‘C’ category items can be subject to

periodical checkups since its value is negligible.

Exercise 11-10

`
( )

Average Stock = (Opening stock + Closing stock)/2

Year 1 (90,000 + 1,10,000)/2 1,00,000

Year 2 (1,10,000 + 1,30,000)/2 1,20,000

Year 3 (1,30,000 + 1,70,000)/2 1,50,000

Cost of Goods Sold = Average stock × Stock turnover

Year 1 (1,00,000 × 20) 20,00,000

Year 2 (1,20,000 × 25) 30,00,000

Year 3 (1,50,000 × 20) 30,00,000

 `
( )

Sales

Year 1 (20,00,000 × 100/60) 33,33,333

Year 2 (30,00,000 × 100/70) 42,85,714

Year 3 (30,00,000 × 100/80) 37,50,000

Statement of Profitability `
( )

Particulars Year 1 Year 2 Year 3

Sales 33,33,333 42,85,714 37,50,000

Less: Cost of goods sold 20,00,000 30,00,000 30,00,000

Gross profit 13,33,333 12,85,714 7,50,000

Less: Administration expenses 3,33,333 4,28,571 3,75,000

Profit before tax 10,00,000 8,57,143 3,75,000

Less: Tax @ 40% 4,00,000 3,42,857 1,50,000

N
Profit after tax 6,00,000 5,14,286 2,25,000

N
Analysis - It is observed from the above that even though there is a marginal increase in sales of year 3 is there over

year 1 sales, the cost of goods sold is increased by 50%. As a result, the profit after is fallen from ` 6,00,000 in year

A
1 to ` 2,25,000 in year 3.

M
Exercise 11-11

Calculation of Cost of Goods Sold `

( )

X
Current (4,50,000 × 70/100) + 10,000 3,25,000

A
A (5,00,000 × 70/100) + 10,000 3,60,000

T
B (5,40,000 × 70/100) + 10,000 3,88,000

C (5,65,000 × 70/100) + 10,000 4,05,500

Level of Investment Involved in Various Inventory Policies `

( )

Current (3,25,000/10) 32,500

A (3,60,000/8) 45,000

B (3,88,000/6) 64,667

C (4,05,500/4) 1,01,375

Evaluation of Inventory Policies `

( )

Particulars Current A B C

Sales 4,50,000 5,00,000 5,40,000 5,65,000

Cost of goods sold 3,25,000 3,60,000 3,88,000 4,05,500

Contribution 1,25,000 1,40,000 1,52,000 1,59,500

Less: Inventory carrying cost @ 5% 1,625 2,250 3,233 5,069

Profit before Tax 1,23,375 1,37,750 1,48,767 1,54,431

Less: Tax 49,350 55,100 59,507 61,771

Profit after Tax 74,025 82,650 89,260 92,660

Incremental profit - 8,625 6,610 3,400

Incremental investment - 12,500 19,667 36,708

Incremental return % - 69% 33.6% 9.3%

Analysis - The incremental rate of return is maximized if inventory policy ‘A’ is adopted.
 Key to Short Answer Questions

True or False Statements

1. False - The firm is having high current ratio. Current ratio indicates proportion of current assets to current

liabilities. But the firm have a very low liquid ratio. The liquid ratio indicates proportion of liquid

assets to current liabilities. The liquid assets represent current assets less stock. Therefore, low liquid
ratio indicates the funds are locked-up in inventories.

2. False - Obsolete stock is a dead stock, and for its existing stock no further demand can be foreseen. It

represents money spent on the inventory that cannot be realized but it occupies useful space.

3. True - The economic order quantity (EOQ) is the optimum size of the order for a particular item of inventory

calculated at a point where the total inventory costs are at a minimum for that particular stock item.

4. False - Items in class ‘A’ constitute the most important class of inventories so far as the proportion of the total

N
value of inventory. The ‘A’ items consist of approximately 15% of the total items, accounts for 80%

of the total material usage.

N
5. False - The stock turnover ratio indicates the movement of average stock holding of each item of material in

relation to its consumption during the accounting period. The slow moving materials will have a low

A
turnover ratio.

6. False - The inventory of a manufacturing concern into raw material stock, work-in-progress and finished

M
goods stock.

X
7. False - The basic objective of working capital management is by optimizing the investment in current assets

and by reducing the level of current liabilities, the company can reduce the locking-up of funds in

A
working capital thereby, it can improve the return on capital employed in the business.

T
8. True - ‘A’ class items merit a tightly controlled inventory system with constant attention by the purchase and

stores management. A larger effort per item on only a few items will cost only moderately, but the

effort can result in large savings.

9. True - EOQ is the reorder quantity, indicates the optimum size of the order for a particular item of inventory,

at that point the ordering costs and carrying costs of inventory are minimized.

10. True - Stock turnover ratio indicates the number of times the average stock is held as compared to the annual

consumption of raw materials.

11. False - The inventory management looks into the aspect of optimization of investment in inventory, proper

accounting and control of inventory, avoid stock-out situation, avoid overstocking, regular monitor-

ing of stock levels, availability of materials in time etc.

12. False - Stock turnover ratio is used to indicate and identify obsolete stocks, by taking the movement of

average stock holding of each item of material in relation to its consumption during the accounting

period.

13. False - The maximum stock level represents the upper limit beyond which the quantity of any item is not

normally allowed to rise to ensure that unnecessary working capital is not blocked in stock items.

14. False - Safety stock is also called as buffer stock or minimum stock. It is the lower limit below which the stock

of any stock item should not normally be allowed to fall.

15. False - ABC analysis divides the inventory into three classes, A, B, and C in order of the consumption value

i.e. value of usage.

16. True - A low inventory turnover indicates high level of carrying inventory, which result in high level of

carrying costs.
Choose Correct Word

1. average

2. input-output

3. optimum

4. 800

5. direct

6. centralized

7. indirect

8. minimizes

9. stockout

10. buffer level

11. higher

12. moderate

N
13. customer

N
Choose Correct Answer

1. (D) all of the above

A
2. (B) profit and loss account

3. (D) all of the above

M
4. (C) loose control

X
5. (C) inventory is growing or sales are dropping

A
6. (B) reorder level

T
7. (C) production cost per unit

8. (A) slow moving stocks

9. (C) ABC analysis

10. (B) inventory control

11. (D) optimize investment in inventory

12. (D) all of the above

13. (C) 2,700 units

14. (B) 2,500 kgs.

15. (D) all of the above

 Practical Exercises

Exercise 12-1 High Vision Ltd. has current sales of ` 20,00,000. The company is planning to introduce a cash

discount policy of 2/10, net 30. As a result, the company expects the average collection period to go down by 10 days

and 80% of the sales opt for the cash discount facility.

If the company’s required return on investment in receivables is 20%, should it introduce the new discount policy?

Exercise 12-2 In order to increase sales from the normal level of ` 2.4 lakhs per annum, the Marketing Manager

submits a proposal for liberalizing credit policy as under:

Normal sales - ` 2.4 lakhs Normal credit period - 30 days

Proposed increase in credit Relevant increase over

period beyond normal 30 days normal sales ( ) `

N
15 days 12,000

30 days 18,000

N
45 days 21,000

A
60 days 24,000

1
The P.V. ratios of the company is 33 /3%. The company expects a pre-tax return of 20% on investment.

M
Evaluate the above four alternatives and advise the management (assume 360 days a year).

X
Exercise 12-3 Unani Cosmetics, manufacturer of herbal cosmetic products, has an annual sales of ` 50 lakh. It offers
30 days credit on sales. The fixed costs are ` 5 lakh and the variable costs are 80% of the sales.

A
The company is considering a change in its credit policy. Based upon its knowledge of market response, it has

T
estimated likely sales figures against each of the proposed collection period as follows:

Policy Collection period Projected sales

(days) ( ` lakhs)

A 45 56

B 60 60

C 75 62

D 90 63

If the expected rate of return is 20%, which policy should be adopted and why?

Exercise 12-4 ABC firm is considering to make certain relaxation in its credit policy. The ABC management has

evaluated two new policies. From the following details advise the ABC management which policy has to be adopted:

(i) Annual credit sales at present ` 87.5 lakhs

(ii) Proposed credit sales : Under alternative -I ` 105 lakhs; Under alternative-II ` 118 lakhs

(iii) Accounts receivable turnover ratio and bad debts losses.

Existing Alternative I Alternative II

7 Times 5.25 times 4.2 times

` 2.63 lakhs ` 5.25 lakhs ` 7.88 lakhs

(iv) The ABC is required to give a return over 30% on the investment in new accounts receivable.

(v) Its PV ratio is 30%.

Exercise 12-5 A dealer having annual sales of ` 50 lakh extends 30 days credit period to its debtors. The variable

cost is estimated at 80% on sales and fixed costs are ` 6,00,000. The dealer intends to change the credit policy for which
the following information is given:

Credit policy Average collection Annual sales

period (Days) ( ` in lakhs)

A 45 56

B 60 60

C 75 62

Rate of return (pre-tax) required on investment is 20%.

You are required to assess the most profitable policy with the help of incremental approach. Calculations may be

restricted to two decimal places.

Exercise 12-6 Sales Manager of a company proposes to sell goods to a group of new customers with 10% risk of non-

payment. This group would require one and a half month’s credit and is likely to increase sales by ` 1,00,000 per

annum. Production and selling expenses amount to 80% of sales and income- tax rate is 30%. The company’s

N
minimum required rate of return after tax is 25%.

N
Should the Sales Manager’s proposal be accepted ?

Find the degree of risk of non-payment that the company should be willing to assume, if required rate of return (after

A
tax) is (i) 30%; (ii) 40%; or (iii) 60%.

Exercise 12-7 ` 80 lakhs, its average

M
The present credit terms of Creation Ltd. are 1/10, net 30. Its annual sales are

collection period is 20 days. Its variable costs and average total costs to sales are 0.85 and 0.95 respectively and its

X
cost of capital is 10%. The proportion of sales on which customers currently take discount is 0.5. Creation Ltd. is

considering relaxing its discount terms to 2/10, net 30. Such relaxation is expected to increase sales by ` 5 lakh, reduce

A
the average collection period to 14 days and increase the proportion of discount sales to 0.8. What will be the effect

of relaxing the discount policy on company’s profit? Take an year as of 360 days.

T
 Key to Practical Exercises

Exercise 12-1

Investment in Debtors Balances

 EBZT
(i) Before Introduction of Cash Discount Policy = C    × = ` 1,66,666
 EBZT

 EBZT
(ii) After Introduction of Cash Discount Policy = C    × = ` 1,11,111
 EBZT

Decrease of Investment in Debtors Balances = 1,66,666 - 1,11,111 = ` 55,555

Saving in Cost of Funds, by reducing debtors balances = ` 55,555 × 20/100 = ` 11,111

Cost of Extending Discount = ` 20,00,000 × 80/100 × 2/100 = ` 32,000

Net Loss on Introduction of Cash Discount Policy = 32,000 - 11,111 = ` 20,889

Analysis - Since the introduction of cash discount policy results in a net loss of ` 20,889, it is suggested not to introduce
the cash discount policy.

Exercise 12-2

Evaluation Alternative Credit Periods ( ` lakhs)

Existing policy Proposed policies

Credit period (days) 30 45 60 75 90

Sales 2.40 2.52 2.58 2.61 2.64

Contribution (Sales × P/V ratio) (a) 0.80 0.84 0.86 0.87 0.88

 $SFEJU QFSJPE 
Debtors balance
 4BMFT ×  0.200 0.315 0.430 0.544 0.660
  

Cost of funds invested in

debtors balances @ 20% (b) 0.040 0.063 0.086 0.109 0.132

Net contribution (a) - (b) 0.760 0.777 0.774 0.761 0.748

Analysis - Since the net contribution is highest if credit period allowed is 45 days. It is suggested to increase the credit

period by 15 days from the existing credit period of 30 days.

Exercise 12-3

Evaluation of Credit Policies ( ` lakhs)

Current Policy A Policy B Policy C Policy D

Policy

Credit period (days) 30 45 60 75 90

Projected sales 50.0 56.0 60.0 62.0 63.0

Less: Variable cost 80% 40.0 44.8 48.0 49.6 50.4

Contribution 10.0 11.2 12.0 12.4 12.6

Less: Fixed cost 5.0 5.0 5.0 5.0 5.0

Net profit 5.0 6.2 7.0 7.4 7.6

 (` lakhs)

Current Policy A Policy B Policy C Policy D

Policy

Credit period (days) 30 45 60 75 90

Cost of sales (Variable cost + Fixed cost) 45.0 49.8 53.0 54.6 55.4

Investment in debtors

 $SFEJU QFSJPE 
 $PTU PG TBMFT ×  3.75 6.225 8.833 11.375 13.85
  EBZT 
 
Net profit 5.00 6.200 7.000 7.400 7.600

Less: Cost of funds in debtors 0.75 1.245 1.767 2.275 2.77

balances @ 20%

Net return 4.25 4.955 5.233 5.125 4.83

Analysis - Since the net return is highest for credit policy B, it is suggested to extend the credit period upto 60 days,

to maximize the company’s profitability.

Exercise 12-4

Calculation of Debtors Balance

Credit sales
= Debtors turnover ratio
Debtors

(i) Debtors Balance under existing Credit Policy

87,50,000
= 7 (given)
Debtors

7 × Debtors = 87,50,000

Debtors = 87,50,000/7 = ` 12,50,000

(ii) Debtors Balance under Alternative I

1,05,00,000
= 5.25 (given)
Debtors

Debtors = ` 20,00,000

(iii) Debtors Balance under Alternative II

1,18,00,000
= 4.2 (given)
Debtors

Debtors = ` 28,09,524

Expected Return on Investment in Debtors Balances

Existing policy = 12,50,000 × 30/100 = ` 3,75,000

Alternative I = 20,00,000 × 30/100 = ` 6,00,000

Alternative II = 28,09,524 × 30/100 = ` 8,42,857

Calculation of Debtors Collection Period

Debtors
= × 12 = Average collection period
Credit sales

12,50,000
Existing = × 12 = 1.71 months
87,50,000

20,00,000 28,09,524
Alternative I = × 12 = 2.29 months Alternative II = × 12 = 2.86 months
1,05,00,000 1,18,00,000
Evaluation of Credit Policies ( ` lakhs)

Existing Alternative I Alternative II

Credit period (months) 1.71 2.29 2.86

Credit sales 87.50 105.00 118.00

Less: Variable cost (70%) 61.25 73.50 82.60

Contribution (a) 26.25 31.50 35.40

Cost of funds invested in debtors balance @ 30% 3.75 6.00 8.43

Bad debts 2.63 5.25 7.88

(b) 6.38 11.25 16.31

Net contribution (a) - (b) 19.87 20.25 19.09

Analysis - The company can maximize its profits by allowing a credit period of 2.29 months, under alternative I.

Exercise 12-5

Evaluation of Proposed Credit Policies ( ` lakhs)

Credit policy Present A B C

Period (days) 30 45 60 75

Annual sales (a) 50.00 56.00 60.00 62.00

Variable cost (80% of sales) 40.00 44.80 48.00 49.60

Fixed cost 6.00 6.00 6.00 6.00

Cost of sales (b) 46.00 50.8 54.00 55.60

Profit (a) - (b) 4.00 5.20 6.00 6.40

Incremental profit (c) - 1.20 2.00 2.40

 $PTU PG TBMFT × $PMMFDUJPO QFSJPE 

Average investment debtors   3.78 6.26 8.88 11.42

  
Incremental investment in debtors balance - 2.48 5.10 7.64

Return on investment required

(20% of incremental investment) (d) - 0.50 1.02 1.53

Excess returns (c) - (d) - 0.70 0.98 0.87

Suggestion - Since the policy B yields maximum profit, it is suggested to adopt 60 days as credit period.

Exercise 12-6

Profitability of Additional Sales ( )`

Increase in sales per annum 1,00,000

Less: Bad debt losses (10% of sales) 10,000

Net sales 90,000

Less: Production and selling expenses (80% of sales) 80,000

Profit before tax 10,000

Less: Income tax @ 30% 3,000

Profit after tax 7,000

Average investment in additional receivables:

Period of credit = 1.5 months

Receivables turnover = 12/1.5 = 8

Average amount of receivables = ` 1,00,000/8 = ` 12,500 (at selling price)

Average investment in receivables = ` 12,500 × 80% = ` 10,000 (at cost price)

C  
Available rate of return = ×  = 70%
C  

Since the available rate of return is 70% which is higher than required rate of return of 25%, the sales manager’s

proposal can be accepted.

Acceptable degree of risk of non-payment for different required rate of returns (after tax)

Particulars 30% 40% 60%

Average investment in debtors 10,000 10,000 10,000

Required profit after tax 3,000 4,000 6,000

Profit before tax (grossed up by 70%) 4,286 5,714 8,571

Production and selling expenses 80,000 80,000 80,000

Required sales revenue to achieve desired return 84,286 85,714 88,571

Additional total sales expected 1,00,000 1,00,000 1,00,000

Acceptable degree of risk of non-payment 15,714 14,286 11,429

Acceptable degree of risk (%) 15.71% 14.28% 11.42%

Exercise 12-7

Present investment in debtors balance = ` 80,00,000 × 95/100 × 20/360 = ` 4,22,222

Proposed investment in debtors balance = [( ` 80,00,000 × 95/100) + (` 5,00,000 × 85/100)] × 14/360

= ` 3,12,083

Incremental investment in debtors balance = ` 4,22,222 - ` 3,12,083 = ` 1,10,139

Saving of cost of investment = ` 1,10,139 × 10/100 = ` 11,014

Incremental contribution = ` 5,00,000 × 15/100 = ` 75,000

Total Savings due to swithchover = ` 11,014 + ` 75,000 = ` 86,014 ....... (a)

Present discount on sales = ` 80,00,000 × 50/100 × 1/100 = ` 40,000

Proposed discount on sales = ` 85,00,000 × 80/100 × 2/100 = ` 1,36,000

Net increase in discount = ` 1,36,000 - ` 40,000 = ` 96,000 ....... (b)

Net increase in profit [(a) - (b)] = ` 86,014 - ` 96,000 = (-) ` 9,986

Suggestion - Since the change in discount policy leads to reduction in current profit, it is suggested to continue the

present discount policy.

 Key to Short Answer Questions

True or False Statements

1. False - Debtors turnover ratio which measures whether the amount of resources tied up in debtors is

reasonable and whether the company has been efficient in converting debtors into cash.

2. False - The management of receivables broadly covers the study of credit policy, credit analysis, credit

control, management of investment in debtors balances.

3. True - A liberal credit policy increases the sales as well as the profitability of the firm. But simultaneously

it should consider the costs involved in liberal credit policy which leads to increased investment

in receivables balances, risk of bad debts, costs of administration of receivables, the problems of

liquidity etc.

4. False - High risk customers are often profitable, if risk is properly managed.

5. False - The carrying cost of debtors includes interest on capital blocked in receivables balances, cost of

keeping the records of credit sales and payments, cost of collection of payments from customers,

opportunity cost of capital for amounts locked in receivables balance which can be profitability

employed elsewhere.

6. False - In a competitive market, if the competitors grant credit, it will be difficult to deny credit to customers.

The reduction in sales limits the profitability of the firm.

7. False - Cash discounts are costs to the seller and benefit to the buyer. To consider whether the offer of a

discount for early payment is financially worthwhile it is necessary to compare the cost of the discount

with the benefit of a reduced investment in debtors.

8. False - The days sales in debtors ratio represents the length of the average credit period taken by the

customers.

9. False - Discriminate analysis is a tool used in discriminating between good and bad accounts taking into

account the readily available information from financial data relating to size of firm, acid test ratio,

creditors payment period etc.

10. True - But, if the firm goes on increasing the cost of collection of debts, after some point, there would not be

further decrease of bad debts. This point is called saturation point.

11. False - Before setting up a credit policy the firm should consider the factors like sales, market share, profit,

return on capital employed, competition, risks involved etc.

Choose Correct Word

1. cash

2. cash discount

3. ageing

4. saturation

5. count back

6. credit

7. credit standards

8. low

9. bad debts
10. credit

11. increase

12. open account

Choose Correct Answer

1. (D) as stated in (A) and (C)

2. (A) credit terms

3. (A) creditors

4. (C) bad debts to sales ratio

5. (C) net 30

6. (A) 2/10 net 30

7. (D) debtors collection period

8. (A) credit period

9. (C) implicit costs

10. (B) sales ledger staff

11. (C) ACP is affected by the seasonality of sales whereas DSO is not

12. (C) opportunity cost of extending credit

 Practical Exercises

Exercise 13-1 A firm maintains a separate account for cash disbursement. Total disbursements are ` 2,62,500 per
month. Administrative and transaction cost of transferring cash to disbursement account is ` 25 per transfer.

Marketable securities yield is 7.5% per annum. Determine the optimum cash balance according to J Baumol model.

Exercise 13-2 JPL has two dates when it receives its cash inflows, i.e., Feb. 15 and Aug. 15. On each of these dates,

it expects to receive ` 15 crore. Cash expenditure are expected to be steady throughout the subsequent 6 month

period.

Presently, the ROI in marketable securities is 8% per annum, and the cost of transfer from securities to cash is ` 125
each time a transfer occurs.

(i) What is the optimal transfer size using the EOQ model? What is the average cash balance?

(ii) What would be your answer to part (i), if the ROI were 12% per annum and the transfer costs were ` 75? Why

N
do they differ from those in part (i) ?

N
Exercise 13-3 The annual cash requirement of A Ltd. is 10 lakhs. The company has marketable securities in lot

sizes of ` 50,000, `1,00,000, ` 2,00,000, ` 2,50,000 and ` 5,00,000. Cost of conversion of marketable securities per lot

A
is ` 1,000. The company can earn 5% annual yield on its securities.

You are required to prepare a table indicating which lot size will have to be sold by the company. Also show that the

M
economic lot size can be obtained by the Baumol Model.

X
Exercise 13-4 Sunshine Ltd. expects its cash flows to behave in a random manner, as assumed by the Miller and Orr

model. The company wants you to establish (i) the ‘Return Point’ and the ‘Upper control limit’. It provides the

A
following information as requested by you:

(a) The annual yield on marketable securities is 12 per cent.

T
(b) The fixed cost of effecting a marketable securities transaction is ` 1600.

(c) The standard deviation of the change in daily cash balance is ` 5000.

(d) The management of Sunshine Ltd. would like to maintain a minimum cash balance of ` 50,000.

Exercise 13-5 Ramesh & Co. Ltd. manufactures water filters. The current ratio at the end of the last year was 3:1

which appeared to be comfortable. However, the cash flow position, in reality, is rather weak and the company finds

it difficult to effect payments to the suppliers and workers on time.

The composition of working capital as per the last Balance sheet is provided here: `
( )

Current Assets:

Inventories 18,00,000

Receivables 12,00,000

Cash and bank balances 1,00,000

Loans and advances 20,00,000

51,00,000

Current Liabilities 17,00,000

Mention specific possibilities of what might be causing cash flow difficulties in this context. Suggest any better ratios

which the company might use to gauge its liquidity in future.

Exercise 13-6 Beta Limited has an annual turnover of ` 84 crores and the same is spread over evenly each of the 50
weeks of the working year. However, the pattern within each week is that the daily rate of receipts on Mondays and

Tuesdays is twice that experienced on the other three days of the week. The cost of banking per day is estimated at
` 2,500. It is suggested that banking should be done daily or twice a week. Tuesdays and Fridays as compared to the
current practice of banking only on Fridays. Beta Limited always operates on bank overdraft and the current rate

of interest is 15% per annum. This interest charge is applied by the bank on a simple daily basis.

Ignoring taxation, advise Beta Limited the best course of banking. For your exercise, use 360 days a year for

computational purposes.

Exercise 13-7

(i) Beauty Ltd. has an excess cash of ` 16,00,000 which it wants to invest in short-term marketable securities.

Expenses relating to investment will be ` 40,000. The securities invested will have an annual yield of 8%.

The company seeks your advice as to the period of investment so as to earn a pre-tax income of 4%.

(ii) Also, find the minimum period for the company to break-even its investment expenditure. Ignore time value

of money.

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 Key to Practical Exercises

Exercise 13-1

The optimum level of cash balance is found to be:

 "5
C =
*
Where, C = Optimum level of cash balance

A = Annual cash payments estimated i.e. ` 2,62,500 × 12 = ` 31,50,000

T = Cost per transaction of purchase or sale of marketable securities i.e. ` 25

I = Carrying cost per rupee of cash i.e. 7.5%

× C    × C 

N

C = = ` 45,826


N
Exercise 13-2

A
(i) Calculation of Optimal Transfer Size using EOQ Model

M
 '5
C =
*

X
Where,

A
C = Optimal transfer size i.e. Cash required each time to restore

balance to minimum cash

T
T = Total cash required during the year i.e., ` 30,00,00,000

F = Fixed cost per transaction i.e., ` 125

I = Rate of interest on securities i.e., 8% p.a.

 ×      × 
C = = ` 9,68,245


Average cash balance = 9,68,245/2 = ` 4,84,123

(ii) Calculation of Optimal Transfer Size using EOQ Model if rate of Interest is 12% and the Transfer Cost is ` 75.

 ×     × 
C = = ` 6,12,372


Average cash balance = 6,12,372/2 = ` 3,06,186

Reasons for Difference

¾ The opportunity cost of holding cash is high in case of part (ii), which requires to maintain lesser cash balance.

¾ The transaction is also lower in case of part (ii) which allows the frequent conversion of securities in cash and

therefore less cash balance can be maintained.

Exercise 13-3

Calculation of Economic Lot Size of Securities `

( )

(a) Annual requirement of cash 10,00,000 10,00,000 10,00,000 10,00,000 10,00,000

(b) Lot size of securities 50,000 1,00,000 2,00,000 2,50,000 5,00,000

(c) Number of lots (a)/(b) 20 10 5 4 2

(d) Conversion cost per lot 1,000 1,000 1,000 1,000 1,000

(e) Total conversion cost (c) × (d) 20,000 10,000 5,000 4,000 2,000

(f) Interest charges [(b)/2] × (5/100) 1,250 2,500 5,000 6,250 12,500

(g) Total cost (e) + (f) 21,250 12,500 10,000 10,250 14,500

Analysis - From the above calculation it is observed that when the lot of size of securities is ` 2,00,000, the total costs
are minimum at ` 10,000 and hence it is an economic lot size of selling securities.

Calculation of economic lot size by applying Baumol Model is as follows:

 '5
C =

N
*
Where, C = Optimal transaction size

N
F = Fixed cost per transaction i.e., ` 1,000

A
T = Estimated annual requirement of cash i.e., ` 10,00,000

I = Interest earned marketable securities i.e., 5% p.a. or 0.05

M
 ×   ×   
C = = ` 2,00,000

X


A
Exercise 13-4


 Cα 

T
(i) Return point (RP) = + --
 *
Where, b = Fixed cost of effecting a marketable securities transaction i.e. ` 1,600

α 2
= Variance of daily changes in the expected cash balance i.e. ( ` 5,000)
2

I = Daily interest rate earned on marketable securities i.e. 0.12/360

LL = Lower control limit i.e. ` 50,000


 ×   ×  

 
  ×    
RP = +   = +  
 
 ×  

= 44,964.43 + 50,000 = ` 94,964.43 say ` 94,964

(ii) Upper Control Limit (UL)

= 3RP - 2LL = (3 × 94,964) - (2 × 50,000) = 2,84,892 - 1,00,000 = ` 1,84,892

Exercise 13-5

Composition of Current Assets

Item of Current Asset Amount ( ) ` Proportion (%)

Inventories 18,00,000 35.3

Receivables 12,00,000 23.5

Cash and bank balance 1,00,000 2.0

Loans and advances 20,00,000 39.2

51,00,000 100.0
 Cash and bank balances 1,00,000
Absolute Liquid Ratio = = = 0.059 : 1
Current liabilities 17,00,000

Analysis - From the analysis of composition of current assets, we can observe that 74.5% of current assets are locked

up in inventories, as well as, loans and advances. 23.5% of current assets are in the form of receivables, which are also

readily not available in liquid form. The cash and bank balances are insufficient to meet the current liabilities. The

management is suggested to take the following actions:

(a) Increase the inventory and debtors turnover by reducing the investment in inventories and debtors.

(b) Collect the loans and advances and bring them to liquid form.

Exercise 13-6

(i) Weekly Sales = Annual sales/50 weeks of working year = ` 8,400 lakhs/50 weeks = ` 168 lakhs

(ii) Daily Sales

Day Proportion Sales ( ` lakhs)

Monday 2 48

Tuesday 2 48

N
Wednesday 1 24

N
Thursday 1 24

Friday 1 24

A
Total weekly sales 168

M
(iii) Cost of Banking (per day)

X
Interest cost on delayed banking = Nil Cost of banking = 5 × ` 2,500 = ` 12,500
(iv) Cost of Banking Tuesdays & Fridays `
( )

A
Interest cost on delayed banking

T
Monday ( ` 48,00,000 × 1/360 × 15/100) 2,000

Wednesday ( ` 24,00,000 × 2/360 × 15/100) 2,000

Thursday ( ` 24,00,000 × 1/360 × 15/100) 1,000

Cost of banking (2 × ` 2,500) 5,000

10,000

(v) Cost of Banking on Fridays only `

( )

Interest cost on delayed banking

Mondays ( ` 48,00,000 × 4/360 × 15/100) 8,000

Tuesdays `
( . 48,00,000 × 3/360 × 15/100) 6,000

Wednesdays ( ` 24,00,000 × 2/360 × 15/100) 2,000

Thursdays ( ` 24,00,000 × 1/360 × 15/100) 1,000

Cost of banking 2,500

19,500

Analysis - Banking on Tuesdays & Fridays is suggested.

Exercise 13-7

Pre-tax income required on short-term marketable securities = ` 16,00,000 × 4/100 = ` 64,000

Let ‘p’ be the required period (in months) of investment so as to earn ` 64,000.
 ∴     × ×
1  
 = 64,000
  
 


16,00,000 × 0.08333P × 0.08 = 64,000 + 40,000

10,666.24P = 1,04,000 P = 1,04,000/10,666.24 = 9.75

Therefore, the period of investment is 9.75 months.

The required minimum period to break-even the investment expenditure will be

    × 1 ×   = 0
  
 


16,00,000 × 0.08333P × 0.08 = 40,000

10,666.24 P = 40,000 P = 40,000/10,666.24 = 3.75

∴ The minimum period of the company to break-even its investment expenditure is 3.75 months.

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 Key to Short Answer Questions

True or False Statements

1. True - Liquidity refers to company’s ability to meet expected as well as unexpected requirement of cash.

Profitability refers to a situation in terms of efficiency in utilization of resources to achieve profit

maximization for the owners. The higher the liquidity the lower will be the profitability and vice versa.

Liquidity and profitability are competing goals for Finance Manager.

2. True - Liquidity and profitability are competing goals for Finance Manager. There is an inverse relationship

between profitability and liquidity. The higher the liquidity the lower will be the profitability and vice

versa.

3. False - Net float is the total amount in a bank account. It is calculated by subtracting the disbursement float

money spent but not yet taken out of the account from the collection float money deposited but not

yet cleared. The net float, when added to or subtracted from previous balance, shows how much

N
money is in the bank account. The net float is important when an account holder deal primarily

N
in cheques.

4. True - The treasury management mainly deals with working capital management and financial risk

A
management. The treasurer would be responsible for providing the business with forecasts of

exchange rate movements, exposure to currency risk and interest rate risk.

M
5. True - Liquidity ensures the ability of the firm to honour its short-term commitments. Under profitability

X
objective, the finance manager has to utilize the funds in such a manner as to ensure the highest return.

6. False - Too little liquidity may lead to frustration in business operations, reduced rate of return, loss of

A
business opportunities, lowering the employee morale etc.

T
7. True - The surplus balance of cash should be suitably invested in marketable investments to earn atleast some

return on idle cash, if cash cannot be invested profitably elsewhere.

8. False - EOQ model of inventory is adopted by William J. Baumol in conceiving the cash management model.

9. True - The existence of free market for marketable securities is a prerequisite of the Baumol model.

10. False - Under Miller-Orr model, the higher the variability in cash flows and transaction cost, the wider and

higher the control limits will be. Conversely, the higher the interest rate, the lower and closer they will

become.

11. True - Float refers to the amount of money tied up between the time a payment is initiated and cleared funds

become available in the company’s bank account.

12. True - A firm with a positive net float can use it to its advantage and maintain a smaller cash balance than

it would have in the absence of the float.

Choose Correct Word

1. optimization

2. liquidity

3. opportunity

4. freely

5. marginal

6. profitability

7. more
 8. technical

9. inverse

10. EOQ

11. Baumol’s

12. purchase

13. cash budget

14. cash budget

15. float

Choose Correct Answer

1. (D) liquidity

2. (C) competing

3. (A) liquidity

4. (C) return point

N
5. (B) lock box system

N
6. (D) treasurer

7. (A) playing the float

A
8. (D) liquidity

M
9. (B) treasury manager

10. (A) speculation motive

X
11. (C) lower limit

A
12. (B) net float

` 8,500

T
13. (A)

14. (B) to improve liquidity ratio

15. (A) payments position cannot be assessed reasonably

 Practical Exercises

Exercise 14-1 The data of ABC Ltd. is as under:

Production for the year 69,000 units Credit given to debtors 3 months

Finished goods inventory 3 months Selling price per unit ` 50 each

Raw materials inventory 2 months consumption Raw material 50% of selling price

Production process 1 month Direct wages 10% of selling price

Credit allowed by creditors 2 months Overheads 20% of selling price

There is regular production and sales cycle, and wages and overheads accrue evenly. Wages are paid in the next

month of accrual. Material is introduced in the beginning of production cycle. Work-in-process involves use of full

N
unit of raw materials in the beginning of manufacturing process and other conversion costs equivalent to 50%.

You are required to find out:

N
(i) its working capital requirement, and

A
(ii) its permissible bank borrowing as per 1st and 2nd method of lending under the Tandon Committee norms.

Exercise 14-2 XYZ Co. Ltd. is a pipe manufacturing company. Its production cycle indicates that materials, are

M
introduced in the beginning of the production cycle, wages and overhead accrue evenly through out the period of

the cycle. Wages are paid in the next month following the month of accrual. Work-in-process includes full units of

X
raw materials used in the beginning of the production process and 50% of wages and overheads are supposed to be

A
conversion costs. Details of production process and the components of working capital are as follows:

T
Production of pipes 12,00,000 units Finished goods inventory held for 2 months

Duration of the production cycle 1 month Credit allowed by creditors 1 month

Raw materials inventory held 1 month consumption Credit given to debtors 2 months

Cost price of raw materials ` 60 p.u. Direct wages ` 10 p.u.

Overheads ` 20 p.u. Selling price of finished pipes ` 100 p.u.

Required to calculate:

(i) The amount of working capital required for the company.

(ii) Its maximum permissible bank finance under all the three methods of lending norms as suggested by the

Tandon Committee, assuming the value of core current assets: ` 1,00,00,000.

Exercise 14-3 A newly formed company has applied to the commercial bank for the first time for financing its

working capital requirements. The following information is available about the projections for the current year.

Elements of cost ( ` per unit)

Raw material 40

Direct labour 15

Overhead 30

Total cost 85

Profit 15

Sales 100
Other information:

Raw material in stock : average 4 weeks consumption, Work-in-progress (completion stage 50%), on an average half

a month. Finished goods in stock : on an average one month.

Credit allowed by suppliers is one month. Credit allowed to debtors is two months.

Average time lag in payment of wages is 1½ weeks and 4 weeks in overhead expenses.

Cash in hand and at bank is desired to be maintained at ` 50,000. All sales are on credit basis only.

Required:

(i) Prepare statement showing estimate of working capital needed to finance an activity level of 96,000 units of

production. Assume that production is carried on evenly throughout the year, and wages and overheads accrue

similarly. For the calculation purpose 4 weeks may be taken as equivalent to a month and 52 weeks in a year.

(ii) From the above information calculate maximum permissible bank finance by all three methods for working

capital as per Tandon Committee norms; assume the core current assets constitute 25% of the current assets.

Exercise 14-4 MNO Ltd. has furnished following data relating to the year ending of 31st March, 2016 ( ` lakhs)

Sales 450

N
Material consumed 150

Direct wages 30

N
Factory overheads (100% variable) 60

A
Office and Administration overheads (100% variable) 60

Selling overheads 50

M
The company wants to make a forecast of working capital needed for the next year and anticipates that:

(a) Sales will go up by 100%.

X
(b) Selling expenses will be ` 150 lakhs.

A
(c) Stock holdings for the next year will be: raw materials for two and half months, work-in-progress for one

month, finished goods for half month and book debts for one and half months.

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(d) Lags in payment will be 3 months for creditors, 1 month for wages and half month for factory, office and

administrative and selling overheads.

You are required to:

(i) Prepare statement showing working capital requirements for next year, and

(ii) Calculate maximum permissible bank finance as per Tandon Committee guidelines assuming that core

current assets of the firm are estimated to be ` 30 lakhs.

Exercise 14-5 A Bank is analyzing the receivables of Jackson Company is order to identify acceptable collateral for

a short-term loan. The company’s credit policy is 2/10 net 30. The bank lends 80% on accounts where customers are

not currently overdue and where the average payment period does not exceed 10 days past the net period. A schedule

of Jackson’s receivables has been prepared. How much will the bank lend on a pledge of receivables, if the bank uses

a 10% allowance for cash discount and returns?

Account Amount Days outstanding Average payment

`
( ) (in days) (period historically)

74 25,000 15 20

91 9,000 45 60

107 11,500 22 24

108 2,300 9 10

114 18,000 50 45

116 29,000 16 10

123 14,000 27 48

1,08,800
Exercise 14-6 Under an advance factoring arrangement Bharat Factors Ltd. (BFL) has advanced a sum of ` 14 lakhs
against the receivables purchased from ABC Ltd. The factoring agreement provides for an advance payment of 80%

(maintaining ‘factor reserve’ of 20% to provide for disputes and deductions relating to the bills assigned) of the value

of factored receivables and for guaranteed payment after three months from the date of purchasing the receivables.

The advance carries a rate of interest of 20% per annum compounded quarterly and the factoring commission is 1.5%

of the value of factored receivables. Both the interest and commission are collected up-front.

(i) Compute the amount of advance payable to ABC Ltd.

(ii) Calculate per annum the effective cost of funds made available to ABC Ltd.

(iii) Calculate the effective cost of funds made available to ABC Ltd. assuming that the interest is collected in arrear

and commission is collected in advance.

Exercise 14-7 Bansali textile has annual sales of ` 200 crores. About 80% of its sales is on credit, and the average

collection period is 90 days. The company’s bad debts, as the past trend reveals, are around 0.9% of credit sales. The

company’s annual cost of administering credit sales is ` 75 lakhs. It is possible to save ` 55 lakhs, out of the bad debts
and sales administering costs, if the company avails of full-factor service from a factoring company. The company

has approached a factoring company and got the following terms:

N
Advance payment 80% Discount rate 14% p.a. Commission for service 1.0% (to be paid upfront)

(i) What will be the effective cost of factoring on an annual basis (assume 360 day in a year) ?

N
(ii) Bansali Textile can borrow the advance payment offered by the factoring company from a bank at 14% p.a.

A
Should the company avail of the factoring service ? Give reasons.

Exercise 14-8 The turnover of Bharat Ltd. is ` 240 crores of which 80% is on credit. Debtors are allowed 90 days to

M
clear off the dues. The company’s annual cost of administering credit sales is ` 90 lakhs. It is possible to save ` 66 lakhs

X
out of the sales administering costs and avoid bad debts at 1% on credit sales (dues) if the company avails of full-factor

service from a factor company. The company has approached Indbank Factors Ltd. (factor company) and got the

A
following terms:

T
Advance payment 90% Discount rate 15% p.a. Commission for service 1.0% (to be paid up-front)

A bank has come forward to make an advance equal to 90% of the debts at an annual interest rate of 13%.

Should the company avail of the factoring service or the offer of the bank ? Give reasons (Assume 360 days in a year).

Exercise 14-9 The annual turnover of Vibgyor Ltd. is ` 12 million of which 80% is on credit. Debtors are allowed one
month to clear off the dues. Allbank Factors Ltd. (a factor company) is willing to advance 90% of the bill raise on

credit for a fee of 2% a month plus a commission of 3% on the total amount of debts. Vibgyor Ltd. as a result of this

arrangement, is likely to save ` 43,200 annually in management costs and avoid bad debts at 1% on the credit sales.
A scheduled bank has come forward to make an advance equal to 90% of the debts at an interest rate of 12 per cent

p.a. However its processing fee will be at 2 per cent on the debts. Should the company avail of the factoring service

or the offer of the bank? Give reasons.

Exercise 14-10 Progressive Ltd. sells its products to wholesale distributors. The management is worried over the

liquidity and is exploring methods of improving the cash flow, by speeding up collection from debtors. The following

table summarizes its turnover and profits for the last two years and comparable debtors level as at the end of last

two years.The alternatives before the management are:

(i) Offer a 2% discount to customers who settle within 10 days of invoicing. It is estimated that 50% of customers

would take advantage of this offer.

(ii) Seek the services of a factor, who will operate on a “service only” basis, administering and collecting payments

from customers. Savings are expected to be ` 5,00,000 annually; also debtor days will come down to 45 days.

Charges payable to the factor would be 1.5% of turnover. Progressive Ltd. can borrow from bank at 15% per

annum. (` ’000)
 Year 0 Year 1

Turnover 60,000 80,000

Profits 11,500 15,000

Debtors 8,000 13,000

Required : Analyze the costs and benefits of both alternatives and state the preferred course of action.

[Note: Take 365 days in a year]

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 Key to Practical Exercises

Exercise 14-1

(i) Statement Showing Computation of Working Capital Requirement `

( )

Current Assets:

Raw materials stock (69,000 units × ` 25 × 2/12) 2,87,500

Work-in-process (69,000 units × ` 32.50 × 1/12) 1,86,875

Finished goods stock (69,000 units × ` 40 × 3/12) 6,90,000

Sundry debtors (69,000 units × ` 50 × 3/12) 8,62,500

(a) 20,26,875

Current Liabilities:

Creditors for raw materials (69,000 units × ` 25 × 2/12) 2,87,500

N
Creditors for wages (69,000 units × ` 5 × 1/12) 28,750

(b) 3,16,250

N
Working Capital (a) - (b) 17,10,625

A
(ii) Computation of Maximum Permissible Bank Finance (MPBF)

1st Method of Lending `

( )

M
Working capital gap 17,10,625

X
Less: 25% from long-term funds 4,27,655

A
Maximum Permissible Bank Finance 12,82,970

T
2nd Method of Lending `
( )

Working capital gap 17,10,625

Less: 25% current assets (20,26,875 × 25/100) 5,06,719

Maximum Permissible Bank Finance 12,03,906

Exercise 14-2

(i) Calculation of Amount of Working Capital Requirement `

( )

Current Assets:

Raw material inventory (12,00,000 × ` 60 × 1/12) 60,00,000

Work-in-progress

Raw materials (12,00,000 × ` 60 × 1/12) 60,00,000

Wages (12,00,000 × ` 10 × 1/12 × 50/100) 5,00,000

Overheads (12,00,000 × ` 20 × 1/12 × 50/100) 10,00,000 75,00,000

Finished goods inventory (12,00,000 × `. 90 × 2/12) 1,80,00,000

Debtors (12,00,000 × ` 90 × 2/12) 1,80,00,000

(a) 4,95,00,000

Current Liabilities:

Creditors for raw materials (12,00,000 × ` 60 × 1/12) 60,00,000

Creditors for wages (12,00,000 × ` 10 × 1/12) 10,00,000

(b) 70,00,000

Net Working Capital (a) - (b) 4,25,00,000

 (ii) Computation of Maximum Permissible Bank Finance (MPBF)

Ist Method of Lending `

( )

Current assets 4,95,00,000

Less: Current liabilities 70,00,000

Working capital gap 4,25,00,000

Less: 25% from long-term sources 1,06,25,000

MPBF 3,18,75,000

IInd Method of Lending `

( )

Current assets 4,95,00,000

Less: Current liabilities 70,00,000

Working capital gap 4,25,00,000

Less: 25% of current assets 1,23,75,000

MPBF 3,01,25,000

N
IIIrd Method of Lending `
( )

N
Total current assets 4,95,00,000

Less: Core current assets 1,00,00,000

A
3,95,00,000

Less: 25% of ` 3,95,00,000 98,75,000

M
2,96,25,000

X
Less: Current liabilities 70,00,000

MPBF 2,26,25,000

T A
Exercise 14-3

Calculation of Working Capital Requirement `

( )

Current Assets:

Stock of materials (96,000 × 40 × 4/52) 2,95,385

Work-in-progress

Material (96,000 × 40 × 2/52) × 50/100 73,846

Labour (96,000 × 15 × 2/52) × 50/100 27,692

Overhead (96,000 × 30 × 2/52) × 50/100 55,385 1,56,923

Finished stock (96,000 × 85 × 4/52) 6,27,692

Debtors (96,000 × 85 × 8/52) 12,55,385

Cash in hand and at bank 50,000

(a) 23,85,385

Current Liabilities:

Creditors (96,000 × 40 × 4/52) 2,95,385

Lag in Payment for expenses:

Overheads (96,000 × 30 × 4/52) 2,21,538

Labour (96,000 × 15 × 3/104) 41,538 2,63,076

(b) 5,58,461

Net working capital (a) - (b) 18,26924

Calculation of Maximum Permissible Bank Finance as per Tandon Committee Norms

Ist Method of Lending `

( )

Total current assets 23,85,385

Less: Current liabilities 5,58,461

18,26,924

Less: 25% from long-term sources 4,56,731

MPBF 13,70,193

IInd Method of Lending `

( )

Total current assets 23,85,385

Less: 25% from long-term sources 5,96,346

17,89,039

Less: Current liabilities 5,58,461

MPBF 12,30,578

N
IIIrd Method of Lending `
( )

N
Total current assets 23,85,385

A
Less: Core current assets (23,85,385 × 25/100) 5,96,346

17,89,039

M
Less: 25% from long-term sources 4,47,260

X
13,41,779

Less: Current liabilities 5,58,461

A
MPBF 7,83,318

T
Exercise 14-4

Statement showing Projected Cost and Profitability for next year ending 31st March 2017 ( ` lakhs)

Particulars Year ended Year ending Per month

31-3-2016 31-3-2017

(actuals) (forecast)

Sales (a) 450 900 75

Costs:

Direct materials 150 300 25

Direct wages 30 60 5

Prime cost 180 360 30

Add: Factory overheads 60 120 10

Factory cost 240 480 40

Add: Office and administration overheads 60 120 10

Cost of production 300 600 50

Add: Selling overheads 50 150 12.50

Total cost (b) 350 750 62.50

Profit (a) - (b) 100 150 12.50

(i) Statement showing working capital requirement for the year ending 31-3-2017 ( ` lakhs)

Current Assets:

Raw materials (25 × 2.5) 62.50

Work-in-progress:

Raw material (25 × 1) 25.00

Direct wages (5 × 1) 5.00

Factory overheads (10 × 1) 10.00 40.00

Finished goods (600 × 0.5/12) 25.00

Debtors (900 × 1.5/12) 112.50

(a) 240.00

Current Liabilities:

Creditors (300 × 3/12) 75.00

Wages (60 × 1/12) 5.00

Factory overheads (120 × 0.5/12) 5.00

N
Office and Admn. overheads (120 × 0.5/12) 5.00

Selling overhead (150 × 0.5/12) 6.25

N
(b) 96.25

A
Net working capital (a) - (b) 143.75

(ii) Calculation of Maximum Permissible Bank Finance as per Tandon Committee Guidelines

M
Ist Method of Lending ( ` lakhs)

X
Total current assets 240.00

Less: Current liabilities 96.25

A
143.75

T
Less: 25% from long-term sources 35.94

MPBF 107.81

IInd Method of Lending ( ` lakhs)

Total current assets 240.00

Less: 25% from long-term sources 60.00

180.00

Less: Current liabilities 96.25

MPBF 83.75

IIIrd Method of Lending ( ` lakhs)

Total current assets 240.00

Less: Core current assets 30.00

210.00

Less: 25% from long-term sources 52.50

157.50

Less: Current liabilities 96.25

MPBF 61.25
Exercise 14-5

Calculation amount to be lent by bank on pledge of receivables

Jackson Company’s Credit Policy 2/10 net 30 with another 10 days as Allowance

Account No. Analysis

74 Not overdue currently and in past

91 Overdue currently and in past

107 Not overdue currently and in past

108 Not overdue currently and in past

114 Overdue currently and in past

116 Not overdue currently and in past

123 Not overdue currently but overdue in the past

From the above analysis, we can observe that Account Nos. 91, 114 and 123 are not eligible for bank finance. Account

N
Nos. 74, 107, 108 and 116 are only eligible for bank finance on pledge of receivables.

Calculation of amount which can be lent by Bank to Jackson Company on pledge of its Receivable

N
Particulars Account Nos.

A
74 107 108 116

Invoice amount 25,000 11,500 2,300 29,000

M
Less: Allowance for cash discount and returns (10%) 2,500 1,150 230 2,900

X
22,500 10,350 2,070 26,100

Eligible bank finance (80% of the above) 18,000 8,280 1,656 20,880

A
` 48,816 to Jackson Company on pledge of its receivables to the bank.

T
Analysis - Therefore, the bank can finance upto

Exercise 14-6

(i) Computation of Advance Payable to ABC Ltd. ( ` lakhs)

Value of factored receivable ( ` 14 lakhs/0.8) 17.50

Maximum permissible advance 14.00

Less: Commission @ 1.5 per cent ( ` 17.50 lakhs × 0.015) 0.26

13.74

Less: Discount charge ( ` 14 lakhs × 0.2 × 90/360) 0.70

Funds made available to ABC Ltd. 13.04

(ii) Effective Cost

Discount charge expressed as a percentage of funds made available to ABC Ltd.

= 0.7/13.04 = 5.37% per quarter

4
The annualized rate of interest = [(1.00537) - 1] = 23.27

Hence cost of funds = 23.27%

(iii) Effective Cost When Interest in Arrears and Commission in Advance ( ` lakhs)

Maximum permissible advance 14.00

Less: Commission payable up-front ( ` 17.50 lakhs × 0.015) 0.26

Funds made available to ABC Ltd. 13.74

Interest charges collected in arrears (i.e., ` 14 lakhs × 0.20 × 90/360) 0.70

 Interest charges expressed as a percentage of funds made available

= 70/13.74 = 5.095 per quarter

4
Annualized interest cost = [(1.05095) - 1] × 100 = 21.99%

Exercise 14-7

Credit sales = ` 200 crores × 80/100 = ` 160 crores

Average receivables = ` 160 crores × 90/360 = ` 40 crores

Calculation of Factoring Cost ( ` crores)

Advance payment ( ` 40 crores × 80/100) 32.00

Less : Discount ( ` 32 crores × 14/100 × 3/12) 1.12

Commission ( ` 40 crores × 1/100) 0.40 1.52

30.48

Add : Saving in administration cost 0.55

31.03

N

Cost for a period of 3 months =  = 1.03126 - 1 = 0.03126 or 3.126%

N


4
Annualized cost = (1 + 0.03126) - 1 = 0.1310 or 13.1%

A
Analysis - Bank borrowing rate of 14% is higher than the effective cost of factoring. Therefore, the company can avail

the factoring service instead of bank borrowing.

M
Exercise 14-8

X
Credit sales = ` 240 crores × 80/100 = ` 192 crores

A
Average receivables = ` 192 crores × 90/360 = ` 48 crores

T
Alternative I - Avail Factoring Service `
( )

Advance payment ( ` 48 crores × 90/100) 43.20

Less: Discount ( ` 43.20 crores × 15/100 × 3/12) 1.62

Commission ( ` 48 crores × 1/100) 0.48 2.10

41.10

Add: Saving in cost

Administering cost 0.66

Bad debts ( ` 48 crores × 1/100) 0.48 1.14

Net realization 42.24


Cost for a period of 3 months =  = 0.02273 or 2.273%


Annualized cost = (1 + 0.02273)

4 - 1 = 0.09407 or 9.41% p.a.

Bank advance rate = 13% p.a.

Suggestion - Since the bank advance rate is higher than the effective cost of factoring, it is suggested to avail factoring

service.

Exercise 14-9

Credit sales = ` 1,20,00,000 × 80/100 = ` 96,00,000

Debtors = ` 96,00,000 × 1/12 = ` 8,00,000

Alternative I - Avail Factoring Service

Calculation of Cost of Factoring `

( )

Factoring fee ( ` 8,00,000 × 2/100 × 90/100) 14,400

Commission ( ` 8,00,000 × 3/100) 24,000

38,400

Less : Saving in cost

Saving management cost ( ` 43,200/12) 3,600

Saving in Bad debts ( ` 8,00,000 × 1/100) 8,000 11,600

Net cost of factoring 26,800

Alternative II - Avail Bank Finance

Calculation of Cost of Bank Finance `

( )

Interest ( ` 8,00,000 × 90/100 × 12/100 × 1/12) 7,200

Processing fee ( ` 8,00,000 × 2/100) 16,000

Bad debts loss ( ` 8,00,000 × 1/100) 8,000

N
Cost of Bank finance 31,200

N
Suggestion - Since the cost of factoring is less than cost of bank finance, it is suggested to avail factoring service.

A
Exercise 14-10

Alternative I - Offer 2% Discount to Customers

M
Turnover in year 1 = ` 800 lakhs

X
Debtors in year 1 = ` 130 lakhs



A
Average collection period = ×  = 59 days


T
 
2% discount will lower the debtors period to = + = 34.5 days
 
Cost of discount = ` 800 lakhs × 2/100 × 50/100 = 8.00 lakhs

Revised Debtors value = ` 800 lakhs - ` 8 lakhs = 792.00 lakhs

 
Average Debtors level = ` 792 lakhs × = 74.86 lakhs


Saving of interest = (130 - 74.86) × 15/100 = ` 8.271 lakhs

Net saving = Interest saving - Cost of discount

= ` 8.271 lakhs - ` 8 lakhs = ` 0.271 lakhs

Alternative II - Avail Services of a Factor

Reduction in Debtors = 59 days - 45 days = 14 days


Reduction in Debtors = ` 800 lakhs × = ` 30.685 lakhs

Interest savings = ` 30.685 lakhs × 15/100 = ` 4.603 lakhs

Savings in administrative cost = ` 5 lakhs

Service charges = ` 800 lakh × 1.5/100 = ` 12 lakhs

Net cost of Factoring = 12 - (4.603 + 5) = ` 2.397 lakhs

Suggestion - Since the cost of availing factoring service is higher than offering discount to customers, it is suggested

to offer 2% discount to customers who settle within 10 days of invoicing.

 Key to Short Answer Questions

True or False Statements

1. True - Cash credit facility will be given by the banker to the customers by giving certain amount of credit

facility on continuous basis on the basis of investment in current assets. The cash credit will be given

on moving stock which has been paid, as far as inventories are concerned.

2. True - Under maximum permissible bank finance (MPBF) approach, the banks will fix the working capital

finance limits of a firm at either 75% of the company’s current asset or the difference between 75% of

current asset and non-bank current liabilities. Therefore, net working capital represents the margin

money to be financed by the business firms.

3. True - Trade credit, credit from employees, credit from suppliers of services etc. are the examples of

spontaneous financing, which contributes about one-third of the total short-term credit.

False

N
4. - Non-fund credit facilities are made available only by commercial banks who render working capital

financing to the customer firms.

N
5. True - The non-fund credit facilities include bank guarantees, bankers acceptance, letter of credit etc. These

A
commitments do not appear in the banks main balance sheet except by way of contingent liabilities

in the ‘Notes’ attached to it.

False

M
6. - A cash credit is a running account for drawing within a specified credit limit sanctioned by the bank

against the security of stocks and book debts. Overdraft means drawing from a current account over

X
and above the credit balance therein, it may be secured or unsecured.

True

A
7. - A bill bearing a reputable bank’s name can be sold in the money markets at a lower discount rate than

a bill bearing the name of a company.

T
8. True - Guarantees should be covered by a counter guarantee by a customer giving the bank absolute right

of payment under guarantee on the happening of contingency guaranteed against.

9. False - The minimum current ratio under second method of MPBF works out to 1.33:1.

10. False - Factoring is a specialized activity whereby a firm converts its receivables into cash by selling them to

a factoring organization. It is also termed as invoice factoring.

11. False - A factor assumes the risk of collection and in the event of nonpayment by the customers/debtors bears

the risk of bad debt losses. In case of factoring, the receivables are not supported by negotiable

instruments, namely, bills. In case of receivables backed by bills, the firm resorts to the practice of bill

discounting with its bankers.

12. True - Forfaiting is a technique to help the exporter to sell his goods on credit and yet receive the cash well

before the due date.

Choose Correct Word

1. pledge

2. trade

3. negotiated

4. depreciation

5. kept in the

6. cash credit

7. reduces
 8. more

9. credit

10. debt administration

11. factoring

12. cycle

Choose Correct Answer

1. (B) bills discounting

2. (C) sight draft

3. (B) notified factoring

4. (C) discounting of bills

5. (C) working capital finance from bank

6. (A) retained profit

7. (A) invoice amount

N
8. (A) bank guarantee

N
9. (D) cash credit

10. (B) bills discounting

A
11. (C) bank

12. (A) suppliers are willing to supply on too long credit period

M
13. (B) 75% of (Current assets - Current liabilities other than bank borrowings)

X
14. (C) Cash credit operates against hypothecation of inventory and debtors while overdraft requires pledge of

A
securities, insurance policies etc.

T
 Practical Exercises

Exercise 16-1 Following information has been extracted from the books of Unique Fashioners Ltd.: ( ) `

Equity capital 4,00,00,000

12% Debentures 4,00,00,000

18% Term loan 12,00,00,000

20,00,00,000

The company has been paying 20% dividend per annum constantly. Compute average cost of capital if the current

market price of a share of ` 100 is ` 160.

Exercise 16-2 Following are the extracts from financial statements of Zipway Ltd.: ( ` lakhs)

N
Earnings before interest and tax 250

Less: Interest on debentures 50

N
Earnings before tax 200

A
Less: Income-tax (40%) 80

Net profit 120

M
Equity share capital (shares of ` 10 each) 500

X
Reserve and surplus 250

10% Non-convertible debentures 500

A
1,250

T
The market price per equity share is ` 15 and per debenture is ` 95. Calculate the following:

(i) earnings per share; and

(ii) percentage of cost of capital to the company for debenture fund and the equity.

Exercise 16-3 H Ltd. and Z Ltd. have the same levels of business risk and their market values and earnings are

summarized below: `
( )

Particulars H Ltd. Z Ltd.

Market values: Equity 6,00,000 3,00,000

Debt - 2,50,000

6,00,000 5,50,000

Earnings 90,000 90,000

Less: Interest - 22,000

90,000 68,000

Calculate the post-tax cost of equity, cost of debt and weighted average cost of capital of both the companies. Assume

that the income-tax rate on the company is 35% and the additional tax on dividend distribution is 20%.

Exercise 16-4 You are required to determine the weighted average cost of capital (K ) of the K.C. Ltd. using (i) book
o
value weights; and (ii) market value weights. The following information is available for your perusal.
The K.C. Ltd.’s present book value capital structure is: ( ) `

Debentures ( ` 100 per debenture) 8,00,000

Preference shares ( ` 100 per share) 2,00,000

Equity shares ( ` 10 per share) 10,00,000

20,00,000

All these securities are traded in the capital markets. Recent prices are debentures @ ` 110, preference shares @ ` 120
and equity shares @ ` 22. Anticipated external financing opportunities are:

(i) ` 100 per debenture redeemable at par : 20-year maturity, 8% coupon rate, 4% flotation costs, sale price ` 100.

(ii) ` 100 preference share redeemable at par : 15-year maturity, 10% dividend rate, 5% flotation costs, sale price
` 100.

(iii) Equity shares ` 2 per share flotation costs, sale price ` 22.

In addition, the dividend expected on the equity share at the end of the year ` 2 per share, the anticipated growth

rate in dividends is 5% and the company has the practice of paying all its earnings in the form of dividends. The

N
corporate tax rate is 50%.

Exercise 16-5 M/s. Albert & Co. has the following capital structure as on 31st March, 2016 `

N
( )

10% Debentures 3,00,000

A
9% Preference shares 2,00,000

Equity (5,000 shares of ` 100 each) 5,00,000

M
10,00,000

X
The equity shares of the company are quoted at ` 102 and the company is expected to declare a dividend of ` 9 per

A
share for 2016.

T
(i) Assuming the tax rate applicable to the company at 50%. Calculate the weighted average cost of capital. State

your assumptions, if any.

(ii) Assuming in the exercise, that the company can raise additional term loan at 12% for ` 5,00,000 to finance an
expansion, calculate the revised weighted cost of capital. The company’s assessment is that it will be in a

position to increase the dividend from ` 9 per share to ` 10 per share, but the business risk associated with new
financing way bring down the market price from ` 102 to ` 96 per share.

Exercise 16-6 The capital structure of Swan & Co. comprising of 12% debentures, 9% preference shares and equity

shares of ` 100 each is in the proportion of 3 : 2 : 5. The company is contemplating to introduce further capital to
meet the expansion needs by seeking 14% term loan from financial institutions. As a result of this proposal, the

proportions of debentures, preference shares and equity would get reduced by 1/10, 1/15 and 1/6 respectively.

In the light of above proposal, calculate the impact on weighted average cost of capital assuming 50% tax rate,

expected dividend of ` 9 per share at the end of the year and growth rate of dividends 5%. No change in dividend,

dividend growth rate and market price of share is expected after availing the proposed term loan.

Exercise 16-7 Three companies A, B & C are in the same type of business and hence have similar operating risks.

However, the capital structure of each of them is different and the following are the details: ( `)

Particulars A B C

Equity share capital (face value ` 10 per share) 4,00,000 2,50,000 5,00,000

Market value per share 15 20 12

Dividend per share 2.70 4 2.88

Particulars A B C

Debentures (face value per debenture ` 100) Nil 1,00,000 2,50,000

Market value per debenture - 125 80

Interest rate - 10% 8%

Assume that the current levels of dividends are generally expected to continue indefinitely and the income-tax rate

at 50%. You are required to compute the weighted average cost of capital of each company.

Exercise 16-8 The following is the capital structure of Simons Company Ltd. as on 31-03-2016 `
( )

Equity shares: 10,000 shares (of ` 100 each) 10,00,000

10% Preference shares (of ` 100 each) 4,00,000

12% Debentures 6,00,000

20,00,000

The market price of the company’s share is ` 110 and it is expected that a dividend of `10 per share would be declared
for the year 2016-17. The dividend growth rate is 6%:

N
(i) If the company is in the 50% tax bracket, compute the weighted average cost of capital.

N
(ii) Assuming that in order to finance an expansion plan, the company intends to borrow a fund of ` 10 lakh

bearing 14% rate of interest, what will be the company’s revised weighted average cost of capital ? This

A
financing decision is expected to increase dividend from ` 10 to ` 12 per share. However, the market price of
equity share is expected to decline from ` 110 to ` 105 per share.

M
Exercise 16-9 The following items have been extracted from the ‘liabilities’ side of balance sheet of XYZ Company

X
as at 31st March, 2016 `
( )

A
Paid-up capital (4,00,000 Equity shares of 10 each) 40,00,000

Reserves and surplus 60,00,000

T
Loans: 15% Non-convertible debentures 20,00,000

14% Institutional loans 60,00,000

Other information about the Company as relevant is given below: `

( )

Year ended 31st March Dividend Earnings Average market

per share per share price per share

2015 4.00 7.50 50.00

2014 3.00 6.00 40.00

2013 4.00 4.50 30.00

You are required to calculate the weighted average cost of capital, using book values as weights and earnings/price

ratio (E/P) as the basis of cost of equity.

Exercise 16-10 A company is considering raising of funds of about ` 100 lakhs by one of two alternative methods, viz.,
14% institutional term loan and 13% non-convertible debentures. The term loan option would attract no major

incidental cost. The debentures would have to be issued at a discount of 2.5% and would involve cost of issue of ` 1 lakh.
Advise the company as to the better option based on the effective cost of capital in each case. Assume a tax rate of 50%.
 Key to Practical Exercises

Exercise 16-1
D
1
` 20
Calculation of Cost of Equity (K ) = = = 0.125 or 12.5%
`
e
P 160
0

Calculation of Weighted Average Cost of Capital

Sources of Capital Amount Cost of capital Proportion Cost

( ` lakhs) (%) to total

Equity capital 400 12.5 0.20 2.50

12% Debentures 400 12.0 0.20 2.40

18% Term loan 1,200 18.0 0.60 10.80

2,000 15.70

N
The weighted average cost of capital is 15.7%.

N
Exercise 16-2

A
(i) Calculation of EPS

Net profit available to Equity shareholders = ` 1,20,00,000

M
No. of Equity shares = ` 5,00,00,000/ ` 10 = 50,00,000 shares

X
1,20,00,000
EPS = = ` 2.40
50,00,000 shares

A
(ii) Calculation of Cost of Capital

T
EPS ` 2.40
Cost of Equity capital (K ) = = = 0.16 or 16%
`
e
Market price 15

Interest (1 - Tax rate)

Cost of Debentures (K ) =
d
Debenture fund

(a) At book value (b) At market value

` 50,00,000 (1 - 0.40) ` 50,00,000 (1 - 0.40)

= = 0.06 or 6% = = 0.0631 or 6.31%
` 5,00,00,000 ` 4,75,00,000

Exercise 16-3
`
( )

Particulars H Ltd. Z Ltd.

Earnings 90,000 68,000

Less: Taxes @ 35% 31,500 23,800

58,500 44,200

Less: Additional tax on dividend (20/120) 9,750 7,367

Net earnings 48,750 36,833

(a) Cost of Equity H Ltd. Z Ltd.

Net earnings 48,750 36,833

K = = = 8.125% = = 12.28%
e
Market value 6,00,000 3,00,000
 (b) Cost of Debt

Interest (1 - t) 22,000 (1-0.35)

K = = Nil = = 5.72%
d
Debt 2,50,000

(c) Weighted Average Cost of Capital

H Ltd. = 8.125%

30 25
Z Ltd. = [ 0.1228 × 55
] + [ 0.0572 × 55
]= 0.067 + 0.026 = 0.093 or 9.3%

Exercise 16-4

(i) Cost of Equity Capital (K )

e

D 2
1
K = + g = + 0.05 = 0.15 or 15%
e
NP 20

(ii) Cost of Debentures (K )

d

  3W 4W  
 * +  /    U
     
  +     

N





K =
 3W + 4W  = = = 0.0418 or 4.18%
  +  

N

d

    


A
(iii) Cost of Preference Shares (K )
p

3W 4W    
%+   + 

M
 /      + 

X
K = = = = 0.1059 or 10.59%
p
 3W + 4W    +   

     

T A
(1) WACC (based on book values)

Source of capital Book value Weight Cost of capital % Weighted

`
( ) cost (%)

Equity capital 10,00,000 0.50 15.00 7.50

Preference capital 2,00,000 0.10 10.59 1.06

Debentures 8,00,000 0.40 4.18 1.67

20,00,000 1.00 WACC = 10.23%

(2) WACC (based on market values)

Source of capital Market value Proportion Cost of capital Weighted

`
( ) (%) cost (%)

Equity share capital 22,00,000 .6626 15.00 9.94

Preference share capital 2,40,000 .723 10.59 0.77

Debentures 8,80,000 .2651 4.18 1.11

33,20,000 1.00 WACC = 11.82%

Exercise 16-5

(i) Calculation of WACC Before Raising Additional Finance

Source of finance Weight Post-tax Weighted

cost % cost %

Debentures (10%) 0.3 5.0 1.5

Preference shares (9%) 0.2 9.0 1.8

Equity shares 0.5 13.8 6.9

1.0 WACC = 10.2%

Cost of Debentures (K ) = I (1 - t) = 10% - (1 - 0.50) = 5%

d

D 9
1
Cost of Equity Capital (K ) = + g = + 0.05 = 0.138 or 13.8%
e
P 102
0

(ii) Calculation of WACC After Raising a Term Loan of ` 5,00,000 @ 12% p.a.

Source of finance Weight Post-tax Weighted

N
cost % cost %

Debentures (10%) 0.200 5.0 1.0

N
Term loan (12%) 0.333 6.0 2.0

A
Preference shares (9%) 0.133 9.0 1.2

Equity 0.334 15.4* 5.1

M
1.000 WACC = 9.3%

X
D 10
1
*Cost of Equity Capital (K ) = + g = + 0.05 = 0.154 or 15.4%
e
P 96

A
0

T
Exercise 16-6

Cost of Capital Before Raising Term Loan

Source of finance Weight Post-tax Weighted

cost % cost %

Debentures (12%) 0.3 6.0 1.8

Preference shares (9%) 0.2 9.0 1.8

Equity 0.5 13.2 6.6

1.0 WACC = 10.2%

Cost of Equity Capital is calculated as below:

Let us assume the market price of equity is ` 110. Then, the cost of equity capital under Gordon Growth Model:

D 9
1

K = + g = + 0.05 = 0.132 or 13.2%

e
P 110
0

Cost of Capital After Raising Term Loan

Source of finance Weight Post-tax Weighted

cost % cost %

Debenture (12%) 0.200 6.0 1.20

Preference shares (9%) 0.133 9.0 1.20

Term loan (14%) 0.333 7.0 2.33

Equity 0.334 13.2 4.40

WACC = 9.13%
Analysis - With the raising of term loan @ 14% p.a., the company’s weighted cost of capital has got reduced from 10.2%

to 9.13%.

Exercise 16-7
D
1

(a) Cost of Equity (K ) = × 100

e
P
0

A = (2.70/15) × 100 = 18% B = (4/20) × 100 = 20% C = (2.88/12) × 100 = 24%

I (1 - t)
(b) Cost of Debt (K ) = × 100
d
MV

10 (1 - 0.50) 8 (1 - 0.50)
Company B = × 100 = 4% Company C = × 100 = 5%
125 80

(at market value)

Name of company Equity Debt

`
( ) (%) `
( ) (%)

A 6,00,000 100 - -

B 5,00,000 80 1,25,000 20

N
C 6,00,000 75 2,00,000 25

N
K (at market values) = (Cost of Equity × % of Equity) + (Cost of Debt × % of Debt)
o

A = (18% × 1.00) = 18%

A
B = (20% × 0.80) + (4% × 0.20) = 16.8%

C = (24% × 0.75) + (5% × 0.25) = 19.25%

M
Exercise 16-8

X
(i) Current Finance Scheme

A
D 10
1
Cost of Equity Shares (K ) = + g = + 0.06 = 0.1509 or 15.09%
e
P 110

T
0

Source of Finance Amount Weight Post-tax Weighted

`
( ) cost (%) cost (%)

Equity shares 10,00,000 0.50 15.09 7.54

10% Preference shares 4,00,000 0.20 10.00 2.00

12% Debentures 6,00,000 0.30 6.00 1.80

20,00,000 1.00 WACC = 11.34%

(ii) Revised Finance Scheme

12
K = + 0.06 = 0.1742 or 17.42%
e
105

Source of Finance Amount Weight Post-tax Weighted

`
( ) cost (%) cost (%)

Equity shares 10,00,000 0.333 17.42 5.80

10% Preference shares 4,00,000 0.134 10.00 1.34

12% Debentures 6,00,000 0.200 6.00 1.20

14% Loan 10,00,000 0.333 7.00 2.33

30,00,000 1.000 Revised WACC = 10.67%

Exercise 16-9

EPS 7.50
Cost of Equity (including Reserves and Surplus) (K ) = = = 0.15 or 15%
e
Market price 50

Cost of Convertible Debentures (K ) = I (1 - t) = 15% (1 - 0.50) = 7.5%

d

Cost of Institutional Loans (K ) = I (1 - t) = 14% (1 - 0.50) = 7%

t

The corporate tax rate is assumed to be 50%.

WACC Based on Book Values

Source of finance Book values Cost of capital Product

( )` `
( )

Equity funds 1,00,00,000 0.150 15,00,000

15% Non-convertible debentures 20,00,000 0.075 1,50,000

14% Institutional loans 60,00,000 0.070 4,20,000

1,80,00,000 20,70,000

20,70,000

N
WACC (K ) = × 100 = 11.5%
o
1,80,00,000

N
Exercise 16-10

Evaluation of Raising ` 100 lakhs Based on Effective Cost of Capital ( ` lakhs)

A
Particulars Option 1 Option 2

14% Term loan 13% NCD

M
Face value of amount 100.00 100.00

X
Less: Discount - 2.50

100.00 97.50

A
Less: Cost of issue - 1.00

T
Net effective amount raised (i) 100.00 96.50

Interest charges p.a. on face value 14.00 13.00

Less: Savings in tax @ 50% 7.00 6.50

Net interest cost (ii) 7.00 6.50

Effective cost of capital (ii)/(i) × 100 7% 6.74%

Recommendation - The cost of capital to the company is lower i.e., 6.74% if the company raises 13% non-convertible

debentures (NCDs) and hence it is suggested to raise funds by issue of NCDs.

 Key to Short Answer Questions

True or False Statements

1. False - The corporate tax rate will have impact on the cost of debt.

2. False - The price-earning ratio indicates the market price of equity share to the earnings per share. It

measures the number of times the earnings per share discounts the market price of an equity share.

The ratio indicates how much an investor is prepared to pay per rupee of earnings. Therefore, P/E

ratio can be considered as opportunity cost of capital. The ratio reflects the market’s confidence on

company’s equity.

3. False - Any payment towards interest will reduce the profit and ultimately the company’s liability towards

taxes would decrease. This phenomenon is called ‘tax shield’. It will reduce the overall cost of capital

but not the cost of equity capital.

True

N
4. - The retained earnings are accumulated over years of the company by keeping a part of the funds

generated without distribution. So long as the retained earnings are not distributed to the sharehold-

N
ers, the company can use the funds within the company for further profitable investment opportunity.

The intrinsic value of the share will increase and therefore, its market price will also be higher due to

A
higher book value and higher earning capacity. There is no need for calculating separate cost for

retained earnings, when cost of equity capital is calculated on the basis of the market value of equity

M
shares.

5. False - CAPM divides the cost of capital into two components, the near risk-free return and risk premium.

X
The return estimated under CAPM depends on the risk attached to the investments cash flows.

A
WACC of a company is calculated by aggregating together costs of each individual source of finance

and weighted by their relative proportions to total amount of long-term funds raised. Therefore, the

T
return estimated from CAPM is different from WACC of the company.

6. True - Cost of capital is the minimum rate of return that a firm must earn on its investments so that market

value per share remain unchanged. For an investment to be worthwhile, the expected return on capital

must be greater than the cost of capital.

7. False - The dividend yield model assumes that the future dividend per equity share is expected to be constant

and the company is expected to earn atleast this yield to keep the equity shareholders content.

8. True - This phenomenon is called tax shield. The tax shield is viewed as a benefit accrues to the company

which is geared.

9. True - These bonds are issued at large discount and no interest is payable on them during their tenure of life.

At the time of redemption, the nominal value of the bond will be repaid to the bond holders.

10. False - In floating rate debt, keeping a certain rate of interest rate as fixed element, the lender will charge extra

rate of interest depending on the money market and economic conditions of the country.

11. False - The relative worth of a project is determined using WACC as the discounting rate.

12. False - All the projects that have an internal rate of return greater than its marginal cost of capital would be

accepted. Only when the returns of a particular project is in excess of its marginal cost of capital, can

add to the total value of the firm.

Choose Correct Word

1. opportunity

2. marginal

3. cost of capital
 4. NPV

5. IRR

6. maximize

7. more

8. equity shareholders

9. opportunity

10. WACC

11. increase

12. increase

13. capital asset pricing

Choose Correct Answer

1. (B) hurdle rate

2. (C) lower

N
3. (A) tax shield

N
4. (C) risk adjusted return

5. (D) internal rate of return

A
6. (D) hurdle rate

7. (C) internal investment

M
8. (B) increases

X
9. (C) personal tax rate on interest payments

A
10. (A) a reduction in the market-risk premium

T
 Practical Exercises

Exercise 17-1 One-up Ltd. has equity share capital of ` 5,00,000 divided into shares of ` 100 each. It wishes to raise
further ` 3,00,000 for expansion-cum-modernization scheme. The company plans the following financing alternatives:
(i) By issuing equity shares only.

(ii) ` 1,00,000 by issuing equity shares and ` 2,00,000 through debentures or term loan @ 10% per annum.

(iii) By raising term loan only at 10% per annum.

(iv) ` 1,00,000 by issuing equity shares and ` 2,00,000 by issuing 8% preference shares.

You are required to suggest the best alternative giving your comment assuming that the estimated ‘earning before

interest and taxes’ (EBIT) after expansion is ` 1,50,000 and corporate rate of tax is 35%.

Exercise 17-2 The capital structure of Asha Ltd. is as under: `

( )

N
Equity shares of ` 100 each 40,00,000

Retained earnings 20,00,000

N
8% Preference shares 24,00,000

A
7% Debentures 16,00,000

1,00,00,000

M
The company earns 12% on its capital. The tax rate applicable is 35%. The company requires a sum of ` 50,00,000
for which following options are available to it:

X
(i) Issue of 40,000 equity shares at a premium of ` 25 per share.

A
(ii) Issue of 9% preference shares.

(iii) Issue of 8% debentures.

T
It is estimated that the P/E ratios in the cases of equity share, preference share and debenture financing would be

22.5, 18.5 and 15.2 respectively. Which of the three financing alternatives would you recommend and why ?

Exercise 17-3 Three Star Co. is to decide between debt funding and equity funding for its expansion program.

Its current position is as under: `

( )

5% Debt 4,00,000

Equity capital ( ` 10/share) 10,00,000

Surplus 6,00,000

Total capitalization 20,00,000

Sales 60,00,000

Less: Costs 53,80,000

Profit before interest and taxes (PBIT) 6,20,000

Less: Interest 20,000

Profit before taxes (PBT) 6,00,000

Less: Income-tax @ 33.99% 2,03,940

Profit after tax (PAT) 3,96,060

The expansion program is estimated to cost ` 10,00,000. If it is financed through debt, the rate of interest of new debt
will be 7%. If the expansion program is financed through fresh equity shares, the new shares can be sold netting

` 25/share. The expansion will generate additional sales of ` 3,00,000 with after tax return of 5%.
If the company is to follow a policy of maximizing the market value of its shares, which form of financing should

it choose and why? (Price-earnings ratio is given to be 15).

Exercise 17-4 Super Ltd. is considering three financing plans:

Financial plans Equity Debt Preference

A 100% - -

B 50% 50% -

C 50% - 50%

Total funds to be raised ` 200 crore Corporate tax rate 35%

Rate of interest on debt 12% Dividend on preference shares 9%

Face value of equity shares of ` 10 each. These shares will be issued at a premium of ` 10 per share. The expected EBIT
is ` 80 crore.

Determine: (i) EPS and financial break-even point for each plan. (ii) Indifference points between financial plans

A and B; and A and C.

N
Exercise 17-5 Following information is available regarding Faxfit Ltd.:

N
Earnings before interest and tax (EBIT) ` 100 lakh Income-tax ` 27.36 lakh

A
Interest on debentures @ 10% ` 4.00 lakh Market price per share ` 20.00

Interest on term loan @ 12% `4.80 lakh Number of equity shares (face value ` 10) 20 lakhs

M
The company has undistributed reserves and surplus of ` 70 lakh. It is in need of ` 130 lakh to pay off debentures

X
and modernize plants. The company is considering following alternatives of financing:

- Raising entire amount as term loans @ 14% per annum.

A
- Issuing 4 lakh shares @ ` 18 per share and rest of the amount as loan @ 14% per annum.

T
As a result of modernization, the return on capital employed is likely to improve by 2.5%. In case the total amount

is raised in the form of term loans, the P/E ratio of the company is likely to decline by 10%.

You are required to: (i) advise the company on financial plan to be selected; and (ii) find out the indifference level

of EBIT.

Exercise 17-6 Company X and Company Y are in the same risk class and identical in all respects except that

Company X uses debts while Company Y does not. Levered company has ` 9 lakh debentures, carrying 10% rate of
interest. Both companies earn 20% before interest and taxes on their total assets of ` 15 lakh. Assume perfect capital
markets, tax rate of 50% and capitalization rate of 15% for an all-equity company.

(i) Compute the value of both the companies using Net Income (NI) approach.

(ii) Compute the value of both the companies using Net Operating Income approach, and

(iii) Using Net Operating Income approach, calculate the overall cost of capital for both the companies.

Exercise 17-7 Merry Ltd. has earning before interest and taxes (EBIT) of ` 30,00,000 and a 40% tax rate. Its required
rate of return on equity in the absence of borrowing is 18%.

In the absence of personal taxes, what is the value of the company in an MM world (i) with no leverage; (ii) with

` 40,00,000 in debt; and (iii) with ` 70,00,000 in debt?

Exercise 17-8 Following is the data relating to Azad Ltd. and Bharat Ltd. belonging to the same risk class:

Particulars Azad Ltd. Bharat Ltd.

No. of equity shares 9,00,000 1,50,000

Market price per share ( ) ` 15 9

6% Debentures ( ) ` 8,00,000 -

Profit before interest ( ) ` 2,00,000 2,00,000

Dividend payout ratio 100% 100%

Explain how under the MM approach, an investor holding 10% shares in Azad Ltd. will be better of in switching his

holding to Bharat Ltd.

Exercise 17-9 Two companies - P Ltd. and Q Ltd. belong to the equivalent risk group. The two companies are

identical in every respect except that Q Ltd. is levered, while P Ltd. is unlevered. The outstanding amount of debt

of the levered company is ` 6,00,000 in 10% debentures. The other information for the two companies are as follows:

Particulars P Ltd. Q Ltd.

N
Net operating income (EBIT) ( ) ` 1,50,000 1,50,000

N
`
Interest ( ) - 60,000

A
Earnings to equity-holders ( ) 1,50,000 90,000

Equity capitalization rate (Ke) 0.15 0.20

M
Market value of equity ( ) ` 10,00,000 4,50,000

Market value of debt ( ) ` - 6,00,000

X
Total value of firm ( )` 10,00,000 10,50,000

A
Overall capitalization rate (K = EBIT/V) 15% 14.3%
o

T
Debt-equity ratio 0 1.33

An investor owns 5% equity shares of Q Ltd. Show the process and the amount by which he could reduce his outlay

through use of the arbitrage process. Is there any limit to the process?
 Key to Practical Exercises

Exercise 17-1

`
( )

Financing Alternatives

Particulars I II III IV

Equity - Existing 5,00,000 5,00,000 5,00,000 5,00,000

- New 3,00,000 1,00,000 - 1,00,000

80% Preference shares - - - 2,00,000

10% Term Loan/Debentures - 2,00,000 3,00,000 -

Total investment 8,00,000 8,00,000 8,00,000 8,00,000

Preference dividend - - - 16,000

N
Interest on term loan or debentures - 20,000 30,000 -

Number of equity shares (i) 8,000 6,000 5,000 6,000

N
EBIT 1,50,000 1,50,000 1,50,000 1,50,000

A
Less: Interest - 20,000 30,000 -

EBT 1,50,000 1,30,000 1,20,000 1,50,000

M
Less: Tax @ 35% 52,500 45,500 42,000 52,500

X
EAT 97,500 84,500 78,000 97,500

Less: Preference dividend - - - 16,000

A
Earning available for equity shareholders(ii) 97,500 84,500 78,000 81,500

T
EPS (ii)/(i) 12.19 14.08 15.60 13.58

Analysis - From the above analysis it is observed that EPS is highest with III Alternative i.e., further financing of

` 3,00,000 can be done by raising term only at 10% per annum.

Exercise 17-2

Current Profit before interest and tax = ` 1,00,00,000 × 12/100 = ` 12,00,000

PBIT after expansion = ` 1,50,00,000 × 12/100 = ` 18,00,000

The following finance options are available for the company to raise ` 50,00,000.

Option I - Issue 40,000 Equity shares of ` 100 each at a premium of ` 25 per share

Option II - Issue 9% Preference shares at par

Option III - Issue 8% Debentures

Calculation of EPS and Market price of shares, under different financing options

Particulars Current Option I Option II Option III

EBIT @ 12% 12,00,000 18,00,000 18,00,000 18,00,000

Less: Interest: Old 1,12,000 1,12,000 1,12,000 1,12,000

New - - - 4,00,000

Profit before tax 10,88,000 16,88,000 16,88,000 12,88,000

Less: Tax @ 35% 3,80,800 5,90,800 5,90,800 4,50,800

Profit after tax 7,07,200 10,97,200 10,97,200 8,37,200

Particulars Current Option I Option II Option III

Less: Preference Dividend: Old 1,92,000 1,92,000 1,92,000 1,92,000

New - - 4,50,000 -

Profit available to Equity shareholders 5,15,200 9,05,200 4,55,200 6,45,200

No. of Equity shares 40,000 80,000 40,000 40,000

EPS 12.88 11.32 11.38 16.13

P/E ratio 22.5 18.5 15.2

Market price per share - 254.70 210.53 245.18

Suggestion - Since the market price of share is highest under option I, it is suggested to issue 40,000 equity shares of
` 100 each at a premium of ` 25 per share.

Exercise 17-3

`
( )

N
Old EBIT 6,20,000

 C    ×  

N
Add: New EBIT   22,724
  


A
Total EBIT after expansion 6,42,724

M
(Shares)

X
No. of shares outstanding:

Existing 1,00,000

A
`
New shares to be issued ( 10,00,000/ ` 25) 40,000

T
No. of shares outstanding after expansion 1,40,000

Evaluation of Finance Options `

( )

Particulars If 7% debt If Equity shares

is issued are issued

EBIT 6,42,724 6,42,724

Less: Interest:

On Old debt 20,000 20,000

On New debt 70,000 -

EBT 5,52,724 6,22,724

Less: Tax @ 33.99% 1,87,870 2,11,664

EAT 3,64,854 4,11,060

No. of equity shares outstanding 1,00,000 1,40,000

EPS 3.65 2.94

P/E ratio 15 15

Market price of share ` 54.75 ` 44.10

Suggestion - The market value of share is higher if debt financing of expansion project is undertaken. Therefore, it

is suggested to raise 7% new debt of ` 10,00,000 instead of fresh issue of shares at a premium of ` 15.
Exercise 17-4

Funds to be raised ( ` crores)

Financial plans

Capital structure A B C

Equity share capital 100 50 50

Equity share premium 100 50 50

9% Preference share capital - - 100

12% Debt - 100 -

200 200 200

Number of equity shares 10 crores 5 crores 5 crores

Calculation of EPS ( ` crores)

Financial plans

Particulars A B C

N
EBIT 80.00 80.00 80.00

N
Less: Interest (12%) - 12.00 -

EBT 80.00 68.00 80.00

A
Less: Tax (@ 35%) 28.00 23.80 28.00

EAT 52.00 44.20 52.00

M
Less: Preference dividend (9%) - - 9.00

X
Earnings available to equity shareholders 52.00 44.20 43.00

Number of equity shares (in crores) 10 5 5

A
EPS `
( ) 5.20 8.84 8.60

T
Calculation of Financial Break-even Point for Each Plan

Plan A : Since Plan A does not consist any debt component, its financial break-even point is zero.

Plan B : Break-even EBIT = Interest charge = ` 100 crores × 12% = ` 12 crores

Plan C : Financial break-even point EBIT

D ` 9,00,00,000 ` 9,00,00,000
`
p
= = = 13.85 crores
(1 - t) (1 - 0.35) 0.65

(ii) Calculation of Indifference Points between Financial Plans A and B; and A and C

(a) Indifference Point between Financial Plans A & B (in crores)

x (1 - t) (x - I) (1 - t)
=
N N
1 2

x (1 - 0.35) (x - 12) (1 - 0.35)

=
10 5

0.65x (x - 12) (0.65)

=
10 5

5 (0.65x) = 10 (0.65x - 7.8)

3.25x = 6.5x - 78

6.5x - 3.25x = 78

3.25x = 78

x = 24 ∴ x= ` 24 crores
 (b) Indifference Point between Financial Plans A & C (in crores)

x (1 - t) x (1 - t) - D
p
=
N N
1 2

x (1 - 0.35) x (1 - 0.35) - 9
=
10 5

0.65x 0.65x - 9
=
10 5

5 × 0.65 x = 10 (0.65x - 9)

3.25x = 6.5x - 90

6.5x - 3.25x = 90

3.25x = 90

x = 90/3.25 = 27.69 ∴ x = ` 27.69 crores

Exercise 17-5

Present Profitability Statement `

( )

N
EBIT 1,00,00,000

N
Less: Interest on debentures @ 10% 4,00,000

A
Interest on term loan @ 12% 4,80,000 8,80,000

EBT 91,20,000

M
Less: Income tax @ 30% 27,36,000

Profit available to equity shareholders 63,84,000

X
No. of equity shares outstanding 20,00,000

A
EPS 3.192

T
Market price per share 20

P/E ratio ( ` 20 / `3.192) 6.27

Present capital structure `

( )

Equity share capital 2,00,00,000

10% Debentures ( ` 4,00,000 × 100/10) 40,00,000

12% Term loan ( ` 4,80,000 × 100/12) 40,00,000

Reserves and surplus 70,00,000

Capital employed 3,50,00,000

EBIT ` 1,00,00,000
Return on Capital Employed = × 100 = × 100 = 28.57%
Capital employed ` 3,50,00,000

Revised Capital Structure `

( )

Existing capital employed 3,50,00,000

Less: Redemption of debentures 40,00,000

3,10,00,000

Add: Additional funds required 1,30,00,000

Revised capital employed 4,40,00,000

Revised EBIT = ` 1,00,00,000 × 102.5/100 = ` 1,02,50,000

New ROCE = 28.57% + 2.5% = 31.07%

New EBIT = ` 4,40,00,000 × 31.07/100 = ` 1,36,70,800

Financing Alternatives

Option I - Raise entire amount as term loan @ 14% p.a.

Option II - Issue 4,00,000 equity shares of `10 each per share at a premium of ` 18 and the rest of the amount as loan
@ 14% p.a.

`
( )

Share capital 40,00,000

Share premium 32,00,000

14% Term loan 58,00,000

1,30,00,000

Interest on New term loan

Option I = ` 1,30,00,000 × 14/100 = ` 18,20,000

Option II = ` 58,00,000 × 14/100 = ` 8,12,000

P/E ratio for Option I = 6.27 × 90/100 = 5.64

N
Calculation of EPS and Market Value of shares under Option I and Option II `
( )

N
Particulars Option I Option II

EBIT 1,36,70,800 1,36,70,800

A
Less: Interest on term loan Existing 4,80,000 4,80,000

New 18,20,000 8,12,000

M
EBT 1,13,70,800 1,23,78,800

X
Less: Tax @ 30% 34,11,240 37,13,640

EAT 79,59,560 86,65,160

A
No. of equity shares 20,00,000 24,00,000

T
EPS 3.98 3.61

Expected P/E ratio 5.64 6.27

Expected market price per share 22.45 22.63

Suggestion - Since the expected market value of share is more for Option II, it is suggested to issue 4,00,000 equity
shares @ ` 18 and the balance amount to be raised as term loan @ 14% p.a.

(ii) Calculation of Indifference level of EBIT of Option I and Option II

(EBIT -I ) (1-T) (EBIT -I ) (1-T)

1 2
=
N N
1 2

(EBIT - 23) (1- 0.3) (EBIT - 12.92) (1- 0.30)

=
20 24

0.7EBIT - 16.1 0.7EBIT - 9.044

=
20 24

24 (0.7 EBIT - 16.1) = 20 (0.7 EBIT - 9.044)

16.8 EBIT - 386.4 = 14 EBIT - 180.88

16.8 EBIT - 14 EBIT = 386.4 - 180.88

2.8 EBIT = 205.52

EBIT = 205.52/2.8 = 73.4

EBIT = ` 73.4 lakhs

At this EBIT, the EPS under both options would be ` 1.76.

Exercise 17-6

Company X `
( )

Equity share capital 6,00,000

10% Debentures 9,00,000

Total assets 15,00,000

EBIT (20% on total assets) 3,00,000

Tax rate 50%

Company Y `
( )

Equity share capital 15,00,000

Total assets 15,00,000

EBIT (20% on total assets) 3,00,000

Tax rate 50%

Capitalization rate 15%

N
(i) Value of Both Companies under Net Income Approach (NI)

Company X (geared company) `

( )

N
EBIT (20% of Total assets) 3,00,000

A
Less: Interest on debentures 90,000

EBT 2,10,000

M
Less: Tax @ 50% 1,05,000

X
Earnings available to equity shareholders 1,05,000

Equity capitalization rate 15%

A
Market value of equity (S) (1,05,000/0.15) 7,00,000

T
Market value of debt (B) 9,00,000

Market value of firm V = (S + B) 16,00,000

Company Y (ungeared company) `

( )

EBIT (20% of Total assets) 3,00,000

Less: Tax @ 50% 1,50,000

Earnings available to equity shareholders 1,50,000

Equity capitalization rate 15%

Market value of equity (S) (1,50,000/0.15) 10,00,000

Market value of firm (V = S) 10,00,000

(ii) Value of Both Companies under Net Operating Income Approach (NOI)

Company X

EBIT (1 - T) 3,00,000 (1 - 0.50)

Value of equity = = = ` 10,00,000
K 0.15
e

Value of debt = 9,00,000 × 0.50 = ` 4,50,000

Value of firm = 10,00,000 + 4,50,000 = ` 14,50,000

Company Y

EBIT (1 - T) 3,00,000 (1 - 0.50)

Value of equity = = = ` 10,00,000
K 0.15
e

\Value of firm = Value of equity = ` 10,00,000

(iii) Calculation of Overall Cost of Capital of Both Companies under Net Operating Income Approach (NOI)

Company X

Earnings available to equity shareholders

K =
e
Market value of equity

Market value of equity

= M.V. of firm - M.V. debentures = 14,50,000 - 9,00,000 = ` 5,50,000

1,05,000
∴K e
= × 100 = 19.09%
5,50,000

K = 10% (1 - 0.5) = 5%
i

Overall cost of capital (K )

o

9,00,000 5,50,000
K
o
= 5% ( 14,50,000 ) + 19.09% ( 14,50,000 ) = (0.05 × 0.62) + (0.1909 × 0.38) = 10.3%

Company Y

Overall cost of capital (K ) = 15%

N
o

Exercise 17-7

N
(i) Value of the Company, if unlevered `
( )

A
EBIT 30,00,000

Less: Interest Nil

M
Profit before tax 30,00,000

X
Less: Taxes @ 40% 12,00,000

Profit after tax 18,00,000

A
Required equity return 0.18

T
Value of Unlevered Company (18,00,000/0.18) = 1,00,00,000

(ii) Value of Company with ` 40,00,000 in Debt

Value if unlevered + Value of tax shield

Value = ` 1,00,00,000 + 0.40 (` 40,00,000) = ` 1,16,00,000

(iii) Value with ` 70,00,000 in Debt

Value = ` 1,00,00,000 + 0.40 (` 70,00,000) = ` 1,28,00,000

With the advantage of tax shield, the firm is able to increase its value in a linear manner with more and more debt

in the capital structure.

Exercise 17-8

In the problem given, arbitrage process will work as follows:

(i) The investor in shares of Azad Ltd. holding to the extent of 10% of total shares of the company, will dispose

of in the market. The amount realized by him would be ` 13,50,000 (i.e. 90,000 shares @ ` 15 per share). He
will also dispose his 10% investment in debentures for ` 80,000. Now the total fund available with him is
` 14,30,000.
(ii) He purchases 10% stake is 15,000 shares of Bharat Ltd. at a market price of ` 9 per share. His investment

amounts to ` 1,35,000.
(iii) Though the above shift in investment from Azad Ltd. to Bharat Ltd., the investor will gain as follows: ( `)

(a) Present income in Azad Ltd. (PBIT - Interest)

Dividend ( ` 2,00,000 - ` 48,000) × 10/100 15,200

Interest ( ` 8,00,000 × 6/100 × 10/100) 4,800 20,000

(b) Proposed income in Bharat Ltd. ( ` 2,00,000 × 10/100) 20,000

Thus the income of the investor remains the same and at the same time he is left with ` 12,95,000 (i.e. ` 14,30,000
- ` 1,35,000) of funds which can be invested elsewhere for generating additional income.

Exercise 17-9

An investor owns 5% equity shares of Q Ltd. He sells his shares for ` 22,500 (i.e. ` 4,50,000 × 5/100). He wishes to
purchase 5% equity shares in P Ltd. which will cost him ` 50,000 ( ` 10,00,000 × 5/100).

He borrows an amount of ` 27,500 @ 10% p.a. and invests ` 50,000 i.e. 5% equity shares in P Ltd.

Particulars P Ltd. Q Ltd.

Dividend income 7,500 4,500

N
Less: Interest ( ` 27,500 × 10/100) 2,750 -

N
Net income 4,750 4,500

A
Thus the income of the investor increases by switching from Q Ltd. to P Ltd. The above arbitrage process would

continue till the price of the two companies comes to a common equilibrium total value.

X M
T A
 Key to Short Answer Questions

True or False Statements

1. True - The first proposition of MM theory on capital structure reads as ‘the market value of any firm is

independent of its capital structure, changing the gearing ratio cannot have any effect on the

company’s annual cash flows. The change in the debt-equity ratio does not have effect on the cost of

capital and market value of the firm. Therefore, the value of firm’s equity is equal to the value of the

firm less the value of non-equity claims.

2. False - The operating free cash flow represents EBIDT as reduced by annual capital expenditure and

extraordinary items, which can be ascertained from published financial statements. Interest on debt

is one of the components of firm’s capital structure. Therefore, a firm’s capital structure will have

impact on its operating free cash flows.

3. True - With corporate taxation incorporates into MM hypothesis, the rate of return required by the geared

N
company’s shareholders is less than that in the all equity company, reflecting the tax benefits. A

further effect of corporate taxation is to lower WACC which will fall continuously as gearing

N
increases.

True

A
4. - The firm should identify optimum capital structure which is a combination of debt and equity that

leads to the maximization of value of the firm. The company’s long-term survival and growth depends

M
upon design of optimum capital structure.

5. True - Earnings capacity is a matter of business risk and cash flow ability is a matter of financial risk. To serve

X
the debt the company should have enough cash flow ability. Therefore, the earning capacity becomes

a less important factor than cash flow ability while designing the capital structure of a business.

A
6. True - The volatility in operating profits will increase financial risk due to firm’s obligation to pay interest

T
and repayment of debt in time. If the level of gearing increases, the expected return of equity

shareholders will also increase, along with the increase in financial risk and bankruptcy risk due to

higher levels of debt component in total capital and the expectation will be more to compensate for

taking higher levels of financial and bankruptcy risk. Therefore, the ROE of an unlevered firm is

higher than ROE of a levered firm, when the ROI is lower than the cost of debt.

7. False - The term ‘total capital structure’ denotes mix of owners’ funds and outsiders’ funds or it is

proportionate relationship of firm’s permanent long-term financing represented by equity and debt.

8. False - The optimum capital structure should lead to maximization of the value of the firm.

9. False - The basic assumption of all capital structure theories is that the company distributes all its earnings

as dividends to its shareholders and no consideration of dividend and retention policies.

10. True - Under NOI approach, optimal capital structure does not exist as average cost of capital remains

constant for varied types of financing mix. As the debt proportion is increased, the cost of equity also

increases.

11. True - Till the optimum level reaches a firm can rise its debt component to minimize WACC. After the

optimum level, a further increase in debt increases the risk to the equity holders.

12. True - The debt is less expensive than equity. Increase in debt level will cause to increase the cost of debt. The

increased debt will increase the financial risk of the firm and expectations of the equity holders will

be more. Thus, the average cost of capital will remain constant for all levels of leverage.

13. True - The market value of the firm is determined by the assets in which the company has invested and not

how those assets are financed.

14. True - It refers to a situation where two identical commodities are selling in the same market for different

prices, then the market will reach equilibrium by the dealers start buy at the lower price and sell at the

higher price, thereby making profit.

Choose Correct Word

1. geared

2. financial distress

3. lowest

4. capital

5. debt-equity

6. financial distress

7. net income

8. NEDC

9. minimum

N
10. capital

11. maximization

N
12. cheaper

A
13. WACC

14. efficient

M
15. arbitrage

X
16. equilibrium

17. minimize

A
18. levered

T
19. external

20. WACC

21. increases

Choose Correct Answer

1. (D) all of the above

2. (C) debt-equity

3. (C) industry norm

4. (B) weighted average cost of capital

5. (A) increase

6. (C) Software

7. (A) capital markets are imperfect

8. (B) EPS will be negative

9. (B) financial indifference point

10. (C) optimum capital structure

11. (D) all of the above

12. (D) the marginal tax benefit is equal to marginal cost of financial distress

13. (D) increase the earnings available for equity shareholders

14. (D) all of the above

15. (A) the use of debt financing would be advantageous

 Practical Exercises

Exercise 18-1 The shares of a chemical company are selling at ` 20 per share. The firm had paid dividend @ ` 2 per
share last year. The estimated growth of the company is approximately 5% per year.

(i) Determine the cost of equity capital of the company.

(ii) Determine the estimated market price of the equity share if the anticipated growth rate of the firm (a) rises to

8% and (b) fall to 3%.

Exercise 18-2 A company is planning to raise ` 20,00,000 additional long-term funds to finance its additional

capital budget of the current year. The debentures of the company to be sold on a 14% net yield basis to the company,

and equity shares to be sold at ` 50 per share net to the company, are the alternatives being considered by the

company. The company expects to pay dividend of ` 5 per share at the end of coming year. The expansion is expected
to carry the company into a new-higher risk class. The required rate of return expected from the point of view of the

investment community is 16%.

N
(i) Determine the growth rate of the company, which the market is anticipating.

(ii) Management is anticipating 8% growth rate. On this basis, at what price should the equity share be sold by the

N
company?

(iii) Assuming that management is anticipating growth rate of only 4% per year, what form of financing would you

A
recommend?

M
Exercise 18-3 The required rate of return of investors is 15%. ABC Ltd. declared and paid annual dividend of ` 4

per share. It is expected to grow @ 20% for the next 2 years and 10% thereafter.

X
Compute the price at which the shares should sell.

A
Note: P.V. factor @ 15% for Year 1 = 0.8696 and Year 2 = 0.7561.

T
Exercise 18-4 R Dotcom Ltd. is foreseeing a growth rate of 12% per annum in the next two years. The growth rate

is likely to fall to 10% for the third year and the fourth year. After that the growth rate is expected to stabilize at 8%

per annum. If the last dividend was ` 1.50 per share and the investor’s required rate of return is 16%, determine the
current value of its equity share.

The PV factors at 16% are:

Year 1 2 3 4

P.V. factor 0.862 0.743 0.641 0.552

Exercise 18-5 The dividends of Nelson Company Ltd. are expected to grow at a rate of 25% for 2 years, after which

the growth rate is expected to fall to 5%. The dividend paid last period was ` 2. The investor desires a 12% return.
You are required to find the value of this stock. PV Factor @ 12% is as under:

Year 1 2 3

Value 0.893 0.797 0.712

Exercise 18-6 A large sized chemical company has been expected to grow at 14% per year for the next 4 years and

then to grow indefinitely at the same rate as the national economy, i.e., 5%. The required rate of return on the equity

shares is 12%. Assume that the company paid a dividend of ` 2 per share last year (D0 = 2). Determine the market
price of the shares today.

Exercise 18-7 The earnings per share (EPS) of a company is ` 10. It has an internal rate of return of 15% and the

capitalization rate of its risk class is 12.5%. If Walter’s model is used:

 (i) What should be the optimum payout ratio of the company?

(ii) What would be the price of the share at this payout?

(iii) How shall the price of the share be affected, if a different payout were employed?

Exercise 18-8 The earning per share of a company is ` 16. The market capitalization rate applicable to the company
is 12.5%. Retained earnings can be employed to yield a return of 10%. The company is considering a payout of 25%,

50% and 75%. Which of these would maximize the wealth of shareholders as per Walter’s model?

Exercise 18-9 Details regarding three Companies are given below:

A Ltd. B Ltd. C Ltd.

r = 15% r = 10% r = 8%

K = 10% K = 10% K = 10%

e e e

E = ` 10 E = ` 10 E = ` 10

By using Walter’s model, you are required to:

(i) Calculate the value of an equity share of each of these companies when dividend payout ratio is (a) 20%,

N
(b) 50%, (c) 0%, and (d) 100%.

(ii) Comment on the result drawn.

N
Exercise 18-10 Bestbuy Auto Ltd. has outstanding 1,20,000 shares selling at ` 20 per share. The company hopes to

A
make a net income of ` 3,50,000 during the year ended 31st March, 2016. The company is considering to pay a

dividend of ` 2 per share at the end of current year. The capitalization rate for risk class of this company has been

M
estimated to be 15%. Assuming no taxes, answer the questions listed below on the basis of the MM-Dividend

valuation model:

X
(i) What will be the price of a share at the end of 31st March, 2015 (a) if the dividend is paid, and (b) if the dividend

is not paid?

A
(ii) How many new shares must the company issue if the dividend is paid and company needs ` 7,40,000 for an

T
approved investment expenditure during the year?

Exercise 18-11 Exponent Ltd. had 50,000 equity shares of ` 10 each outstanding on 1st April. The shares are being
quoted at par in the market. The company intends to pay a dividend of ` 2 per share for current financial year. It

belongs to a risk class whose appropriate capitalization rate is 15%.

Using Modigliani-Miller model and assuming no taxes, ascertain in price of company’s share as it is likely to prevail

at the end of the year when (i) dividend is declared; and (ii) no dividend is declared.

Also find out number of new equity shares that the company must issue to meet its investment needs of ` 2,00,000
assuming net income of ` 1,10,000 and assuming that the dividend is paid.

Exercise 18-12 RST Ltd. has a capital of ` 10,00,000 in equity shares of ` 100 each. The shares are currently quoted
at par. The company proposes declaration of a dividend of ` 10 per share. The capitalization rate for the risk class

to which the company belongs is 12%.

What will be the market price of the share at the end of the year, if - (i) no dividend is declared; and (ii) 10% dividend

is declared?

Assuming that the company pays the dividend and has net profits of ` 5,00,000 and makes new investments of

` 10,00,000 during the period, how many new shares must be issued? Use the M.M. Model.
 Key to Practical Exercises

Exercise 18-1

(i) Determination of Cost of Equity Capital

D (1 + g) 2 (1 + 0.05)
0
K = + g = + 0.05 = 15.5%
e
P 20
0

(ii) Determination of Estimated Market Price of the Equity Share if anticipated growth rate rises or falls

D
1
P =
0
K - g
e

(a) If the growth rate raises to 8%: (b) If growth rate of the firm falls:

2.16 2.06
= ` 28.8 = ` 16.48
0.155 - 0.08 0.155 - 0.03

N
Exercise 18-2

N
(i) Calculation of Growth rate of the company

A
K = + g
e
P
o

M
0.16 = + g
50

0.16 = 0.10 + g g = 0.16 - 0.10 = 0.06 or 6%

X
(ii) Calculation of market price of equity share when growth rate is 8%

A
5
0.16 = + 0.08

T
P
o

D 5
P
o
= = = ` 62.50
K - g 0.16 - 0.08
e

(iii) Calculation of market price of share when growth rate is 4%

D 5
P
o
= = = ` 41.67
K - g 0.16 - 0.04
e

When the growth rate is 4%, the market price of equity share fall below its face value. Then it should go with

debenture issue instead of equity issue.

Exercise 18-3

D = Dividend declared and paid i.e. 15% ( ` 4 per share)

0

G = Growth rate (20% for next 2 years and 10% thereafter)

Calculation of Dividend Per Share

D = D (1 + g) = 4 (1 + 0.20) = ` 4.80
1 0

D = D (1 + g) = 4.80 (1 + 0.20) = ` 5.76

2 1

D = D (1 + g) = 5.76 (1 + 0.10) = ` 6.34

3 2

Present Value of Dividends for the first 2 years

= (4.80 × 0.8696) + (5.76 × 0.7561) = 4.174 + 4.355 = ` 8.53

Price of Stock (P )
2

D 6.34 6.34
P =
3
= = = ` 126.80
2 r - g 0.15 - 0.10 0.05

P.V. of stock = 126.80 × 0.7561 = ` 95.87 Value of stock = 8.53 + 95.87 = ` 104.40

Exercise 18-4

Calculation of Dividend Per Share during 1 - 5 years

Dividend Per Share is calculated follows:

D
1
= D
0
(1 + g) = 1.50(1 + 0.12) = ` 1.68

D
2
= D
1
(1 + g) = 1.68(1 + 0.12) = `1.88
D
3
= D
2
(1 + g) = 1.88(1 + 0.10) = ` 2.07

D
4
= D
3
(1 + g) = 2.07(1 + 0.10) = ` 2.28

D
5
= D
4
(1 + g) = 2.28(1 + 0.08) = ` 2.46

Calculation of Present Value of Dividends during 1 - 4 years

N
Years Dividend P.V. factor Total P.V.

`
( ) @ 16% `
( )

N
1 1.68 0.862 1.45

A
2 1.88 0.743 1.40

3 2.07 0.641 1.33

M
4 2.28 0.552 1.26

X
Total present value of 1-4 years dividends 5.44

Calculation of Present Value of Expected Market Price of Share at the end of year 4 based on Constant Growth Rate of 8%

A
D
5

T
P =
4
(K - g)
e

Where, P = Expected market price of share at the end of year 4 K = Cost of equity i.e. 16% or 0.16
4 e

D
5
= Dividend per share for year 5 i.e. ` 2.46 g = growth rate expected i.e. 8% or 0.08

2.46 2.46
P
4
= = = ` 30.75
0.16 - 0.08 0.08

Present Value of Market Price of Share = ` 30.75 × 0.552 = ` 16.97

Present Value of Equity Share of X Ltd.

= P.V. of Dividends during 1-4 years + P.V. of Market Price of share = ` 5.44 + ` 16.97 = ` 22.41

Exercise 18-5

D = Dividend of last year

o

D
1
= Dividend of 1st year D =
1
D (1+g) =
o
2 (1+0.25) = ` 2.50
D
2
= Dividend of second year D =
2
D (1+g) =
1
2.50 (1+0.25) = ` 3.125
D
3
= Dividend of third year D =
3
D (1+g) =
2
3.125 (1+0.05) = ` 3.28
g = Growth rate r = Return

D 3.28 3.28
` 46.86
3
Price of Stock at the end of second year P = = = =
2
K - g 0.12 - 0.05 0.07
e
Calculation of Present Value of Stock Price (P.V. factor @ 12%) `
( )

1st year (2.50 × 0.893) 2.23

2nd year (3.125 × 0.797) 2.49

(46.86 × 0.797) 37.34

Present value of stock 42.06

Exercise 18-6

The share value under Gordon dividend growth valuation model can be ascertained as follows:

D D (1 + g)
1 0
P = or
0
K - g K - g
e e

1
Year D = D (1 + g) P/V factor Total PV
t 0

at 12% `
( )

1 2(1 + 0.14) = 2.28 0.893 2.0360

2
2 2(1 + 0.14) = 2.5992 0.797 2.0715

N
3
3 2(1 + 0.14) = 2.9631 0.712 2.1097

N
4 2(1 + 0.14) = 3.3779 0.636 2.1483

8.3655

A
D D (1 + g) 3.3779 (1 + 0.05) 3.546795
`
5 4
P = = = = = 50.67
4

M
K - g K - g 0.12 - 0.05 0.07
e e

X
PV of market price of share at the end of year 4 = 50.67 × 0.636 = 32.25

Market price of shares = PV of dividends + PV of share price = 8.3655 + 32.25 = ` 40.62

T A
Exercise 18-7

Calculation of Share Price under Walter’s Model

R
a
D + (E - D)
R
c
P =
R
c

(i) Since R > R (i.e. 15% > 12.5%), to maximize the share price the company should retain all its earnings and its
a c

optimum payout ratio is zero.

(ii) Calculation of Share Price at Optimum Payout Rate i.e. if no dividend is declared.

0.15
0 + (10 - 0)
0.125 12
P = = = ` 96
0.125 0.125

(iii) Impact on Share Price, if dividend is paid @ 30%

0.15
3 + (10 - 3)
0.125 11.4
P = = = ` 91.20
0.125 0.125

Exercise 18-8

Shareholders’ wealth would be maximized only when the market value (price) per share of common stock of the

company is maximized. Walter’s model help in ascertaining the market price of shares under various payout ratios.

The market price of each share under various payout ratio using the above model
 R
a
D + (E - D)
R
c
P =
R
c

D/P Ratio 25% D/P Ratio 50% D/P Ratio 75%

0.10 0.10 0.10

4 + (16 - 4) 8 + (16 - 8) 12 + (16 - 12)
0.125 0.125 0.125
= ` 108.80 = ` 115.20 = ` 121.60
0.125 0.125 0.125

Analysis - The above calculations show that the wealth of the shareholders would be maximized when the company

adopts 75% payout ratio.

Exercise 18-9

(i) As per Walter’s Model, the Value of Shares as under:

R
a
D + (E - D)
R
c
P =
R

N
c

A Ltd. B Ltd. C Ltd.

N
(a) When D/P ratio is 20%

A
0.15 0.10 0.08
2 + (10 - 2) 2 + (10 - 2) 2 + (10 - 2)
0.10 0.10 0.10
= ` 140 = ` 100 = ` 84

M
0.10 0.10 0.10

(b) When D/P ratio is 50%

X
0.15 0.10 0.08
5 + (10 - 5) 5 + (10 - 5) 5 + (10 - 5)

A
0.10 0.10 0.10
= ` 125 = ` 100 = ` 90
0.10 0.10 0.10

T
(c) When D/P ratio is 0%

0.15 0.10 0.08

0 + (10 - 0) 0 + (10 - 0) 0 + (10 - 0)
0.10 0.10 0.10
= ` 150 = ` 100 = ` 80
0.10 0.10 0.10

(d) When D/P ratio is 100%

0.15 0.10 0.08

10 + (10 - 10) 10 + (10 - 10) 10 + (10 -10)
0.10 0.10 0.10
= ` 100 = ` 100 = ` 100
0.10 0.10 0.10

Comments
¾ Company A Ltd. is growth firm (r > K ), company B Ltd. is a normal firm (r = K ), and Company C Ltd. is a
e e

declining firm (r < K ). For Company A Ltd., the value of share is inversely related to D/P ratio. As the pay out
e

ratio increases from 0 to 100%, the market value of share declines from ` 150 to ` 100. When all earnings are
distributed its value is lowest. In other words, optimum pay out ratio is zero.

¾ For Company B Ltd. (a normal firm), the market value of share is constant irrespective of D/P ratio. In other

words, the market price is not affected by D/P ratio. It is ` 100 in all cases. So there is no optimum dividend
policy or D/P ratio.

¾ For Company C Ltd. (a declining firm), the D/P ratio and the value of shares are positively related. As pay out

ratio increases from 0 to 100%, the market price of the shares also increases from ` 80 to ` 100. In this case

optimum dividend policy is given by D/P ratio of 100%.

Exercise 18-10

(i) Calculation Market Price of share under MM - Dividend Irrelevancy Model

P + D
1 1
P =
0
1 + K
e

(a) If Dividend is paid

P + 2
`
1
20 = 20 × 1.15 = P + 2 P = 21
1 1
1 + 0.15

(b) If Dividend is not paid

P + 0
`
1
20 = 20 × 1.15 = P + 0 P = 23
1 1
1 + 0.15

(ii) Calculation of number of new shares to be issued, if the dividend is paid and company needs ` 7,40,000 for

investment expenditure.

I - (E - nD )
∆N
1
=
P

N
1

7,40,000 - [3,50,000 - (1,20,000 × 2)] 7,40,000 - 1,10,000

= = = 30,000 shares

N
21 21

Therefore, the company has to issue 30,000 new shares to meet its capital expenditure, after payment of dividend.

A
Exercise 18-11

M
(Dividend per share at time 1 +

Market price per share at time 1)

Market Price Per Share at 0 time =

X
1 + Capitalization rate

D + P

A
1 1
P =
0
1 + K

T
e

(1) Price Per Share when Dividends are paid

D + P 2 + P
∴ ∴
1 1 1
P = 10 = P = 9.5
0 1
( 1 + K ) 1.15
e

(2) Price Per Share when Dividends are not paid

P + 0
` ∴ ` 11.5
1
10 = P =
1
1.15

(3) Number of New Equity Shares to be issued

Volume of investment - (Net income earned during

the period - Dividend paid on outstanding shares)

Number of New shares =
Market price per at time 1

I - (E - nD ) 2,00,000 - (1,10,000 - 1,00,000)

∆
1
N = = = 20,000 shares
P 9.5
1

Thus, 20,000 new equity shares will have to be issued to meet the investment needs of the company.

Exercise 18-12

(i) Calculation of Share Price under MM - Dividend Irrelevancy Model

P + D
1 1
P =
o
1 + K
e
 (a) When Dividend is not declared

P + 0
`
1
100 = P = 100 × 1.12 P = 112
1 1
1 + 0.12

(b) When Dividend is declared

P + 10
`
1
100 = P + 10 = 100 × 1.12 P = 102
1 1
1 + 0.12

(ii) Calculation of Number of Shares to be Issued `

( )

Particulars If no dividend If dividend

declared declared

Net Income 5,00,000 5,00,000

Less: Dividend paid - 1,00,000

Retained earnings 5,00,000 4,00,000

New investments 10,00,000 10,00,000

Amount to be raised by issues of new shares (i) 5,00,000 6,00,000

N
Market price per share (ii) 112 102

No. of new shares to be issued (i)/(ii) 4,464 5,882

N
Alternatively

A
No. of shares to be issued can also be calculated by applying the following formula:

I - (E - nD )
∆N

M
1
=
P
1

X
Where,

∆N = Change in the number of shares outstanding during the period

A
n = Number of shares outstanding at the beginning of the period i.e. 10,000 shares

T
I = Investment amount required for capital budget i.e. ` 10,00,000

E = Earning of the firm during the period i.e. ` 5,00,000

P
1
= Market price of share at the end of period one (i) if no dividend declared - ` 112 (ii) if dividend declared - ` 102
D
1
= Dividend to be received at the end of period one i.e. ` 10

(i) When Dividend is not declared

10,00,000 - (5,00,000 - 10,000 × 0) 10,00,000 - 5,00,000

∆N = = = 4,464 shares
112 112

(ii) When Dividend is declared

10,00,000 - (5,00,000 - 10,000 × 10) 10,00,000 - 4,00,000

∆N = = = 5,882 shares
102 102

Verification of M.M. Dividend Irrelevancy Theory

Particulars If dividend If dividend

not declared declared

Existing shares 10,000 10,000

New shares 4,464 5,882

Total number of shares at the year end (i) 14,464 15,882

Market price per share (ii) ` 112 ` 102

Total market value of shares at the end of year (i) × (ii) ` 16,20,000 16,20,000

Analysis - The market value of shares at the end of year will remain the same whether dividends are distributed or

not declared.
 Key to Short Answer Questions

True or False Statements

1. False - As per Gordon’s model, the growth rate is determined by the product of retention ratio and rate of

return on investment.

2. True - According to MM approach it is earning potentiality and investment policy of firm rather than

pattern of distribution of earning that affects value of firm.

3. True - The assumption of dividend discount model is that external financing is not used in the firm. Retained

earnings represent the only source of financing. The growth rate of the firm is the product of retention

ratio and its rate of return. Therefore, payment of high dividends will reduce the value of the share

under dividend discount model.

4. False - Dividend valuation model assumes a constant level of growth in dividends in perpetuity. The model

N
incorporates the retention of earnings and growth in dividends in valuation of share price. Therefore,

the market sentiment will not depress the stock price.

False

N
5. - The dividend growth model assumes a constant level of growth in dividends in perpetuity and the

value of share reflects the value of future dividends accruing to that share. The model further assumes

A
that a constant retention ratio and a constant return on new investment projects. The model can also

be applied to value high growth company that pays low or no dividends.

M
6. True - Under dividend growth rate model, the dividend payments and its growth are relevant in valuation

of shares. In real world, the constant dividend growth and earnings growth is fallacy.

X
7. False - Cash inflows are generated from the successful operation of business which are used for payment of

A
dividend to its shareholders. Dividend paid represents a cash outflow which depletes the cash

resources. Retentions are used to finance capital projects. Therefore, dividend payment is not the

T
determinant of the shareholders’ wealth.

8. True - It has been observed that an increase in the dividend is often accompanied by an increase in the price

of the stock, while a dividend cut generally leads to a stock price decline. A change in dividend policy

may convey information to the stock market.

9. True - Under dividend growth valuation model, the basic assumption is that future annual growth rate

dividend is expected to be constant. The value of a share reflects the value of the future dividends

accruing to that share. Therefore, the dividend payments and its growth are relevant in valuation of

shares.

10. True - The Gordon growth model assumes that a constant retention ratio and a constant return on capital

invested. The model assumes that dividends will grow at a constant rate but a rate that is less than the

required return.

11. False - The implications of the dividend discount model is that when the rate of return is greater than the

discount rate, the price per share increases as dividend ratio decreases and if the return is less than

discount rate it is vice versa.

12. True - Dividend valuation model assumes, a constant level of growth in dividends in perpetuity. The model

is also called as Gordon growth valuation model or Constant dividend growth valuation model.

13. True - Walter model is based on the argument that in the long-run the share prices reflect only the present

value of expected dividends. Retentions influence stock price only through their effect on future

dividends.
14. False - Modigliani and Miller has argued that a firm’s dividend policy has no effect on its value of assets. For

example, if rate of dividend declared by a company is less, its retained earnings will increase and so

also the net worth and vice versa. Their argument is that the value of the firm is unaffected by dividend

policy.

15. False - As per Walter’s valuation model, when the rate of return on investments (R ) exceeds the cost of
a
capital (R ), the price per share increases as the dividend payout ratio decreases. In such cases, the
c
shareholders would not prefer for higher dividend to increase their stock’s price.

16. True - When the return on equity is higher than the cost of equity, the growth firms retain the earnings

to enable them to plough back the earnings. Therefore, the price to book value of the growth firms will

be higher.

17. False - As per Gordon dividend growth valuation model the price of share rises with retention of earnings,

which leads to alter the expectations of investors to get the large dividends in future. Therefore, low

paid dividends will not likely to undervalue the share of a company with high price earning ratio.

18. True - The stability of dividends ensures the consistency of future stream of income to the shareholders.

Small shareholders generally do not prefer variability in their future earnings in the form of dividends.

Stability of dividends increases the investors’ confidence in company’s performance.

N
19. True - Walter’s valuation model based on the argument that in the long-run the share prices reflect only the

N
present value of expected dividends. Retentions influence stock price only through their effect on

future dividends.

A
Choose Correct Word

1. certainty

M
2. dividend

X
3. terms

A
4. equity

T
5. cover

6. low

7. divisible

8. payout

9. price earning

10. low

11. yield

12. dividend growth

13. retained

14. personal

15. future

16. growth

17. constant

18. 100%

19. irrelevancy

20. business

21. MM

22. internal

23. divisible
24. dividend clientele

25. indifferent

26. relevance

27. equalization

28. greater

29. payout

30. dividend

31. liberal

32. yield

33. capital

34. AGMs

35. ignored

36. irrelevant

N
37. liberal

38. dividends

N
39. signalling

A
40. market

41. equity

M
Choose Correct Answer

X
1. (A) earnings per share

A
2. (A) liberal

T
3. (A) higher

4. (A) equity

5. (A) dividend payout ratio

6. (A) marginal

7. (B) dividend yield ratio

8. (A) dividend discount

9. (D) decrease in shareholder’s return expectations

10. (D) high market discounting

11. (B) market price per equity share

12. (A) EPS/K

e

13. (B) Modigliani-Miller approach

14. (C) the equity cost of capital

15. (C) Profitable investment opportunities

16. (C) 66.67%

17. (A) ` 14.40

18. (C) 12.80%

19. (A) 17.6%

20. (B) 4 times

21. (C) ` 15.60

22. (D) Possibly increase, possibly decrease, or possibly remain unchanged

23. (D) There is asymmetric information between the managers and investors

24. (B) The results are accurate when the dividend payout ratio is 100 percent

25. (C) resort to dividend cuts as and when needed

N N
M A
A X
T
 Practical Exercises

Exercise 20-1 ITC Ltd. have decided to purchase a machine to augment the company’s installed capacity to meet

the growing demand for its products. There are three machines under consideration of the management. The

relevant details including estimated yearly expenditure and sales are given below : All sales are on cash. Corporate

income-tax rate is 40%. Interest on capital may be assumed to be 10%. `

( )

Particulars Machine 1 Machine 2 Machine 3

Initial investment required 3,00,000 3,00,000 3,00,000

Estimated annual sales 5,00,000 4,00,000 4,50,000

Cost of production (estimated):

Direct materials 40,000 50,000 48,000

Direct labour 50,000 30,000 36,000

N
Factory overheads 60,000 50,000 58,000

Administration costs 20,000 10,000 15,000

N
Selling and distribution costs 10,000 10,000 10,000

A
` 40,000, ` 25,000,
The economic life of Machine 1 is 2 years, while it is 3 years for the other two. The scrap values are

and ` 30,000 respectively. You are required to find out the most profitable investment based on ‘payback method’.

M
Exercise 20-2 A Ltd. is considering the question of taking up a new project which requires an investment of ` 200

X
lakhs on machinery and other assets. The project is expected to yield the following gross profits (before depreciation

and tax) over the next five years: ( ` lakhs)

A
Year 1 2 3 4 5

T
Gross profit 80 80 90 90 75

The cost of raising the additional capital is 12% and the assets have to be depreciated at 20% on ‘written down value’

basis. The scrap value at the end of the five-year period may be taken as zero. Income-tax applicable to the company

is 50%. Calculate the net present value of the project and advise the management whether the project has to be

implemented. Also calculate the Internal Rate of Return of the project.

Present value of ` 1 at different rates of interest are as follows:

Year 10% 12% 14% 16%

1 0.91 0.89 0.88 0.86

2 0.83 0.80 0.77 0.73

3 0.75 0.71 0.67 0.67

4 0.68 0.64 0.59 0.55

5 0.62 0.57 0.52 0.52

Exercise 20-3 XY Ltd. wants to install a new machine in the place of an existing old one which has become obsolete.

The company made extensive enquiries and from the replies received, short-listed two offers. The two models differ

in cost, output and anticipated net revenue. The estimated life of both the machines is five years. There will be only

negligible salvage value at the end of the fifth year. Further details are as follows: ( ` lakhs)
Machine Cost Anticipated after-tax cash flow

Year 1 Year 2 Year 3 Year 4 Year 5

A 25 - 5 20 14 6

B 40 10 14 16 17 8

The company’s cost of capital is 16%. You are required to make an appraisal of the two offers and advise the firm

by using the following: (i) Payback period, (ii) Net present value, (iii) Profitability index, (iv) Internal rate of return.

Note - Present value of ` 1

End of year 16% 18% 20%

1 0.862 0.847 0.833

2 0.743 0.718 0.694

3 0.641 0.609 0.579

4 0.552 0.516 0.482

5 0.476 0.437 0.402

N
Exercise 20-4 A company is contemplating to purchase a machine. Two machines A and B are available, each

N
costing ` 5 lakhs. In comparing the profitability of the machines, a discounting rate of 10% is to be used and machine
is to be written off in five years by straight line method of depreciation with nil residual value. Cash inflows after tax

A
are expected as follows: ( ` lakhs)

Year Machine A Machine B

M
1 1.5 0.5

X
2 2.0 1.5

3 2.5 2.0

A
4 1.5 3.0

T
5 1.0 2.0

Indicate which machine would be profitable using the following methods of ranking investment proposals:

(i) Payback method, (ii) Net present value method, (iii) Profitability index method, and (iv) Average rate of return

method.

The discounting factors at 10% are:

Year 1 2 3 4 5

Discounting factor 0.909 0.826 0.751 0.683 0.621

Exercise 20-5 Modern Electronics wants to take up a new project of the manufacture if an electronic device which

has good market. Further details are given below:

(i) Cost of the Project as estimated ( ` lakhs)

Land 2.00 (will be incurred at the beginning of year 1)

Buildings 3.00 (will be incurred at the end of year 1)

Machinery 10.00 (will be incurred at the end of year 2)

Working capital (margin money) 5.00 (will be incurred at the beginning of year 3)

20.00
 (ii) The project will go into production from the beginning of year 3 and will be operational for a period of 5 years.

The annual working results are estimated as follows: ( ` lakhs)

Sales 20.00

Less: Variable cost 8.00

Fixed cost (excluding depreciation) 4.00

Depreciation of assets 2.00

(iii) At the end of the operational period, it is expected that the fixed assets can be sold for ` 5 lakhs (without any
profit)

(iv) Cost of capital of the firm is 10%. Applicable tax rate is 50%.

(v) Present value of ` 1 at 10%

At the end of year P.V. At the end of year P.V.

1 0.909 5 0.621

2 0.826 6 0.564

N
3 0.751 7 0.513

4 0.683 8 0.467

N
You are required to evaluate the proposal, by working out the net present value and advise the firm.

A
Exercise 20-6 Following are the data on a capital project being evaluated by the management of X Ltd.:

Project M

M
Annual cost saving ` 40,000 Cost of capital ?

X
Useful life 4 years Cost of project ?

A
I.R.R. 15% Payback ?

Profitability Index (PI) 1.064 Salvage value 0

T
NPV ?

Find the missing values considering the following table of discount factor only:

Discount factor 15% 14% 13% 12%

1 year 0.869 0.877 0.885 0.893

2 year 0.756 0.769 0.783 0.797

3 year 0.658 0.675 0.693 0.712

4 year 0.572 0.592 0.613 0.636

2.855 2.913 2.974 3.038

Exercise 20-7 A Ltd. has an investment budget of ` 25 lakhs for next year. It has under consideration three projects
A, B and C (B and C are mutually exclusive) and all of them can be completed within a year. Further details are given

below: ( ` lakhs)

Project Investment required Net present value

A 14 5.6

B 12 7.2

C 10 5.0

Recommend the best policy to utilize the investment budget, supported by proper reasoning.
Exercise 20-8 In a capital rationing situation (investment limit ` 25 lakhs), suggest the most desirable feasible

combination on the basis of the following data (indicate justification):

( ` lakhs)

Project Initial outlay NPV

A 15 6

B 10 4.5

C 7.5 3.6

D 6 3

Projects B and C are mutually exclusive.

Exercise 20-9 Five Projects M, N, O, P and Q are available to a company for consideration. The investment required

for each project and the cash flows it yields are tabulated below. Projects N and Q are mutually exclusive. Taking

the cost of capital @ 10%, which combination of projects should be taken up for a total capital outlay not exceeding

` 3 lakhs on the basis of NPV and Benefit-Cost Ratio (BCR) ? `

( )

N
Project Investment Cash flow p.a. No. of years P.V. @ 10%

M 50,000 18,000 10 6.145

N
N 1,00,000 50,000 4 3.170

A
O 1,20,000 30,000 8 5.335

P 1,50,000 40,000 16 7.824

M
Q 2,00,000 30,000 25 9.077

X
Exercise 20-10 S Ltd. has ` 10,00,000 allocated for capital budgeting purposes. The following proposals and

A
associated profitability indexes have been determined:

T
Project Amount ( ) Profitability Index

1 3,00,000 1.22

2 1,50,000 0.95

3 3,50,000 1.20

4 4,50,000 1.18

5 2,00,000 1.20

6 4,00,000 1.05

Which of the above investments should be undertaken? Assume that projects are indivisible and there is no

alternative use of the money allocated for capital budgeting.

Exercise 20-11 Five projects A, B, C, D and E with the following characteristics are available to an organization:

Project A B C D E

Investment ( )` 20,000 45,000 75,000 1,00,000 1,40,000

Annual cash inflow ( ) ` 6,000 8,000 15,000 15,000 25,000

Life (in years) 5 10 8 12 7

Salvage value 5,000 - - 15,000 50,000

Project B is a prerequisite for Project E and projects C & D are mutually exclusive. If the cost of capital is 10% and

the total investment available is ` 2,00,000 find out the feasible combination of projects and rank them on the basis
of Net Present Value (NPV) as well as Benefit Cost Ratio (BCR).

Note: Extracted from table:

Year 5 10 8 12 7

PVIFA at 10% 3.791 6.145 5.335 6.814 4.868

Exercise 20-12 KPR is evaluating six capital investment projects. The company has allocated ` 20,00,000 for capital
budgeting purposes. The relevant particulars of the projects, which are independent of one another, are as follows:

Project `
Investment needed ( ) Profitability index

P 10,00,000 1.21
1

P 3,00,000 0.94
2

P 7,00,000 1.20
3

P 9,00,000 1.18
4

P 4,00,000 1.20
5

P 8,00,000 1.05
6

If there is strict capital rationing, which of the projects should be undertaken ?

N
Exercise 20-13 Electrofast Ltd. is a manufacturing organization. It is manufacturing electronic equipments in

N
which a Component-X is used which is purchased from a local supplier at a cost of ` 40 each. In order to bring down
the cost and improve its competitiveness, the company has a proposal to install a machine for the manufacture of

A
Component-X. It has the following two options:

Option I Installation of semiautomatic machine involving an annual fixed expenses of ` 22 lakh and a

M
variable cost of ` 18 per component manufactured.

X
Option II Installation of automatic machine involving an annual fixed cost of 40 lakh and a variable cost

of ` 15 per component manufactured.

A
You are required to:

T
(i) Find the annual requirement of Component-X to justify a switch over from purchase of components to

manufacture of the same by installing (i) semiautomatic machine; and (ii) automatic machine.

(ii) If the annual requirements of the Component-X is 8,00,000 units, which machine would you advise the

company to install?

Exercise 20-14 Growell Ltd. has a machine which has been in operation for 2 years and its remaining estimated

useful life is 4 years with no salvage value at the end. Its current market value is ` 1,00,000.

The management is considering a proposal to purchase an improved model of similar machine, which gives

increased output. The relevant particulars are as follows:

Particulars Existing machine New machine

Purchase price ( ) ` 2,40,000 4,00,000

Estimated life (years) 6 4

Salvage value Nil Nil

Annual operating hours 2,000 2,000

Selling price per unit ( ) ` 10 10

Material cost per unit ( ) ` 2 2

Output per hour (units) 15 30

Labour cost per hour ( ) ` 20 40

Consumable stores per year ( ) ` 2,000 5,000

Repairs and maintenance per year ( ) ` 9,000 6,000

Working capital ( ) ` 25,000 40,000

The company follows the written down value method of depreciation @ 25% and is subject to 35% tax. Should the

existing machine be replaced ? Assume that the company’s required rate of return is 15% and the company has

several assets in the 25% block.

Exercise 20-15 Akshay Machine Ltd. currently manufactures 10,000 units annually on a machine which has book

value of ` 60,000 (it was purchased for ` 1,20,000 six years ago). This machine is not fully depreciated for tax purposes.
The manufacturing cost per unit is as under: `
( )

Direct labour and material 24

Variable overheads 24

Fixed overheads 16

It is expected that old machine can be used for indefinite period after suitable repairs at estimated cost of ` 40,000
per annum. On the other hand, Modern Machine Tools offers a machine with latest technology at ` 3,00,000 after
trading off old machine for ` 30,000. The new machine is expected to last for 10 years at the end of which its salvage
value will be ` 20,000. However, the old machine can be sold for ` 40,000 in open market.
The projected cost per unit on the new machine will be as under: `
( )

N
Direct labour and material 14

N
Variable overheads 24

Fixed overheads 20

A
The fixed overheads are allocated from other departments plus depreciation on machinery. The cost of old and new

machinery will be depreciated in 10 years for tax purposes and the tax rate will be 30%. The minimum rate of return

M
is expected to be 10% and the annual production will stay at 10,000 units. Ignoring capital gains, advise whether new

machine should be installed or not.

X
Exercise 20-16 A company is considering a cost saving project. This involves purchasing a machine costing ` 7,000,

A
which will result in annual savings on wage costs of `1,000 and on material costs of ` 400.

T
The following forecasts are made of the rates of inflation each year for the next 5 years:

Wages costs 10% Material costs 5% General prices 6%

The cost of capital of the company, in monetary terms, is 15%.

Evaluate the project, assuming that the machine has a life of 5 years and no scrap value.

Exercise 20-17 A company is considering a new project. The project would involve an initial investment of

` 1,20,000 in equipment which would have a life of 5 years and no scrap value. The selling price now (year 0) would
be ` 60 and is expected to increase in line with the retail price index. Sales are expected to be constant at 2000 units

each year. The following estimates about unit costs are available:

Cost element `
Cost at year 0 prices ( ) Rate of increases

Wages 20 2% per annum faster than retail prices

Other 25 In line with retail prices

Total 45

All transactions take place at yearly intervals on the last day of the year. No increase in working capital will be

required. The following estimates of the rate of increase in retail prices and of interest rates are available:
 Year Rates of increase in retail prices Interest rate

(%) (%)

1 15 16

2 20 20

3 25 22

4 40 20

5 30 18

Exercise 20-18 A firm has projected the following cash flows from a project under evaluation:

Year 0 1 2 3

` lakhs (70) 30 40 30

The above cash flows have been made at expected prices after recognizing inflation. The firm’s cost of capital is 10%.

The expected annual rate of inflation is 5%. Show how the viability of the project is to be evaluated.

N
Exercise 20-19 S Engineering Company is considering to replace or repair a particular machine, which has just

broken down. Last year this machine costed ` 20,000 to run and maintain. These costs have been increasing in real

N
terms in recent years with the age of the machine. A further useful life of 5 years is expected, if immediate repairs

of `19,000 are carried out. If the machine is not repaired it can be sold immediately to realize about ` 5,000 (Ignore

A
loss/gain on such disposal).

Alternatively, the company can buy a new machine for ` 49,000 with an expected life of 10 years with no salvage value

M
after providing depreciation on straight line basis. In this case, running and maintenance costs will reduce to `14,000
each year and are not expected to increase much in real terms for a few years at least. S Engineering Company regard

X
a normal return of 10% p.a. after tax as a minimum requirement on any new investment. Considering capital

A
budgeting techniques, which alternative will you choose ? Take corporate tax rate of 50% and assume that

depreciation on straight line basis will be accepted for tax purposes also.

T
Given cumulative present value of ` 1 p.a. at 10% for 5 years ` 3.791, 10 years ` 6.145.

Exercise 20-20 X & Co. is contemplating whether to replace an existing machine or to spend money in overhauling

it. X & Co currently pays no taxes. The replacement machine costs ` 95,000 and requires maintenance of ` 10,000
every year at the year end for eight years. At the end of eight years, it would have a salvage value of ` 25,000 and would

be sold. The existing machine requires increasing amounts of maintenance each year and its salvage value falls each

year as follows:

Year Maintenance ( ) ` Salvage ( ) `

Present 0 40,000

1 10,000 25,000

2 20,000 15,000

3 30,000 10,000

4 40,000 0

The opportunity cost of capital for X & Co. is 15%. You are required to state, when should the firm replace the

machine.

(Given: Present value of an annuity of ` 1 per period for 8 years at interest rate of 15% - 4.4873; Present value of

` 1.00 to be received after 8 years at interest rate of 15% - 0.3269).

Exercise 20-21 A machine used on a production line must be replaced at least every four years. Costs incurred to

run the machine according to its age are: `

( )
 Age of the machine (Years)

0 1 2 3 4

Purchase price 60,000 - - - -

Maintenance - 16,000 18,000 20,000 20,000

Repair - 0 4,000 8,000 16,000

Scrap value - 32,000 24,000 16,000 8,000

Future replacement will be with identical machine with same cost. Revenue is unaffected by the age of the machine.

Ignoring inflation and tax, determine the optimum replacement cycle. PV factors of the cost of capital of 15% for

the respective four years are 0.8696, 0.7561, 0.6575 and 0.5718.

N N
M A
A X
T
 Key to Practical Exercises

Exercise 20-1

Calculation of Payback Period of Machines ( )`

Machine 1 Machine 2 Machine 3

Initial Investment (i) 3,00,000 3,00,000 3,00,000

Sales (a) 5,00,000 4,00,000 4,50,000

Costs:

Direct material 40,000 50,000 48,000

Direct labour 50,000 30,000 36,000

Factory overhead 60,000 50,000 58,000

Depreciation 1,30,000 91,667 90,000

N
Administration cost 20,000 10,000 15,000

Selling and distribution 10,000 10,000 10,000

N
Interest on capital 30,000 30,000 30,000

A
Total cost (b) 3,40,000 2,71,667 2,87,000

Profit before tax (a) - (b) 1,60,000 1,28,333 1,63,000

M
Less: Tax @ 40% 64,000 51,333 65,200

X
Profit after tax 96,000 77,000 97,800

Add: Depreciation 1,30,000 91,667 90,000

A
Net cash flow (ii) 2,26,000 1,68,667 1,87,800

T
Payback period (years) (i)/(ii) 1.33 1.78 1.60

Analysis - Machine 1 having low pay back period, hence it is preferred to the other two machines.

Exercise 20-2

Calculation of Net Cash flow ( ` lakhs)

Year Profit before Depreciation PBT PAT Net cash flow

depreciation and tax 20% W.D.V. (3)+(5)

(1) (2) (3) (4) (5) (6)

1 80 40.00 40.00 20.00 60.00

2 80 32.00 48.00 24.00 56.00

3 90 25.60 64.40 32.20 57.80

4 90 20.48 69.52 34.76 55.24

5 75 81.92* (-) 6.92 (-) 3.46 78.46

*Including depreciation and loss on disposal of assets.

Calculation of Net Present Value ( ` lakhs)

Year C.F D.F P.V D.F. P.V D.F P.V

12% 14% 16%

0 (200.00) 1.00 (200.00) 1.00 (200.00) 1.00 200.00

1 60.00 0.89 53.40 0.88 52.80 0.86 51.60

2 56.00 0.80 44.80 0.77 43.12 0.74 41.44

 ( ` lakhs)

Year C.F D.F P.V D.F. P.V D.F P.V

12% 14% 16%

3 57.80 0.71 41.04 0.67 38.73 0.64 36.99

4 55.24 0.64 35.35 0.59 32.59 0.55 30.38

5 78.46 0.57 44.72 0.52 40.80 0.48 37.66

N.P.V. 19.31 8.04 (-) 1.93

Net present value at 12% = ` 19.31 lakhs

8.04
I.R.R. = 14% + × 2% = 15.6%
10.02

Exercise 20-3

(i) Payback Period ( ` lakhs)

Machine A Machine B

N
Year Cash Cumulative Cash Cumulative

inflow cash inflow inflow cash inflow

N
1 - - 10 10

2 5 5 14 24

A
3 20 25 16 40

4 14 39 17 57

M
5 6 45 8 65

X
Payback period is 3 years for both machines.

A
(ii) Net Present Value ( lakhs)

DCF Machine A Machine B

T
Year @ 16% Cash flow Present Cash flow Present

value value

1 0.862 - - 10 8.620

2 0.743 5 3.715 14 10.402

3 0.641 20 12.820 16 10.256

4 0.552 14 7.728 17 9.384

5 0.476 6 2.856 8 3.808

Total present value 27.119 42.470

Less: Initial cost 25.000 40.000

Net Present Value 2.119 2.470

(iii) Profitability Index = NPV/Investment ( ` lakhs)

27.119 42.470
Machine A = = 1.085 Machine B = = 1.062
25 40

(iv) Internal Rate of Return

Machine A ( ` lakhs)

Year Cash inflow DCF P.V. DCF P.V.

@ 18% @ 20%

1 - 0.847 - 0.833 -

2 5 0.718 3.590 0.694 3.470

 Machine A (` lakhs)

Year Cash inflow DCF P.V. DCF P.V.

@ 18% @ 20%

3 20 0.609 12.180 0.579 11.580

4 14 0.516 7.224 0.482 6.748

5 6 0.437 2.622 0.402 2.412

Total present value 25.616 24.210

Less: Initial investment 25.000 25.000

Net Present Value 0.616 (-) 0.790

0.616
IRR = 18% + × 2% = 18.88%
0.616 + 0.790

Machine B (` lakhs)

Year Cash inflow DCF P.V. DCF P.V.

@ 18% @ 20%

N
1 10 0.847 8.470 0.833 8.330

N
2 14 0.718 10.052 0.694 9.716

3 16 0.609 9.744 0.579 9.264

A
4 17 0.516 8.772 0.482 8.194

5 8 0.437 3.496 0.402 3.216

M
Total present value 40.534 38.720

X
Less: Initial investment 40.000 40.000

Net Present Value 0.534 (-) 1.28

A
0.534

T
IRR = 18% + × 2% = 18.59%
0.534 + 1.28

Summary of Investment Appraisal

Particulars Machine A Machine B

(i) Payback period 3 years 3 years

(ii) Net present value (@ 16%) ` 2.119 lakhs ` 2.47 lakhs

(iii) Profitability index 1.085 1.062

(iv) IRR 18.88% 18.59%

Suggestion - From the analysis of the above it is observed that Profitability Index and IRR are greater in case of

Machine A. Hence, Machine A is to be selected even though NPV of it is slightly lesser than Machine B. Payback

period of both the machines is equal.

Exercise 20-4

Initial Investment
(i) Payback Period =
Annual cash inflows

Calculation of Payback Period

Machine A (` lakhs)

Year Cash inflows Payback

Total Needed years required

1 1.50 1.50 1 year

2 2.00 2.00 1 year

3 2.50 1.50 (1.50/2.50) × 12 = 7.2 months

 ∴ Payback Period for Machine A = 2 years 7.2 months

Machine B ( ` lakhs)

Year Cash inflows Payback

Total Needed years required

1 0.50 0.50 1 year

2 1.50 1.50 1 year

3 2.00 2.00 1 year

4 3.00 1.00 (1/3) × 12 = 4 months

5.00

∴ Payback period for Machine B = 3 years 4 months

Rank : Machine A - I, Machine B - II. Machine A is more profitable.

(ii) Calculation of Net Present Value of Cash Inflows for Machine A and Machine B ( ` lakhs)

N
Year Cash Inflows Discount P. V. of cash inflows

Machine A Machine B factor @ 10% Machine A Machine B

N
1 1.5 0.5 .909 1.36 0.45

A
2 2.0 1.5 .826 1.65 1.24

3 2.5 2.0 .751 1.88 1.50

M
4 1.5 3.0 .683 1.02 2.05

5 1.0 2.0 .621 0.62 1.24

X
6.53 6.48

A
Total present value of cash inflows

T
Less: Initial investment 5.00 5.00

Net Present Value 1.53 1.48

Rank : Machine A - I, Machine B - II

Since Machine A has greater NPV compared to Machine B, Machine A is more profitable.

(iii) Calculation of Profitability Index ( ` lakhs)

Particulars Machine A Machine B

Present value of cash inflows 6.53 6.48

Profitability Index = = 1.306 = 1.296
Present value of cash inflows 5.00 5.00

Rank I II

Machine A is more profitable.

Average annual earnings

(iv) Calculation of Average Rate of Return = × 100
Initial cost

( ` lakhs)

Particulars Machine A Machine B

Total cash inflow 8.50 9.00

Less: Depreciation for 5 years 5.00 5.00

Net earning after tax and depreciation 3.50 4.00

Life of machine (years) 5 5

Average earnings per year 0.70 0.80

Initial cost 5 5
 ( ` lakhs)

Particulars Machine A Machine B

ARR (0.70/5.00) × 100 = 14% (0.80/5.00) × 100 = 16%

Rank II I

Suggestion - Machine B is more profitable

Exercise 20-5

Calculation of P.V. of Cash Outflow ( ` lakhs)

Land (2 × 1.000) 2.00

Buildings (3 × 0.909) 2.73

Machinery (10 × 0.826) 8.26

Working capital (5 × 0.826) 4.13

P.V. of cash outflow 17.12

Calculation of Annual Cash Inflow ( ` lakhs)

N
Sales 20

N
Less: Cost of sales 12

PBDT 8

A
Less: Depreciation 2

PBT 6

M
Less: Tax @ 50% 3

X
PAT 3

Add: Depreciation 2

A
Annual cash inflow 5

T
Calculation of NPV ( ` lakhs)

Year Cash inflow P.V. factor @ 10% P.V.

3 5.0 0.751 3.755

4 5.0 0.683 3.415

5 5.0 0.621 3.105

6 5.0 0.564 2.820

7 5.0 0.513 2.565

7 (salvage value) 5.0 0.513 2.565

7 (working capital recovered) 5.0 0.513 2.565

P.V. of cash inflow 20.79

Less: P.V. of cash outflow 17.12

NPV 3.67

Analysis - Since NPV is positive, the project can be taken up.

Exercise 20-6

Calculation of cost of project i.e., initial cash outlay of Project M

Annual cost saving ` 40,000 Useful life 4 years I.R.R. 15%

At 15% I.R.R., the total present value of cash inflows is equal to initial cash outlay.

Total present value of cash inflows @ 15% for 4 years is 2.855 = 40,000 × 2.855 = ` 1,14,200

∴ Project cost is ` 1,14,200

Calculation of Payback Period of Project M

Cost of project ` 1,14,200

Payback period = = = 2.855 or 2 years 11 months (approx.)
Annual cost saving ` 40,000
Calculation of Cost of Capital

Discounted cash inflows

Profitability Index = = 1.064 given
Cost of project

Cost of Project = ` 1,14,200

Present value of cash inflows
1.064 =

` 1,14,200

Present value of cash inflows = 1.064 × ` 1,14,200 = ` 1,21,509

Cumulative Discount Factor for 4 years

Present value of cash inflows ` 1,21,509

= = = 3.038
Annual cost saving ` 40,000
Looking at present value table at discount compound discount factor for 4 years is 3.038. ∴ Cost of capital = 12%

N
NPV of Project = P.V. of total cash inflows - Cost of project = ` 1,21,509 - ` 1,14,200 = ` 7,309

N
Exercise 20-7

A
Investment Allocation Strategy under Capital Rationing Situation ( ` lakhs)

Projects Investment required NPV Comment

M
(i) A & B 26 12.8 Funds available is only ` 25 lakhs and this proposal is

X
not possible to implement.

(ii) B & C 22 12.2 Since B & C are mutually exclusive, it is not possible to

A
take up B & C simultaneously.

T
(iii) A & C 24 10.6 The possible option is only to take up A & C, even

though NPV is lowest.

Exercise 20-8

Determination of Feasible Combination in Capital Rationing Situation (Investment limit ` 25 lakhs) ( ` lakhs)

Combination of Projects Total outlay NPV

A & B 25.00 10.50

A & C 22.50 9.60

A & D 21.00 9.00

B & D 16.00 7.50

C & D 13.50 6.60

Analysis - From the above analysis it is observed that Projects A and B combination give highest NPV of ` 10.50 lakhs.
Therefore, by undertaking Projects A and B, the wealth maximization is possible.

Exercise 20-9

Total capital outlay < ` 3.00 lakhs

Computation of Net Present Value and Benefit-Cost Ratio for five Projects `
( )

Project Investment Cash flow No. of P.V. @ 10% P.V. NPV BCR (PV/

p.a. years. Investment)

M 50,000 18,000 10 6.145 1,10,610 60,160 2.212

N 1,00,000 50,000 4 3.170 1,58,500 58,500 1.585

 ( ) `

Project Investment Cash flow No. of P.V. @ 10% P.V. NPV BCR (PV/

p.a. years. Investment)

O 1,20,000 30,000 8 5.335 1,60,050 40,050 1.334

P 1,50,000 40,000 16 7.824 3,12,960 1,62,960 2.086

Q 2,00,000 30,000 25 9.077 2,72,310 72,310 1.362

Statement Showing Feasible Combination of Projects and their NPV, BCR

Feasible combination Investment NPV Rank BCR Rank

of projects `
( ) `
( )

(i) M, N and P 3,00,000 2,82,070 1 1.940 1

(ii) M, N and O 2,70,000 1,59,160 4 1.589 4

(iii) O & P 2,70,000 2,03,010 3 1.752 3

(iv) M & Q 2,50,000 1,32,920 5 1.532 5

N
(v) N & P 2,50,000 2,21,460 2 1.886 2

(vi) N & Q 3,00,000 1,30,810 6 1.436 6

N
Comment - The optimum combination of projects, is Projects M, N and P with total investment of ` 3.00 lakhs since

A
it has highest NPV & BCR of ` 2,82,070 and 1.940 respectively. Hence, the same should be taken up.

Exercise 20-10

M
Statement Showing Ranking of Projects on the basis of Profitability Index

X
Project Amount ( ) ` Profitability Index Rank

A
1 3,00,000 1.22 1

2 1,50,000 0.95 5

T
3 3,50,000 1.20 2

4 4,50,000 1.18 3

5 2,00,000 1.20 2

6 4,00,000 1.05 4

Statement Showing NPV of Projects ( ) `

Project Amount Profitability Index Cash inflow N.P.V.

(2) × (3) (4) - (2)

(1) (2) (3) (4) (5)

1 3,00,000 1.22 3,66,000 66,000

2 1,50,000 0.95 1,42,500 (-) 7,500

3 3,50,000 1.20 4,20,000 70,000

4 4,50,000 1.18 5,31,000 81,000

5 2,00,000 1.20 2,40,000 40,000

6 4,00,000 1.05 4,20,000 20,000

Selection Projects

¾ Profitability Index Method - Assuming the projects are indivisible and there is no alternative use of unutilized

amount, S Ltd. is advised to undertake investments in projects 1, 3 and 5, which will give N.P.V. of ` 1,76,000
and unutilized amount will be ` 1,50,000.
 ¾ Net Present Value Method - As per this method projects 3, 4 and 5 can be undertaken which will be `1,91,000
and no money will remain unspent.

Suggestion - From the above analysis, we can observe that, selection of projects under N.P.V. method will maximize

S Ltd.’s net cash inflow by ` 15,000 (i.e., 1,91,000 - 1,76,000). Hence, it is suggested to undertake investments in

Projects 3, 4 and 5.

Exercise 20-11

Calculation of NPV and Benefit Cost Ratio (BCR) of different Projects

Project A (5 years)

NPV = [(6,000 × 3.791) + (5,000 × 0.6209)] - 20,000

= (22,746 + 3,105) - 20,000 = 25,851 - 20,000 = ` 5,851

BCR = 25,851/20,000 = 1.29

Project B (10 years)

NPV = (8,000 × 6.145) - 45,000 = 49,160 - 45,000 = ` 4,160

BCR = 49,160/45,000 = 1.09

N
Project C (8 years)

NPV = (15,000 × 5.335) - 75,000 = 80,025 - 75,000 = ` 5,025

N
BCR = 80,025/75,000 = 1.067

A
Project D (12 years)

NPV = [(15,000 × 6.814) + (15,000 × 0.319)] - 1,00,000

M
= (1,02,210 + 4,785) - 1,00,000 = 1,06,995 - 1,00,000 = ` 6,995

X
BCR = 1,06,995/1,00,000 = 1.07

Project E (7 years)

A
NPV = [(25,000 × 4.868) + (50,000 × 0.513)] - 1,40,000

T
= (1,21,700 + 25,650) - 1,40,000 = 1,47,350 - 1,40,000 = ` 7,350

BCR = 1,47,350/1,40,000 = 1.05

Feasible Combinations `
( )

Project Total Total Rank BCR Rank based

 /17 + * 
combinations outlay (I) NPV based on NPV
  on BCR
 * 
A + B 65,000 10,011 7 1.154 1

A + C 95,000 10,876 6 1.114 2

A + D 1,20,000 12,846 3 1.107 3

B + C 1,20,000 9,185 8 1.077 5

B + D 1,45,000 11,155 5 1.077 5

B + E 1,85,000 11,510 4 1.062 6

A + B + C 1,40,000 15,036 2 1.107 3

A + B + D 1,65,000 17,006 1 1.103 4

Analysis - The optimum combination of projects A, B & D with total investment of ` 1,65,000.
Exercise 20-12

Calculation of NPV of Projects ( ) `

Project Total cash inflow Initial cash outflow Net present values

(a) (b) (a) - (b)

P 10,00,000 × 1.21 = 12,10,000 10,00,000 2,10,000

1
P 3,00,000 × 0.94 = 2,82,000 3,00,000 (-)18,000
2
P 7,00,000 × 1.20 = 8,40,000 7,00,000 1,40,000
3
P 9,00,000 × 1.18 = 10,62,000 9,00,000 1,62,000
4
P 4,00,000 × 1.20 = 4,80,000 4,00,000 80,000
5
P 8,00,000 × 1.05 = 8,40,000 8,00,000 40,000
6

Ranking of Projects based on NPV and Profitability Index

Project Initial investment NPV ( ) ` Rank Profitability Index Rank

P 10,00,000 2,10,000 1 1.21 1

1

N
P 3,00,000 (-)18,000 6 0.94 6
2
P 7,00,000 1,40,000 3 1.20 2.5
3

N
P 9,00,000 1,62,000 2 1.18 4
4
P 4,00,000 80,000 4 1.20 2.5
5

A
P 8,00,000 40,000 5 1.05 5
6

M
If the projects are chosen based on Profitability Index (PI)

Project Investment ( ) ` PI NPV ( ) `

X
P 10,00,000 1.21 2,10,000
1

A
P 7,00,000 1.20 1,40,000
3

T
17,00,000 3,50,000

If projects are chosen based on the principle of full budget utilization

Project Investment ( ) ` PI NPV ( ) `

P 7,00,000 1.20 1,40,000
3
P 4,00,000 1.20 80,000
5
P 9,00,000 1.18 1,62,000
4

20,00,000 3,82,000

Analysis - If full budget utilization is warranted, projects P , P and P are to be selected to maximise NPV.
3 5 4

Exercise 20-13

(i) Statement Showing Comparative Output Required

Particulars Semi automatic Automatic

machine machine

Purchase price of component 40.00 40.00

Less: Variable cost per component 18.00 15.00

Saving 22.00 25.00

Components required to be produced to justify

the installation of the machine (Fixed cost/Savings) ` 22,00,000/22 ` 40,00,000/25

= 1,00,000 units = 1,60,000 units
 (ii) Selection of machine (when annual requirement is 8,00,000 units)

Particulars Semi-automatic Automatic

machine machine

Variable cost: (8,00,000 × ` 18); (8,00,000 × ` 15) 1,44,00,000 1,20,00,000

Fixed cost 22,00,000 40,00,000

Total cost 1,66,00,000 1,60,00,000

The total cost in case of automatic machine is less, hence it will be beneficial to install automatic machine.

Exercise 20-14

Cash Outflows `
( )

Purchase price of new machine 4,00,000

Add: Additional working capital 15,000

Less: Sale value of old machine 1,00,000

3,15,000

N
Incremental Cash Inflows Before Taxes ( ) `

N
Particulars Existing New Differential

Machine Machine cash flow

A
Annual operating hours 2,000 2,000

M
Output per hour (units) 15 30 15

Total output (units) 30,000 60,000 30,000

X
Selling price per unit 10 10 10

A
Total sale revenue 3,00,000 6,00,000 3,00,000

T
Less: Expenses:

Material cost 60,000 1,20,000 60,000

Labour cost 40,000 80,000 40,000

Consumable stores 2,000 5,000 3,000

Repairs & maintenance 9,000 6,000 (3,000)

Total expenses 1,11,000 2,11,000 1,00,000

Cash flows before taxes 1,89,000 3,89,000 2,00,000

Computation of NPV of Incremental Cash flows ( ) `

Particulars Year 1 Year 2 Year 3 Year 4

Incremental cash flows before taxes 2,00,000 2,00,000 2,00,000 2,00,000

Less: Incremental depreciation 75,000 56,250 42,187 31,641

Earnings before taxes 1,25,000 1,43,750 1,57,813 1,68,359

Less: Taxes @ 35% 43,750 50,312 55,235 58,926

EAT 81,250 93,438 1,02,578 1,09,433

CFAT (EAT + Depreciation) 1,56,250 1,49,688 1,44,765 1,41,074

Release of working capital - - - 15,000

1,56,250 1,49,688 1,44,765 1,56,074

P.V. factor @ 0.15 0.8696 0.7561 0.6575 0.5718

P.V. of cash flows after tax 1,35,875 1,13,179 95,183 89,243

Computation of NPV of Incremental Cash flows `
( )

Particulars Year 1 Year 2 Year 3 Year 4

Total P.V. of cash flows after tax 4,33,480

Less: Cash outflows 3,15,000

NPV 1,18,480

Suggestion - Since the NPV of incremental cash flows is positive, it is suggested to replace the existing machine with

new machine.

Depreciation base of New Machine `

( )

WDV of existing machine (2,40,000 - 60,000 - 45,000) 1,35,000

Add: Cost of new machine 4,00,000

Total 5,35,000

Less: Sale value of old machine 1,00,000

4,35,000

N
Base for Incremental Depreciation = ( ` 4,35,000 - ` 1,35,000 WDV of existing machine) = ` 3,00,000

N
Exercise 20-15

Calculation of Variable Cost

A
Variable cost p.u. = Direct material & labour + Variable overheads p.u.

Old machine = ` 24 + ` 24 = ` 48 New machine = ` 14 + ` 24 = ` 38

M
Calculation of Depreciation

X
Old machine = ` 60,000/10 years = ` 6,000
New machine = ( ` 3,00,000 + ` 30,000 - ` 20,000)/10 years = ` 31,000

A
Evaluation of Replacement of Old machine `
( )

T
Particulars Old machine New machine

No. of units 10,000 10,000

Variable cost 4,80,000 3,80,000

Add: Annual repairs 40,000 -

Depreciation 6,000 -

Total cost 5,26,000 4,11,000

Tax saving on cost @ 30% 1,57,800 1,23,300

Add back depreciation 6,000 31,000

Total cash saving 1,63,800 1,54,300

Net decrease in cash flow = ` 1,63,800 - ` 1,54,300 = ` 9,500

`
( )

P.V. of total decrease in cash flow in 10 years ( ` 9,500 × 6.145) 58,378

P.V. of salvage value ( ` 20,000 × 0.3855) 7,711

Total cash outflow over 10 years 66,089

Less: Initial cost of machine 3,00,000

Net present value 3,66,089

Suggestion - Since NPV is negative it is suggested not to replace the old machine with new machine.
Exercise 20-16

Calculation of Net Present Value ( )`

Year Labour cost Material cost Total DCF Present

saving saving savings @ 15% values

1 1000 × (1.1) = 1,100 400 × (1.05) = 420 1,520 0.870 1,322

2 2
2 1000 × (1.1) = 1,210 400 × (1.05) = 441 1,651 0.756 1,248

3 3
3 1000 × (1.1) = 1,331 400 × (1.05) = 463 1,794 0.658 1,180

4 4
4 1000 × (1.1) = 1,464 400 × (1.05) = 486 1,950 0.572 1,115

5 5
5 1000 × (1.1) = 1,610 400 × (1.05) = 510 2,120 0.497 1,054

Present value of total savings 5,919

Less: Initial cash outflow 7,000

Net present value (negative) (-) 1,081

Analysis - Since the present value of cost of project exceeds the cost of savings form it is not suggested to purchase

the machine.

N
Exercise 20-17

N
Assuming Purchasing Power Parity Theorem holds in the present case, changes in interest rates will affect the money

A
value. Hence, cost of capital is taken in money terms.

Year 0 1 2 3 4 5

M
Inflation rate for contribution before wages

X
(increase over previous year) 1.15 1.20 1.25 1.40 1.30

Inflation rate for wages

A
(increase over previous year) 1.17 1.22 1.27 1.42 1.32

T
` ` ` ` ` `

Contribution before wages, per unit sold 35 40.25 *48.30 60.38 84.53 109.88

Wages per unit 20 23.40 28.55 **36.26 51.49 67.97

Contribution after wages, per unit sold 15 16.85 19.75 24.12 33.04 41.91

Total contribution from 2000 units sold 30,000 33,700 39,500 48,240 66,080 83,820

* 35 × 1.15 × 1.20 and so on. ** 20 × 1.17 × 1.22 × 1.27 and so on.

Calculation of Net Present Value using Money Estimates ( )`

Year Money cash flow Money discount factor Present value

0 (1,20,000) 1.000 (1,20,000)

1 33,700 0.862 [1 × 1/1.16] 29,049

2 39,500 0.718 [0.862 × 1/1.2] 28,361

3 48,240 0.589 [0.718 × 1/1.22] 28,413

4 66,080 0.491 [0.589 × 1/1.2] 32,445

5 83,820 0.416 [0.491 × 1/1.18] 34,869

NPV 33,137

Analysis - Since the NPV is Positive, the project is worthwhile.

Exercise 20-18

Calculation Present Value Factors @ 10%

Year 1 = 1/1.10 = 0.909 Year 2 = 1/1.102 = 0.826 Year 3 = 1/1.103 = 0.751

Calculation P.V.F @ 10% adjusted by the Inflation Factor i.e. 5%

0.909 0.826 0.751

Year 1 = = 0.866 Year 2 = = 0.749 Year 3 = = 0.649
2 3
1 + 0.05 (1 + 0.5) (1 + 0.5)

Calculation of Inflation Adjusted NPV ( ` lakhs)

Year Nominal P.V. factor @ 10% P.V.

cash flows (inflation adjusted)

0 (70) 1.000 (70.00)

1 30 0.866 25.98

2 40 0.749 29.96

3 30 0.649 19.47

Net Present Value 5.41

Alternatively, NPV can be calculated by converting nominal cash flows into real cash flows, after adjusting for

inflation.

2 3
Year 1 = 30 × 1/1.05 = 28.57 Year 2 = 40 × 1/1.05 = 36.28 Year 3 = 30 × 1/1.05 = 25.92

N
Calculation Inflation Adjusted NPV ( ` lakhs)

Year Real cash flows P.V. factor @ 10% P.V. of cash flows

N
0 (70.00) 1.000 (70.00)

A
1 28.57 0.909 25.97

2 36.28 0.826 29.97

M
3 25.92 0.751 19.47

Net Present Value 5.41

X
Suggestion - Since NPV is positive, it is suggested to undertake the project.

A
Exercise 20-19

T
Evaluation of Alternative Proposals

Alternative I Repairs to Existing Machine `

( )

Cost of repairs ( ` 19,000 × 50/100 = ` 9,500)

Equivalent annual cost for 5 years ( ` 9,500/3.791) 2,506

Add: Running and maintenance cost p.a. net of tax ( ` 20,000 × 50/100) 10,000

Present value of cash outflows p.a. 12,506

Alternative II Replace the Old Machine `

( )

Purchase cost of new machine 49,000

Less: sale proceeds of old machine 5,000

Net cash outflow 44,000

Equivalent annual cost for 10 years ( ` 44,000/6.145) 7,160

Add: Running and maintenance cost p.a. net of tax ( ` 14,000 × 50/100) 7,000

14,160

Less: Tax saving on depreciation ( ` 49,000/10) × 50/100 2,450

Present value of cash outflow p.a. 11,710

Analysis - From the above analysis it is observed that Alternative-II i.e., replacement of old machine with a new

machine is more profitable, since the cash outflow p.a. will decrease by ` 796 (i.e., ` 12,506 - ` 11,710) if old machine
is replaced with new machine.
Exercise 20-20

Calculation of equivalent cost of New machine `

( )

Cost of new machine at present 95,000

Add: P.V. of annual repairs @ ` 10,000 p.a. for 8 years ( ` 10,000 × 4.4873) 44,873

1,39,873

Less: P.V. of salvage value at the end of 8th year ( ` 25,000 × 0.3269) 8,173

1,31,700

Equivalent annual cost = ` 1,31,700/4.4873 = ` 29,350

Equivalent Annual Cost (EAC) of keeping the machine `

( )

Particulars I year II year III year IV year

Salvage value 40,000 25,000 15,000 10,000

Add: P.V. of annual maintenance (AM/1.15) 8,696 17,391 26,087 34,783

Total 48,696 42,391 41,087 44,783

N
Less: P.V. of salvage values at end of the year (SV.1.15) 21,739 13,043 8,696 Nil

N
26,957 29,348 32,391 44,783

1.15 1.15 1.15 1.15

A
Equivalent annual cost 31,000 33,750 37,250 51,500

M
Analysis - Since the equivalent annual cost of new machine is 29,350 and equivalent annual cost of keeping the

machine is more in all the four years. Therefore, it is suggested to replace the old machine with the new machine

X
immediately.

A
Exercise 20-21

The possible replacement options of the machine are every one, two, three and four years. The annual equivalent

T
cost of each of these replacement policies are as follows:

(i) Replacement every year `

( )

Year 0 1

Cost (60,000) -

Maintenance and repair - (16,000)

Residual value - 32,000

Total (60,000) 16,000

DCF @ 15% 1.0000 0.8696

P.V. of cash flows (60,000) 13,914

Total present value of cash outflows = ` 46,086

Equivalent annual cost = ` 46,086/0.8696 = ` 52,997

(ii) Replacement Every Two years

Year 0 1 2

Cost (60,000) - -

Maintenance and repair - (16,000) (22,000)

Residual value - - 24,000

Total (60,000) (16,000) 2,000

DCF @ 15% 1.0000 0.8696 0.7561

P.V. of cash flows (60,000) (13,914) 1,512

 Total present value of cash outflows = ` 72,402
Equivalent annual cost = ` 72,402/1.6257 = ` 44,536

(iii) Replacement Every Three years `

( )

Year 0 1 2 3

Cost (60,000) - - -

Maintenance and Repair - (16,000) (22,000) (28,000)

Residual value - - - 16,000

Total (60,000) (16,000) (22,000) (12,000)

DCF @ 15% 1.0000 0.8696 0.7561 0.6575

P.V. of cash flows (60,000) (13,914) (16,634) (7,890)

Total present value of cash outflows = ` 98,438

Equivalent annual cost = ` 98,438/2.2832 = ` 43,114

(iv) Replacement Every Four years `

( )

N
Year 0 1 2 3 4

N
Cost (60,000) - - - -

Maintenance and Repair - (16,000) (22,000) (28,000) (36,000)

A
Residual value - - - - 8,000

Total (60,000) (16,000) (22,000) (28,000) (28,000)

M
DCF @ 15% 1.0000 0.8696 0.7561 0.6575 0.5718

X
P.V. of cash flows (60,000) (13,914) (16,634) (18,410) (16,010)

A
Total present value of cash outflows = ` 1,24,968

T
Equivalent annual cost = ` 1,24,968/2.855 = ` 43,772

Suggestion - Since least equivalent annual cost is ` 43,114, it is suggested to replace the machine every three years.
 Key to Short Answer Questions

True or False Statements

1. True - Annual capital charge provided basis of comparing projects whose life span are otherwise different.

2. True - The NPV method discounts the net cash flows from the investment by a minimum required rate of

return and deducts the initial investment to give the yield from the funds invested. If yield is positive

the project is acceptable. If it is negative the project is unable to pay for itself and is thus unacceptable.

3. False - The test of profitability of a project is the relationship between the IRR (%) of the project and the

minimum acceptable rate of return (%). IRR is called as ‘cut off rate’ for accepting the investment

proposals, using IRR all projects which yield an internal rate of return in excess of the firm’s cost of

capital will be chosen.

4. False - When evaluating mutually exclusive projects, the one with the highest IRR not be the one with best

N
NPV. The conflict between NPV and IRR for evaluation of mutually exclusive projects is due to

reinvestment assumption: (a) NPV assumes cash flows reinvested at the cost of capital, (b) IRR

N
assumes cash flows reinvested at the internal rate of return.

True

A
5. - IRR is a percentage discount rate used in capital investment appraisals which brings the cost of a

project and its future cash inflows into equality. IRR is the rate of return which equates the present

value of anticipated net cash flows with the initial outlay. IRR is also defined as the rate at which the

M
net present value is zero.

True

X
6. - We know that Profitability Index (PI) = PV of cash inflow/PV of cash outflow. So, if PI is 1, then cash

inflow and cash outflow would be equal.

A
7. False - Profitability index is the present value of anticipated cash inflows divided by the initial investment.

T
A project with an index of more than 1 will be selected.

8. True - The discounted cash flow (DCF) analysis requires projections of the future free cash flows of a project

or investment which are discounted back to the present by an applicable cost of capital. In case of

companies with higher risk level, the higher discount rate will be adopted.

9. False - IRR is a percentage discount rate used in capital investment appraisals which brings the cost of a

project and its future cash inflows into equality. IRR does not consider the cost of capital into

consideration. IRR is the rate which NPV is zero. In appraising the investment proposals, IRR is

compared with the desired rate of return or weighted average cost of capital, to ascertain whether the

project can be accepted or not. IRR is also called as cutoff rate for accepting the investment proposals.

10. False - The payback period is usually expressed in years, which it takes the cash inflows from a capital

investment project to equal the cash outflows. The NPV method discounts the net cash flows from the

investment by the minimum required rate of return, and deducts the initial investment to give the

yield from the invested funds. Given two mutually exclusive projects and a zero cost of capital,

payback period is most preferable over NPV method.

11. False - Capital rationing refers to a situation where a company cannot undertake all positive NPV projects

it has identified because of shortage of capital. Under this situation, a decision-maker is compelled to

reject some of the projects having positive NPV because of shortage of funds. The aim is to maximize

the wealth of the company by selecting those projects which will maximize overall NPV of the

concern.

12. True - WACC is considered as the minimum rate of return required from project to pay off the expected

return of the investors and as such WACC is generally referred to as the ‘required rate of return’.

Therefore, if IRR is less than the firm’s cost of capital, the project should be rejected.
Choose Correct Word

1. capital

2. profitability index

3. rationing

4. negative

5. NPV

6. discounting

7. equal to

8. payback period

9. payback period

10. shortest

11. capital

12. NPV

N
13. end

N
14. NPV

15. benefit-cost ratio

A
16. IRR

17. cutoff

M
18. IRR

X
19. conflicting

A
20. greater

21. indivisible

T
22. NPV

23. constant

24. NPV

25. low

26. cost of capital

Choose Correct Answer

1. (A) The NPV will be zero

2. (C) higher

3. (D) retained earnings

4. (A) zero

5. (C) Capital rationing

6. (B) T = P (1 + r)
n
n o
7. (C) Reinvested at a rate equal to the internal rate of return of the firm

8. (D) Economically dependent

9. (A) The discount rate decreases

10. (B) All else equal, a project’s NPV increases as the cost of capital declines
 Practical Exercises

Probability and Expe cte d Value

Exercise 21-1 The following table presents the proposed cash flows for projects M and N with their associated

probabilities. Which project has a higher preference for acceptance?

Project M Project N

Possibilities Cash flow Probability Cash flow Probability

( ` lakhs) ( ` lakhs)

1 7,000 0.10 12,000 0.10

2 8,000 0.20 8,000 0.10

3 9,000 0.30 6,000 0.10

N
4 10,000 0.20 4,000 0.20

5 11,000 0.20 2,000 0.50

N
Exercise 21-2 A company is considering the purchase of a new machine, which has a three year life and will lead

A
to increase the profit in each of the next 3 years. However, due to uncertainty in demand, the annual additional cash

flow resulting from the purchase of the new machine cannot be determined with certainty and have, therefore, been

M
estimated probabilistically as under:

Year I Year II Year III

X
Annual cash Probability Annual cash Probability Annual cash Probability

A
flow ( ` lakhs) flow ( ` lakhs) flow ( ` lakhs)

T
10 0.30 10 0.10 10 0.20

15 0.50 20 0.30 20 0.50

20 0.20 30 0.40 30 0.30

40 0.20

The cost of the new machine is ` 42 lakhs and will have no salvage value at the end of the 3rd year. Based on the average
cash flow for each year, advise whether it would be advisable to purchase the machine. The company’s cost of capital

is 15%. Present value of ` 1 at 15% discount rate is:

Year I II III

P.V. 0.8696 0.7561 0.6575

Exercise 21-3 A tender has been floated for purchase of a component. The demand is 8,000 units of the component.

The tenderer will accept the lowest bid. The estimates of probabilities of bids at various levels are:

Price bid ( ` p.u.) 90 100 110 120 130 140 150

Probability of bid 0.05 0.10 0.20 0.25 0.25 0.10 0.05

The variable cost is ` 64 per unit. Determine the price bid at which profits can be maximized.

Exercise 21-4 A company has estimated the following demand level of its product:

Sales volume (units) 10,000 12,000 14,000 16,000 18,000

Probability 0.10 0.15 0.25 0.30 0.20

It has assumed that the sales price of ` 6 per unit, marginal cost ` 3.50 per unit, and fixed costs ` 34,000. What is

the probability that: (a) the company will break-even in the period? (b) the company will make a profit of at least

` 10,000?

Exercise 21-5 PQR Ltd. is considering the introduction of a new product. The anticipated demand, probability of

demand and profits for each product are given below. Choice is to be made between Product X and Y.

Product X Product Y

Demand Probability Profit Demand Probability Profit

(units) of demand (%) `

( ) (units) of demand (%) ( )`

50,000 20 -8,000 30,000 15 -12,000

60,000 10 -5,000 40,000 15 -10,000

70,000 30 11,000 50,000 40 14,000

80,000 20 14,000 60,000 20 16,000

90,000 20 17,000 70,000 10 18,000

100 100

N
Exercise 21-6 A company has estimated the unit variable cost of a Product to be ` 10, and the selling price is ` 15

N
per unit. Budgeted sales for the year are 20,000 units. Estimated fixed costs are as follows:

A
`
Fixed costs p.a. ( ) 50,000 60,000 70,000 80,000 90,000

Probability 0.1 0.3 0.3 0.2 0.1

M
What is the probability that the company will equal or exceed its target profit of ` 25,000 for the year.

X
Exercise 21-7 Gadgets Ltd. which makes and sells only one product, sold 1,20,000 units incurring a loss of `
` `

A
1,20,000. The variable cost per unit of the product is 8 and the fixed costs are 3,60,000.

The company has estimated its sales demand as under:

T
Sales (units) 1,20,000 1,44,000 1,68,000 1,92,000 2,16,000

Probability 0.10 0.15 0.20 0.30 0.25

Requirements: (i) What is the probability that the company will continue to make losses ? (ii) What is the prob-

ability that the company will make a profit of atleast ` 72,000 ?

Exercise 21-8 A firm wants to avoid risk and choose between either of two alternative products. Both the products

have the same contributory margin of ` 4 per unit, the same increment in annual fixed costs (` 4 lakhs) and require
similar amounts of processing facilities. Both the products will have the same break-even volume of one lakh units

and for any levels of sales will yield the same profit contribution.

Given the probability distribution of sales for Products 1 and 2, as under, which product the firm will prefer?

Units sold 50,000 75,000 1,00,000 1,25,000 1,50,000 2,25,000

Product 1 0.1 0.2 0.3 0.3 0.1 0

Product 2 0.2 0.3 0.2 0.1 0.1 0.1

Pessimistic, Most Likely and Optimistic Estimate s

Exercise 21-9 Forward Looking Ltd. is preparing their budget for 2016. In the preparation of the budget, they

would like to take no chances, but would like to envisage all sorts of possibilities and incorporate them in the budget.

Their estimates are as under:

 (a) If the worst possible happens, sales will be 8,000 units at a price of ` 19 per unit. The material cost will be ` 9
per unit, the direct labour ` 2 per unit and the variable overheads will be ` 1.50 per unit. The fixed cost will be
` 60,000 p.a.

(b) If the best possible happens sales will be 15,000 units at a price of ` 20 per unit. The material cost will be ` 7
per unit, direct labour ` 3 per unit and variable overhead will be ` 1 per unit. The fixed cost will be ` 48,000 p.a.
(c) It is most likely however that the sales will be 2,000 units above the worst possible level at a price of ` 20 per
unit. The material cost, direct labour and variable overheads will be respectively ` 8, ` 3 and Re. 1 per unit. The
fixed cost will be ` 50,000 p.a.

(d) There is a 20% probability that the worst will happen a 10% probability that the best will happen and a 70%

probability that the most likely out come will occur.

What will be the expected value of profit as per the budget for 2016?

Exercise 21-10 Venkatesh Ltd. is always discarding old lines and introducing new lines of products and is

considering at present three alternative promotional plans for ushering in new products. Various combinations of

prices, development expenditure and promotional outlays are involved in these plans. High, medium and low

forecast of revenues under each plan have been formulated and their respective probabilities of occurrence have

N
been estimated. Their budgeted revenues and probabilities along with other relevant data are : ( ` lakhs)

Particulars Plan I Plan II Plan III

N
Budgeted revenue with probability:

A
High 30 (0.3) 24 (0.2) 50 (0.2)

Medium 20 (0.3) 20 (0.7) 25 (0.5)

M
Low 5 (0.4) 15 (0.1) 0 (0.3)

X
Variable cost as percentage of revenue 60% 75% 70%

Initial investment 25 20 24

A
Life in years 8 8 8

T
The company’s cost of capital is 12% and the income-tax rate is 40%. Investment in promotional programs will be

amortised by the straight line method. The company will have net taxable income each year, regardless of the success

or failure of the new products.

(i) Substantiating with figures, make a detailed analysis and find out which of the promotional plans is expected

to be the most profitable ?

(ii) In the worst event, which of the plans would result in maximizing the profits.

Value of Pe rfe ct Info rm ation

Exercise 21-11 A Ltd. has a choice between three projects X, Y and Z. The following information has been

estimated:

Market demand Profit ( ` ’000)

Projects D D D
1 2 3

X 190 50 15

Y 110 200 160

Z 150 140 110

Probabilities are D = 0.6, D = 0.2, D = 0.2

1 2 3

Which projects should be undertaken if decision is made by expected value approach?

Calculate the expected value of perfect information?

Exercise 21-12 Toys for Tiny Tots Ltd. manufactures high-quality toys for children, which are sold by mail order

and through departmental stores. Kiddy Products is prepared to sell the design and manufacturing rights for three

products. However it will only sell the rights to one product, not two or three. The costs of the rights are:

Pussy Cat = ` 62,500 Teddy Bear = ` 75,000 Jack in Box = ` 52,500

Toys for Tiny Tots Ltd. feel that any of these products would make an attractive addition to its range, though the

products would have a sales life of only one year and wish to select the best of the three products.

The following information has been made available: `

( )

Particulars Pussy Cat Teddy Bear Jack in Box

Selling price p.u. 199 140 115

Variable cost p.u. 98 75 65

Fixed production costs 70,000 95,000 60,000

Advertising 55,000 40,000 20,000

These figures have been worked out with great care and circumspection. But when it comes to sales volumes, the

Sales manager could provide only the following analysis of possibilities:

N
Pussy Cat Teddy Bear Jack in Box

N
Volume Probability Volume Probability Volume Probability

A
(units) (units) (units)

2,000 0.7 Nil 0.1 2,500 0.1

M
3,000 0.2 3,000 0.4 3,000 0.3

4,000 0.1 6,000 0.5 4,000 0.4

X
5,000 0.2

A
You are required to:

(a) Advise the company of the best course of action based on the above information.

T
(b) In the case of Teddy Bear it is felt that the company should launch a market research study costing ` 20,000

which would be able to determine precisely whether the sales would be nil, 3,000 or 6,000 units. Is it worthwhile

to undertake the study? Assume all costs are avoidable.

Exercise 21-13 X Ltd. must choose whether to go ahead with either of two mutually exclusive projects A and B.

The expected profits are as follows: `

( )

Particulars Profit if there is Profit/(Loss) if there is

strong demand weak demand

Project A 4,000 (1,000)

Project B 1,500 500

Probability of demand 0.3 0.7

(i) What would be the decision based on expected values, if no information about demand were available ?

(ii) What is the value of perfect information about the demand ?

Standard Deviation of Cash Fl ows

Exercise 21-14 Pioneer Projects Ltd. is considering accepting one of two mutually exclusive projects X & Y. The

cash flow and probabilities are estimated as under:

 Project X Project Y

Probability Cash flow Probability Cash flow

0.10 12,000 0.10 8,000

0.20 14,000 0.25 12,000

0.40 16,000 0.30 16,000

0.20 18,000 0.25 20,000

0.10 20,000 0.10 24,000

Advise Pioneer Projects Ltd.

Exercise 21-15 Ankit Ltd. is considering to take up Project-X or Project-Y. Both the projects have same life, require

equal investment of ` 80 lakh and have almost same yield. An attempt is made to use Probability Theory to analyze
the pattern of cash flow from either project during first year of operation. This pattern is likely to continue during

life of these projects. The results of analysis are as follows:

Project X Project Y

N
Cash flow ( ) ` Probability Cash flow ( )` Probability

N
12,00,000 0.10 8,00,000 0.10

A
14,00,000 0.20 12,00,000 0.25

16,00,000 0.40 16,00,000 0.30

M
18,00,000 0.20 20,00,000 0.25

20,00,000 0.10 24,00,000 0.10

X
80,00,000 1.00 80,00,000 1.00

A
You are required to decide as to which project is riskier to be dropped by the company.

T
Sensitivity Analysis

Exercise 21-16 X Ltd. is considering a project with the following cash flow: `
( )

Year Purchase of plant Running cost Savings

0 70,000 - -

1 - 20,000 60,000

2 - 25,000 70,000

The cost of capital is 8%. Measure the sensitivity of the project to changes in the level of running cost, savings and

plant cost. Which factor is the most sensitive.

The present values of Re. 1 at 8% for year 1 and year 2 are respectively 0.9259 and 0.8573.

Exercise 21-17 From the following project details calculate the sensitivity of the (a) Project cost, (b) Annual cash

flow, and (c) Cost of capital. Which variable is the most sensitive?

Project cost ` 12,000 Annual cash flow ` 4,500

Life of the project 4 years Cost of capital 14%

The annuity factor at 14% for 4 years is 2.9137 and at 18% for 4 years is 2.6667.
Exercise 21-18 The budget for Product P is given as follows: `
( )

Sales 3,00,000

Direct material 1,00,000

Labour 60,000

Variable overhead 40,000

Fixed overhead 50,000

Profit 50,000

Required: Test the sensitivity of the budget to 10% changes of : (i) Material, (ii) Labour, (iii) Variable overhead,

(iv) Fixed overhead, (v) Sales price, and (vi) Sales volume.

Which is the most sensitive variable ?

Ce rtainty Equivalent (CE)

Exercise 21-19 A Project requires an initial cash outlay of ` 50,000 and offers an annual expected cash inflow of `

N
40,000 for three years and has no salvage value. The risk coefficients for three years are estimated to be 0.80, 0.70 and

0.65 respectively. The risk-free rate of interest is estimated to be 15%.

N
Given the PV factor @ 15% as 0.870 for 1st year, 0.756 for 2nd year, 0.658 for 3rd year.

A
Calculate the NPV of the Project.

M
Exercise 21-20 Delta Corporation is considering an investment in one of the two mutually exclusive proposals:

Project A It involves initial outlay of ` 1,70,000 Project B It requires initial outlay of ` 1,50,000

X
The certainty-equivalent approach is employed in evaluating risky investments. The current yield on treasury bills

A
is 5% and the company uses this as riskless rate. Expected values of net cash inflow with their respective certainty-

equivalents are:

T
Year Project A Project B

Cash inflow Certainty Cash inflow Certainty

`
( ) equivalent `
( ) equivalent

1 90,000 0.8 90,000 0.9

2 1,00,000 0.7 90,000 0.8

3 1,10,000 0.5 1,00,000 0.6

Answer the following with reasons:

(i) Which project should be acceptable to the company ?

(ii) Which project is riskier and why ? Explain.

(iii) If the company was to use the risk-adjusted discount rate method, which project would be analyzed with higher

rate ?
 R isk Adjuste d Disco u nt Rate (RADR)

Exercise 21-21 Determine the risk adjusted net present value of the following projects:

Particulars Project A Project B Project C

`
Net cash outlay ( ) 1,00,000 1,20,000 2,10,000

Project life (years) 5 5 5

Annual cash inflow ( ) ` 30,000 42,000 70,000

Coefficient of variation 0.4 0.8 1.2

The company selects the risk adjusted discount rate (RADR) on the basis of coefficient of variation:

Coefficient of variation 0.0 0.4 0.8 1.2 1.6 2.0 > 2.0

RADR 10% 12% 14% 16% 18% 22% 25%

Exercise 21-22 Fast-run Automobiles Spares Ltd. (FASL) is considering investment in one of three mutually

N
exclusive projects Zeta-10, Meta-10 and Neta-10. The company’s cost of capital is 15% and the risk-free rate of return

is 10%. The income-tax rate for the company is 40%. FASL has gathered the following basic cash-flow and risk index

N
data for each project.

`
( )

A
Project Zeta-10 Meta-10 Neta-10

Initial investment 15,00,000 11,00,000 19,00,000

M
Cash inflows after-tax for year: 1 6,00,000 6,00,000 4,00,000

X
2 6,00,000 4,00,000 6,00,000

3 6,00,000 5,00,000 8,00,000

A
4 6,00,000 2,00,000 12,00,000

T
Risk Index 1.80 1.00 0.60

Using the risk adjusted discount rate, determine the risk adjusted NPV for each of the project. Which project should

be accepted by the company? Give reasons.

Note: Present value of Re. 1 for five years:

Rate Year 1 Year 2 Year 3 Year 4 Year 5

9% 0.9174 0.8417 0.7722 0.7084 0.6499

11% 0.9009 0.8116 0.7312 0.6587 0.5935

13% 0.8850 0.7831 0.6931 0.6133 0.5428

15% 0.8696 0.7561 0.6575 0.5718 0.4972

17% 0.8547 0.7305 0.6244 0.5337 0.4561

19% 0.8403 0.7062 0.5934 0.4987 0.4190

D ecision Tre e

Exercise 21-23 A product with a unit contribution of ` 10 will sell either 4,000 units or 8,000 units with the

probability of 0.5 for each level. But, if additional ` 5,000 were spent on improving the design then the probability
of selling on the higher level would change to 0.7. Alternatively, if ` 1 per unit were spent on better packing and `
500 on promotion propaganda, the probability would yet again change to 0.9 for selling at the higher level. Use a

decision tree to determine the best strategy.

Exercise 21-24 A firm has an investment proposal, requiring an outlay of ` 40,000. The investment proposal is

expected to have 2 years’ economic life with no salvage value. In Year-1, there is a 0.4 probability that cash flow after

tax (CFAT) will be ` 25,000 and 0.6 probability that CAFT will be ` 30,000. The probabilities assigned to CAFT for
the Year-2 are as follows:

If CFAT = ` 25,000 If CFAT = ` 30,000

Amount ( ) ` Probability Amount ( ) ` Probability

12,000 0.2 20,000 0.4

16,000 0.3 25,000 0.5

22,000 0.5 30,000 0.1

The firm uses a 10% discount rate for this type of investment. You are required to:

(a) Present the above information in the form of a decision tree.

(b) Find out the NPV under (a) the worst outcome; and (b) under the best outcome.

(c) Find out the profitability or otherwise of the above investment proposal.

N
Exercise 21-25 Mr. X is trying to decide whether to travel to Sri Lanka from Delhi to negotiate the sale of a shipment

of China novelties. He holds the novelties in stock and is fairly confident but by no means sure that if he makes the

N
trip, he will sell the novelties at a price that will give him a profit of ` 3,00,000. He puts the probability of obtaining
the order at 0.6. If he does not make the trip, he will certainly not get the order.

A
If the novelties are not sold in Sri Lanka, there is an Indian customer, who will certainly buy them at a price that leaves

him a profit of `1,50,000 and his offer will be open at least till Mr. X returns from Sri Lanka. Mr. X estimates the

M
expenses of trip to Sri Lanka at ` 25,000. He is however, concerned that his absence, even for only three days, may
lead to production inefficiencies in the factory. These could cause him to miss the deadline on a contract, with the

X
consequences that a late penalty of ` 1,00,000 will be invoked. Mr. X assesses the probability of missing the deadline
under these circumstances at 0.4. Further, he believes that in his absence, there will be a lower standard of

A
housekeeping in the factory and the raw material and labour costs on the other contract will raise by about ` 20,000

T
above the budgeted figure.

Draw an appropriate decision tree for Mr X’s problem and using the Expected Monetary Value (EMV) as the

appropriate criterion for decision and find the appropriate initial decision.

Exercise 21-26 A company is considering whether to develop and make new product. Development costs are

estimated to be ` 1,80,000 and there is a 0.75 probability that the development effort will be successful and a 0.25

probability that development effort will be unsuccessful. If the development is successful, the product will be

marketed, and it is estimated that:

(i) If the product is very successful profit will be ` 5,40,000.

(ii) If the product is moderately successful profit will be ` 1,00,000.

(iii) If the product is a failure there will be a loss of ` 4,00,000.

Each of the above profit and loss calculation is after taking into account the development costs of ` 1,80,000. The

estimated probabilities of each of the above events are as follows:

Very successful 0.4 Moderately successful 0.3 Failure 0.3

Required: (i) Prepare decision tree, (ii) Offer your comments.

Simulation

Exercise 21-27 Shree Lakshmi Finance Corporation is an investment company. The management of the company

wants to study the investment in a project based on the following three factors: (a) Market demand, (b) Profitability,

and (c) Amount of investment required.

In analyzing a new consumer product, the Corporation estimates the following probability distributions:

Annual Demand Profit per unit Investment required

Units Probability ` Probability ` Probability

20,000 0.05 3.00 0.10 17,50,000 0.25

25,000 0.10 5.00 0.20 20,00,000 0.50

30,000 0.20 7.00 0.40 25,00,000 0.25

35,000 0.30 9.00 0.20

40,000 0.20 10.00 0.10

45,000 0.10

50,000 0.05

The following random numbers are to be used:

(a) For Demand 28 57 60 17 64 20 27 58 61 30

(b) For Profit 19 07 90 02 57 28 29 83 58 41

N
(c) For Investment 18 67 16 71 43 68 47 24 19 97

N
Required: Using simultaneous technique, repeat the trial ten times, compute the return on investment for each trial

considering these three factors into account. Approximately what is the highest likely return ?

A
Exercise 21-28 The top management of a company is considering the problem of marketing a new product. The

investment or the fixed cost, required in the project is ` 15,000. The three factors that are uncertain are the selling

M
price, variable cost and the annual sales volume. The product has a life of only one year. The management has

collected the following data regarding the possible levels of these three factors. The factors are independent of each

X
other:

A
Selling price Probability Variable cost Probability Sales volume Probability

` `

T
per unit ( ) per unit ( ) units

14 0.35 2 0.30 3,000 0.25

15 0.50 3 0.50 4,000 0.40

16 0.15 4 0.20 5,000 0.35

Using the Monte Carlo Simulation, determine the expected profit from the above investment on the basis of 10 trials

and using the following 3 series of ten Random numbers each.

Series 1 : 18, 71, 32, 55, 31, 20, 48, 73, 75, 03

Series 2 : 81, 93, 18, 97, 21, 83, 94, 19, 90, 02

Series 3 : 67, 63, 39, 55, 29, 78, 70, 06, 78, 76

Exercise 21-29 The top management of Zasleen Ltd. is considering the problem of marketing a new product. The

fixed cost required in the project is ` 1,50,000. The three factors that are uncertain are selling price, variable cost and
the annual sales volume. The product has a life of only one year.

The management has collected the following data regarding the possible levels of these three factors:

Selling Probability Variable Probability Sales volume Probability

price/unit ( ) ` cost/unit ( ) ` (units)

(series 1) (series 2) (series 3)

14 0.35 2 0.30 30,000 0.25

15 0.50 3 0.50 40,000 0.40

16 0.15 4 0.50 50,000 0.35

Consider the following three series of random numbers:

Series 1 82 84 28 82 36 92 73 91 63 29 (to be used for selling price)

Series 2 27 26 92 63 83 03 10 39 10 10 (to be used for variable cost)

Series 3 23 57 99 84 51 29 41 11 66 30 (to be used for sales volume)

Required: Using Monte Carlo simulation technique, determine the expected profit for the above project on the basis

of 10 trials.

Adjusted NPV

Exercise 21-30 Madhuri Ltd. is evaluating a project for which the initial investment required is ` 50 lakh to be met
by internally generated funds of ` 10 lakh, from a rights issue of ` 15 lakh and the rest from a term loan @ 12 % per
annum. Rights issue will involve flotation cost of 5% and the term loan processing will cost 1%. Corporate tax rate

is 40%. The risk-free rate of interest is 6.5%, market return is 15% and the relevant asset beta for the investment is

estimated to be 1.5. Net operating cash inflows after tax from the project are:

Year1 - ` 15 lakh; Year 2 - ` 35 lakh; Year 3 - ` 15 lakh.

N
Besides these cash inflows, residual value of ` 5 lakh (net of taxes) is also expected at the end of third year. Should

N
the project be taken up ?

A
NPV of the Project using EVA Ap p ro a c h

` 50

M
Exercise 21-31 Magnavision Corporation Ltd. (MCL) is considering a new project involving an investment of

million for which the following information is available:

X
Project life 4 years

A
Salvage value Nil

Depreciation (for tax purposes) Straight line

T
Annual revenues ` 60 million

Annual costs (excluding depreciation, interest and taxes) ` 40 million

Debt-Equity ratio 4 : 5 Risk-free rate of return 6%

Interest rate on debt (post tax) 9% Market risk premium 8%

Tax rate 40% Beta of MCL’S Equity 1.5

You are required to: (i) Compute the EVA of the project over its life, and (ii) Calculate the NPV of the project using

EVA approach.

Note: Extracted from the table of PV of ` 1

PVIF/Year 0 1 2 3 4

at 14% 1.000 0.877 0.769 0.675 0.592

at 15% 1.000 0.870 0.756 0.658 0.572

 Abandonment Option

Exercise 21-32 Kitkat Ltd. made an investment of ` 65,000 in a new machine that is expected to bring in the

following cash flows in years 1 and 2: `

( )

Particulars Cash flow Cash flow Residual

value

Favourable (60%) 52,000 39,000 2,600

Unfavourable (40%) 26,000 19,500 1,300

Should the environment turnout to be unfavourable, the company will dispose of the machine for a value of ` 32,500
at the end of year 1. They can nevertheless continue with the machine, if they so choose. Reckoning the cost of capital

at 15%, evaluate the overall investment decision, and decide the course of action for the owner of the project.

[Note: Discounting/PV factor for Year 1 = 0.870; Year 2 = 0.756]

Exercise 21-33 The projected cash flows and the expected net abandonment values for a project are given below:

` `

N
Year Cash inflows ( ) Abandonment Value ( )

0 (-) 1,00,000 Nil

N
1 35,000 65,000

A
2 30,000 45,000

3 25,000 20,000

4 20,000 Nil

M
Should the project be abandoned and if so, when? Cost of Capital may be taken as 10%.

X
Given:

A
Year 0 1 2 3 4

T
PV factor @ 10% 1.000 0.909 0.826 0.751 0.683
 Key to Practical Exercises

Probability and Expe cte d Value

Exercise 21-1

Calculation of Expected Value of Cash flow ( ` lakhs)

Project M Project N

Possibilities Cash flow Probability Expected Cash flow Probability Expected

value value

1 7,000 0.1 700 12,000 0.10 1,200

2 8,000 0.2 1,600 8,000 0.10 800

3 9,000 0.3 2,700 6,000 0.10 600

N
4 10,000 0.2 2,000 4,000 0.20 800

5 11,000 0.2 2,200 2,000 0.50 1,000

N
1.0 EV = 9,200 1.00 EV = 4,400

A
Analysis - The expected monetary value of Project M is greater than Project N. Therefore, Project M has a higher

preference for acceptance.

M
Exercise 21-2

X
EV of annual cash flow ( ` lakhs)

Year 1 = 10 × 0.30 + 15 × 0.50 + 20 × 0.20 = 14.50

A
Year 2 = 10 × 0.10 + 20 × 0.30 + 30 × 0.40 + 40 × 0.20 = 27.00

T
Year 3 = 10 × 0.20 + 20 × 0.50 + 30 × 0.30 = 21.00

Calculation of NPV ( ` lakhs)

Year 1 (14.50 × 0.8696) 12.61

Year 2 (27.00 × 0.7561) 20.41

Year 3 (21.00 × 0.6575) 13.81

Total P.V. 46.83

Less: Cost of new machine 42.00

NPV 4.83

Analysis - Since NPV of the proposal is positive, it is suggested to purchase the new machine.

Exercise 21-3

Determination of Price Bid at which Profits can be maximized for 8,000 units `
( )

Selling Variable Contribution p.u. Total Probability Expected value of

price p.u. cost p.u. contribution contribution

90 64 26 2,08,000 1.00 2,08,000

100 64 36 2,88,000 0.95 2,73,600

110 64 46 3,68,000 0.85 3,12,800

120 64 56 4,48,000 0.65 2,91,200

130 64 66 5,28,000 0.40 2,11,200

140 64 76 6,08,000 0.15 91,200

150 64 86 6,88,000 0.05 34,400

∴ Profit is maximum at a price of ` 110.

Exercise 21-4

To break-even, the company must earn enough total contribution to cover its fixed costs. The contribution to fixed

costs and profit is ` 2.50 per unit (i.e. 6 - 3.5).

Contribution required ` 34,000

To break-even, sales must be = = = 13,600 units
Contribution per unit ` 2.50

The probability that sales will equal or exceed 13,600 units is the probability that sales will be 14,000, 16,000 or 18,000

units, which is (0.25 + 0.30 + 0.20) = 0.75 or 75%

To earn profit of `10,000, the company must earn enough contribution to cover its fixed costs ( ` 34,000) and then
make the profit, so total contribution must be ` 44,000.
To earn this contribution, sales must be = ` 44,000/2.50 = 17,600 units

The probability that sales will equal or exceed 17,600 units is the probability of sales being 18,000 units, which is

0.20 or 20%.

Exercise 21-5

N
Expected Profit

` 7,400

N
Product X = 0.20 (- 8,000) + 0.10 (-5,000) + 0.30 (11,000) + 0.20 (14,000) + 0.20 (17,000) =

Product Y = 0.15 (-12,000) + 0.15 (-10,000) + 0.40 (14,000) + 0.20 (16,000) + 0.10 (18,000) = ` 7,300

A
Analysis - Based on the above data, the choice will be made for Product X.

Exercise 21-6

M
The different outcomes for fixed cost are mutually exclusive events. If fixed costs are ` 50,000 for example, they can’t

X
be anything else as well.

Budgeted sales = 20,000 units Budgeted unit contribution = 15 - 10 = ` 5

A
`
( )

T
Budgeted total contribution (20,000 × 5) 1,00,000

Target profit 25,000

Maximum fixed costs if target is to be achieved 75,000

The probability that fixed costs will be ` 75,000 or less is:

= P (50,000 or 60,000 or 70,000) = P (50,000) + P (60,000) + P (70,000) = 0.1 + 0.3 + 0.3 = 0.7 or 70%

Exercise 21-7

Sales revenue = F.C. + V.C. - Loss = 3,60,000 + 9,60,000 - 1,20,000 = ` 12,00,000

Selling price per unit = ` 12,00,000/1,20,000 units = ` 10

Contribution per unit = ` 10 - ` 8 = ` 2 Break-even point units = ` 3,60,000/` 2 = 1,80,000 units

(i) Calculation of probability that the company will continue to make losses

Sales units Probability

1,20,000 0.10

1,44,000 0.15

1,68,000 0.20

0.45

(ii) Probability that the company will make a profit of atleast ` 72,000

Desired sales = ( ` 3,60,000 + ` 72,000)/` 2 = 2,16,000 units

The probability for sales units being 2,16,000 units is 0.25.

Exercise 21-8

Computation of Expected Sales of the Products

Product 1 Product 2

Units Probability Total Units Probability Total

50,000 0.1 5,000 50,000 0.2 10,000

75,000 0.2 15,000 75,000 0.3 22,500

1,00,000 0.3 30,000 1,00,000 0.2 20,000

1,25,000 0.3 37,500 1,25,000 0.1 12,500

1,50,000 0.1 15,000 1,50,000 0.1 15,000

2,25,000 0 - 2,25,000 0.1 22,500

1,02,500 1,02,500

Both the products have the same expected sales of 1,02,500 units, same break-even point of 1,00,000 units and same

expected profit of ` 10,000 (i.e. 2,500 × 4). However, Product 2 seems to be riskier than Product 1 since the probability
of sales being 1,00,000 units is 0.2 only in case of Product 2 as compared to 0.3 in case of Product 1. Moreover, Product

N
2 has a total probability 0.5 of sales being less than 1,00,000 units as compared to 0.3 in case of Product 2. Product

2 has, therefore, more chances of making a loss as compared to Product 1. Product 2 has also more variation in its

N
sales as compared to Product 1. Thus, on the whole if the firm wants to have less risk, it will prefer Product 1.

A
Pessimistic, Most Likely and Optimistic Estimate s

Exercise 21-9

M
Profitability Statement Under Three Estimates `
( )

X
Pessimistic Most Likely Optimistic

8,000 units 10,000 units 15,000 units

A
Selling price (per unit) 19 20 20

T
Variable cost (per unit) 12.50 12 11

Sales 1,52,000 2,00,000 3,00,000

Less: Variable cost 1,00,000 1,20,000 1,65,000

Contribution 52,000 80,000 1,35,000

Less: Fixed cost 60,000 50,000 48,000

Profit (loss) (8,000) 30,000 87,000

Calculations of Expected Value of Profit

Outcome Profit/(loss) Probability Expected

`
( ) value

Pessimistic (8,000) 0.2 (1,600)

Most likely 30,000 0.7 21,000

Optimistic 87,000 0.1 8,700

Expected value of profit 28,100

Exercise 21-10

(i) Statement of Profitability of Different Plans `

( )

Particulars Plan I Plan II Plan III

Budgeted revenue with probability:

High 9,00,000 4,80,000 10,00,000

Medium 6,00,000 14,00,000 12,50,000

 `
( )

Particulars Plan I Plan II Plan III

Low 2,00,000 1,50,000 -

Expected revenue 17,00,000 20,30,000 22,50,000

Contribution(%) 40% 25% 30%

Contribution 6,80,000 5,07,500 6,75,000

Less: Depreciation 3,12,500 2,50,000 3,00,000

PBT 3,67,500 2,57,500 3,75,000

Less: Tax @ 40% 1,47,000 1,03,000 1,50,000

PAT 2,20,500 1,54,500 2,25,000

Add: Depreciation 3,12,500 2,50,000 3,00,000

Average yearly cash inflow 5,33,000 4,04,500 5,25,000

P.V. factor @ 12% for 8 years 4.9676 4.9676 4.9676

N
P.V. of Cash inflows 26,47,731 20,09,394 26,07,990

Initial investment 25,00,000 20,00,000 24,00,000

N
Net present value 1,47,731 9,394 2,07,990

A
Profitability Index 1.059 1.005 1.087

Plan III has the highest present value index and also the highest NPV, hence most profitable.

M
(ii) Computation of maximum loss under different plans `
( )

X
Particulars Plan I Plan II Plan III

A
Low forecast 5,00,000 15,00,000 -

Contribution(%) 40 25 30

T
Contribution 2,00,000 3,75,000 -

Less: Depreciation 3,12,500 2,50,000 3,00,000

Profit/(loss) (1,12,500) 1,25,000 3,00,000

Less: Tax/(Tax shield) @ 40% 45,000 50,000 (1,20,000)

Net profit after tax (loss) (67,500) 75,000 (1,80,000)

Add: Depreciation 3,12,500 2,50,000 3,00,000

Annual cash inflow 2,45,000 3,25,000 1,20,000

P.V. factor @ 12% for 8 years 4.9676 4.9676 4.9676

P.V. of cash inflows 12,17,062 16,14,470 5,96,112

Initial outlay 25,00,000 20,00,000 24,00,000

Net present value (12,82,938) (3,85,530) (18,03,888)

Analysis - From the above calculations it is observed that the negative NPV is the lowest in case of Plan II. Hence it

is comparatively better.

Value of Pe rfe ct Info rm ation

Exercise 21-11

The elements of the material should be identified-profits, demand, probabilities, action (Project X, Y or Z) and

outcomes (expected values).

 Profit EV

Particulars ( ` ’000) Probability ( ` ’000)

Project X D 190 0.6 114

1

D 50 0.2 10
2

D 15 0.2 3
3

EV = 127

Project Y D 110 0.6 66

1

D 200 0.2 40
2

D 160 0.2 32
3

EV = 138

Project Z D 150 0.6 90

1

D 140 0.2 28
2

D 110 0.2 22
3

EV = 140

N
Analysis - Project Z should be chosen because it has the highest EV of ` 1,40,000.

N
Perfect Information: In order to obtain perfect information about future states of demand from market researchers,

a company has to pay for the information. The maximum value of this perfect information will be equal the EV with

A
the information less the EV without information.

Demand Choose Profit ( ` ’000) Probability EV ( ` ’000)

M
D X 190 0.6 114
1

X
D Y 200 0.2 40
2

D Y 160 0.2 32

A
3

EV with Perfect Information = 186

T
∴ EV of the Perfect Information = 186 - 140 = ` 46 i.e. ` 46,000

Exercise 21-12

(a) Statement of Expected Profit from Different Products ( )`

Particulars Pussy Cat Teddy Bear Jack in Box

Expected sales (units) (Volume × Probability) 1,400 - 250

600 1,200 900

400 3,000 1,600

- - 1,000

Total sales (units) 2,400 4,200 3,750

Contribution per unit (Selling price - Variable cost) 101 65 50

Total contribution (a) 2,42,400 2,73,000 1,87,500

Total fixed costs:

Cost of rights 62,500 75,000 52,500

Fixed production costs 70,000 95,000 60,000

Advertising 55,000 40,000 20,000

Total costs (b) 1,87,500 2,10,000 1,32,500

Expected profit (a) - (b) 54,900 63,000 55,000

The above table shows that the highest expected profit arises from acquiring the rights to manufacture Teddy Bear.

Statement of Expected Profit from Teddy Bear at Different Sales Levels `

( )

Sales × Unit Total Fixed cost Profit Probability Expected profit

contribution contribution (Loss) (Loss)

0 0 2,10,000 (2,10,000) 0.1 (21,000)

3,000 × 65 1,95,000 2,10,000 15,000 0.4 (6,000)

6,000 × 65 3,90,000 2,10,000 1,80,000 0.5 90,000

63,000

The above table shows that there are equal chances of profit or loss. If sales are 0 to 3,000 (combined probability is

0.5 (i.e. 0.1 + 0.4) there will be losses. If sales are 6,000 (probability 0.5) there will be substantial profit.

(b) It is worth while to spend ` 20,000 on market research in respect of the product Teddy Bear since all costs are

avoidable. This will help in substituting a product expected to make a loss by a product which is expected to make

a profit. For example, if the survey shows that sales of Teddy Bear will not exceed 3,000 units, the company can go

to next best product Jack in Box. The company’s net cost of survey would amount only to ` 14,000 (i.e. 20,000 less
` 6,000). Moreover, the product Jack in Box gives a profit of ` 55,000. If a decision is taken to purchase

N
loss avoided

the rights of Jack in Box, the company would finally end with additional net profit of ` 41,000 (i.e. ` 55,000 - ` 14,000).

N
Exercise 21-13

A
(i) If there were no information to help with the decision, the project with the higher EV of profit would be

selected. `
( )

M
Project A Project B

X
Probability Profit EV Profit EV

0.3 4,000 1,200 1,500 450

A
0.7 (1,000) (700) 500 350

T
1.0 500 800

As the EV of B is more than those of project A, therefore project B would be selected.

Option of project B is clearly the better option, if the demand turns out to be weak. However, if the demand

were to turn out to be strong. Project A would be more profitable. There is a 30% chance that this could happen.

(ii) Perfect information will indicate for certain whether demand will be weak or strong. If demand is forecast as

‘weak’, project B would be selected. If the demand is projected as ‘strong’, project A would be selected. Perfect

information would improve the profit from ` 1,500 which would have been earned, by selecting B to ` 4,000
from A.

Forecast demand Probability Project chosen Profit EV of profit

Weak 0.7 B 500 350

Strong 0.3 A 4,000 1,200

EV of profit with perfect information 1,550

`
( )

EV of profit without perfect information (i.e. choose B all the time) 800

EV of profit with perfect information 1,550

Value of perfect information 750

Suggestion - Provided that the information does not cost more than ` 750 to collect, it would be worth it.
 Standard Dev i ation of Cash Fl ow s

Exercise 21-14

Calculation of Standard Deviation

Project X

p x EV (x - Y) (x - Y) 2
p(x - Y) 2

(x × p) (’000)

0.10 12,000 1,200 -4 16 1.6

0.20 14,000 2,800 -2 4 0.8

0.40 16,000 6,400 0 0 0

0.20 18,000 3,600 2 4 0.8

0.10 20,000 2,000 4 16 1.6

Y = 16,000 Variance = 4.8

Standard Deviation ( σ) =   = 2.19

N
σ 2.19
Coefficient of Variation = × 100 = × 100= 13.68%

N
EV 16

Project Y

A
p x EV (x - Y) (x - Y) 2
p(x - Y) 2

(x × p) (’000)

M
0.10 8,000 800 -8 64 6.4

X
0.25 12,000 3,000 -4 16 4.0

0.30 16,000 4,800 0 0 0

A
0.25 20,000 5,000 4 16 4.0

T
0.10 24,000 2,400 8 64 6.4

Y = 16,000 Variance = 20.8

Standard Deviation ( σ) =  = 4.56

σ 4.56
Coefficient of Variation = × 100 = × 100 = 28.58%
EV 16

Analysis - Project Y is more risky as it is more succeptible to wider degree of variation around the most likely outcome

than Project X. Therefore, Project X should be preferred.

Exercise 21-15

Calculation of Standard Deviation ( ` lakhs)

Project X

Cashflow Probability EV (x - Y) (x - Y) 2
p(x - Y) 2

x p (x × p)

12 0.1 1.2 - 4 16 1.6

14 0.2 2.8 - 2 4 0.8

16 0.4 6.4 0 0 0

18 0.2 3.6 + 2 4 0.8

20 0.1 2.0 + 4 16 1.6

80 EV = 16 Variance = 4.8

Y = 80/5 = 16 Standard Deviation of Project X =  = ` 2.19 lakhs

Project Y

Cashflow Probability EV (x - Y) (x - Y)
2
p(x - Y)
2

x p (x × p)

8 0.10 0.8 - 8 64 6.4

12 0.25 3.0 - 4 16 4.0

16 0.30 4.8 0 0 0

20 0.25 5.0 + 4 16 4.0

24 0.10 2.4 + 8 64 6.4

80 EV = 16 Variance = 20.8

Y = 80/5 = 16 Standard Deviation of Project Y =  = ` 4.56 lakhs

Standard Deviation
Coefficient of Variation = × 100
EV of Cash flow

2.19
Project X = × 100 = 13.69%
16

N
4.56
Project Y = × 100 = 28.5%
16

N
Analysis - Project Y is more risky than Project X and the risk involved in it is more than double.

A
S ensitivity An a l ysis

M
Exercise 21-16

`
( )

X
P.V. of Savings

A
Year 1 (60,000 × 0.9259) 55,554

Year 2 (70,000 × 0.8573) 60,011

T
1,15,565

Less: P.V. of Running Cost

Year 1 (20,000 × 0.9259) 18,518

Year 2 (25,000 × 0.8573) 21,432 39,950

Net savings 75,615

Less: Purchase cost of plant 70,000

Net present value 5,615

(a) Sensitivity for Plant Cost: If the purchase cost of plant increases by ` 5,615, the NPV of the project will become
zero. The sensitivity for plant cost is:

5,615
× 100 = 8.02%
70,000

(b) Sensitivity for Running Cost: If the present value of running cost increases by ` 5,615, the NPV of the project will
become zero. Therefore, the sensitivity for running cost is:

5,615
× 100 = 14.06%
39,950

(c) Sensitivity for Savings: If the savings decrease by ` 5,615, the NPV becomes zero. Therefore, the sensitivity for
savings is:

5,615
× 100 = 4.86%
1,15,565

Analysis - Savings is most sensitive.

Exercise 21-17

`
( )

Annual cash inflow (4,500 × 2.9137) 13,112

Less: Project cost 12,000

Net present value 1,112

(i) Sensitivity for project cost - If the project cost is increased by ` 1,112, the NPV of the project will become zero.
Therefore, sensitivity for project cost is:

1,112
× 100 = 9.27%
12,000

(ii) Sensitivity for annual cash inflow - If the present value of annual cash inflow is lower by ` 1,112, the NPV of the
project will become zero. Therefore, the sensitivity for annual cash flow is:

1,112
× 100 = 8.48%
13,112

(iii) Sensitivity for cost of capital - Let ‘x’ be the annuity factor which gives a zero NPV i.e. ‘x’ is the IRR

N
-12,000 + 4,500x = 0

4,500x = 12,000

N
x = 12,000/4,500 = 2.6667

A
Hence, x = 2.6667 and at 18% for 4 years, the annuity factor is 2.6667

18% - 14%
Sensitivity % = = 29%

M
14%

Analysis - The cash inflow is more sensitive, since only 8.5% change in cash inflow will make the NPV of the project

X
zero.

A
Exercise 21-18

T
Sensitivity = Change in profit ÷ Original profit (expressed as a %)

Material 29% (10,000/50,000) Fixed overheads 10% (5,000/50,000)

Labour 12% (6,000/50,000) Sales price 60% (30,000/50,000)

Variable overheads 8% (4,000/50,000) Sales volume 20% (10,000/50,000)

So, selling price is the most sensitive element.

`
( )

Revised sale 3,30,000

Material (revised) 1,10,000

Labour (revised) 66,000

Variable overhead (revised) 44,000

Fixed overhead 50,000

Profit 60,000

Increase in profit due to volume increase of sales = ` 60,000 - ` 50,000 = ` 10,000

 Ce rtainty Equivalent (CE)

Exercise 21-19

Calculation of risk adjusted NPV `

( )

Year Cash Risk Certainty P.V. factor Present

flow coefficient equivalent @ 15% values

1 40,000 0.80 32,000 0.870 27,840

2 40,000 0.70 28,000 0.756 21,168

3 40,000 0.65 26,000 0.658 17,108

Total present value 66,116

Less: Initial cash outflow 50,000

Risk adjusted NPV 16,116

Exercise 21-20

N
Determination of NPV

Project A

N
Year Cash inflows Certainty Adjusted P.V. factor Total P.V.

` ` `

A
( ) equivalent cash inflow ( ) @ 5% ( )

1 90,000 0.8 72,000 0.9524 68,573

M
2 1,00,000 0.7 70,000 0.9070 63,490

3 1,10,000 0.5 55,000 0.8638 47,509

X
1,79,572

A
∴ NPV = 1,79,572 - 1,70,000 = ` 9,572

T
Project B

Year Cash inflows Certainty Adjusted P.V. factor Total P.V.

`
( ) equivalent cash inflow ( )` @ 5% `
( )

1 90,000 0.9 81,000 0.9524 77,144

2 90,000 0.8 72,000 0.9070 65,304

3 1,00,000 0.6 60,000 0.8638 51,828

1,94,276

∴ NPV = 1,94,276 - 1,50,000 = ` 44,276

Analysis: (a) Project B should be acceptable as its NPV is greater. (b) Project A is riskier because its certainty

equivalents are lower. (c) Project A being more risky, as it would be analyzed with higher discount rate.

R isk Adjuste d Disco u nt Rate (RADR)

Exercise 21-21

Calculation of Risk Adjusted Cash Flow

Project Annual Coefficient of Risk adjusted P.V. factor Discounted

cash inflow variation rate of discount 1 - 5 years cash inflow

A 30,000 0.4 12% 3.6048 1,08,144

B 42,000 0.8 14% 3.4331 1,44,190

C 70,000 1.2 16% 3.2743 2,29,201

Calculation of NPV of Projects

Project A = 1,08,144 - 1,00,000 = ` 8,144

Project B = 1,44,190 - 1,20,000 = ` 24,190
Project C = 2,29,201 - 2,10,000 = ` 19,201

Exercise 21-22

The Risk Adjusted Discount Rate (RADR) is determined by the following formula:

RADR = R + [R × (K - R )]
f i 0 f

Where, R = Risk free rate K = Cost of capital R = Risk index for the project
f 0 i

Zeta-10 = 10 + [1.80 × (0.15 - 0.10)] = 0.19 or 19%

Meta-10 = 10 + [1.00 × (0.15 - 0.10)] = 0.15 or 15%

Neta-10 = 10 + [0.60 × (0.15 - 0.10)] = 0.13 or 13%

Calculation of Risk Adjusted NPV of Three Projects

Zeta-10 `
( lakhs)

N
Year Cash inflows after tax P.V. factor @ 19% Present value

N
1 6 0.8403 5.0418

2 6 0.7062 4.2372

A
3 6 0.5934 3.5604

4 6 0.4987 2.9922

M
Total P.V. of Cash Inflows 15.8316

X
Less: Total Investment 15.0000

NPV 0.8316

A
`

T
Meta-10 ( lakhs)

Year Cash inflows after tax P.V. factor @ 15% Present value

1 6 0.8696 5.2176

2 4 0.7561 3.0244

3 5 0.6575 3.2875

4 2 0.5718 1.1436

Total P.V. of Cash Inflows 12.6731

Less: Total Investment 11.0000

NPV 1.6731

Neta-10 `
( lakhs)

Year Cash inflows after tax P.V. factor @ 13% Present value

1 4 0.8850 3.5400

2 6 0.7831 4.6986

3 8 0.6931 5.5448

4 12 0.6133 7.3596

Total P.V. of Cash Inflows 21.1430

Less: Total Investment 19.0000

NPV 2.143

Analysis - From the above calculations it is observed that NPV of Neta-10 is highest and hence project Neta-10 is

suggested to be implemented.
 D ecision Tre e

Exercise 21-23

Let us draw the Decision tree as under:

` `

0.5 4,000 × ` 10 = 20,000

Do Nothing 60,000

0.5
8,000 × ` 10 = 40,000

0.3 4,000 × ` 10 = 12,000

` 5,000
START Improve Design 68,000

0.7
8,000 × ` 10 = 56,000
`
5
0
0

Better packing + 0.1

4,000 × `9 = 3,600

Promotion 68,400

propaganda 0.9
8,000 × `9 = 64,800

N
From the above Decision tree, the outcomes are interpreted as under: ( ) `

N
State Cash inflow Cost Expected value of

net contributions

A
Do Nothing 60,000 - 0 = 60,000

Improve Design 68,000 - 5,000 = 63,000

M
Better packing + Promotion propaganda 68,400 - 500 = 67,900

X
Analysis - Since the better packing and promoting propaganda of the product leads to the highest net expected value

of contribution i.e. ` 67,900 so it is the best strategy for the firm.

A
Exercise 21-24

T
Year 1 Year 2 Path No. Joint probability

Year 1 and Year 2

0.2 12,000 1 0.08

` 25,000
0.3 16,000 2 0.12

Cash outlay

` 40,000 0.5 22,000 3 0.20

0.4 20,000 4 0.24

0.5 25,000 5 0.30

` 30,000
0.1 30,000 6 0.06

1.00

The decision tree given above shows that there are six possible outcomes each represented by a path.

(ii) The Net Present Value (NPV) of each path at 10% discount rate is given below: ( ) `
Path P.V. of cash inflow P.V. of cash inflow P.V. of total Cash N.P.V.

of year 1 of year 2 cash inflow outflow

1 25,000 × 0.909 = 22,725 12,000 × 0.826 = 9,912 32,637 40,000 - 7,363

2 25,000 × 0.909 = 22,725 16,000 × 0.826 = 13,216 35,941 40,000 - 4,059

3 25,000 × 0.909 = 22,725 22,000 × 0.826 = 18,172 40,897 40,000 897

4 30,000 × 0.909 = 22,270 20,000 × 0.826 = 16,520 43,790 40,000 3,790

5 30,000 × 0.909 = 22,270 25,000 × 0.826 = 20,650 47,920 40,000 7,920

6 30,000 × 0.909 = 22,270 30,000 × 0.826 = 24,780 52,050 40,000 12,050

 (a) If the worst outcome is realized, the NPV which the project will yield is ` 7,363 (negative).

(b) The best outcome will be path 6 when NPV is highest i.e. ` 12,050 (positive).

(iii) Statement showing the Expected Net Present Value

Path NPV @ 10% Joint probability Expected PV

(a) (b) (a) × (b)

1 - 7,363 0.08 - 589.04

2 - 4,059 0.12 - 487.08

3 897 0.20 179.40

4 3,790 0.24 909.60

5 7,920 0.30 2,376.00

6 12,050 0.06 723.00

Expected NPV 1.00 3,111.88

Suggestion - Since the expected NPV is positive, it is suggested to accept the project.

N
Exercise 21-25

Calculation of EMV by following roll-back technique:

N
At A = 3,00,000 × 0.6 + 1,50,000 × 0.4 = 1,80,000 + 60,000 = 2,40,000

A
At B = 3,00,000 × 0.6 + 1,50,000 × 0.4 = 1,80,000 + 60,000 = 2,40,000

At C = (2,40,000 × 0.6) + (2,40,000 × 0.4) - (1,00,000 × 0.4) = 1,44,000 + 96,000 - 40,000 = 2,00,000

M
A + D (Go) = 2,00,000 - (25,000 + 20,000) = 2,00,000 - 45,000 = 1,55,000

A + D (Not go) = 1,50,000

A X
Order obtained

† 3,00,000

0.6

T
A
t

†
p
e

Sell to Indian customer

k
e

†
n

1,50,000
li

0.4
d

.6
a

0
e
D

C
†

D
e
a
d
li
n
o

e
G

(-

m
0

0
0

Order obtained
1
,0

is
.4
0

,0

†
5

s
,0

3,00,000
0

e
2

,0

d
0
)

0.6
0
(-

0
)

)
(-

D
B

Order not obtained

† Sell to Indian customer 1,50,000

0.4
N
o
t
G
o

Sell to Indian customer

† 1,50,000

Analysis - Hence ‘x’ should proceed to Sri Lanka, as the EMV will be ` 1,55,000 if he goes, as against the EMV of

` 1,50,000 if he does not go.

Exercise 21-26

(i) Decision Tree

Possible Probability Payoff

outcomes (Profit) expected

(P = 0.4) Very successful

† ` 5,40,000 0.300 ` 1,62,000

(p = 0.3) Moderately successful

† ` 1,00,000 0.225 ` 22,500
t

†
n
e
m

s
p

d
lo

e
c
e

c
v

su
e
D

(p = 0.75) (p = 0.3) Failure

† ( ` 4,00,000) 0.225 ( ` 90,000)
†
t
c
u
d
ro

N
p
p

(p = 0.25) Development fails

lo

` 1,80,000) ` 45,000)
e

†
v

( 0.250 (
e
D

N
1.000 ` 49,500

M A
Do not develop product

X
† 0 0.000 0

A
(ii) Comments - The total expected value for the decision to develop the product is ` 49,500. It is assumed that there

T
are no other alternatives available except inaction, i.e. not to develop - which will yield a zero value. As against

the zero value, it is obviously preferable that the product be developed. However, it does not mean that an

outcome of ` 49,500 profit is guaranteed. The expected value calculation indicates that if the probabilities are
correct and the decision was repeated on many occasions, an average profit of ` 49,500 would result.

Simulation

Exercise 21-27

The return per annum can be determined by the formula:

Return (R) = [Profit per unit × No. of units demanded] ÷ Investment

To determine a cumulative probability distribution corresponding to each of the three factors, we assign an

appropriate set of random numbers representing each of the three factors as shown hereinafter:

Allocation of Random Numbers for Annual Demand

Annual demand Probability Cumulative Random number

probability interval

20,000 0.05 0.05 00-04

25,000 0.10 0.15 05-14

30,000 0.20 0.35 15-34

35,000 0.30 0.65 35-64

40,000 0.20 0.85 65-84

45,000 0.10 0.95 85-94

50,000 0.05 1.00 95-99

Allocation of Random Numbers for Profit per Unit

Profit per unit Probability Cumulative Random number

probability interval

3.00 0.10 0.10 00-09

5.00 0.20 0.30 10-29

7.00 0.40 0.70 30-69

9.00 0.20 0.90 70-89

10.00 0.10 1.00 90-99

Allocation of Random Numbers for Investment required

Investment Probability Cumulative Random number

required probability interval

17,50,000 0.25 0.25 00-24

20,00,000 0.50 0.75 25-74

N
25,00,000 0.25 1.00 75-99

The simulation worksheet is prepared for 10 trials. The simulated return (r) is also calculated by using the above

N
formula. The results of simulation are as follows:

A
Simulation for 10 Trails

Trail R.N. for Simulated R.N. for Simulated Simulated R.N. for Simulated Return on

M
No. demand demand profit profit p.u. total profit investment investment investment

(000 units) `
( ) (` 000) (` 000) (%)

X
1 28 30 19 5.00 150 18 1,750 8.57

2 57 35 07 3.00 105 67 2,000 5.25

A
3 60 35 90 10.00 350 16 1,750 20.00

T
4 17 30 02 3.00 90 71 2,000 4.50

5 64 35 57 7.00 245 43 2,000 12.25

6 20 30 28 5.00 150 68 2,000 7.50

7 27 30 29 5.00 150 47 2,000 7.50

8 58 35 83 9.00 315 24 1,750 18.00

9 61 35 58 7.00 245 19 1,750 14.00

10 30 30 41 7.00 210 97 2,500 8.40

From the above simulation, we can observe that the highest likely return is 20% and its corresponding demand is

35,000 units, resulting in a profit of ` 10 per unit and the investment required to meet the demand is ` 17,50,000.

Exercise 21-28

Allocation of Random Numbers for Selling Price

Selling price Probabilities Cumulative Random

`
( /unit) probability numbers

14 0.35 0.35 00-34

15 0.50 0.85 35-84

16 0.15 1.00 85-99

Allocation of Random Numbers for Variable Cost

Variable cost Probabilities Cumulative Random

`
( /unit) probability numbers

2 0.30 0.30 00-29

3 0.50 0.80 30-79

4 0.20 1.00 80-99

Allocation of Random Numbers for Sales Volume

Sales volume Probabilities Cumulative Random

(units) probabilities numbers

3,000 0.25 0.25 00-24

4,000 0.40 0.65 25-64

5,000 0.35 1.00 65-99

Calculation of Expected Profit using Monte Carlo Simulation on the basis of 10 trails

N
Trail Series 1 Selling Series 2 Variable Series 3 Sales Fixed Profit

No. R.N. price R.N. cost R.N. volume cost

N
`
( ) `
( ) (units) `
( ) `
( )

A
1 18 14 81 4 67 5,000 15,000 35,000

2 71 15 93 4 63 4,000 15,000 29,000

M
3 32 14 18 2 39 4,000 15,000 33,000

X
4 55 15 97 4 55 4,000 15,000 29,000

5 31 14 21 2 29 4,000 15,000 33,000

A
6 20 14 83 4 78 5,000 15,000 35,000

T
7 48 15 94 4 70 5,000 15,000 40,000

8 73 15 19 2 06 3,000 15,000 24,000

9 75 15 90 4 78 5,000 15,000 40,000

10 03 14 02 2 76 5,000 15,000 45,000

3,43,000

Expected profit = 3,43,000/10 = ` 34,300

Exercise 21-29

Selling price Probability Cumulative Random Numbers

`
( ) probability assigned

14 0.35 0.35 00 - 34

15 0.50 0.85 35 - 84

16 0.15 1.00 85 - 99

Variable cost ( ) `
2 0.30 0.30 00 - 29

3 0.50 0.80 30 - 79

4 0.20 1.00 80 - 99
 Selling price Probability Cumulative Random Numbers

`
( ) probability assigned

Sales volume

(units)

30,000 0.25 0.25 00 - 34

40,000 0.40 0.65 35 - 84

50,000 0.35 1.00 85 - 99

Simulation using 3 series of 10 Random numbers each

Run Random Price Random Variable Random Sales Fixed Profit

numbers `
( ) numbers cost numbers units cost `
( )

Series 1 Series 2 `
( ) Series 3 `
( )

(1) (2) (3) (4) (5) (6) (7) (2)-(4)× (6)-(7)

1 82 15 27 2 23 30,000 1,50,000 2,40,000

N
2 84 15 26 2 57 40,000 1,50,000 3,70,000

3 28 14 92 4 99 50,000 1,50,000 3,50,000

N
4 82 15 63 3 84 40,000 1,50,000 3,30,000

A
5 36 15 83 4 51 40,000 1,50,000 2,90,000

6 92 16 03 2 29 40,000 1,50,000 4,10,000

M
7 73 15 10 2 41 40,000 1,50,000 3,70,000

8 91 16 39 3 11 30,000 1,50,000 2,40,000

X
9 63 15 10 2 66 40,000 1,50,000 3,70,000

A
10 29 14 10 2 30 40,000 1,50,000 3,30,000

T
33,00,000

Therefore, the expected profit (average) = 33,00,000/10 = ` 3,30,000

Working Notes

Profit = (Selling price - Variable cost) × Sales volume - Fixed cost

`
( )

Trial 1 = (15 - 2) × 30,000 - 1,50,000 = 2,40,000

2 = (15 - 2) × 40,000 - 1,50,000 = 3,70,000

3 = (14 - 4) × 50,000 - 1,50,000 = 3,50,000

4 = (15 - 3) × 40,000 - 1,50,000 = 3,30,000

5 = (15 - 4) × 40,000 - 1,50,000 = 2,90,000

6 = (16 - 2) × 40,000 - 1,50,000 = 4,10,000

7 = (15 - 2) × 40,000 - 1,50,000 = 3,70,000

8 = (16 - 3) × 30,000 - 1,50,000 = 2,40,000

9 = (15 - 2) × 40,000 - 1,50,000 = 3,70,000

10 = (14 - 2) × 40,000 - 1,50,000 = 3,30,000

 Adjuste d N P V

Exercise 21-30

Initial investment required = ` 50,00,000 Equity shares through rights issue = ` 15,00,000

Internal accruals = ` 10,00,000 12% Term loan = ` 25,00,000

Corporate tax rate = 40% Market rate of return (R ) = 15%

m

Risk-free rate of interest (R )

f
= 6.5% Beta of the investment ( β) = 1.5

K
e
= R +
f
β (R m
- R)
f
= 6.5 + 1.5 (15 - 6.5) = 19.25%

Calculation of NPV at 19.25%

15,00,000 35,00,000 15,00,000 + 5,00,000

= + + - 50,00,000
1 2 3
(1.1925) (1.1925) (1.1925)

15,00,000 35,00,000 20,00,000

= + + - 50,00,000
1.1925 1.422 1.696

= (12,57,862 + 24,61,322 + 11,79,245) - 50,00,000 = 48,98,429 - 50,00,000 = - ` 1,01,571

N
Impact of Financing

` 25,00,000

N
Loan amount = = ` 25,25,253
(1 - 0.01)

A
Tax shield = ` 25,25,253 × 12/100 × 40/100 = ` 1,21,212 p.a.

P.V. of tax shield (for 3 years @ 12%) = ` 1,21,212 × 2.4018 = ` 2,91,127

M
Cost of Rights issue = ` 15,00,000 × 5/95 = ` 78,947
Cost of Debt = ` 25,00,000 × 1/99 = ` 25,253

X
Calculation of Adjusted NPV ( ) `

A
Base NPV (negative) 1,01,571

T
Add: Floatation cost of rights issue 78,947

Processing cost of term loan 25,253

2,05,771

Less: Tax shield 2,91,127

Adjusted NPV 85,356

Suggestion - Since adjusted NPV is positive, it is suggested to take up the project.

NPV of the Project using EVA Ap p ro a c h

Exercise 21-31

Calculation of Cost of Equity = 6% + 1.5(8%) = 18%

  ×   +   ×  
Calculation of WACC =     = 0.04 + 0.10 = 0.14 or 14%
     

Calculation of Economic Value Added ( ` million)

Years 1 2 3 4

Revenues 60.00 60.00 60.00 60.00

Less: Costs 40.00 40.00 40.00 40.00

PBIDT 20.00 20.00 20.00 20.00

Less: Depreciation 12.50 12.50 12.50 12.50

PBIT 7.50 7.50 7.50 7.50

 `
( million)

Years 1 2 3 4

Less: Tax @ 40% 3.00 3.00 3.00 3.00

NOPAT (a) 4.50 4.50 4.50 4.50

Add: Depreciation 12.50 12.50 12.50 12.50

Cash flow 17.00 17.00 17.00 17.00

Capital at charge 50.00 37.50 25.00 12.50

Capital charge @ 14% (b) 7.00 5.25 3.50 1.75

Economic Value Added (a) - (b) (2.50) (0.75) 1.00 2.75

Calculation of NPV of Project using EVA approach

= [(2.5) × 0.877] + [(0.75) × 0.769] + (1.00 × 0.675) + (2.75 × 0.592)

= (2.19) + (0.58) + 0.67 + 1.63 = (-) ` 0.47 million (negative NPV)

N
Ab a n d o n m e nt O p t i o n

N
Exercise 21-32

A
Calculation of expected value of cash inflow

Year 1 = ( ` 52,000 × 0.60) + (` 26,000 × 0.40) = ` 41,600

M
Year 2 = ( ` 39,000 × 0.60) + (` 19,500 × 0.40) = ` 31,200
` 2,600 × 0.60) + (` 1,300 × 0.40) ` 2,080

X
Year 2 = ( =

Calculation of NPV of Investment ( ) `

A
Year Cash inflow P.V. factor Present

T
@ 15% values

1 41,600 0.870 36,192

2 31,200 0.756 23,587

3 2,080 0.756 1,572

Present value of cash inflow 61,351

Less: Initial investment 65,000

Net present value (3,649)

Analysis - Since NPV of the investment proposal is negative, it is suggested not accept the proposal.

Calculation of NPV if project is abandoned at the end of 1st year in unfavourable environment ( `)

Cash inflow in favourable conditions in 2 years:

Year 1 ( ` 52,000 × 0.60 × 0.870) 27,144

Year 2 ( ` 39,000 × 0.60 × 0.756) 17,690

Year 2 ( ` 2,600 × 0.60 × 0.756) 1,180

46,014

Add: Cash inflow under unfavourable

environment if leading to abandon

project at year end 1 [( ` 26,000 + ` 32,500) × 0.40 × 0.870] 20,358

66,372

Less: Initial investment 65,000

Net present value 1,372

Advice - If project is unsuccessful, it can be abandoned at the end of first year, since its NPV is positive. If project is

continued for 2nd year in unfavourable conditions, the project generates negative NPV of ` 3,649.

Exercise 21-33

Calculation of Expected NPV over 4 years of Economic Life `

( )

Year Cashflow Abandonment P.V. factor Present value of

`
( ) value ( ) ` @ 10% Cashflow Abandon value

0 (1,00,000) - 1.000 (1,00,000) -

1 35,000 65,000 0.909 31,815 59,085

2 30,000 45,000 0.826 24,780 37,170

3 25,000 20,000 0.751 18,775 15,020

4 20,000 - 0.683 13,660 -

Net present value (10,970)

From the above table, the total NPV of the project (NPV of cash flows + NPV of abandonment value) at the end of

N
each year are computed as shown below:

N
( )

Year Total NPV at the end of

A
3 years 2 years 1 year

0 (1,00,000) 1,00,000 (1,00,000)

M
1 31,815 31,815 31,815

X
59,085 (A.V.)

2 24,780 24,780

A
37,170 (A.V.)

T
3 18,775

15,020 (A.V.)

Total (9,610) (6,235) (9,100)

Note: A.V. = Abandonment value

Analysis - The project generates negative abandonment value in all three years. However, the negative NPV is lowest

if the project is abandoned at the end of 2nd year.

 Key to Short Answer Questions

True or False Statements

1. True - The word uncertainty to cover all future outcomes which cannot be predicted with accuracy.

Uncertainty arises from a lack of previous experience and knowledge.

2. True - Sensitivity analysis is a modelling procedure used in forecasting whereby changes are made in

estimates of the variables to establish whether any will critically affect the outcome of the forecast.

Sensitivity analysis involves identification of all those variables having influence on the project’s NPV

or IRR.

3. False - Sensitivity analysis is used in determination of risk factor in capital budgeting decisions. It aids in

identifying the most sensitive factor, that may cause the error in estimation. Sensitivity analysis tells

about the responsiveness of each factor on the project’s NPV or IRR.

False

N
4. - Simulation does not always offers a guaranteed and the best solution.

5. True - Simulation is not an optimizing technique. It simply allows us to select the best of the alternative

N
systems examined. The simulation model does not produce answers by itself. Managers must generate

all the conditions and constraints for solutions they want to examine.

A
6. True - Simulation is the imitation of the operation of a real-world process or system over time. The act of

simulating something first requires that a model be developed; this model represents the key

M
characteristics or behaviours of the selected physical or abstract system or process. The model

X
represents the system itself, whereas the simulation represents the operation of the system over time.

7. True - Risk occurs where future outcomes of current actions are unknown, but the probabilities of these

A
future outcomes can be reasonably estimated from a knowledge of past and current events. Uncer-

T
tainty occurs where the probabilities of future outcomes cannot be predicted from past or current

events, because no probability estimates are available.

8. True - Probability analysis is basically a statistical technique to measure probability of occurrence of an event

and probability of its non-occurrence.

9. True - An optimistic decision-maker consider the best estimates and a pessimistic decision-maker will

consider the worst estimates.

10. False - The value of outcome should always be more than expenditure incurred for collecting the perfect

information. The management should decide whether obtaining information would be worth the cost

of its collection.

11. False - The project with lesser standard deviation in cash flows carries less risk and uncertainty.

Choose Correct Word

1. uncertainty

2. uncertainty

3. risk

4. probability

5. absolute

6. more

7. NPV

8. certainty equivalent
 9. more

10. RADR

11. outcomes

12. simulation

13. volatility

Choose Correct Answer

1. (A) standard deviation

2. (C) problems cannot be solved mathematically

3. (B) R
f
β p
(R
m
- R)
f

4. (C) forecasting the future cash flows

5. (A) normal distribution

6. (B) pessimistic estimate

7. (B) news paper reports

N
8. (B) β>1

N
9. (D) all of the above

10. (D) all of the above

A
11. (D) any one of the above three

12. (A) when an organization has to take interrelated decisions

X M
T A
 Practical Exercises

Exercise 22-1 Superior Engineering proposes a Project with the following data:

(a) Total outlay: ` 450 lakhs ( ` 250 lakhs of fixed assets and ` 200 lakhs of current assets).

(b) Scheme of financing: ` 100 lakhs equity, ` 200 lakhs term loan, ` 100 lakhs working capital advance and

` 50 lakhs trade creditors.

(c) Interest rates: Term loan 12% p.a. and working capital advance: 15% p.a.

(d) Term loan is repayable in 5 equal instalments, commencing from 3rd year of operations. (assume that

instalment for each year is paid on the last day of the year).

(e) Depreciation: 30% on written down value

(f) Production is expected to reach 60% of capacity in the 1st year of operations, 70% in the 2nd year and 80% from

the 3rd year onwards.

N
(g) Expected revenue from the project will be ` 500 lakhs p.a. on 100% capacity utilization and corresponding
direct costs are ` 200 lakhs. Fixed costs are ` 100 lakhs p.a. Working capital advance of ` 100 lakhs is on 80%

N
capacity and proportionately reduced in the first two years.

A
(h) Tax rate applicable is 50%

Assuming that each year’s production is sold away in the same year, draw the projected profit & loss account for each

M
year of operation and the operational cashflow. Also calculate the Debt Service Coverage Ratio.

X
Exercise 22-2 Find the capitalised project cost of a 25,000 tones p.a. carbon black project in A.P. from the following

information. Assume proper percentage wherever data are missing.

A
Land - 0.80 acres @ ` 20,000 per bigha

T
Site development - ` 17.5 lakhs

Interest during contraction - ` 9 crores

Preliminary expenses - ` 16 lakhs

Building and civil works - 14% of plant and equipment including spares

Plant and machinery including spares ex-works - ` 30 crores (consider average E.D. @ 16%)

Start up and commissioning - @ 10% of ex-works price of plant and equipment

Construction, water, power and approach road etc. - ` 10 lakhs

Engineering consultancy fee - @ 2% of applicable project cost

Foreign technical know-how and training - US $ 1,00,000

Contingencies - @ 5% on land, building and site development and on balance @ 10%

Miscellaneous fixed assets - ` 35 lakhs

Environment cost - ` 250 lakhs

Working capital - ` 2,400 lakhs

Arrange the items of project cost in the manner desired by financial institution (Ignore octroi). [1 U.S. $ = ` 48]

Exercise 22-3 Toy Ltd. has a new project for the manufacture of computerised toy. The product is a novelty in the

toy market. The company had already spent an amount of ` 7,20,000 in developing the product and is eager to place
it in the market as quickly as possible. The company estimates a five-year market life for the product. The maximum

number it can produce in any given year is limited to 36 lakh units. The expected market scenario will support a sale
equivalent of 20%, 50%, 100%, 100%, and 30% of the capacity in 1st year, 2nd year, 3rd year, 4th year and 5th year

respectively. Investment in the project is expected to be completed in one year and will have the following major

components: ( ` lakhs)

Land, buildings and civil works 12.50

Machinery and equipments 87.50

Interest during construction 8.00

Cost structure of the toy is as given below:

Materials ` 2.00 Conversion cost excluding depreciation ` 1.00

Materials are required to be held in stock for 15 days at an average while finished goods may be held for up to 60 days.

Production cycle is 12 days. Credit expectancy of the market is 30 days both on sales and purchases. It is the usual

practice of the company to keep a cash-in-hand reserve for 15 days’ expenses not provided for specifically elsewhere

in the working capital estimates. Working capital requirement should be worked out on the above basis for the first

year. Same level in terms of money will be maintained in the subsequent years, though composition may change.

The following assumptions are made:

N
(1) The project will be financed by a combination of equity and term loans in a ratio as close to 30:70 as practicable.

(2) Loans will carry an interest of 20% p.a.

N
(3) Loan disbursement will be uniform throughout the period of construction, simple interest at the same rate will

A
be applied.

(4) Selling price per unit will be ` 6.

M
(5) One year moratorium on the principal will be available.

` 2.00 lakhs, ` 1.00 lakh and ` 0.50 lakh respectively.

X
(6) Product promotion expenses for the first three years will be

(7) Production is prorated every month equally.

A
(8) The factory operates one shift for 360 days in a year.

T
(9) Ignore interest on overdraft.

(10) Working capital requirement will not increase after the initial first year.

Workout:

(a) Initial working capital required.

(b) Total financial investment in the project and its financing.

(c) Profit before depreciation and interest charges for 5 years.

(d) Debts service coverage ratio.

Exercise 22-4 Sunrise Ltd. is setting up a new project for manufacturing two products:

Product A - 1,500 tons; Product B - 2,500 tons

The cost of the project after capitalising interest and preoperative expenses are as under: ( ` lakhs)

Cost of Project

Land and site development 26

Buildings 34

Plant and machinery 290

Miscellaneous fixed assets 12

Preliminary expenses 3

365
Means of Finance:

Equity share capital 125

Term loan 240

365

Assumptions:

(a) Capacity utilization of both the products is:

Year 1 - 50%, Year 2 - 60%, Year 3 (onwards) - 70%

(b) Raw materials requirement:

Product A ` 30/kg., Product B ` 80/kg.

(c) Total cost of power is ` 30 lakhs in year 1 with an increase of 10% thereafter every year.

(d) Repairs and maintenance ` 50 lakhs per year.

(e) Administration overheads of ` 40 lakhs per year with 10% increase every year.

(f) Salaries and wages are estimated at ` 100 lakhs in the year 1 with an increase of 20% thereafter.

N
(g) Selling expenses are estimated at 10% of sales.

(h) Selling prices for each product is estimated as:

N
Product A ` 40/kg. Product B ` 120/kg.

A
(i) Depreciation is on straight line method

Buildings 5%, Plant and machinery 10%, and Miscellaneous assets 15%

M
(j) Interest on term loans is @ 17.5% on average balance. Term loans are repayable over 5 years in equal

instalments, commencing from year 2.

X
(k) Bank borrowing carries interest @ 18%. Bank borrowings are:

` `

A
Year 1 - 375 lakhs, Year 2 - 465 lakhs, and Year 3 - 535 lakhs

(l) All expenses are estimated to remain constant for this purpose of appraisal except interest on term loan from

T
3 year onwards.

From the above information prepare a cost and profitability statement for seven years.

Exercise 22-5 A newly incorporated company intends to set up a project for the manufacture of three varieties of

products. The company has already purchased land and all site development work has been completed and paid from

equity fund. The cost of the project is estimated to be as follows: ( ` lakhs)

Land and site development 13.30

Building and civil works 14.30

Plant and machinery 129.35

Utilities and fixed assets 10.95

Contingencies and escalations (10% on items 2 and 4 and 5% on item 3) 9.00

Preliminary and preoperatives 12.30

Interest during construction 10.10

Margin money for working capital 15.70

215.00

The above project to be financed as per the following: ( ` lakhs)

Equity share capital 58.80

Interest free loans from promoters 19.50

Term loans 136.70

215.00
As a Project manager you are required to prepare a statement showing cost of production and profitability (before

tax) and debt service coverage ratio on the basis of the following assumptions for consideration of the Board:

(a) The installed capacity of the plant would be 846 MT comprising the following:

Product A - 216 MT Product B - 336 MT Product C - 294 MT

(b) Capacity utilization has been assumed as follows:

First year - 50% of each product

Second year - 60% of each product

Third year to sixth year - 70% of each product

(c) Requirement of raw material at full capacity utilization has been estimated as follows for the three products

in aggregate:

Sl. No. Item Annual requirement (tones) Unit rate ( ) `

1 X 504.0 2,600

2 Y 8.4 7,000

N
3 Z 200.0 19,000

4 P 38.2 91.600

N
5 Q 50.4 27,500

A
(d) Requirement of packing material at full capacity utilization has been estimated at ` 111.80 lakhs.

(e) The total cost of power and fuel oil has been estimated at ` 4.60 lakhs at full capacity utilization.

M
(f) Repair and maintenance have been estimated at 1% on building, 2% on plant and machinery and miscella-

X
neous fixed assets.

(g) Administrative and other overheads have been estimated at ` 2.00 lakhs and an annual increase of 15% has been

A
considered during subsequent years.

T
(h) Salary and wages have been estimated at ` 10.00 lakhs and an increase of 10% per year has been considered in
subsequent years.

(i) Selling expenses have been considered at 10% of the total sales.

(j) Selling price for the product has been estimated as under:

Product A - ` 30/kg. Product B - ` 70/kg. Product C - ` 45/kg.

(k) For the purpose of projections depreciation to be considered on straight line basis (assuming the life of the

project as 10 years and a scrap value of 5%).

(l) Interest on term loan has been considered at 14% and the interest on bank borrowings have been considered

at 16.5%.

(m) Working capital loan for different capacity utilization level has been assumed as follows:

50% level - ` 25 lakhs 60% level - ` 30 lakhs 70% level - ` 35 lakhs

(n) Term loan to be repaid within 6 years from the date of commencement of commercial production.

(o) The calculations to be made for 6 years and relevant assumptions may be made.
 Key to Practical Exercises

Exercise 22-1

Projected Profit and Loss account and Operational Cashflow ( ` lakhs)

Year of operation 1 2 3 4 5 6 7

Capacity utilization (%) 60 70 80 80 80 80 80

Revenue (a) 300.00 350.00 400.00 400.00 400.00 400.00 400.00

Costs:

Variable costs 120.00 140.00 160.00 160.00 160.00 160.00 160.00

Fixed costs 100.00 100.00 100.00 100.00 100.00 100.00 100.00

Interest on working

capital advance 11.25 13.13 15.00 15.00 15.00 15.00 15.00

N
(b) 231.25 253.13 275.00 275.00 275.00 275.00 275.00

N
PBIDT (a) - (b) 68.75 96.87 125.00 125.00 125.00 125.00 125.00

Less: Interest on term loan 24.00 24.00 24.00 19.20 14.40 9.60 4.80

A
PBDT 44.75 72.87 101.00 105.80 110.60 115.40 120.20

Less: Depreciation 75.00 52.50 36.75 25.73 18.01 12.61 8.82

M
PBT (30.25) 20.37 64.25 80.07 92.59 102.79 111.38

X
Less: Tax @ 50% - 10.19 32.13 40.04 46.30 51.40 55.69

PAT (30.25) 10.18 32.12 40.03 46.29 51.40 55.69

A
Add: Interest on term loan 24.00 24.00 24.00 19.20 14.40 9.60 4.80

T
Depreciation 75.00 52.50 36.75 25.73 18.01 12.61 8.82

(a) Operation cash inflow 68.75 86.68 92.87 84.96 78.70 73.61 69.31

(b) Payments:

Interest on term loan 24.00 24.00 24.00 19.20 14.40 9.60 4.80

Repayment of term loan - - 40.00 40.00 40.00 40.00 40.00

24.00 24.00 64.00 59.20 54.40 49.60 44.80

DSCR (a)/(b) 2.86 3.61 1.45 1.44 1.45 1.48 1.55

5PUBM PQFSBUJPO DBTI JOGMPX C  MBLIT

Average DSCR = = = 1.73
5PUBM QBZNFOU BHBJOTU EFCUT C  MBLIT

Exercise 22-2

(1) Plant and Machinery (including spares) ( ` lakhs)

Ex. works cost 3,000.00

Add: Excise duty @ 16% 480.00

3,480.00

Add: Sales tax @ 4% 139.20

3,619.20

Add: Transport and insurance @ 3% 108.58

Landed cost 3,727.78

Add: Installation cost (4%) 149.11

Total cost of plant and machinery 3,876.89

(2) Land Cost

80a × 3b = 240 bighas

240 bighas × ` 20,000 = ` 48 lakhs

(3) Buildings and Civil Works

14% of Plant and equipment (including spares) = ` 3,876.89 lakhs × 14/100 = ` 542.76 lakhs

(4) Calculation of Engineering Consultancy Fees ( ` lakhs)

Site development 17.50

Building and civil works 542.76

Plant and machinery 3,876.89

Miscellaneous fixed assets 35.00

Environmental cost 250.00

Start up and commission 300.00

5,022.15

Engineering consultancy fee = 5,022.15 × 2/100 = ` 100.44 lakhs

N
(5) Preoperative Expenses ( ` lakhs)

N
Start up and commission 300

Interest during construction 900

A
Construction water, power and approach road 10

1,210

M
(6) Contingencies ( ` lakhs)

X
5% on Land, buildings and site development (48 + 17.50 + 542.76) × 5/100 30.41

A
10% on balance items:

T
Plant and machinery 3,876.89

Miscellaneous fixed assets 35.00

Environment cost 250.00

Technical know-how 148.44

Preoperative expenses (1,210 - 900) 310.00

Preliminary expenses 16.00

4,636.33

(4,636.33 × 10/100) 463.63

494.04

(7) Margin Money of Working Capital = ` 2,400 lakhs × 25/100 = ` 600 lakhs

Ascertainment of Cost of Project ( ` lakhs)

Land 48.00

Site development 17.50

Buildings and civil works 542.76

Plant and machinery including spares 3,876.89

Miscellaneous fixed assets 35.00

Environmental cost 250.00

Technical know-how and training:

Foreign know-how 48.00

Engineering consultancy 100.44

 ( ` lakhs)

Preoperative expenses 1,210.00

Preliminary expenses 16.00

Contingencies 494.04

Margin money 600.00

Total project cost 7,238.63

Exercise 22-3

(a) Computation of Initial Working Capital required 1st year production and sales

= 36,00,000 units × 20/100 = 7,20,000 units

Particulars Norm `
( )

Materials 15 days (7,20,000 × 2 × 15/360) 60,000

Work-in-progress 12 days (7,20,000 × 1.5 × 12/360) 36,000

N
Finished goods 60 days (7,20,000 × 3 × 60/360) 3,60,000

Debtors 30 days (7,20,000 × 3 × 30/360) 1,80,000

N
Cash 15 days (7,20,000 × 1 × 15/360) 30,000

A
6,66,000

Assumption - 360 days in a year and 30 days in a month.

M
(b) Statement Showing Investment in the Project and its financing `
( )

X
Cost of Project

Land, building and civil works 12,50,000

A
Machinery and equipments 87,50,000

T
Product development 7,20,000

Interest during construction 8,00,000

Initial working capital 6,66,000

1,21,86,000

Means of Finance

Equity capital 33,86,000

Loans 80,00,000

Overdraft for interest 8,00,000

1,21,86,000

Debt-equity ratio is 7 : 3 (basing on long-term debt of ` 80 lakhs).

(c) Statement Showing Profit Before Depreciation and Interest Charges for 5 years ( ` lakhs)

Year 1 2 3 4 5

Sales (units in lakhs) 7.20 18.00 36.00 36.00 10.80

Sales revenue (a) 43.20 108.00 216.00 216.00 64.80

Expenses

Materials 14.40 36.00 72.00 72.00 21.60

Conversion expenses 7.20 18.00 36.00 36.00 10.80

Promotion 2.00 1.00 0.50 - -

(b) 23.60 55.00 108.50 108.00 32.40

Profit before depreciation and interest (a) - (b) 19.60 53.00 107.50 108.00 32.40
 (d) Statement Showing Debt Service Coverage Ratio (DSCR) ( ` lakhs)

Year 1 2 3 4 5

Profit before interest and depreciation (a) 19.60 53.00 107.50 108.00 32.40

Finance charges:

Interest 16.00 16.00 12.00 8.00 4.00

Principal repayment - 20.00 20.00 20.00 20.00

(b) 16.00 36.00 32.00 28.00 24.00

DSCR (a)/(b) 1.225 1.472 3.359 3.857 1.350

Exercise 22-4

Particulars Year 1 Year 2 Year 3

Production

Product A

Utilization (%) 50 60 70

N
Quantity (tons) 750 900 1,050

N
Product B

Utilization % 50 60 70

A
Quantity (tons) 1,250 1,500 1,750

Sales

M
Product A

Quantity 750 900 1,050

X
Rate (per kg.) 40 40 40

A
Value ( ` lakhs) (a) 300 360 420

T
Product B

Quantity 1,250 1,500 1,750

Rate (per kg.) 120 120 120

Value ( ` lakhs) (b) 1,500 1,800 2,100

Total sales (a) + (b) 1,800 2,160 2,520

Expenses

Power 30 33 36

Repairs and maintenance 50 50 50

Salaries and wages 100 120 144

Administrative overheads 40 44 48

Selling expenses 180 216 252

Depreciation Cost Rate Amount

Buildings 34 5% 1.70

Plant and machinery 290 10% 29.00

Miscellaneous assets 12 15% 1.80

32.50

Rounded off 33.00

Repayment of Term Loan and Interest @ 17.5%

Year 1 2 3 4 5 6 7

Principal 240 240 192 144 96 48 -

Repayment - 48 48 48 48 48 -

Balance 240 192 144 96 48 - -

Average balance - 216 168 120 72 24 -

Interest (on average balance) 42 38 29 21 13 4 -

Cost and Profitability Statement

Year 1 2 3 4 5 6 7

Product A (tons) 750 900 1,050 1,050 1,050 1,050 1,050

Product B (tons) 1,250 1,500 1,750 1,750 1,750 1,750 1,750

Utilization (%) 50 60 70 70 70 70 70

Cost of Production ( ` lakhs)

N
Raw materials 1,225 1,470 1,715 1,715 1,715 1,715 1,715

Salaries and wages 100 120 144 144 144 144 144

N
Power and fuel 30 33 36 36 36 36 36

Repairs and maintenance 50 50 50 50 50 50 50

A
Administrative overhead 40 44 48 48 48 48 48

Selling expenses 180 216 252 252 252 252 252

M
(a) 1,625 1,933 2,245 2,245 2,245 2,245 2,245

Interest

X
On term loans 42 38 29 21 13 4 -

A
On working capital 68 84 96 96 96 96 96

(b) 110 122 125 117 109 100 96

T
Depreciation (c) 33 33 33 33 33 33 33

Total cost (a) + (b) + (c) = (d) 1,768 2,088 2,403 2,395 2,387 2,378 2,374

Total sales (e) 1,800 2,160 2,520 2,520 2,520 2,520 2,520

Net profit (12 - 11) (e) - (d) 32 72 117 125 133 142 146

Exercise 22-5

(1) Allocation of Contingencies of ` 9 lakhs ( ` lakhs)

Item of asset Original Contingencies Amount Total value

estimate provisions rounded off of assets

Land and site development 13.30 - - 13.30

Building and civil works 14.30 10% 1.43 15.73

Plant and machinery 129.35 5% 6.47 135.82

Miscellaneous fixed assets 10.95 10% 1.10 12.05

167.90 9.00 176.90

(2) Allocation of Interest During Construction ` 10.10 lakhs ( ` lakhs)

Items of asset Asset value Interest allocated Value of assets

Building and civil works 15.73 0.97 16.70

Plant and machinery 135.82 8.39 144.21

Miscellaneous fixed assets 12.05 0.74 12.79

163.60 10.10 173.70

 Value of Assets After Allocation of Interest During Construction ( ` lakhs)

Land and site development 13.30

Building and civil works 16.70

Plant and machinery 144.21

Miscellaneous fixed assets 12.79

187.00

Value of Depreciable Assets ( ` lakhs)

Building and civil works 16.70

Plant and machinery 144.21

Miscellaneous fixed assets 12.79

173.70

(3) Allocation of Preoperative Expenses

As per section 35D of the Income-tax Act, 1961 2.5% of the “cost of the project” can be written off over a period

` 215 lakhs × 2.5% = ` 5.37 lakhs can be written off over a period 10 years. The balance amount

N
of 10 years. Thus

of preoperative ` 6.93 (i.e. ` 12.30 - 5.37) lakhs is to be capitalised and is to be allocated over fixed assets. The

N
capitalization should be done over the site development also. However, for the sake of convenience the

capitalization is done over the following three category of assets:

A
Building and civil works, Plant and machinery, and Miscellaneous fixed assets

This may be allocated in the ratio of value of depreciable assets as follows: ( ` lakhs)

M
Item of asset Ratio for allocation Amount allotted Total

X
Building and civil works 16.70 0.67 17.37

A
Plant and machinery 144.21 5.75 149.96

Miscellaneous fixed assets 12.79 0.51 13.30

T
173.70 6.93 180.63

Value of Fixed Assets After Allocation of Preoperatives ( ` lakhs)

Land and site development 13.30

Building and civil works 17.37

Plant and machinery 149.96

Miscellaneous fixed assets 13.30

193.93

Thus, the total value of assets after capitalization of Contingencies, Interest during construction, and

Preoperative etc. are ` 193.93 lakhs.

(4) Checking the accuracy of capitalization to check the accuracy of the allocation the following approach can be

adopted:

Value of Assets after allocation

= Cost of Project - Margin Money for working capital to be written off

= 215 - 15.70 - 5.37 = ` 193.93 lakhs

Hence, the value of the assets capitalised above is correct.

(5) Depreciation

Depreciation is to be calculated on the straight line basis. Assuming the life of the project is 10 years and the

scrap value is 5% the value of the depreciable assets would be:

= 193.93 - 13.30 = ` 180.63 lakhs

 Building ` 17.37 lakhs

Others ` 163.36 lakhs

Scrap value @ 5% = ` 9.03 lakhs

Annual depreciation = (180.63 - 9.03) ÷ 10 = 17.16 lakhs

(6) Raw Material

Raw Material Requirement at 100%

Item Quantity Price at 100% capacity

(MT) `
( ) `
( )

X 504.00 2,600 13,10,400

Y 8.40 7,000 58,800

Z 200.00 19,000 38,00,000

P 38.20 91,600 34,99,120

Q 50.40 27,500 13,86,000

1,00,54,320

N
Raw Material Requirement ( ` lakhs)

N
at 50% capacity 50.27

A
at 60% 60.33

at 70% 70.38

M
(7) Packing Expenses ( ` lakhs)

X
at 100% 111.80

at 50% 55.90

A
at 60% 67.08

T
at 70% 78.26

(8) Power and Fuel Expenses

At 100% Capacity the expenses on power and fuel would be ` 4.60 lakhs.

Capacity utilization 50% 60% 70%

Power and fuel ( ` lakhs) 2.30 2.76 3.22

(9) Repairs and Maintenance Expenses ( ` lakhs)

Building and civil works (17.37 × 1/100) 0.17

Plant and machinery (including miscellaneous fixed assets) (163.26 × 2/100) 3.27

3.44

(10) Sales Realization at 100% capacity `

( )

Product A (216 M.T. × ` 30,000) 64,80,000

Product B (336 M.T. × ` 70,000) 2,35,20,000

Product C (294 M.T. × ` 45,000) 1,32,30,000

4,32,30,000

Sales Realization at Different Levels of Capacity ( ` lakhs)

Capacity utilization 50% 60% 70%

Sales realization 216.15 259.38 302.61

(11) Estimation of Selling Expenses

Selling expenses are to be calculated at 10% of the sales realization ( ` lakhs)

Particulars 1 year 2 year 3 to 6 years

Capacity utilization 50% 60% 70%

Sales realization 216.15 259.38 302.61

Selling expenses (10% of sales) 21.62 25.94 30.26

(12) Power and Fuel ( ` lakhs)

Capacity utilization 100% 50% 60% 70%

Power and fuel 4.6 2.3 2.76 3.22

(13) Administration and Other Overheads ( ` lakhs)

Years 1 2 3 4 5 6

Administration and other overheads 2 2.3 2.65 3.04 3.5 4.02

N
(15% increase p.a.)

(14) Salary and Wages ( ` lakhs)

N
Year 1 2 3 4 5 6

A
Salary and wages (10% increase p.a.) 10.00 11.00 12.10 13.31 14.64 16.10

M
(15) Interest on Working Capital Loan ( ` lakhs)

X
Capacity utilization 50% 60% 70%

Working capital loan 25.00 30.00 35.00

A
Interest on working capital loan @ 16.5% 4.13 4.95 5.78

T
(16) Interest on Term Loan ( ` lakhs)

Year Payment Balance Interest @ 14%

1 - 136.70 19.14

2 - 136.70 19.14

3 34.00 102.70 19.14

4 34.00 68.70 14.38

5 34.00 34.70 9.62

6 34.70 - 4.86

136.70 86.28

(17) Depreciation on Buildings ( ` lakhs)

Particulars 1 2 3 4 5 6

Opening balance 17.37 15.72 14.07 12.42 10.77 9.12

Depreciation from year 1 to 6 1.65 1.65 1.65 1.65 1.65 1.65

WDV 15.72 14.07 12.42 10.77 9.12 7.47

Repairs and maintenance 1% on op. balance 0.17 0.16 0.14 0.12 0.11 0.09
(18) Depreciation on Plant and Machinery ( ` lakhs)

Particulars 1 2 3 4 5 6

Opening balance 163.26 147.75 132.24 116.73 101.22 85.71

Depreciation 15.51 15.51 15.51 15.51 15.51 15.51

WDV 147.75 132.24 116.73 101.22 85.71 70.20

2% on opening balance for repairs etc. 3.27 2.96 2.65 2.33 2.02 1.71

(19) Repairs and Maintenance 1 2 3 4 5 6

`
( lakhs) 3.44 3.12 2.79 2.45 2.13 1.80

Statement of Cost of Production and Profitability Before Tax ( ` lakhs)

Years 1 2 3 4 5 6

Raw materials 50.27 60.33 70.38 70.38 70.38 70.38

Packing materials 55.90 67.08 78.26 78.26 78.26 78.26

N
Power and fuel 2.30 2.76 3.22 3.22 3.22 3.22

Repairs and maintenance 3.44 3.12 2.79 2.45 2.13 1.80

N
Administration and other overheads 2.00 2.30 2.65 3.04 3.50 4.02

A
Salaries 10.00 11.00 12.10 13.31 14.64 16.11

Selling expenses 21.62 25.94 30.26 30.26 30.26 30.26

M
Interest on ways and means 4.13 4.95 5.78 5.78 5.78 5.78

Interest on term loans 19.14 19.14 19.14 14.38 9.62 4.86

X
Depreciation 17.16 17.16 17.16 17.16 17.16 17.16

A
Cost of production (a) 185.96 213.78 241.74 238.24 234.95 231.85

Sales (b) 216.15 259.38 302.61 302.61 302.61 302.61

T
Profit before tax (b) - (a) 30.19 45.60 60.87 64.37 67.66 70.76

Tax @ 50% (assumed) 15.09 22.80 30.44 32.19 33.83 35.38

Profit after tax (PAT) 15.10 22.80 30.43 32.18 33.83 35.38

Available cash inflow

(PAT + Depreciation + Interest on term loan) 51.40 59.10 66.73 63.72 60.61 57.40

Necessary payments

(Term loan repayment + Interest) 19.14 19.14 53.14 48.38 43.62 39.56

Available total cash inflow 358.96

Debt Service Coverage (DSCR) Ratio = = = 1.61
Total necessary payments 222.98
 Key to Short Answer Questions

True or False Statements

1. False - Interest cover indicates how many times a company can cover its current interest payments out of

current profits. A very high ratio indicates that the firm is conservative in using debt and a very low

ratio indicates excessive use of debt.

2. False - A very high interest coverage ratio indicates that the firm is conservative in using debt. The lower the

debt in the total capital structure means the firm is loosing the advantage of trading on equity.

3. True - The debt service coverage ratio (DSCR) indicates whether the business is earning sufficient profits to

pay not only the interest charges but also the installments due of the principal amount. A ratio of 2

is considered satisfactory by financial institutions. The greater DSCR indicates the better debt

servicing capacity of the organization.

False

N
4. - The pre-operative expenses include salaries, establishment expenses, rent, trail-run expenses and

other miscellaneous expenses incurred before the commercial production. The pre-operative ex-

N
penses are also considered as part of the cost of project.

False

A
5. - Detailed project report (DPR) contains the details about the plan of action, details about technical,

financial, marketing, management and social aspects. DPR is prepared only after feasibility report of

the project comes out positive.

M
6. True - Normally the cash flows are estimated and projected income statement and balance sheet are prepared

X
without considering the uncertainty in projections due to inflation factor.

True

A
7. - The resourcefulness, competence and integrity of the management, the experience and capability of

the promoters will enable to implement and run the project successfully.

T
8. False - An entrepreneur who promotes the project will also participate in the scheme of the project. The

extent of promoter’s participation is considered as sign of interest the promoters show in the project.

9. True - The banks and financial institutions asks the promoter to bring in margin money, as a safeguard from

the changes in the value of assets that are being financed and provided as a security.

10. True - The multinational companies which are making foreign direct investment must assess the political

risk, before any such investments are made.

Choose Correct Word

1. cash flow

2. project

3. covenants

4. cost of project

5. appraisal

6. project report

7. country

8. external

9. force majeure

10. pre-operative

11. debt-equity

12. margin money

Choose Correct Answer

1. (A) liquidity risks

2. (D) incremental cash flows

3. (D) default risk

4. (A) political risks

5. (B) technical appraisal

6. (C) critical success factors

7. (D) payback period

8. (A) raw materials consumption

9. (A) foreign collaborator’s participation

10. (A) inter corporate deposits

11. (A) income-tax receipts and payments

12. (B) Impact of the project on the wealth of the shareholders

N N
M A
A X
T
 Practical Exercises

Exercise 24-1 The balance sheet of Galaxy Ltd. as on 31st March, 2016 is as follows:

Liabilities ` lakhs Assets ` lakhs

Share capital 400 Fixed assets 900

Reserves 300 Inventories 500

Long-term debt 700 Receivables 400

Short-term debt 400 Cash and bank 200

Payables 100

Provisions 100

2,000 2,000

The current year sales were ` 1,200 lakh. For the next year ending 31st March, 2017 sales and assets are expected to

N
increase by 20%. The net profit margin after taxes and dividend payout are expected to be 10% and 50% respectively.

You are required to determine for the year 2016-17:

N
(i) The external fund requirement.

(ii) The mode of raising funds given the following parameters:

A
(a) Current ratio should be 1.5.

(b) Ratio of fixed assets to long-term loans should be 1.5.

M
(c) Long-term debt to equity ratio should not exceed 0.9.

X
(d) The funds are to be raised in the order of (i) short-term bank borrowings, (ii) long-term loans, and

(iii) equities.

A
Exercise 24-2 The balance sheet of Smart Ltd. as on March 31, 2016 is as follows:

T
Liabilities ` lakhs Assets ` lakhs

Share capital 200 Fixed assets 500

Reserves 140 Inventories 300

Long-term loans 360 Receivables 240

Short-term loans 200 Cash and bank 60

Payables 120

Provisions 80

1,100 1,100

Sales for the year were ` 600 lakhs. For the year ending on March 31, 2017 sales are expected to increase by 20%. The
profit margin and dividend payout ratio are expected to be 4% and 50% respectively. You are required to:

(i) Quantify the amount of external funds required.

(ii) Determine the mode of raising the funds given the following parameters: (a) Current ratio should atleast be

1.33. (b) Ratio of fixed assets to long-term loans should be 1.5. (c) Long-term debt to equity ratio should not

exceed 1.05.

(iii) The funds are to be raised in the order of short-term bank borrowings, long-term loans and equities.

Exercise 24-3 IOPS has an equity capital of 12 million, total debt of 8 million and sales last year were 30 million:

(i) It has a target Assets-to-Sales ratio of 0.667, a target Net Profit margin of 0.04, a target D.E. ratio of 0.667 and

target earnings retention rate of 0.75. In a steady state, what is its sustainable growth rate?
(ii) Suppose the company has established for the next year a target Assets-to-Sales ratio of 0.62, a target Net Profit

margin of 0.05, and a target D.E. ratio of 0.80. It wishes to pay an annual dividend of 0.3 million and raise

1 million in equity capital next year. What is its sustainable growth rate for next year ? (Million = Million

Rupees)

N N
M A
A X
T
 Key to Practical Exercises

Exercise 24-1

Current year sales = ` 1,200 lakhs

Projected sales for next year = ` 1,200 × 120/100 = ` 1,440 lakhs

Current year assets = ` 2,000 lakhs

Projected assets for next year = ` 2,000 lakhs × 120/100 = ` 2,400 lakhs

Additional assets to be acquired to meet additional sales

= ` 2,400 lakhs - ` 2,000 lakhs = ` 400 lakhs

It is assumed that payables and provisions will also increase pari pasu with sales.

Projected profit for next year = ` 1,440 lakhs × 10/100 = ` 144 lakhs

N
Dividend payable for next year = ` 144 lakhs × 50/100 = ` 72 lakhs

` ` `

N
Next year retained earnings = 144 lakhs - 72 lakhs = 72 lakhs

Calculation of External Funds Requirement ( ` lakhs)

A
Projected level of assets 2,400

Less: Payables and provisions 240

M
Retained earnings 72

X
Existing fund used (400 + 300 + 700 + 400) 1,800 2,112

External Funds required 288

A
Parameters for mode of raising funds:

T
(a) Current ratio should be 1.5.

(b) Ratio of fixed assets to long-term loans should be 1.5.

(c) Long-term debt to equity ratio should not exceed 0.9.

Projected level of current assets = (500 + 400 + 200) × 120/100 = ` 1,320 lakhs

Projected level of Payables and Provisions = (100 + 100) × 120/100 = ` 240 lakhs

Now, we can determine the level of short-term borrowings.

Calculation of additional short-term borrowings

CA
1.5 =
CL

1,320
1.5 =
240 + STL

1.5 (240 +STL) = 1,320

360 + 1.5 STL = 1,320

STL = 960/1.5 = 640

Therefore, projected short-term loan is ` 640 lakhs.

Additional short-term loan = ` 640 lakhs - ` 400 lakhs = ` 240 lakhs

Calculation of Additional Long-term Debt

 Fixed assets
1.5 =
Long-term loans

Projected fixed assets = ` 900 lakhs × 120/100 = ` 1,080 lakhs

1,080
1.5 =
LTL

LTL = 1,080/1.5 = 720

Additional long-term loan = 720 - 700 = ` 20 lakhs

Calculation of Additional Equity Funds ( ` lakhs)

Total additional external fund required 288

Less: Additional short-term borrowing 240

Additional long-term loan 20 260

Equity capital to be issued 28

New level of Equity funds = ` 428 + `. 372 lakhs = ` 800 lakhs

N
New level of long-term debt = ` 720 lakhs

New debt-equity ratio = 720/800 = 0.9

N
The third parameter as to debt-equity ratio (0.9) is also satisfied.

A
Exercise 24-2

(i) Quantification of the Amount of External Funds Required

M
The external funds requirement (EFR), is calculated by applying the following formula:

X
( )
A L
EFR = - ∆S - MS 1
(1 - D)
S S

A
Where,

T
A = Total assets = 1,100 lakhs

L = Payables and provisions = ` 120 lakhs + ` 80 lakhs

S = Sales for current year = ` 600 lakhs

S
1
= Projected sales for next year = ` 720 lakhs

∆S = Expected increase in sales = ` 120 lakhs

M = Profit Margin = 4% or 0.04

D = Dividend payout ratio = 50% or 0.5

1,100 200
EFR =
( 600
-
600
) 120 - (0.04 × 720 × 0.5)

= (1.5 × 120) - 14.4 = 180 - 14.4 = 165.60

∴ External funds requirement = ` 165.60 lakhs

(ii) Determination of Mode of Raising Funds

(a) Short-term Borrowings

Current ratio should at least be 1.33

600 × 1.2
1.33 =
200 × 1.2 + Short-term bank borrowings (x)

1.33 720
=
1 240 + x

1.33 (240 + x) = 720

319.2 + 1.33 x = 720

 1.33 x = 720 - 319.2

1.33 x = 400.8

x = 400.8/1.33 = 301.35

∴ Short-term Bank Borrowings = ` 301.35 lakhs

( ` lakhs)

Short-term bank borrowings (Desired) 301.35

Less: Existing short-time loans 200.00

Additional Short-term Borrowings 101.35

(b) Long-term Debt

Ratio of Fixed Assets to Long-term Loans should be 1.5

500 × 1.2
1.5 =
Long-term Loans (y)

1.5 y = 500 × 1.2

y = 600/1.5 = 400

N
∴ Long-term Loans = ` 400 lakhs

N
( ` lakhs)

Total Long-term Loans (desired) 400

A
Less: Existing Long-term Loans 360

Additional Long-term Borrowings 40

M
(c) Equity ( ` lakhs)

X
External Funds Requirement 165.60

A
Less: Additional Short-term Borrowings 101.35

T
Additional Long-term Borrowings 40.00 141.35

Balance to be Raised as Equity Capital 24.25

Long-term Debt to Equity Ratio should not exceed 1.05

(360 + 40)
=
(200 + 24.25) + [140 + (20% of 140)]

400
= = 1
224.25 + 168

400
= = 1.02
392.25

∴ Long-term Debt to Equity Ratio is satisfied to the norm.

(iii) Funds to be Raised in order of STBB, LTL and Equity ( ` lakhs)

Short-term Bank borrowings 101.35

Long-term Loans 40.00

Equity 24.25

Total Funds to be raised 165.60

Exercise 24-3

(i) Sustainable Growth Rate (SGR)

/1   % 
C     + 
 4   &R 
=

 "   C  /1    + %  
     
 4    4   &R  

Where, b = Retention rate of earnings (1 - b is the Dividend Payout Ratio) i.e. 0.75

NP/S = Net profit margin (Net profit/Sales) i.e. 0.04

D/Eq = Debt - Equity Ratio i.e. 0.667

S = Annual Sales

A/s = Assets to Sales ratio i.e. 0.667

 
 + 

SGR = = 0.0811 or 8.11%

<  

 + 
>

N
(ii) Sustainable Growth Rate for Next Year

N
  %  4 
 &R  + /FX &R %JW
  +    
 &R   "     

A

  4  


SGR =

 /1   %  4 
    +   
 4   &R   " 

M
 

X
NP/S. D/Eq, S, A/S are the same as stated in (i) above

A
Where, S = Most recent annual sales
0

Eq = Equity in the beginning

T
0

Now, Here A/s = 0.62, NP/S = 0.05, D/Eq = 0.80, Div = 3 million and

New Eq = ` 1 million S = 30 million

0

  +  
 + 

   
SGR =     = 0.4377 or 43.77%

  < 


>    
 Key to Short Answer Questions

True or False Statements

1. True - Strategy defines where the organization wants to go to fulfil its purpose and achieve its mission and

provides the framework for guiding choices.

2. True - The strategic financial planning should enable the firm in early identification of shifts in environ-

ment, counter possible actions of competitor, reduction in financing costs, effective use of funds

deployed, identification of business and financial risk etc.

3. False - Financial sector reforms aim at promoting a diversified, efficient and competitive financial sector

with ultimate objective of improving the allocative efficiency of available resources, increasing the

return on investments and promoting an accelerated growth of real sectors of economy.

4. True - The investment decisions create cash flow, which is central to the success of the firm, the finance

N
decisions influence the cost of capital.

5. True - Non-financial measures are directly traceable to key success factors like customer satisfaction, market

N
leadership, manufacturing excellence, quality and technological competence. Non-financial mea-

A
sures may predict better future cash flow of the firm.

6. False - There always must be some range of error allowed in forecast. While forecasting one should note that

M
it is impossible to forecast the future precisely.

7. True - Financial forecasting helps making decisions like capital investment, annual production level,

X
operational efficiency required, working capital requirement, assessment of cash flow etc.

False

A
8. - IGR is the maximum growth rate a firm can achieve without going for external financing. All the

financing requirements are met internally from the internal accruals.

T
9. False - SGR is the maximum growth rate which can be achieved by using both internal accruals, as well as,

external debt without increasing the financial leverage.

10. False - Agency theory models a situation in which a principal (owner) delegates decision-making authority

to an agent (managers) who receives a reward in return for performing some activity of the principal.

11. True - Financial engineering is defined as the design and redesign of financial instruments to structure cash

flow to achieve the desired financial goals. It is the process and formulation of creative solutions to

problems in finance.

Choose Correct Word

1. agents

2. external

3. strategic

4. information asymmetry

5. agency

6. principal

7. agency

8. agency

9. external

10. maximum
11. financial

12. incentives

13. control

Choose Correct Answer

1. (C) strategy

2. (A) strategic

3. (C) competitive

4. (C) SWOT

5. (B) strategic

6. (C) incentives

7. (B) threat of providers of debt funds

8. (B) Replacing debt with equity, thus forcing managers to invest in high-yield operational assets

9. (D) all of the above

N
10. (B) Increase in networth of the firm

A N
X M
T A
 Practical Exercises

Exercise 25-1 ` 100 shares of SBC Ltd. were being quoted at ` 180. The company launched an expansion program
worth ` 25 crores and decided to make a public issue. Part of the issue was to be rights. Members were offered one
right share for every six ordinary shares held by them, at a premium of ` 50 per share. Determine the minimum price

that can be expected of the shares after the issue.

Exercise 25-2 The financial data of G.D. Pharma is as follows:

Paid-up capital (4 lakh shares) ` 40 lakhs

Reserve and surplus ` 180 lakhs

Profit after tax ` 32 lakhs

The P/E multiple of the shares of G.D. Pharma is 7. The company has taken up an expansion project at Ghaziabad.

The cost of the project is` 200 lakhs. It proposes to fund it with a term loan of ` 100 lakhs from ICICI and balance

N
by a rights issue. The rights will be priced at ` 25 per share (` 15 premium).

You are required to calculate:

N
(i) The value of the rights and the market capitalization of G.D. Pharma after the rights issue, and

A
(ii) The Net Asset Value (NAV) of the shares after the rights issue.

Exercise 25-3 Ray Gold Ltd. (RL) has a paid-up ordinary share capital of ` 200 lakhs represented by 4 lakh shares

M
of ` 50 each. Earnings after tax in the most recent year (2015-16) were ` 80,00,000 of which ` 26,50,000 was

X
distributed as dividend. The current price/earning ratio of these shares as reported in the financial press is 8.

The company (RL) is planning a major investment that will cost ` 240 lakhs and is expected to produce additional

A
after-tax earnings over the foreseeable future at a rate of 15 percent on the amount invested. The necessary finance

T
is to be raised by a rights issue to the existing shareholders at a price 25 per cent below the current market price of

the company’s shares.

You are required to calculate:

(i) the current market price of the shares already in issue

(ii) the price at which the rights issue will be made

(iii) the number of new shares that will be issued

(iv) the value of the rights

(v) the price at which the shares of the company should theoretically be quoted on completion of the rights issue

(i.e., the ex-rights price), ignoring incidental and transaction costs. Assuming that - the rate of return on

existing funds is 12.5% and the market accepts the company’s forecast of incremental earnings.

Exercise 25-4 Amol Ltd. makes a rights issue at ` 5 a share of one of the new share for every 4 shares held. Before
the issue, there were 10 million shares outstanding and the share price was ` 6. Based on the above information, you
are required to compute:

(i) the total amount of new money raised.

(ii) how many rights are required to buy one new share?

(iii) what is the value of one right?

(iv) what is the prospective ex-rights price?

(v) how far could the total value of the company fall before shareholders would be unwilling to take up their rights?

(vi) whether the company’s shareholders are just as well as off, if right shares are issued at ` 5?
Exercise 25-5 Axles Limited has issued 10,000 equity shares of ` 10 each. The current market price per share is
` 30. The company has a plan to make a rights issue of one new equity share at a price of ` 20 for every four shares
held. You are required to:

(i) Calculate the theoretical post-rights price per share

(ii) Calculate the theoretical value of the rights alone

(iii) Show the effect of the rights issue on the wealth of a shareholder who has 1,000 shares assuming he sells the

entire rights, and

(iv) Show the effect if the same shareholder does not take any action and ignores the issue.

Exercise 25-6 ABC Limited’s shares are currently selling at ` 13 per share. There are 10,00,000 shares outstanding.
The firm is planning to raise ` 20 lakhs to finance a new project.

Required: What is the ex-right price of shares and the value of a right, if

(i) The firm offers one right share for every two shares held.

(ii) The firm offers one right share for every four shares held.

(iii) How does the shareholders’ wealth change from (i) to (ii) ? How does right issue increase shareholders’ wealth ?

N
Exercise 25-7 XYZ company has current earnings of ` 3 per share with 5,00,000 shares outstanding. The company

N
plans to issue 40,000, 7% convertible preference shares of ` 50 each at par. The preference shares are convertible into
2 shares for each preference share held. The equity share has a current market price of ` 21 per share.

A
(i) What is preference share’s conversion value ?

(ii) What is conversion premium ?

M
(iii) Assuming that total earnings remain the same, calculate the effect of the issue on the basic earning per share:

X
(a) before conversion, and (b) after conversion.

(iv) If profits after tax increases by ` 1 million what will be the basic EPS: (a) before conversion, and (b) on a fully

A
diluted basis ?

T
 Key to Practical Exercises

Exercise 25-1

Valuation of Rights Share of SBC Ltd.

MN + SR (180 × 6) + (150 × 1)
P = = = ` 175.71
N + R 6 + 1

∴ The minimum expected price of the share after the rights issue would be ` 175.71.

Exercise 25-2

Term loan to be raised = ` 100 lakhs

Amount to be raised through Rights issue = ` 100 lakhs

Total amount required for expansion project = ` 200 lakhs

N
Rights price (including premium) = ` 25

N
Number of rights shares to be offered = ` 1,00,00,000/` 25 = 4,00,000

Therefore, one rights share to be offered for every one existing share.

A
Existing EPS = ` 32,00,000/4,00,000 shares = ` 8

Price-earning ratio = 7

M
Market price per share = `8×7 = ` 56

1 − 4

X
Value of right (R) =
/ +

A
Where, P = Cum-rights market share price
0

T
S = Subscription price of rights share

N = Number of existing shares required for a rights issue

 − 
R = = ` 15.50
+
/1 + 4  × 
+  
Market value after rights issue = = = = ` 40.50
/ + + 
Number of shares outstanding after rights issue = 8,00,000 shares

Market capitalization = Ex-rights price × No. of shares outstanding

= ` 40.50 × 8,00,000 = ` 3,24,00,000

Calculation of Net asset value per share after rights issue `

( )

Paid up capital 80,00,000

Reserves and Surplus:

Existing 1,80,00,000

Premium rights issue 60,00,000 2,40,00,000

Networth of the company 3,20,00,000

Net asset value per share = ` 3,20,00,000/8,00,000 = ` 40 per share

Exercise 25-3

(i) Calculation of current market price of the shares already in issue

Earnings after tax (2015-16) = ` 80,00,000

No. of shares outstanding = 4,00,000 shares

EPS = ` 80,00,000/4,00,000 shares = ` 20

Price earning ratio = 8 (given)

Market price of share = ` 20 × 8 = ` 160

(ii) Price at which the rights issue will be made = ` 160 × 0.75 = ` 120

(iii) Number of new shares to be issued = ` 2,40,00,000/ ` 120 = 2,00,000 shares

(iv) Calculation of Value of Rights

S . − 4

Value of right =
/+S

Where, r = No. of rights issued N = No. of existing shares

N
M = Market price of share S = Issue price of rights

    − 

N
  
= = = ` 13.33
   +      

A
           
(v) Calculation of Ex-rights Price =   ×  +    × ×  = 106.67 + 48 = ` 154.67
    

M
      

X
Exercise 25-4

No. of shares outstanding = 1,00,00,000

A
Market price of share = ` 6

T
(i) Calculation of total amount of new money raised

    TIBSFT
No. of new shares issued = = 25,00,000 shares
 TIBSFT

New money raised = 25,00,000 shares × ` 5 = ` 1,25,00,000

(ii) No. of rights required to buy one new share = 4 rights

1 − 4 − 
(iii) Calculation of value of one right = = = = ` 0.20
/ +  + 

/1 + 4  × 
+  
(iv) Calculation of prospective ex-rights price = = = = ` 5.80
/ +  + 
(v) Computation of total value of the company fall before shareholders would be unwilling to take up their rights

When the price of share falls to ` 5, it will make rights issue unattractive.

Fall in total value of the company required to make the rights issue unattractive.

= ` 6,00,00,000 - (` 5 × 1,00,00,000) = ` 1,00,00,000

(vi) The rights price does not affect the shareholders’ wealth. Therefore, shareholders will be as well off, if shares

are issued at ` 4.

Exercise 25-5

(i) Calculation of Theoretical Post-rights (ex-right) Price Per Share

MN + SR ( ` 30 × 4) + (` 20 × 1)
Ex-rights value = = = ` 28
N + R 4 + 1
 (ii) Calculation of Theoretical Value of the Rights Alone

= Ex-rights price - Cost of rights share = ` 28 - ` 20 = ` 8

(iii) Calculation of Effect of the Rights Issue on the Wealth of a Shareholder who has 1,000 shares assuming he sells

the entire rights: `

( )

Value of shares before rights issue (1,000 shares × ` 30) 30,000

Value of share after rights issue (1,000 shares × ` 28) 28,000

Add: Sale proceeds of rights (250 rights × ` 8) 2,000

30,000

There is no change in the wealth of the shareholder after the right issue.

(iv) Calculation of Effect if the Shareholder does not take any action and ignores the issue. `
( )

Value of shares before rights issue (1,000 shares × ` 30) 30,000

Value of shares after the rights issue (1,000 shares × ` 28) 28,000

Loss of wealth to shareholder, if rights ignored 2,000

N
Exercise 25-6

N
Current market price of ABC Ltd.’s share = ` 13

` 20,00,000

A
Number of equity shares outstanding = 10,00,000 Investment planning in new project =

Calculation of Ex-rights Price and Value of Right

M
(i) If the firm offers on right share for every two shares held

Number of shares to be issued = 5,00,000

X
` 1,30,00,000 + ` 20,00,000
Ex-rights price = = ` 10

A
15,00,000 shares

Subscription price = ` 20,00,000/5,00,000 = ` 4

T
Value of rights = ( ` 10 - ` 4)/2 = ` 3

(ii) If Firm Offers One Right Share for Every Four Shares Held

Number of shares to be issued = 2,50,000

` 1,30,00,000 + ` 20,00,000
Pre-right price = = ` 12
12,50,000 shares

Subscription on price = ` 20,00,000/2,50,000 = ` 8

Value of right = ( ` 12 - ` 8)/4 = ` 1

(iii) Effect on Shareholders’ Wealth - The shareholders’ wealth will not change whether the rights offer is 1: 2 or

1: 4. Either the wealth created in the company represented in higher market value of share or the benefit of

lower subscription price is passed on to shareholders but then, the share price will be quoted lower. Since the

flotation costs of a rights issue is much lower than the public issue, the benefit can be transferred to existing

shareholders in the form of lower subscription price of rights issue.

Exercise 25-7

(i) Calculation of conversion value of preference share

Conversion value = 2 shares × ` 21 = ` 42

(ii) Calculation of conversion premium

Conversion premium = ( ` 50/ ` 42) - 1 = 19.05%

(iii) Calculation of the effect of the issue on basic earning per share, assuming that total earnings remain the same.

(a) EPS before conversion `

( )

Total earnings (after tax) ( ` 5,00,000 × 3) 15,00,000

Less: Preference dividend 1,40,000

Earnings available to equity shareholders 13,60,000

No. of equity shares outstanding 5,00,000

Existing EPS ` 2.72

(b) EPS after conversion `

( )

Total earnings (after tax) ( ` 5,00,000 × 3) 15,00,000

No. of equity shares outstanding (5,00,000 + 80,000) 5,80,000

Revised EPS ` 2.59

(iv) Calculation of EPS if profit is increased by ` 10,00,000

N
(a) EPS before conversion ( )

Total earnings after tax 25,00,000

N
Less: Preference dividend 1,40,000

A
Earnings available for equity shareholders 23,60,000

No. of equity shares outstanding 5,00,000

M
EPS ` 4.72

X
(b) EPS after conversion

Total earnings after tax ` 25,00,000

A
No. of equity shares outstanding 5,80,000

T
EPS ` 4.31
 Key to Short Answer Questions

True or False Statements

1. False - In the book building process, the investors make the bids, ‘at’ or ‘above’ the floor price. The price opted

by the majority of the bidders shall be decided as the subscription price.

2. False - Shareholder activism is a way that shareholders can claim their power to influence the corporation’s

behaviour and tries to change the status quo through voice, without a change in control of the firm.

3. True - In case of small issues, the companies can adjust the attributes of the offer according to the preferences

of the potential investors. It may not be possible in big issues, since the risk-return preference of the

investors cannot be estimated easily.

4. True - In efficient capital markets situation, the investors are aware of various parameters affecting the

market price of the securities.

N
5. False - The book building commences with appointment of a book running lead manager and submission

N
of a draft prospectus to SEBI. The book runner forms a syndicate of eligible subscribers who are

intermediaries registered with SEBI and who are permitted to carry on activities as underwriters.

A
6. False - The price of the instrument is the weighted average at which the majority of investors are willing to

buy the instrument. The price is investor driven and based on market forces of demand and supply.

M
7. False - ESOP is a stock option plan is used as a tool to retain the best talents with in the organization. It should

X
be exercised before a predetermined future period.

8. True - This is a temporary fall due to uncertainty in the market about the consequences of the issue, with

A
respect to future profits, earnings and dividends. Another reason for fall in price is due to more shares

T
available in the market, and new shares were issued at a discount price.

9. False - A shareholder who does not want to buy the right shares, his right of entitlement can be sold to

someone else.

10. True - The new issues as well as existing companies can determine the denomination of its face value of

shares. However, the shares shall not be issued in the denomination of less than a rupee and no decimal

of a rupee.

11. True - For making such on-line public issues, the appointment of various intermediaries by the issuer is a

prerequisite that such members/registrars have the required facilities to accommodate such an on-

line issue process.

12. False - The Indian companies are not allowed to issue tracking stocks so far, but it is only under consideration

and recommended by the expert committee headed by Dr JJ Irani.

13. False - The non-voting shares are closely akin to preference shares which do not carry any voting rights nor

is the dividend payable predetermined. But preference shares carry a predetermined rate of dividend.

Under Indian law, it is not possible for public limited company to issue non-voting shares.

Choose Correct Word

1. integral

2. financial

3. SEBI

4. higher

5. fall
 6. red-herring

7. 1988

8. coupon

9. rights issue

10. flotation

11. reduced

12. capital

13. explicit

14. equity

15. greater

16. one

17. private placement

Choose Correct Answer

N
1. (C) underwriting

N
2. (C) green option

3. (D) stock broker

A
4. (D) stock bonus plan

M
5. (A) employee stock option plan

6. (D) All of the above

X
7. (C) Central Government

A
8. (D) For all of the above

T
9. (B) follow on public offering

10. (A) of allocating shares in excess of the shares include in the public issue

11. (D) all of the above

12. (D) Both (A) and (B) above

 Practical Exercises

Exercise 26-1 Alpha Company is contemplating conversion of 500 14% convertible bonds of ` 1,000 each. Market
price of the bond is ` 1,080. Bond indenture provides that one bond will be exchanged for 10 shares. Price earning
ratio before redemption is 20 : 1 and anticipating price-earning ratio after redemption is 25 : 1. Number of shares

outstanding prior to redemption are 10,000. EBIT amounts to ` 2,00,000. The company is in the 35% tax bracket.

Should the company convert bond into shares? Give reasons.

Exercise 26-2 An established company is contemplating to issue 10% debentures to raise funds for financing its

ambitious expansion project. The funds ` 1,00,000 to be raised for the purpose will be paid off in 5 equal yearly

installments payable at the year end along with interest. The processing expenses are estimated to be 10% of the face

value of the debentures.

You are required to find out such a rate of return on investment as is sufficient to pay off the interest and principal

due for payment every year. Ignore taxes.

N
Exercise 26-3 Blue Ltd. is contemplating a debenture issue on the following terms:

N
Face value ` 100 per debenture Term to maturity 7 years

A
Coupon: Year 1 - 2 = 8% p.a. 3 - 4 = 12% p.a. 5 - 7 = 15% p.a.

The current market rate of interest on similar debentures is 15% per annum. The company proposes to price the issue

M
so as to yield a (compounded) return of 16% per annum to the investors. Determine the issue price. Assume the

redemption of debenture at a premium of 5%.

X
Exercise 26-4 The following data are available for a bond:

A
Face value ` 1,000

T
Coupon rate 16%

Years to maturity 6

Redemption value ` 1,000

Return to maturity 18%

What is the current market price duration and volatility of this bond? Calculate the expected market price, if increase

in required yield is 80 basis points.

Exercise 26-5 A firm has a bond outstanding ` 3,00,00,000. The bond has 12 years remaining until maturity, has

a 12.5% coupon and is callable at ` 1,050 per bond; it had floatation costs of ` 4,20,000, which are being amortised
at ` 30,000 annually. The floatation costs for a new issue will be ` 9,00,000 and the current interest rate will be 10%.

The after tax cost of the debt is 6%. Should the firm refund the outstanding debt? Show detailed workings. Consider

corporate income-tax rate at 50%.

Exercise 26-6 M/s Agfa Industries is planning to issue a debenture series on the following terms:

Face value ` 100 Term of Maturity 10 years

Years 1 - 4 5 - 8 9 - 10

Yearly coupon rate 9% 10% 14%

The current market rate on similar debentures is 15% p.a.. The company proposes to price the issue in such a manner

that it can yield 16% compounded rate of return to the investors. The company also proposes to redeem the

debentures at 5% premium on maturity. Determine the issue price of the debentures.

Exercise 26-7 ABC Ltd. has ` 300 million, 12 per cent bonds outstanding with six years remaining to maturity.

Since interest rates are falling, ABC Ltd. is contemplating of refunding these bonds with a ` 300 million issue of 6
year bonds carrying a coupon rate of 10 per cent. Issue cost of the new bond will be ` 6 million and the call premium
is 4 per cent. ` 9 million being the unamortized portion of issue cost of old bonds can be written off no sooner the
old bonds are called off. Marginal tax rate of ABC Ltd. is 30 per cent. You are required to analyze the bond refunding

decision.

Exercise 26-8 XYZ company has current earnings of ` 3 per share with 5,00,000 shares outstanding. The company
plans to issue 40,000, 7% convertible preference shares of ` 50 each at par. The preference shares are convertible into
2 shares for each preference share held. The equity share has a current market price of ` 21 per share.
(i) What is preference share’s conversion value ?

(ii) What is conversion premium ?

(iii) Assuming that total earnings remain the same, calculate the effect of the issue on the basic earning per share:

(a) before conversion, and (b) after conversion.

(iv) If profits after tax increases by ` 1 million what will be the basic EPS: (a) before conversion, and (b) on a fully
diluted basis ?

N
Exercise 26-9 Saranam Ltd. has issued convertible debentures with coupon rate 12%. Each debenture has an option

N
to convert to 20 equity shares at any time until the date of maturity. Debentures will be redeemed at ` 100 on maturity
of 5 years. An investor generally requires a rate of return of 8% p.a. on a 5-year security. As an investor when will

A
you exercise conversion for given market prices of the equity share of (i) ` 4, (ii) ` 5 and (iii) ` 6.

Cumulative P.V. factor for 8% for 5 years 3.993

M
P.V. factor for 8% for year 5 0.681

X
Exercise 26-10 A convertible bond with a face value of ` 1,000 is issued at ` 1,350 with a coupon rate of 10.5%. The

A
conversion rate is 14 shares per bond. The current market price of bond and share is ` 1,475 and ` 80 respectively.
What is the premium over conversion value?

T
 Key to Practical Exercises

Exercise 26-1

Analysis of Conversion of Bonds into Equity Shares `

( )

Particulars Pre-redemption Post-redemption

EBIT 2,00,000 2,00,000

Interest @ 14% 70,000 Nil

Taxable Income 1,30,000 2,00,000

Less: Tax @ 35 per cent 45,500 70,000

Net Income after tax 84,500 1,30,000

Outstanding shares (Nos.) 10,000 15,000

N
EPS ( )` 8.45 8.66

P/E Ratio 20 : 1 25 : 1

N
Market Price per share ( )` (P/E Ratio × EPS) 169 216.50

A
Comment - The company is suggested to convert the bond into shares and this will benefit both shareholders and

debentureholders. The post redemption market price of the equity shares would be ` 216.50 and the debenture/

M
bondholders would receive ` 1,690 in stock (i.e. ` 169 × 10 shares) in place of receiving cash ` 1,080 only.

X
Exercise 26-2

`
( )

A
Face value of debentures 1,00,000

T
Less: Processing expenses @ 10% 10,000

Initial cash inflow on issue of 10% Debentures 90,000

Redemption of debentures in 5 equal yearly installments of ` 20,000 (i.e ` 1,00,000/5 years).

Yearly Cash Outflow `

( )

Year Principal Interest Yearly outflow

(a) (b) (a) + (b)

1 20,000 1,00,000 × 10/100 = 10,000 30,000

2 20,000 80,000 × 10/100 = 8,000 28,000

3 20,000 60,000 × 10/100 = 6,000 26,000

4 20,000 40,000 × 10/100 = 4,000 24,000

5 20,000 20,000 × 10/100 = 2,000 22,000

Total cash outflow 1,30,000

Factor to be located = Initial cash inflow/Average cash outflow = 90,000/(1,30,000 ÷ 5 years) = 3.4615

The factor thus calculated (i.e. 3.4615) will be located in the present value table of ` 1 received annually for 5 years
would give the expected rate of interest rate of 14%, which can be used for calculation of IRR.
Calculation of IRR

Year Amount DCF P.V. DCF P.V.

`
( ) @ 14% `
( ) @ 15% `
( )

1 30,000 0.877 26,310 0.870 26,100

2 28,000 0.769 21,532 0.756 21,168

3 26,000 0.675 17,550 0.658 17,108

4 24,000 0.592 14,208 0.572 13,728

5 22,000 0.519 11,418 0.497 10,934

91,018 89,038

91,018 - 90,000
∴ IRR = 14% + × 1 = 14.51%
91,018 - 89,038

Exercise 26-3

Calculation of Present Value of Interest

N
Year Interest P.V. factor Present values

( ) ` @ 16% `
( )

N
1 8 0.8621 6.90

A
2 8 0.7432 5.95

3 12 0.6407 7.69

M
4 12 0.5523 6.63

5 15 0.4761 7.14

X
6 15 0.4104 6.16

A
7 15 0.3538 5.31

T
Total Present Value of Interest 45.78

Redemption price of debentures = ` 105

Present value of redemption price = ` 105 × 0.3538 = ` 37.15

Total present value = ` 37.15 + ` 45.78 = ` 82.93

The issue price of each debenture is to be fixed at ` 82.93.

Exercise 26-4

Current market price is the present value of future cash discounted at the time value of money.

Calculation of Current Market price and Duration

Year Cash flow Discount value Present value Proportion of Proportion

( )` @ 18% `
( ) bond value × Time (year)

1 160 0.8475 135.60 0.146 0.146

2 160 0.7182 114.91 0.124 0.248

3 160 0.6086 97.38 0.105 0.315

4 160 0.5158 82.52 0.088 0.352

5 160 0.4371 69.94 0.075 0.375

6 1,160 0.3704 429.66 0.462 2.772

Total 3.498 930.01 1.000 4.208

Duration 4.208
Volatility = = = 3.57
(1 + Yield) 1.18
Expected market price if yield increase in 80 points

Price will decrease by: Market price × Basis points × Volatility/100

930.01 × 0.80 × 3.57/100 = ` 26.56

New market price = ` 930.01 - ` 26.56 = ` 903.45

Exercise 26-5

(1) Calculation Present Value of Saving in Interest by Issue of New Bonds Replacing Old Bonds

Interest on bond outstanding p.a. = 3,00,00,000 × 12.5/100 = ` 37,50,000

Interest on new bonds p.a. = 3,00,00,000 × 10/100 = ` 30,00,000
Savings in interest by issue of new bonds = (37,50,000 - 30,00,000) (1 - 0.50) = ` 3,75,000
P.V. of savings in interest (@ 6% for 12 years) = 3,75,000 × 8.384 = ` 31,44,000

(2) Saving of Call Premium

Call premium per bond = Callable value - Face value = 1,050 - 1,000 = ` 50

50
or = × 100 = 5%

N
1,000

Total call premium = (3,00,00,000 × 5/100) (1 - 0.50) = ` 7,50,000

N
The call premium can be written of as an expense in the year the call is made.

A
(3) Floatation Costs

The floatation cost of issue of new callable bonds to mobilize ` 300 lakhs will be ` 9,00,000.

M
Amortisation of floatation cost p.a. (after tax) = (9,00,000/12) (1 - 0.50) = ` 37,500

X
P.V. of floatation cost amortised (after tax) (@ 6% p.a. for 12 years) = 37,500 × 8.384 = ` 3,14,400

(4) P.V. of Tax Saving by Amortisation of Outstanding Bonds

A
P.V. of immediate tax savings = ` 1,80,000

T
P.V. of tax saving if outstanding debt is continued = 30,000 × 0.50 × 8.384 = ` 1,25,760

P.V. of net tax saving = 1,80,000 - 1,25,760 = ` 54,240

Calculation of Total Net Savings by Replacing Outstanding Bonds with New Issue of Callable Bonds `
( )

P.V. of interest savings 31,44,000

P.V. of tax savings on floatation cost amortised of old bonds 3,14,400

P.V. of tax savings by amortisation of old debt 54,240

35,12,640

Less: Cash outflow on floatation cost 9,00,000

Call premium 7,50,000 16,50,000

P.V. of net savings if outstanding bonds are replaced with callable bonds 18,62,640

Analysis - It is suggested to replace the outstanding bonds with new debt by issue of callable bonds.

Exercise 26-6

Calculation of Present Value of Interest Payments

Years Cash outflow ( ) ` P.V. Factor @ 16% P.V.

1 9 0.862 7.758

2 9 0.743 6.687

3 9 0.641 5.769

4 9 0.552 4.968
 Years Cash outflow ( ) ` P.V. Factor @ 16% P.V.

5 10 0.476 4.76

6 10 0.410 4.10

7 10 0.354 3.54

8 10 0.305 3.05

9 14 0.263 3.682

10 14 + 105 = 119 0.227 27.013

71.327

Therefore, the issue price of debentures can be fixed at ` 71.327.

Exercise 26-7

(a) Calculation of initial outlay

Cost of calling old bonds with 4% call premium = ` 300 million × 104/100 = ` 312 million

N
Net proceeds of new issue = Gross proceeds of new issue - Issue costs

= ` 300 million - ` 6 = ` 294 million

N
Tax savings on call premium and unamortized cost = ( ` 12 + ` 9) 0.30 = ` 6.3 million

Initial outlay = 312 - 294 - 6.3 = ` 11.7 million

A
(b) Calculation of net present value of refunding the bond ( ` million)

M
Saving in annual interest expenses [300 × (0.12 - 0.10)] 6.00

Less: Tax saving on interest and amortization 0.30 [6 + (9 - 6)/6] 1.95

X
Annual net cash saving 4.05

A
PVIFA (7%, 6 years) (4.766 × 4.05) 19.30

T
Less: Initial outlay 11.70

NPV of refunding the bond 7.6

Decision - The bond should be refunded.

Exercise 26-8

(i) Conversion value of preference share = 2 shares × ` 21 = ` 42

(ii) Conversion premium = ( ` 50/ ` 42) - 1 = 19.05%

(iii) Calculation of the effect of the issue on basic earning per share, assuming that total earnings remain the same.

(a) EPS before conversion `

( )

Total earnings (after tax) ( ` 5,00,000 × 3) 15,00,000

Less: Preference dividend 1,40,000

Earnings available to equity shareholders 13,60,000

No. of equity shares outstanding 5,00,000

Existing EPS ` 2.72

(b) EPS after conversion `

( )

Total earnings (after tax) ( ` 5,00,000 × 3) 15,00,000

No. of equity shares outstanding (5,00,000 + 80,000) 5,80,000

Revised EPS ` 2.59

(iv) Calculation of EPS if profit is increased by ` 10,00,000

(a) EPS before conversion `

( )

Total earnings after tax 25,00,000

Less: Preference dividend 1,40,000

Earnings available for equity shareholders 23,60,000

No. of equity shares outstanding 5,00,000

EPS ` 4.72

(b) EPS after conversion

Total earnings after tax ` 25,00,000

No. of equity shares outstanding 5,80,000

EPS ` 4.31

Exercise 26-9

N
Present value of debentures if not converted `
( )

N
Interest ( ` 12 p.a. for 5 years @ 8% PVF i.e. 3.993) 47.916

` ` 100 × 0.681)

A
Redemption value of 100 at the end of 5th year ( 68.100

P.V. of debenture 116.016

M
Calculation of conversion value

X
No. of equity Market price Total value

shares offered per share ( ) ` after conversion ( ) `

A
20 4 80

T
20 5 100

20 6 120

Analysis - It is suggested that conversion should not be exercised, unless the market price of equity share is at ` 6.

Exercise 26-10

Face value of convertible bond = ` 1,000 Conversion rate per bond = 14 shares

Issue price of convertible bond = ` 1,350 Current market price of bond = ` 1,475
Coupon rate = 10.5% Current market price of share = ` 80

Conversion value = 14 shares × ` 80 = ` 1,120

  −   

Premium over conversion value = ×  = ×  = 31.7%
   
 Key to Short Answer Questions

True or False Statements

1. False - Junk bonds are corporate bonds with low ratings given by major credit rating agencies and not the

investors. High-rated bonds are called investment grade bonds, low rate bonds are called speculative

grade junk bonds.

2. True - Zero coupon bonds refer to those bonds which are sold at discount from their eventual maturity value

and have zero interest rate. The difference between the face value of the bond and the acquisition cost

is the gain to the investors.

3. False - Zero coupon bonds refer to those bonds which are sold at discount from their eventual maturity value

and have zero interest rate. The difference between the face value of the bond and the acquisition cost

is the gain to the investors.

N
4. True - Bonds may be issued, instead of a predetermined rate at which coupons are paid, it is possible to

structure the bonds. The bonds with credit enhancement mechanism (LC, escrow account etc.) are

N
called structured obligation.

A
5. False - CBLO is a negotiable instrument, which is fully collaterized with no credit risk associated with it, since

Clearing Corporation of India Ltd. provides guarantee against default to the counter-parties.

M
6. True - The mezzanine lender stands in line behind the senior lender in case of bankruptcy of the company.

True

X
7. - A call option provides an issuer of the option to redeem a bond, if interest rates decline and to reissue

the bond at a lower coupon.

A
8. False - Firms with low credit rating are willing to pay 3 to 5% more interest than the investment grade debt,

T
to compensate for greater risk.

9. True - The interest paid to the floating rate bond holders changes periodically depending on the market rate

of interest payable on gilt-edged securities. These bonds are also called as adjustable interest bonds.

10. False - SPN is a tradable instrument with detachable warrant against which the holder gets equity shares(s)

after a fixed period of time.

Choose Correct Word

1. zero coupon

2. deep discount

3. interest

4. increase

5. Securities Contracts Regulation

6. above

7. less than

8. amortizing

9. RBI

10. core

11. debt

12. government
13. government

14. negotiated dealing

Choose Correct Answer

1. (A) premium

2. (D) all of the above

3. (B) BBB-

4. (B) less than

5. (A) size of offering

6. (A) junk bonds

7. (C) Prexel Burnham Lambert

8. (B) SEBI

9. (D) all of the above

10. (C) unlisted companies

N
11. (A) stock market

N
12. (B) secured debentures

13. (D) all of the above

A
14. (D) items (A) and (B) only

M
15. (D) subordinated debt is included under Tiers I and II capital for the purpose of determining capital adequacy

of the bank

A X
T
 Practical Exercises

Exercise 27-1 Kastro Ltd. issued commercial paper as per following details:

Date of issue 19th October, 2016 Interest rate 7.25% per annum

Date of maturity 17th January, 2017 Face value of commercial paper ` 10 crore

What was the net amount received by the company on issue of commercial paper?

Exercise 27-2 RBI sold a 91 day T-bill of face value of ` 100 at an yield of 6%. What was the issue price ?

Exercise 27-3 From the following particulars, calculate the effective interest p.a. as well as the total cost of funds

to ABC Ltd., which is planning a CP issue:

Issue price of CP ` 97,350 Face value ` 1,00,000 Maturity period 3 months

N
Issue Expenses:

Brokerage 0.125% for 3 months Rating charges 0.5% p.a. Stamp duty 0.125% for 3 months

N
Exercise 27-4 LMN & Co. plans to issue Commercial Paper (CP) of ` 1,00,000 at a price of ` 98,000.

A
Maturity period : 4 months

Expenses for issues of CP are: (i) Brokerage 0.10%, (ii) Rating charges 0.60% and, (iii) Stamp duty 0.15%.

M
Find the effective interest rate per annum and the cost of Fund.

X
Exercise 27-5

A
(i) Beauty Ltd. has an excess cash of ` 16,00,000 which it wants to invest in short-term marketable securities.

T
Expenses relating to investment will be 40,000. The securities invested will have an annual yield of 8%.

The company seeks your advice as to the period of investment so as to earn a pre-tax income of 4%.

(ii) Also, find the minimum period for the company to break-even its investment expenditure. Ignore time value

of money.

Exercise 27-6 During a year the price of British gilts (face value £ 100) rose from £ 105 to £ 110, while paying a

coupon of £ 8. At the same time the exchange rate moved from $/£ 1.80 to 1.70.

What is the total return to an investor in USA who invested in this security?

Exercise 27-7 9 year Government of India security is quoted at 10.85%. The 364 T-Bill is quoted at 11.30. Last year

Indian National Bank had issued a fixed rate bond under statutory requirement at 16% coupon for a period of 10

years. Now when remaining 9 years are yet to expire, the Bank wants to convert their fixed rate obligation to floating

rate due to anticipation of decline in interest rates. Market quotation for fixed to floating rate swap is T-Bill rate vs.

75 bp over 9 year Government of India security, i.e. T-Bill rate = 11.6%.

If T-Bill declines 20 bp over the current year and rises by 5 bp every year thereafter, what is the effective cost of funds

to Indian National Bank for 10 year period.

 Key to Practical Exercises

Exercise 27-1

No. of days relevant for commercial paper = 13 + 30 + 31 + 16 = 90 days

The net amount received by the company on issue of commercial paper is as follows:

Interest 7.25% p.a.

7.25 × 90
Interest for 90 days = = 1.79%
365

1.79
Hence interest will be = × ` 10,00,00,000 = ` 17,58,522
100 + 1.79

New amount received at the time of issue = ` 10,00,00,000 - ` 17,58,522 = ` 9,82,41,478

Exercise 27-2

N
Issue price of T-bill is at discounted value and redeemed at face value.

N
Maturity period 91 days Face value ` 100 Yield rate 6% or 0.06

A
Let the issue of T-bill be ‘ x ’. Then

100 - x 365
0.06 = × × 100

M
x 91

100 - x

X
0.06 = × 4.011
x

A
0.06x = 401.10 - 4.011x

4.071x = 401.10

T
x = 401.10/4.071 = 98.53

∴ The issue of price of T-bill was ` 98.53.

Exercise 27-3

(a) Calculation of Effective Rate of Interest on CP

( )
Face value - Issue price 12 months
Effective Interest = × × 100
Issue price Maturity period

( )
1,00,000 - 97,350 12
= × × 100 = 10.89%
97,350 3

(b) Calculation of Total Cost of Funds (%)

Effective interest 10.89

Add: Brokerage (0.125 × 4) 0.50

Rating charge 0.50

Stamp duty (0.125 × 4) 0.50

Total cost of funds 12.39

Exercise 27-4

(i) Computation of effective rate of interest per annum

Effective rate of interest p.a.

 ' 1      
× ×

= = × ×  = 0.02041 × 3 × 100 = 6.12% (approx.)
1 N   

(ii) Calculation of Cost of Fund (%)

Effective interest 6.12

Brokerage 0.10

Rating charges 0.60

Stamp duty 0.15

Cost of funds 6.97

Exercise 27-5

(i) Pre-tax Income Required on Investment of ` 16,00,000 = ` 16,00,000 × 4/100 = ` 64,000

Let the period of investment be ‘P’

( )
8 P
16,00,000 × × - 40,000 = 64,000
100 12

N
(16,00,000 × 0.08 × 0.0833 P) - 40,000 = 64,000

N
10,662.40 P - 40,000 = 64,000

10,662.40 P = 64,000 + 40,000

A
P = 1,04,000/10,662.40 = 9.754

∴ To earn a 4% pre-tax return, ` 16,00,000 should be invested in short-term marketable securities for a period

M
9.754 months.

X
(ii) Calculation of Minimum Period to Break-even its Investment Expenditure

( )
8 P

A
16,00,000 × × - 40,000 = 0
100 12

T
10,662.4 P - 40,000 = 0

10,662.4 P = 40,000

P = 40,000/10,662.4 = 3.75

∴ The minimum period to break-even its investment expenditure is 3.75 months.

Exercise 27-6

Let us assume that, the amount invested by investor in USA is $ 1,000

By converting the investment into £ = $ 1,000/£ 1.80 = £ 555.55

Number of British gilts purchased = £ 555.55/£ 105 = 5.291

Calculation of Total Return Earned by USA Investor (£)

Coupon income (5.291 × £ 8) 42.328

Capital gain [5.291 × (£ 110 - £ 105)] 26.455

Redemption value 555.55

624.333

Total Amount Received = £ 624.333 × $ 1.70 = $ 1,061.366

$ 1,061.366 - $ 1,000
Total Return Earned = × 100 = 6.137%
$ 1,000
Exercise 27-7

Coupon rate of fixed rate bond = 16%

Coupon rate declines by 20 bp over the current year (i.e. 2nd year) and rises by 5 bp every year thereafter.

9 year GOI Security i.e. T.Bill rate = 11.6%

9 year GOI quoted at 10.85%; 364 T-Bill quoted at 11.3%

Swap rate on T-Bill = 10.85% + 0.75% = 11.6%

This means the National Bank has to pay T-Bill rate and receive fixed payment of 11.6% in year 2.

Year 1 = Interest cost is fixed rate of 16%

Year 2 = 16% - 11.6% + 11.3% = 15.7%

Year 3 = 16% - 11.6% + 11.1% = 15.5%

Year 4 = 16% - 11.6% + 11.15% = 15.55%

Year 5 = 16% - 11.6% + 11.2% = 15.6%

Year 6 = 16% - 11.6% + 11.25% = 15.65%

N
Year 7 = 16% - 11.6% + 11.3% = 15.7%

Year 8 = 16% - 11.6% + 11.35% = 15.75%

N
Year 9 = 16% - 11.6% + 11.4% = 15.8%

A
Year 10 = 16% - 11.6% + 11.45% = 15.85%

Total 157.1%

M
Effective interest cost = 157.1/10 = 15.71%

A X
T
 Key to Short Answer Questions

True or False Statements

1. False - Commercial Paper (CP) is an unsecured promissory note issued by a firm to raise funds for a short

period, generally varying from a few days to a few months.

2. False - Commercial Paper (CP) is a debt instrument for short-term borrowing. CP is a form of usance

promissory note, negotiable by endorsement and delivery. CP is not tied to any specific transaction.

3. False - Commercial paper is a debt instrument for short-term borrowing, that enables highly-rated corpo-

rate borrowers to diversify their sources of short-term borrowings and provides an additional

financial instrument to investors with a freely negotiable interest rate.

4. True - Repo and reverse repos are commonly used in the money markets as instruments of short-term

liquidity management and can also be termed as a collateralized lending and borrowing mechanism.

N
Banks and financial institutions usually enter into reverse repo transactions to manage their reserve

requirements or to manage liquidity.

N
5. False - Money market deals with the transactions of raising and supplying money in a short period not

exceeding one year though various instruments viz., treasury bills, gilt-edged securities, commercial

A
paper, certificate of deposit, call money etc. All these are unsecured money market instruments.

6. True - The eligible parties to deal in repo market include banks, primary dealers, mutual funds, insurance

M
companies, non-banking finance companies and housing finance companies.

False

X
7. - IBPCs can be issued only by the scheduled commercial banks.

False

A
8. - Participation certificates can be issued by banks against the working capital granted to the business

concerns.

T
9. True - NDS is provided with an objective of creating a broad-based and transparent market in Government

securities and thereby enhancing liquidity in the system.

10. True - CPs are issued by listed companies after obtaining the necessary credit rating for the CP and having

bank’s working capital limits.

11. True - CP is freely transferable and payable to bearer.

12. True - The non-bank entities are allowed to access to the call money market.

Choose Correct Word

1. money

2. disorganized

3. RBI

4. 14 days

5. default

6. one year

7. money

8. 364

9. repo

10. treasury bills

11. statutory liquidity ratio

12. ` 4 crore

13. commercial paper

14. certificate of deposit

15. call money

Choose Correct Answer

1. (B) 5 year public deposit

2. (B) a repurchase agreement

3. (C) Equity Shares

4. (C) usance promissory note

5. (C) 3 to 6 months

6. (A) 180 days

7. (B) 14 days

8. (C) 30 days

N
9. (D) ` 25 lakhs

N
10. (B) 12 months

11. (B) 15 days and above

A
12. (A) permission from RBI

13. (B) Unsecured short-term loan notes

M
14. (C) guaranteed by promoters

X
15. (A) act as a money market instrument

A
16. (A) CP is a negotiable instrument

17. (D) all of the above

T
 Practical Exercises

Exercise 28-1 The closing value of Sensex for the month of October, 2016 is given below:

Date Closing Sensex Value Date Closing Sensex Value

01.10.2016 2800 16.10.2016 3300

03.10.2016 2780 17.10.2016 3450

04.10.2016 2795 19.10.2016 3360

05.10.2016 2830 22.10.2016 3290

08.10.2016 2760 23.10.2016 3360

09.10.2016 2790 24.10.2016 3340

10.10.2016 2880 25.10.2016 3290

N
11.10.2016 2960 29.10.2016 3240

N
12.10.2016 2990 30.10.2016 3140

15.10.2016 3200 31.10.2016 3260

A
You are required to test the week form of efficient market hypothesis by applying the run test at 5% and 10% level

M
of significance.

Following value can be used:

X
Value of ‘t’ at 5% is 2.101 at 18 degrees of freedom Value of ‘t’ at 5% is 2.086 at 20 degrees of freedom

A
Value of ‘t’ at 10% is 1.734 at 18 degrees of freedom Value of ‘t’ at 10% is 1.725 at 20 degrees of freedom

T
 Key to Practical Exercises

Exercise 28-1

Date Closing sensex Sign of price charge

01.10.2016 2800

03.10.2016 2780 -

04.10.2016 2795 +

05.10.2016 2830 +

08.10.2016 2760 -

09.10.2016 2790 +

10.10.2016 2880 +

N
11.10.2016 2960 +

12.10.2016 2990 +

N
15.10.2016 3200 +

A
16.10.2016 3300 +

17.10.2016 3450 +

M
19.10.2016 3360 -

22.10.2016 3290 -

X
23.10.2016 3360 +

A
24.10.2016 3340 -

T
25.10.2016 3290 -

29.10.2016 3240 -

30.10.2016 3140 -

31.10.2016 3260 +

Total of sign of price changes (r) = 08

No. of positive changes = n = 11

1

No. of negative changes = n = 08

2

OO   ×  × 
µr = + = + = 176/10 + 1 = 10.26
O + O   + 

 OO   OO  − O − O 
 ×  × 
 ×  ×  −  − 

σ? =
 =

S O + O
O + O  − 
 + 
 +  − 

 × 
= =  = 2.06




Since too few runs in the case would indicate that the movement of prices is not random. We employ a two-tailed

test the randomness of prices.

Test at 5% level of significance at t.05 using t-table at 18 degrees of freedom.

?
Lower limit = µ − U×σ = 10.26 - 2.101 × 2.06 = 5.932
S
 ?
Upper limit = µ + U×σ = 10.26 + 2.101 × 2.06 = 14.588
S

At 10% level of significance at 18 degrees of freedom

Lower limit = 10.26 - 1.734 × 2.06 = 6.688

Upper limit = 10.26 + 1.734 × 2.06 = 13.832

As seen ‘r’ lies between these limits. Hence, the market exhibits weak form of efficiency.

N N
M A
A X
T
 Key to Short Answer Questions

True or False Statements

1. True - Members of stock exchanges are subject to gross exposure limits. Gross exposure for a member, across

all securities in rolling settlements, is computed as absolute (buy value and sell value), i.e. ignoring +ve

and -ve signs, across all open settlements. Open settlements would be all those settlements for which

trading has commenced and for which settlement pay-in is not completed.

2. True - The market capitalization of a company is said to be its share price multiplied by the number of its

shares outstanding. The market capitalization of each company’s share is calculated discretely and

then added up for finding the total market capitalization.

3. True - The efficient market hypothesis (EMH) implies that new information is revealed about a firm it will

be incorporated into the share price rapidly and rationally, with respect to the direction of the share

N
price movement and the size of that movement.

4. True - The strong form of efficient market hypothesis (EMH) requires all known information to be

N
impounded in the current share price, whether publicly and generally available or not. The basic

assumption of EMH is that in an efficient capital market, prices of traded securities always fully reflect

A
all publicly available information concerning the securities. The developed stock exchange network

will enable the existence of strong form of market efficiency.

M
5. False - The securities that are already outstanding and owned by the investors are usually bought and sold

X
through secondary market. It is also called as stock market.

6. False - The securities of government are traded in the stock market as a separate component, called gilt edged

A
market.

T
7. True - The listing agreement ensures that the company provides all the information pertaining to its working

from time to time and all price sensitive information.

8. True - The principal objective of listing is to provide liquidity and marketability to listed securities and

ensure effective monitoring of trading for the benefit of all participants in the market.

9. True - Short selling is the sale of a security that is not owned by the seller, but with a promise to deliver the

same.

10. True - Day trading is not allowed to the institutional investors, they will be required to fulfil their obligation

on a gross basis.

11. True - The stock market index captures the behaviour of the overall market.

Choose Correct Word

1. stock

2. SEBI

3. T+3

4. index

5. semi-strong

6. over the counter exchange

7. scripless

8. demat

9. internet based
10. margins

11. 50%

Choose Correct Answer

1. (C) Listed

2. (C) mark to market margin

3. (A) T+0

4. (C) 49

5. (D) answer (A) and (B) are correct

6. (A) increase

7. (A) increase

8. (C) no change

9. (B) decrease

10. (B) decrease

N
11. (A) developed

N
12. (A) increase

13. (B) semi-strong form of market efficiency

A
14. (B) semi-strong form of efficiency

M
15. (C) strong form of efficient market hypothesis

16. (C) super strong form of market efficiency

X
17. (C) power to suspend business of a recognized stock exchange

A
18. (B) Positive abnormal returns can be expected from low P/E stock

T
19. (C) Price of one share is independent of the prices of other shares in the market

20. (C) Investors can’t beat the market unless they have better information about the value of the asset

21. (D) market prices contain errors, but these being random cannot be exploited by investors
 Practical Exercises

Exercise 31-1 Your company is considering to acquire an additional computer to supplement its time-share

computer services to its clients. It has two options:

(i) To purchase the computer for ` 22 lakhs.

(ii) To lease the computer for 3 years from a leasing company for ` 5 lakhs as annual lease rent plus 10% of gross
time-share service revenue. The agreement also requires an additional payment of ` 6 lakhs at the end of the
third year. Lease rents are payable at the year-end, and the computer reverts to the lessor after the contract

period.

The company estimates that the computer under review will be worth ` 10 lakhs at the end of the third year. Forecast
revenues are:

Year 1 2 3

N
Amount ( ` lakhs) 22.5 25 27.5

N
Annual operating costs excluding depreciation/lease rent of computer are estimated at ` 9 lakhs with an additional

` 1 lakh for start up and training costs at the beginning of the first year. These costs are to be borne by the lessee. Your

A
company will borrow at 16% interest to finance the acquisition of the computer. Repayments are to be made

according to the following schedule: ( ` ’000)

M
Year end 1 2 3

X
Principal 500 850 850

Interest 352 272 136

A
The company uses straight line method (SLM) to depreciate its assets and pays 50% tax on its income. The

T
management approaches the company secretary for advice. Which alternative would be recommend and why ?

Note - The PV factors at 8% and 16% rates of discount are:

Year 1 2 3

8% 0.926 0.857 0.794

16% 0.862 0.743 0.641

Exercise 31-2 The FFM Ltd. is in the tax bracket of 35% and discounts its cash flows at 16%. In the acquisition of

an asset worth ` 10,00,000, it is given two offers - either to acquire the asset by taking a bank loan @ 15% p.a. repayable
in five yearly instalments of ` 2,00,000 each plus interest or to lease-in the asset at yearly rentals of ` 3,24,000 for five
years. In both cases, the instalment is payable at the end of the year. Applicable rate of depreciation is 15% using

‘written down value’ (WDV) method.

You are required to suggest the better alternative.

Year 1 2 3 4 5

P.V. factor @ 16% 0.862 0.743 0.641 0.552 0.476

Exercise 31-3 ABC Ltd. is considering a proposal to acquire an equipment costing ` 5,00,000. The expected

effective life of the equipment is 5 years. The company has two options - either to acquire it by obtaining a loan of

` 5 lakhs at 12% interest p.a. or by lease. The following additional information are available:

(i) the principal amount of loan will be repaid in 5 equal yearly instalments.

(ii) the full cost of the equipment will be written off over a period of 5 years on straight line basis and it is to be

assumed that such depreciation charge will be allowed for tax purpose.
(iii) the effective tax rate for the company is 40% and the after tax cost of capital is 10%.

(iv) the interest charge, repayment of principal and the lease rentals are to be paid on the last day of each year.

You are required to work out the amount of lease rental to be paid annually, which will match the loan option. The

discount factor at 10% are as follows:

Year 1 2 3 4 5

Discount factor 0.909 0.826 0.751 0.683 0.621

Exercise 31-4 ABC Finance Ltd. is a hire purchase and leasing company. It has been approached by a small business

firm interested in acquiring a machine through leasing. The quoted price of the machine is ` 5,00,000. 10% sale tax
is extra. The lease will be for a primary lease period of 5 years.

The finance company wants 8% post-tax return on the outlay. Its effective tax rate is 35%. The income tax rate of

depreciation on the machine is 25% (WDV). Lease rents are payable in arrear at the end of each year.

Calculate the annual rent to be charged by ABC Finance Ltd.

Exercise 31-5 LB Ltd. has decided to acquire machine M costing ` 63,000. It will have an operational life of 4 years,

N
with nil scrap value. Tax is payable at 30% on operating cash flows in the same year. Capital allowances are available

at 25% a year on a reducing balance basis.

N
The company has the opportunity either to purchase the machine or to lease it under a finance lease arrangement,

` 20,000 for four years, payable at the end of each year. The company can borrow to finance the

A
at an annual rent of

acquisition at 10%. Should the company lease or buy the machine ?

M
Exercise 31-6 Laxmi Enterprise is to acquire a personal computer complete with multimedia kit and a printer. Its

price is ` 60,000. Laxmi Enterprise can borrow ` 60,000 from Punjab National Bank at 12% interest per annum to

X
finance the purchase. The principal sum is to be repaid in 5 equal yearly instalments. Laxmi Enterprise can also have

the computer on lease for 5 years and seeks your advice to know the maximum lease rent per year payable at the end

A
of each year.

T
You collect the following additional information:

(i) Interest on bank loan is payable at the end of each year.

(ii) The full cost of the computer will be written off over the effective life of computer on a straight line basis. This

is allowed for tax purposes.

(iii) At the end of year 5, the computer may be sold for ` 1,500 through second hand dealer who will charge 8%

commission on the sale proceeds.

(iv) The company’s effective tax rate is 30%.

(v) The cost of capital is 11%.

Suggest the maximum lease rental for Laxmi Enterprise.

Exercise 31-7 MB Leasing Company has been approached by a client to write a 5-year lease on an equipment. The

equipment is eligible for depreciation at 25 per cent for Income-tax purpose. In the terminal year, the client will be

required to pay 1 per cent of the equipment cost to acquire the ownership of the asset. The post-tax rate of return

of the leasing company is 12 per cent. Assuming that the lessor is subject to a Corporate tax rate of 35 per cent,

calculate pre-tax annual lease rental payable in arrear, and express the same in terms of standard lease quotation i.e.

rupees per thousand per month.

Note: Extracted from the table:

(i) The present value factors at 12% discount rate for 0 to 5 years are : 1.0000, 0.8928, 0.7972, 0.7118, 0.6355 and 0.5674.

(ii) The present value factor of an annuity of ` 1 for 60 months at 12%

- n
[using the formula : 1-(1+r) /r] = 44.9550]
Exercise 31-8 Titanic Instruments Ltd. is in the business of manufacturing Bearings. Some more product lines are

being planned to be added to the existing system. The company has decided to acquire a machine costing ` 10,00,000
having a useful life of 5 years with the salvage value of ` 2,00,000 (considering short-term capital loss/gain for the

income tax). The full purchase value of machine can be financed by bank loan at the rate of 10% interest p.a. repayable

in five equal instalments falling due at the end of each year. Alternatively, the machine can be produced on 5 years

lease, year end lease rentals being ` 2,50,000 per annum. The company follows the written down value method of

depreciation at the rate of 25 per cent. The company is in the 30 per cent tax bracket.

Requirements:

(i) What is the present value (PV) of cash outflow for each of these financial alternatives using the after-tax cost

of Debt?

(ii) Which of the two alternatives is preferable?

Note : Extracted from the Table of PV:

(i) PVIF at 7% for 0 to 5 years are: 1.000, 0.9346, 0.8734, 0.8163, 0.7629, 0.7130.

(ii) PVIF at 10% for 0 to 5 years are: 1.0000, 0.9091, 0.8264, 0.7513, 0.6830, 0.6209.

(iii) PVIFA for 5 years at 10% = 3.7908.

N
(iv) PVIFA for 5 years at 7% = 4.1002.

N
Exercise 31-9 AB Ltd. is considering to buy an equipment and it has two options. The cost of the equipment is

` 1,00,000.

A
Option I to buy with borrowed funds at a cost of 18% p.a. repayable in five equal instalments of ` 32,000

M
Option II to take the equipment on lease on an annual rental of ` 32,000

X
The salvage value of the equipment at the end of five-year period will be zero. The company uses straight-line

depreciation. Assume tax @ 40%. Which of the two options would you recommend? Discounting factors are:

A
Year 1 Year 2 Year 3 Year 4 Year 5

T
@ 9% 0.917 0.842 0.772 0.708 0.650

@ 11% 0.901 0.812 0.731 0.659 0.593

@ 18% 0.847 0.718 0.609 0.516 0.437

 Key to Practical Exercises

Exercise 31-1

22,00,000 - 10,00,000
Depreciation p.a. = = ` 4,00,000 p.a.
3 years

Effective rate of interest after tax shield = 16% (1 - 0.50) = 8%

Operating and training costs are not considered while calculation of net present value of cash flows of both

alternatives.

Alternative I - Purchase of Computer `

( )

Years 1 2 3

Instalment payment

N
Principal 5,00,000 8,50,000 8,50,000

Interest @ 16% 3,52,000 2,72,000 1,36,000

N
(a) 8,52,000 11,22,000 9,86,000

A
Tax shield 50% on

Interest Payment 1,76,000 1,36,000 68,000

Depreciation ( ` 4 lakh p.a.) 2,00,000 2,00,000 2,00,000

M
Total (b) 3,76,000 3,36,000 2,68,000

X
Net cash outflow (a) - (b) 4,76,000 7,86,000 7,18,000

PV Factor at 8% 0.926 0.857 0.794

A
PV of cash outflow 4,40,776 6,73,602 5,70,092

T
`
( )

Total present value of cash outflow (4,40,776 + 6,73,602 + 5,70,092) 16,84,470

Less: PV of salvage value of computer (10,00,000 × 0.794) 7,94,000

Net PV of cash outflow 8,90,470

Alternative II - Lease the Computer `

( )

Years 1 2 3

Lease rent 5,00,000 5,00,000 5,00,000

10% of gross revenue 2,25,000 2,50,000 2,75,000

Lump sum payment - - 6,00,000

Total payment 7,25,000 7,50,000 13,75,000

Tax shield-50% on lease payment 3,62,500 3,75,000 6,87,500

Net cash outflow 3,62,500 3,75,000 6,87,500

PV Factor at 8% 0.926 0.857 0.794

PV of cash outflow 3,35,675 3,21,375 5,45,875

Total PV of cash outflow = ` 12,02,925

Suggestion - Since the present value of net cash outflow of Alternative I is lowest, it is suggested to purchase the

computer instead of leasing it.

Exercise 31-2

Alternative I - Acquire the Asset by taking a Bank Loan `

( )

Years 1 2 3 4 5

Interest (@ 15% p.a.) (a) 1,50,000 1,20,000 90,000 60,000 30,000

Depreciation (@ 15% WDV) 1,50,000 1,27,500 1,08,375 92,118 78,301

3,00,000 2,47,500 1,98,375 1,52,118 1,08,301

Less: Tax shield (@ 35%) (b) 1,05,000 86,625 69,431 53,241 37,905

Interest less tax shield (a) - (b) 45,000 33,375 20,569 6,759 (-)7,905

Principal repayment 2,00,000 2,00,000 2,00,000 2,00,000 2,00,000

Total cash outflow 2,45,000 2,33,375 2,20,569 2,06,759 1,92,095

N
Discount factor (@ 16%) 0.862 0.743 0.641 0.552 0.476

Present value 2,11,190 1,73,397 1,41,385 1,14,131 91,437

N
P.V. of total cash outflow = ` 7,31,540

A
Alternative II - Acquire Asset on Lease Basis `
( )

Year Rentals Tax shield Net cash @ 35% Discount out flow P.V. @ 16%

M
1 3,24,000 1,13,400 2,10,600 0.862 1,81,537

X
2 3,24,000 1,13,400 2,10,600 0.743 1,56,476

A
3 3,24,000 1,13,400 2,10,600 0.641 1,34,995

T
4 3,24,000 1,13,400 2,10,600 0.552 1,16,251

5 3,24,000 1,13,400 2,10,600 0.476 1,00,246

P.V. of total cash outflow under lease option = ` 6,89,505

Analysis - By making analysis of both the above alternatives, we can observe that the present value of the cash outflow

is lower in Alternative II by ` 42,035 (i.e. ` 7,31,540 - ` 6,89,505). Hence it is suggested to acquire the asset on lease
basis.

Exercise 31-3

Calculation of Interest under Loan Option and Depreciation `

( )

Year Principal amount Repayment Principal at Interest for Depreciation

at beginning of year at end of year end of year year @ 12% for year

1 5,00,000 1,00,000 4,00,000 60,000 1,00,000

2 4,00,000 1,00,000 3,00,000 48,000 1,00,000

3 3,00,000 1,00,000 2,00,000 36,000 1,00,000

4 2,00,000 1,00,000 1,00,000 24,000 1,00,000

5 1,00,000 1,00,000 Nil 12,000 1,00,000

Calculation of Present Value under Loan Option ( )`

Year Repayment Interest Total Tax on Interest Total Net outflow Discount NPV

of principal on loan (1)+(2) depreciation (a)+(b) (3) - (c) factor

(1) (2) (3) (a) (b) (c)

1 1,00,000 60,000 1,60,000 40,000 24,000 64,000 96,000 0.909 87,264

2 1,00,000 48,000 1,48,000 40,000 19,200 59,200 88,800 0.826 73,349

3 1,00,000 36,000 1,36,000 40,000 14,400 54,400 81,600 0.751 61,282

4 1,00,000 24,000 1,24,000 40,000 9,600 49,600 74,400 0.683 50,815

5 1,00,000 12,000 1,12,000 40,000 4,800 44,800 67,200 0.621 41,731

Total present value of cash outflows 3.790 3,14,441

Annual cash outflow after-tax = 3,14,441/3.790 = ` 82,966

82,966
Annual lease rental which will be indifferent to loan option = = ` 1,38,277
1 - 0.40

Exercise 31-4

N
Determination of Cash outflows ( )`

N
Cost of machine inclusive sale tax (10%) 5,50,000

Less: Tax saving on Depreciation (Tax shield Relief) 1,22,284

A
Present value of cash outflows for purchase 4,27,716

M
Computation of Tax Saving on Depreciation of the Machine ( )

Year Cost/WDV Depreciation Tax PV factor P.V. of Dep.

X
@ 25% @ 35% @ 8% tax shield

A
1 5,50,000 1,37,500 48,125 0.926 44,564

2 4,12,500 1,03,125 36,094 0.857 30,933

T
3 3,09,375 77,344 27,070 0.794 21,494

4 2,32,031 58,008 20,303 0.735 14,923

5 1,74,023 43,506 15,227 0.681 10,370

3.993 1,22,284

Calculation of Leasing Rent

Let, the required lease rent per year be ‘R’. ∴ Post-tax rental income p.a. (1 - 0.35) = 0.65R

P.V. of 5 year’s post-tax rental income = 0.65R × 3.993

This sum should be equal to ` 4,27,716

0.675R × 3.993 = 4,27,716

R = 4,27,716/2.59545 = 1,64,795

Hence, the annual rent to be charged by ABC Finance Ltd. is ` 1,64,795.

Exercise 31-5

Calculation of Depreciation and its Tax benefit ( )`

Year WDV Depreciation WDV Tax benefit

at the beginning at the end on depreciation @ 30%

1 63,000 15,750 47,250 4,725

2 47,250 11,813 35,437 3,544

3 35,437 8,859 26,578 2,658

4 26,578 26,578 - 7,973

Marginal cost of borrowing = 10% (1 - 0.30) = 7% Lease rental is subject to tax benefit of 30%.

Evaluation of Lease or Buy proposal `

( )

Year Lease rentals Tax shield Total cash Discount Discounted

(after tax) on depreciation lost outflow factor @7% cashflow

1 14,000 4,725 18,725 0.9346 17,500

2 14,000 3,544 17,544 0.8734 15,323

3 14,000 2,658 16,658 0.8163 13,598

4 14,000 7,973 21,973 0.7629 16,763

Present value of total cash outflow 63,184

NPV = 63,000 - 63,184 = ` 184 (negative)

Suggestion - Since NPV is negative, it is suggested to purchase the equipment to minimize the cash outflow.

Exercise 31-6

Annual loan repayment = ` 60,000/5 = ` 12,000

`
( )

N
Residual sale value at the end of year 5 1,500

N
Less: Commission at 8% 120

1,380

A
Less: Tax at 30% 414

Net cash flow 966

M
Calculation of cash outflow under loan option `
( )

X
Year 1 2 3 4 5 Total

A
Principal repayment 12,000 12,000 12,000 12,000 12,000 60,000

Payment of interest 7,200 5,760 4,320 2,880 1,440 21,600

T
19,200 17,760 16,320 14,880 13,440 81,600

Less: Tax savings on depreciation 3,600 3,600 3,600 3,600 3,600 18,000

Tax savings on interest 2,160 1,728 1,296 864 432 6,480

13,440 12,432 11,424 10,416 9,408 57,120

Discount factor @ 11% 0.901 0.812 0.731 0.659 0.593

Present value of cash outflow 12,109 10,095 8,351 6,864 5,579 42,998

P.V. of cash inflow of residual value = ` 966 × 0.593 = ` 573

P.V. of net cash outflow = ` 42,998 - ` 573 = ` 42,425

C  
Annual equivalent of P.V. of net cash outflow = = ` 11,480


C  
P.V. of pre-tax lease rental per year = = ` 16,400
 

Maximum pre-tax annual rental should be ` 16,400.

Exercise 31-7

Calculation Depreciation on Equipment `

( )

Year WDV at the Depreciation WDV at the

beginning on WDV @ 25% end

1 1,000.0 250.0 750.0

2 750.0 187.5 562.5

3 562.5 140.6 421.9

4 421.9 105.5 316.4

5 316.4 79.1 237.3

Calculation present value of Depreciation @ 12%

= (250 × 0.8928) + (187.5 × 0.7972) + (140.6 × 0.7118) + (105.5 × 0.6355) + (79.1 × 0.5674)

= 223.20 + 149.475 + 100.079 + 67.05 + 44.88 = ` 584.68

Present value of tax saving on depreciation = ` 584.68 × 0.35 = ` 204.64

Present value of residual cashflow = ` 1,000 × 1/100 × 0.5674 = ` 5.67

N
Calculation of amount to be recovered through post-tax lease rental `
( )

N
Value of asset 1,000.00

A
Less: Tax saving on depreciation 204.64

Residual cashflow 5.67 210.31

M
Net post-tax lease rental 789.69

X
C  
Post-tax lease rental = = ` 17.57 (per thousand per month)


A
C 
`

T
Pre-tax lease rental = = 27.03 (per thousand per month)
 − 
Exercise 31-8

Working Notes

Calculation of Depreciation `
( )

Year Opening WDV Depreciation Closing WDV

1 10,00,000 2,50,000 7,50,000

2 7,50,000 1,87,500 5,62,500

3 5,62,500 1,40,625 4,21,875

4 4,21,875 1,05,469 3,16,406

5 3,16,406 79,101 2,37,305

Discounting factor = Cost of finance - Tax = 10% - 30% of 10% = 7%

Debt payment schedule `

( )

Year Opening Interest Installment Principal Closing

end balance @ 10% repayment balance

1 10,00,000 1,00,000 2,63,796 1,63,796 8,36,204

2 8,36,204 83,620 2,63,796 1,80,176 6,56,028

3 6,56,028 65,603 2,63,796 1,98,193 4,57,835

4 4,57,835 45,783 2,63,796 2,18,013 2,39,822

5 2,39,822 23,974 2,63,796 2,39,822 -

Alternative I - Purchase of machine financed by bank loan `
( )

Year Loan Tax shield Tax shield Net cash PVIF Present

end installment on interest on depreciation outflow @ 7% values

1 2,63,796 30,000 75,000 1,58,796 0.9346 1,48,411

2 2,63,796 25,086 56,250 1,82,460 0.8734 1,59,360

3 2,63,796 19,681 42,187 2,01,928 0.8163 1,64,834

4 2,63,796 13,735 31,641 2,18,420 0.7629 1,66,633

5 2,63,796 7,192 23,730 2,32,874 0.7130 1,66,039

Total present value of cash outflows 8,05,277

Less: P.V. of salvage value ( ` 2,00,000 × 0.7130) 1,42,600

6,62,677

Less: P.V. of Tax savings on short-term capital loss[(2,37,305 - 2,00,000) × 0.30 × 0.7130] 7,980

Net present value of cash outflow 6,54,697

N
Alternative II - Obtain the machine on lease basis.

P.V. of lease rent after tax shield for 1-5 years = ` 1,75,000 × 4.1002 = ` 7,17,535

N
Suggestion - Since the net present value of cash outflow is lower in case of alternative I, it is suggested to purchase

A
machine financed by bank loan.

Exercise 31-9

M
Option I - Buy an equipment with borrowed funds

X
Cost of borrowed funds = 18%

After tax cost of borrowed funds = 18%(1 - 0.40) = 10.8% say 11%

A
Depreciation per annum = ` 1,00,000/5 years = ` 2,000 p.a.

T
Schedule of Debt repayment `
( )

Year Op. balance Installment Interest Principal Cl. balance

end of principal repayment of principal

1 1,00,000 32,000 18,000 14,000 86,000

2 86,000 32,000 15,480 16,520 69,480

3 69,480 32,000 12,506 19,494 49,986

4 49,986 32,000 8,997 23,003 26,983

5 26,983 32,000 5,017* 26,983 -

* Balancing figure

Calculation of Present Value of cash outflows `

( )

Year Annual Tax shield Tax shield on Net cash P.V. factor Present

end installment on interest depreciation outflow @ 11% values

1 32,000 7,200 8,000 16,800 0.901 15,137

2 32,000 6,192 8,000 17,808 0.812 14,460

3 32,000 5,002 8,000 18,998 0.731 13,888

4 32,000 3,599 8,000 20,401 0.659 13,444

5 32,000 2,007 8,000 21,993 0.593 13,042

Present value of total cash outflows 69,971

Option II - Take the equipment on lease `
( )

Year Annual Tax Net cash P.V. factor Present

end lease rent shield outflow @ 11% values

1 32,000 12,800 19,200 0.901 17,299

2 32,000 12,800 19,200 0.812 15,590

3 32,000 12,800 19,200 0.731 14,035

4 32,000 12,800 19,200 0.659 12,653

5 32,000 12,800 19,200 0.593 11,386

Present value of total cash outflows 70,963

Suggestion - The present value of total cash outflows is lower in case of Option I. Hence it is suggested to buy the

equipment with borrowed funds.

N N
M A
A X
T
 Key to Short Answer Questions

True or False Statements

1. False - The operating lease agreement gives to the lessee only a limited right to use the asset. The lessor will

enjoy the depreciation claim and the responsibility of the lessee is to maintain and upkeep the asset

properly when the asset is under his control.

2. True - The lease is basically a contract whereby the owner of the asset (the lessor) grants to another party (the

lessee) to exclusive right to use the asset for an agreed period of time. The basic lease period refers to

the period during which the lease is irrevocable.

3. True - Practically all the risks incidental to the asset ownership and all the benefits arising there from is

transferred to the lessee who bears the cost of maintenance, insurance and repairs. Only the title deeds

remain with the lessor under financial lease.

False

N
4. - In lease transactions, the lessor is entitled to claim depreciation allowance and the lease rentals will

be taken into consideration in computation of taxable income.

N
5. False - In a cross boarder lease transaction, the lessor and the lessee are domiciled in different countries, the

domicile of the supplier is immaterial.

A
6. False - In installment sale, the ownership of the asset is transferred to the buyer on payment of the first

installment. In hire purchase the ownership is transferred to the hirer only when he exercises the

M
option to purchase or a payment of the last installment.

X
7. True - The major part of finance is arranged with the financier to whom the title deeds of the asset are

assigned.

A
8. True - In sales aid leasing, the leasing company will enter into an agreement with the seller, usually

T
manufacturer of the equipment, to market the latter’s product through its leasing operations.

Choose Correct Word

1. leveraged

2. greater

3. full title

4. deferred payment

5. stepped-up

6. lease

7. owning

8. business

9. financial

10. irrevocable

11. financial

12. end-consumer

13. efficiency

14. sale and lease back

15. operating

Choose Correct Answer

1. (A) finance lease

2. (D) leveraged lease

3. (B) lessee

4. (D) all of the above

5. (A) equal annual plan

6. (B) on making final payment

7. (A) lessor

8. (A) leasing and borrowing to buy will always be equivalent

9. (B) when the lessee want to own the asset but does not have enough funds to invest

N N
M A
A X
T
 Practical Exercises

Exercise 32-1 A mutual fund that had a net asset value of ` 20 at the beginning of month - made income and capital
gain distribution of ` 0.0375 and ` 0.03 per share respectively during the month, and then ended the month with
a net asset value of ` 20.06. Calculate monthly return.

Exercise 32-2 A mutual fund that had a net asset value of ` 16 at the beginning of a month, made income and capital
gain distribution of ` 0.04 and ` 0.03 respectively per unit during the month, and then ended the month with a net
asset value of ` 16.08. Calculate monthly and annual rate of return.

Exercise 32-3 Mr. X earns 10% on his investments in equity shares. He is considering a recently floated scheme of

a Mutual Fund where the initial expenses are 6% and annual recurring expensed are expected to be 2%. How much

the Mutual Fund scheme should earn to provide a return of 10% to Mr. X ?

Exercise 32-4 An investor purchased 300 units of a Mutual Fund at ` 12.25 per unit on 31st December, 2015. As

N
on 31st December, 2016 he has received ` 1.25 as dividend and ` 1.00 as capital gains distribution per unit.

N
Required:

(i) The return on the investment if the NAV as on 31st December, 2016 is ` 13.00.

A
(ii) The return on the investment as on 31st December, 2016 if all dividends and capital gains distributions are

reinvested into additional units of the fund at ` 12.50 per unit.

M
Exercise 32-5 Mr. Sinha has invested in three Mutual fund schemes as per details below: `
( )

X
Scheme X Scheme Y Scheme Z

A
Date of investment 01.12.2015 01.01.2016 01.03.2016

T
Amount of investment 5,00,000 1,00,000 50,000

Net asset value at entry date 10.50 10.00 10.00

Dividend received upto 31.03.2016 9,500 1,500 Nil

NAV as at 31.03.2016 10.40 10.10 9.80

You are required to calculate the effective yield on per annum basis in respect of each of the three schemes to

Mr. Sinha upto 31.03.2016.

Exercise 32-6 A Mutual Fund having 300 units has shown its NAV of ` 8.75 and ` 9.45 at the beginning and at the
end of the year respectively. The Mutual Fund has given two options:

(i) Pay ` 0.75 per unit as dividend and ` 0.60 per unit as a capital gain, or

(ii) These distributions are to be reinvested at an average NAV of ` 8.65 per unit.

What difference it would make in terms of return available and which option is preferable?

Exercise 32-7 A company has a choice of investments between several different equity oriented mutual funds. The

company has an amount of ` 1 crore to invest. The details of the mutual funds are as follows:

Mutual Fund A B C D E

Beta 1.6 1.0 0.9 2.0 0.6

Required:

(i) If the company invests 20% of its investment in the first two mutual funds and an equal amount in the mutual

funds C, D, and E, what is the beta of the portfolio ?

 (ii) If the company invests 15% of its investment in C, 15% in A, 10% in E and the balance in equal amount in the

other two mutual funds, what is the beta of the portfolio?

(iii) If the expected return of market portfolio is 12% at a beta factor of 1.0, what will be the portfolios expected

return in both the situations given above.

Exercise 32-8 Based on the following information, determine the NAV of a regular income scheme on per unit

basis: ( ` crores)

Listed shares at cost (ex-dividend) 20

Cash in hand 1.23

Bonds and debentures at cost 4.3

Of these, bonds not listed and quoted 1

Other fixed interest securities at cost 4.5

Dividend accrued 0.8

Amount payable on shares 6.32

Expenditure accrued 0.75

N
Number of units ( ` 10 face value) 20 lakhs

Current realizable value of fixed income securities of face value of ` 100 106.5

N
The listed shares were purchased when index was 1,000

A
Present index is 2,300

Value of listed bonds and debentures at NAV date 8

M
There has been a diminution of 20% in unlisted bonds and debentures. Other fixed interest securities are at cost.

X
Exercise 32-9 A mutual fund made an issue of 10,00,000 units of ` 10 each on January 01, 2016. No entry load was
`

A
charged. It made the following investments: ( )

` `

T
50,000 Equity shares of 100 each @ 160 80,00,000

7% Government securities 8,00,000

9% Debentures (unlisted) 5,00,000

10% Debentures (listed) 5,00,000

98,00,000

During the year, dividends of ` 12,00,000 were received on equity shares. Interest on all types of debt securities was
received as and when due. At the end of the year equity shares and 10% debentures are quoted at 175% and 90%

respectively. Other investments are at par.

Find out the Net Asset Value (NAV) per unit given that operating expenses paid during the year amounted to

` 5,00,000. Also find out the NAV, if the Mutual fund had distributed a dividend of ` 0.80 per unit during the year
to the unit holders.

Exercise 32-10 A Mutual Fund Co. has the following assets under it on the close business as on:

1
st February 2016 2
nd February 2016

Company No. of shares Market price per share ( ) ` Market price per share ( ) `

L Ltd 20,000 20.00 20.50

M Ltd 30,000 312.40 360.00

N Ltd 20,000 361.20 383.10

P Ltd 60,000 505.10 503.90

Total No. of units 6,00,000.

 (i) Calculate Net Assets Value (NAV) of the Fund.

(ii) Following information is given: Assuming one Mr. A, submits a cheque of ` 30,00,000 to the Mutual Fund and
the Fund manager of this company purchases 8,000 shares of M Ltd; and the balance amount is held in Bank.

In such a case, what would be the position of the Fund ?

nd
(iii) Find new NAV of the Fund as on 2 February 2016.

N N
M A
A X
T
 Key to Practical Exercises

Exercise 32-1

Calculation of Monthly Return on Mutual Fund

(NAV - NAV ) + I + G
t t-1 t t
r =
NAV
t-1

(20.06 - 20.00) + (0.0375 + 0.03) 0.06 + 0.0675 0.1275

r = = = = 0.006375
20 20 20

r = 0.6375% p.m. or 7.65% p.a.

Exercise 32-2

Calculation of monthly return on the mutual funds

N
/"7U − /"7U −
+ M U + ( U
r =

N
/"7U −

C  − C 
+ C  + C 
+ 

A

= = = 0.009375
 

M
or, r = 0.9375% p.m. or 11.25% p.a.

X
Exercise 32-3

Rate of return the mutual fund should earn (r )

2

A
 
= × r + Recurring expenses = × 0.1 + 0.02 = 0.1264 or 12.64%

T
1
 − *OJUJBM FYQFOTFT  − 

Exercise 32-4

Return for the year (all changes on a per year basis) `

( /unit)

Change in price ( ` 13.00 - ` 12.25) 0.75

Dividend received 1.25

Capital gain distribution 1.00

Total return 3.00


Return on investment = ×  = 24.49%


If all dividends and capital gain are reinvested into additional units at ` 12.50 per unit the position would be:

Total amount reinvested = ` 2.25 × 300 = ` 675

C 
Additional units added = = 54 units


Value of 354 units as on 31.12.2016 = ` 4,602

Price paid for 300 units on 31.12.2015 (300 × ` 12.25) = ` 3,675

C   C   C 

Return = = = 25.22%
C   C  
Exercise 32-5

Calculation of effective yield on per annum basis in respect of three mutual fund schemes to Mr. Sinha upto

31.03.2016

Particulars MFX MFY MFZ

(a) Investments `
( ) 5,00,000 1,00,000 50,000

(b) No. of units 47,619.05 10,000 5,000

(c) Unit NAV on 31.3.2016 `

( ) 10.40 10.10 9.80

(d) Total NAV on 31.3.2016 `

( ) (b) × (c) 4,95,238.12 1,01,000 49,000

(e) Increase/Decrease of NAV `

( ) (a) - (d) (4,761.88) 1,000 (1,000)

(f) Dividend received `

( ) 9,500 1,500 Nil

(g) Total yield `

( ) (e) + (f) 4,738.12 2,500 (1,000)

(h) Number of days 121 90 31

N
Calculation of effective yield p.a.

C    EBZT −

C    EBZT
× ×  × × 

N
MFX = = 2.859% MFZ = = (-) 23.55%
C     EBZT C    EBZT

A
C    EBZT
MFY = × ×  = 10.139%
C     EBZT

M
Exercise 32-6

X
Total Return per annum `
( )

` ` 8.75)

A
Increase in NAV ( 9.45 - 0.70

Dividend received 0.75

T
Capital gain 0.60

Total return 2.05

` 2.05
Effective Rate of Return = × 100 = 23.43%
` 8.75
Calculation of Effective Rate of Return

When Dividend and Capital gain are Reinvested, total dividend and capital gain received

= (Dividend p.u. + Capital gain p.u.) × No. of units = ( ` 0.75 + ` 0.60) × 300 units = ` 405

Total additional units acquired = ` 405/` 8.65 = 46.82 units

Total number of units = 300 + 46.82 = 346.82 units

Value of 346.82 units held at the end of the year = 346.82 units × ` 9.45 = ` 3,277.50

Value of 300 units paid at the beginning = 300 units × ` 8.75 = ` 2,625.00

Increase in investment = ` 3,277.50 - ` 2,625.00 = ` 652.50

` 652.50
Effective Rate of Return = × 100 = 24.86%
` 2,625.00
Suggestion - The effective rate of return is more if dividend and capital gain are reinvested. Hence, it is suggested to

reinvest the distributions at an average NAV of ` 8.65 p.u.

Exercise 32-7

(i) Calculation of Weighted Beta and Expected Return if investment is made as per Plan I

Mutual Investment Beta Weighted

fund ( ` lakhs) investment

A 20 1.6 32

B 20 1.0 20

C 20 0.9 18

D 20 2.0 40

E 20 0.6 12

Total 100 122

Weighted beta = 122/100 = 1.22

(ii) Calculation of Weighted Beta and Expected Return if investment is made as per Plan II

Mutual Investment Beta Weighted

N
fund ( ` lakhs) investment

N
A 15 1.6 24.0

B 30 1.0 30.0

A
C 15 0.9 13.5

D 30 2.0 60.0

M
E 10 0.6 6.0

Total 100 133.5

X
Weighted beta = 133.5/100 = 1.335

A
(iii) Calculation of Expected Return

T
Plan I = 12% × 1.22 = 14.64% Plan II = 12% × 1.335 = 16.02%

Exercise 32-8

Calculation of adjustment value of net assets ( ` crores)

Equity shares 46.00

Cash in hand 1.23

Bonds and debentures not listed 0.80

Bonds and debentures listed 8.00

Dividends accrued 0.80

Fixed income securities 4.50

Sub total assets (a) 61.33

Less: Liabilities

Amount payable on shares 6.32

Expenditure accrued 0.75

Sub total liabilities (b) 7.07

Net assets value (a) - (b) 54.26

No. of units = 20,00,000

Net assets value per unit = ` 54,26,00,000/20,00,000 units = ` 271.30

Exercise 32-9

Calculation of net cash balance at the end `

( )

Cash balance in the beginning (100 lakhs - 98 lakhs) 2,00,000

Dividend received 12,00,000

Interest on 7% Govt. securities 56,000

Interest on 9% Debentures 45,000

Interest on 10% Debentures 50,000

15,51,000

Less: Operating expenses 5,00,000

Net cash balance at the end 10,51,000

Calculation of NAV `
( )

Cash balance 10,51,000

N
7% Govt. securities (at par) 8,00,000

50,000 equity shares @ ` 175 each 87,50,000

N
9% Debentures (unlisted) at cost 5,00,000

10% Debentures @ 90% 4,50,000

A
Total assets (a) 1,15,51,000

M
No. of units (b) 10,00,000

NAV per unit (a)/(b) ` 11.55

X
Calculation of NAV, if dividend of ` 0.80 is paid

A
Net assets ( ` 1,15,51,000 - ` 8,00,000) ` 1,07,51,000

T
No. of units 10,00,000

NAV per unit ` 10.75

Exercise 32-10

C    + C    + C    + C    

(i) NAV of the fund =
  

C    
= = ` 78.84 (approx.)
  

(ii) Revised Position of Fund

Shares No. of shares Price Amount ( ) `

L Ltd. 20,000 20.00 4,00,000

M Ltd. 38,000 312.40 1,18,71,200

N Ltd. 20,000 361.20 72,24,000

P Ltd. 60,000 505.10 3,03,06,000

Cash 5,00,800

5,03,02,000

  
No. of units of fund = 6,00,000 + = 6,38,053

(iii) NAV of Fund on 2-2-2016

Shares No. of shares Price `

Amount ( )

L Ltd. 20,000 20.50 4,10,000

M Ltd. 38,000 360.00 1,36,80,000

N Ltd. 20,000 383.10 76,62,000

P Ltd. 60,000 503.90 3,02,34,000

Cash 5,00,800

5,24,86,800

C    
NAV as on 2-2-2016 = = ` 82.26 per unit
  

N N
M A
A X
T
 Key to Short Answer Questions

True or False Statements

1. True - Mutual fund issues units to the investors in accordance with the quantum of money invested by them.

A mutual fund is a trust that pools together the savings of a number of investors who share a common

financial goal. The fund manager then invests this pool of money (called a corpus) in different

securities. Therefore, investment in mutual fund is an indirect investment.

2. True - A portfolio which consists of investment in debt funds will have a regular flow of earnings but with

increased risk of the portfolio.

3. False - Each mutual fund has its own investment objective. Investors as a part of their own investment

strategies, will choose the appropriate mutual fund in which to invest.

4. True - The investors of mutual funds are known as ‘unit holders’, who share profit and losses in proportion

N
to their investments.

False

N
5. - AMC should satisfy SEBI, for floating no load funds and assured funds, that its present networth

would be adequate to meet any financial obligation which may arise, and if required the networth

A
should be increased.

6. True - The role of sponsor is akin to the promoter of a company, who will establish the mutual fund, get

M
registered with SEBI, forms trust and appoints board of trustees, and then contributes 40% of the

networth of AMC.

X
7. False - The open-ended schemes are available for subscription on continuous basis, which do not have any

A
fixed maturity period.

8. False - The rise or fall will not be exactly same percentage due to some factors known as ‘tracking error’.

T
9. True - Mutual fund houses in India can mobilize rupee funds from Indian residents for investments abroad.

10. True - Mutual funds generally invest in a well diversified portfolio of securities which reduce risk.

11. False - Investments are made into sovereign wealth funds by governments with an aim to benefit the

country’s economy and the citizens as well.

Choose Correct Word

1. mutual fund

2. 1999

3. insurance

4. Three

5. financial

6. AMC

7. Trustees

8. NAV

9. equity index fund

10. NAV

11. market value

12. capital appreciation

13. standard deviation

14. standard deviation

15. alpha

16. hedge

Choose Correct Answer

1. (B) trust

2. (B) Government of India

3. (D) All of the above

4. (A) zero unsystematic risk

5. (C) 1999

6. (B) absolute measure

7. (D) Jensen’s alpha model

8. (A) limited investment horizon

9. (D) yield-to-maturity

10. (B) money market fund

N
11. (B) superior performance of the fund manager

12. (D) are perfectly diversified

N
13. (B) all the year round except during their period of book closing

A
14. (C) key motives for trading are value, information and cash flow

15. (B) open-ended funds can sell unlimited number of units

X M
T A
 Practical Exercises

Exercise 36-1 John inherited the following securities on his uncle’s death:

Type of Security Nos. Annual Maturity Yield

coupon (%) years (%)

Bond A ( ` 1,000) 10 9 3 12

Bond B ( ` 1,000) 10 10 5 12

Preference shares C ( ` 100) 100 11 * 13*

Preference shares D ( ` 100) 100 12 * 13*

*Likelihood of being called at a premium over par. Compute the current value of his uncle’s portfolio.

Exercise 36-2 The Investment portfolio of a bank is as follows:

N
Government Coupon Purchase rate Duration

bond rate (F.V. ` 100 per bond) (years)

N
G.O.I 2009 11.68 106.50 3.50

A
G.O.I 2013 7.55 105.00 6.50

G.O.I 2018 7.38 105.00 7.50

M
G.O.I 2025 8.35 110.00 8.75

G.O.I 2035 7.95 101.00 13.00

X
Face value of total investment is ` 5 crores in each Government bond. Calculate actual investment in portfolio.

A
What is a suitable action to churn out investment portfolio in the following scenario ?

T
(1) Interest rates are expected to lower by 25 basis points.

(2) Interest rates are expected to raise by 75 basis points.

Also calculate the revised duration of investment portfolio in each scenario.

 Key to Practical Exercises

Exercise 36-1

Calculation of Current Value of John’s Portfolio Inherited from his uncle Current value ( `)

Bond A

(i) Interest p.a. (10,000 × 9/100) = ` 900

Compounded @ 12% p.a. for 3 years (900 × 2.402) 2,162

(ii) Current value of bonds amount

received on maturity. P.v. @ 12% on 3rd year (10,000 × 0.712) 7,120

(a) 9,282

Bond B

(i) Interest p.a. (10,000 × 10/100) = ` 1,000

N
Compounded @ 12% p.a. for 5 years (1,000 × 3.605) 3,605

(ii) Current value of bonds value received on

N
maturity. P.v. @ 12% on 5th year (10,000 × 0.567) 5,670

(b) 9,275

A
Preference shares C

` 100 × 100 Nos. × 11% 1,100

M
= (c) 8,462
13% 0.13

X
Preference shares D

` 100 × 100 Nos. × 12% 1,200

A
= (d) 9,231
13% 0.13

T
Current Value of John’s Portfolio (a) + (b) + (c) + (d) 36,250

Exercise 36-2

Calculation of Actual Investment in Portfolio ( ) `

` 5,00,00,000
G.O.I. 2009 × ` 106.50 5,32,50,000
` 100

` 5,00,00,000
G.O.I. 2013 × ` 105 5,25,00,000
` 100

` 5,00,00,000
G.O.I. 2018 × ` 105 5,25,00,000
` 100

` 5,00,00,000
G.O.I. 2025 × ` 110 5,50,00,000
` 100

` 5,00,00,000
G.O.I. 2035 × ` 101 5,05,00,000
` 100

Total investment in portfolio 26,37,50,000

Average duration of total portfolio (in years)

3.5 + 6.5 + 7.5 + 8.75 + 13.00 39.25

= = = 7.85 years
5 5
Suitable Action to churn out Investment Portfolio

Case 1 Interest rates are expected to be lower by 25 basis points

When interest rates are expected to be lower by 25 basis points, increase the average duration of the portfolio

by purchasing G.O.I. 2035 and selling G.O.I. 2009.

Then, revised average duration of portfolio is:

39.25 - 3.5 + 13 48.75

= = = 9.75 years
5 5

Case 2 Interest rates are expected to raise by 75 basis points.

When interest rates are expected to raise by 75 basis points, reduce the average duration of the portfolio by

purchasing G.O.I. 2013 and selling G.O.I. 2035.

Then, revised average duration of portfolio is:

39.25 - 13 + 6.5 32.75

= = = 6.55 years
5 5

N
In this case, purchase of G.O.I. 2008 is not suggested, since its maturity period is very short but the increase

in basis points is comparatively higher.

A N
X M
T A
 Key to Short Answer Questions

True or False Statements

1. False - The efficient market hypothesis is a theory that capital markets operate at a high degree of perfection.

Since the market efficiently prices all the stocks on an ongoing basis, any opportunity for excess

returns derived from fundamental or technical analysis will be almost immediately used away by the

market participants.

2. False - Portfolio balance approach refers to the process of systematically placing of money into various

classes of investments such as stock, bonds and cash equivalents. The purchasing power parity (PPP)

theorem relates to foreign exchange management.

3. True - A portfolio may be represented investment on stocks, shares, investment in projects etc.

4. False - Portfolio management refers to selection of securities and their continuous balancing and shifting to

N
optimize returns to suit the objectives of the investor.

5. False - An aggressive investor may be willing to take a high risk in order to have high capital appreciation.

N
6. True - Higher the risk, higher the return. If one wishes to have higher return from his investments, he should

A
be prepared to carry higher risk also.

7. False - In defensive companies, the future earnings are likely to withstand an economic downturn.

M
8. True - Passive management is the process of managing investment portfolios by trying to match the

X
performance index such as stock market index.

9. True - Growth stocks is basically a currently undervalued stock that has a high probability of being properly

A
valued in the near term.

T
10. False - In reverse asset allocation, where alpha generators constitute the core portfolio instead the satellite

portfolio.

11. False - In rupee cost averaging plan, the investor will go on investing at regular intervals at a fixed amount

of installment.

12. True - It is a passive management strategy which produce substantial returns with least management in

investments.

Choose Correct Word

1. zero

2. 10 : 90

Choose Correct Answer

1. (A) purchasing power risk

2. (C) defensive stock

3. (A) portfolio redemption

4. (A) strategy in which asset mix is held constant

5. (A) pioneering stage

6. (A) insured asset allocation

7. (C) dollar cost averaging

8. (B) rebalancing of existing portfolio

9. (D) all of the above

10. (B) a fixed ratio to the conservative portfolio

11. (D) need for higher expected returns at lower risk

12. (C) the investors to fix their revaluation points

13. (C) both (a) and (b) above

14. (D) aggressive portfolio to the conservative portfolio changes

N N
M A
A X
T
 Practical Exercises

Exercise 37-1 Closing values of BSE Sensex from 6th to 17th day of the month of January of the year 2016 were as

follows:

Days Date Day Sensex

1 6 Thu 14522

2 7 Fri 14925

3 8 Sat No trading

4 9 Sun No trading

5 10 Mon 15222

6 11 Tue 16000

N
7 12 Wed 16400

N
8 13 Thu 17000

9 14 Fri No trading

A
10 15 Sat No trading

M
11 16 Sun No trading

12 17 Mon 18000

X
Calculate Exponential Moving Average (EMA) of Sensex during the above period. The 30 days simple moving

A
average of Sensex can be assumed as 15000. The value of exponent for 30 days EMA is 0.062.

T
Give detailed analysis on the basis of your calculations.
 Key to Practical Exercises

Exercise 37-1

Date Sensex EMA for (1) - (2) (3) × (0.062) EMA

previous day (2) ± (4)

(1) (2) (3) (4) (5)

6 14522 15000 (478) (29.636) (14970.364)

7 14925 14970.364 (45.364) (2.812) 14967.55

10 15222 14967.55 254.45 15.776 14983.32

11 16000 14983.32 1016.68 63.034 15046.354

12 16400 15046.354 1353.646 83.926 15130.28

N
13 17000 15130.28 1869.72 115.922 15246.203

N
17 18000 15246.203 2753.797 170.735 15416.938

A
Analysis - The market is bullish. The market is likely to remain bullish for short-term to medium-term if other factors

remain the same. On the basis of this indicator (EMA) the investors/brokers can take long position.

X M
T A
 Key to Short Answer Questions

True or False Statements

1. False - The fundamental analysis suggests that every stock has intrinsic value, which should be equal to the

present value of the future stream of income from the stock discounted at an appropriate risk related

rate of interest. But in practice the price of a stock depends on supply and demand in the market place.

It has little co-relation with its intrinsic value.

2. False - The market price of a growing company’s share will be higher than its book value since its rate of

return is greater than the discount rate.

3. True - The intrinsic value of every stock is assumed to be equal to the present value of the future stream of

income from the stock discounted at an appropriate risk related rate of interest.

4. False - The prime objective of investment in share is to obtain higher returns by selling the stocks at higher

N
prices subsequently. The receipt of dividends will also form part of the return.

False

N
5. - Analysts perform fundamental analysis since it is largely believed that stock price does not reflect the

value of the company. This true value or the intrinsic value can be estimated only through the

A
fundamental analysis.

6. False - The basic underlying assumption of technical analysis is that the price of a stock depends on supply

M
and demand in the market price. It has little co-relation with its intrinsic value.

7. True - It is the mood of the crowd which determines the way in which prices move and the move can be

X
gauged by analyzing the price movement and volume of transactions.

A
8. True - The chart patterns are used to predict the market movements. The basic concept underlying the chart

T
analysis are (a) persistence of trends, (b) relationship between volume and trend, and (c) resistance

and support levels.

9. False - The moving average is a lagging indicator, which represents an average of a certain series of data that

moves through time.

10. False - The RSI attempts to quantify the degree of oversoldness or overboughtness. Overbought basically

means the market is too high in the respect that it is running out of buyers, in effect about to fall of

its own weight.

11. False - Generally, a short interest ratio is considered to be high when it is greater than 2. This is a bullish

indicator because there are a large number of investors in the market who will have to buyback the

shares that were sold short.

Choose Correct Word

1. higher

2. securities

3. short-term

4. three

5. five

6. uptrend

7. trend

8. green

9. filter rules
10. two

11. 70

12. bullish

Choose Correct Answer

1. (A) long-term

2. (B) momentum

3. (A) high P/E ratios

4. (D) high market discounting

5. (D) there is no steep rise or fall in share price

6. (C) are those who fall outside the standard CAPM

7. (D) all of the above

8. (D) all of the above

9. (B) move smoothly from one period to another as it rises or falls

N
10. (A) he strives to reach long-term buy and hold investment decisions

N
11. (B) supply of stock to be nil below that level of price

12. (C) chart patterns tend to repeat themselves

M A
A X
T
 Practical Exercises

Exercise 38-1

(i) Calculate the market sensitivity index and the expected return on the portfolio from the following data:

Standard deviation of an asset 2.5% Expected return on market portfolio 15.0%

Market standard deviation 2.0% Correlation coefficient of portfolio with market 0.8

Risk-free rate of return 13.0%

(ii) What will be the expected return on the portfolio if portfolio beta is 0.5 and the risk-free return is 10%.

Exercise 38-2 From the following information, calculate the expected rate of return of a portfolio:

Risk-free rate of interest 8% Market standard deviation 2.3%

Expected return of market portfolio 18% Correlation coefficient of portfolio with market 0.8

N
Standard deviation of an asset 2.8%

N
Exercise 38-3 The following information is given:

β of a security

A
Risk-free rate of return 8% Expected rate of return on market portfolio 16% 0.7

(i) Find out the expected rate of return of the security.

M
(ii) If another security has an expected return of 20%, what must be its beta?

X
Exercise 38-4 Calculate the expected rate of return of the security and interpret the same from the following

information:

A
Beta of a security 0.5 Expected rate of return on portfolio 15% Risk-free rate of return 0.06

T
If another security has an expected rate of return of 18%, what would be its beta?

Exercise 38-5 An investor is seeking the price to pay for a security, whose standard deviation is 4%. The correlation

coefficient for the security with the market is 0.9 and the market standard deviation is 3.2%. The return from

government securities is 6.2% and from the market portfolio is 10.8%. The investor knows that, by calculating the

required return, he can then determine the price to pay for the security. What is the required return on the security?

Exercise 38-6 From the following data, compute beta of Security J:

σ = 12%
j
σ m
= 9%

Cor = + 0.72
jm

Exercise 38-7 The market portfolio has a historically based expected return of 0.10 and a standard deviation of 0.04

during a period when risk-free assets yielded 0.03. The 0.07 risk premium is thought to be constant through time.

Riskless investments may now be purchased to yield 0.09. A security has a standard deviation of 0.08 and a coefficient

of correlation with the market portfolio is 0.85. The market portfolio is now expected to have a standard deviation

of 0.04.

You are required to find: (i) market’s return-risk trade-off; (ii) security beta; and (iii) equilibrium required expected

return of the security.

Exercise 38-8 The following information is available in respect of Security X and Security Y:

Security β Expected rate of return

X 1.8 22.00%

Y 1.6 20.40%

Rate of return of market portfolio is 15.3%.If risk-free rate of return is 7%, are these securities correctly priced?

What would be the risk-free rate of return, if they are correctly priced?

Exercise 38-9 Dhanpat, an investor, is seeking the price to pay for a security, whose standard deviation is 5%. The

correlation coefficient for the security with the market is 0.75 and the market standard deviation is 4%. The return

from risk-free securities is 6% and from the market portfolio is 11%. Dhanpat knows that only by calculating the

required rate of return, he can determine the price to pay for the security.

What is the required rate of return on the security ?

Exercise 38-10 The market portfolio has a historically based expected return of 0.095 and a standard deviation of

0.035 during a period when risk-free assets yielded 0.025. The 0.06 risk premium is thought to be constant through

N
time. Riskless investments may now be purchased to yield 0.08. A security has a standard deviation of 0.07 and a 0.75

correlation with the market portfolio. The market portfolio is now expected to have a standard deviation of 0.035.

N
Find out the following: (i) Market’s return-risk trade-off, (ii) Security beta, (iii) Equilibrium required expected

return of the security.

A
Exercise 38-11 Your client is holding the following securities:

M
Particulars of securities `
Cost ( ) `
Dividend ( ) Market price ( ) ` Beta

X
Equity shares

Co. X 8,000 800 8,200 0.8

A
Co. Y 10,000 800 10,500 0.7

Co. Z 16,000 800 22,000 0.5

T
PSU Bonds 34,000 3,400 32,300 1.0

Assuming the risk free rate of 15%, Calculate:

(i) Expected rate of return in each, using the Capital Asset Pricing Model (CAPM).

(ii) Average return of portfolio.

Exercise 38-12 As an Investment Manager, you are given the following information:

Investment in Initial Dividends Market price at the Beta risk

equity shares of `
price ( ) `
( ) `
end of the year ( ) factor

A. Cement Ltd. 25 2 50 0.8

Steel Ltd. 35 2 60 0.7

Liquor Ltd. 45 2 135 0.5

B. Govt. of India Bonds 1000 140 1005 0.99

Risk-free return may be taken at 14%. You are required to calculate:

(i) Expected rate of returns of portfolio in each using capital asset pricing model (CAPM).

(ii) Average return of portfolio.

Exercise 38-13 Tara Ltd. is comprised of only four major investment projects, details of which are as follows:

Project % of market Annual % return Risk % of Correlation with

value during the last 5 years standard deviation the market

Alpha 28 10 15 0.55

Beta 17 18 20 0.75

Gamma 31 15 14 0.84

Delta 24 13 18 0.62

The risk free rate is expected to be 5% per year, the market return is 14% per year and the standard deviation of market

returns is 13%.

Assume that Tara Ltd.’s shares are currently priced based upon the assumption that the last five years experience

of returns will continue for the foreseeable future. Evaluate whether or not the share price of Tara Ltd. is

undervalued/overvalued.

Exercise 38-14 The following particulars about 4 corporate securities (shares) are available: `
( )

N
Security Today’s Predicted Price Expected Dividend

Price a year from today during the coming year

N
A 490 580 7.0

A
B 180 200 7.0

C 570 640 5.0

M
D 220 235 –

X
The most recent beta estimates are:

Security A B C D

A
Beta 1.4 1.2 1.0 0.5

T
Expected return in the market is 14% and the risk-free rate of return is 8%.

You are required to calculate for each security:

(i) the estimated return based on the Capital Asset Pricing Model (CAPM), and

(ii) predicted return.

Also, state, giving reasons, whether the securities are undervalued or overvalued.
 Key to Practical Exercises

Exercise 38-1

(i) Calculation of Market Sensitivity Index (beta) and Expected Rate of Return of Portfolio

σ 0.025
β =
i
× r = × 0.8 = 1
i
σ m
im
0.020

E(R )
i
= R +
f
β i
(R
m
- R)
f
= 13 + 1.0 (15 - 13) = 15%

(ii) Calculation of Expected Rate of Return if Portfolio Beta is 0.5 and the Risk-free return is 10%

ER = 10 + 0.5 (15 -10) = 12.5%

p

Exercise 38-2

N
Calculation of Beta Factor (Market Sensitivity Index)

σ 0.028
β

N
i
= × r = × 0.8 = 0.97
i
σ m
im
0.023

A
Calculation of Expected Rate of Return of Portfolio

E(R )
i
= R +
f
β i
(R
m
- R)
f
= 8 + 0.97 (18 - 8) = 17.7%

M
Exercise 38-3

X
(i) Calculation of Expected Rate of Return of the Security

A
E(R ) = R + (R - R) = 8 + 0.7 (16 - 8) = 13.6%
i f i m f

T
(ii) If a security has an expected return of 20% what must be its beta?

E(R )
i
= R +
f
β i
(R
m
- R )
f

20 = 8 + ß (16 - 8)
i

β i
8 = 20 - 8 β i
= 12/8 = 1.5

Exercise 38-4

Calculation of Expected Rate of Return of the Security

E(R )
i
= R +
f
β i
(R
m
- R)
f
= 6 + 0.5 (15 - 6) = 10.5%

Calculation of Beta of another security, whose expected rate of return is 18%

E(R )
i
= R +
f
β (R - R ) i m f

18 = 6 + β (15 - 6)
i

β i
9 = 18 - 6 β i
= 12/9 = 1.33

Exercise 38-5

(i) Beta Coefficient

σ 0.04
β =
i
× r = × 0.9 = 1.125
i
σ m
im
0.032

(ii) Required Rate of Return on Security

E(R )
i
= R +
f
β i
(R
m
- R)
f
= 6.2 + 1.125 (10.8 - 6.2) = 11.375%
Exercise 38-6
σσ Cov 12 × 9 × 0.72 77.76
β)
J m jm
Calculation of beta of Security J ( = = = = 0.96
j
σ 2

m
9
2
81

Exercise 38-7

R - R
m f

(i) Market’s Return-Risk Trade-off =

σ
Where, R = Market rate of return i.e. 0.10
m

R = Risk free return i.e. 0.03

f

σ = Standard deviation i.e. 0.04

0.10 - 0.03
= = 1.75
0.04

σ
β)
s
(ii) Security Beta ( = × r
1
σ m
m

N
Where, = Beta factor of investment
1

σ s
= Standard deviation of investment in security i.e. 0.08

N
r = Coefficient of correlation with market portfolio i.e. 0.85
m

A
= Market portfolio standard deviation i.e. 0.04
m

0.08
β 1
= × 0.85 = 1.7

M
0.04

(iii) Equilibrium required for expected rate of return on the security

X
E(R )
1
= R +
f
β1
(R
m
- R)
f

A
Where, E(R ) = Expected rate of return on investment
1

T
R = Riskless investments yield = 0.09
f

R = Expected return on market portfolio

m

β 1
= Market sensitive index (beta factor) of investment i.e. 1.7

E(R ) = 0.09 + 1.7 (0.10 - 0.03) = 0.09 + 1.7 (0.07) = 0.09 + 0.119 = 0.209 or 20.9%
1

Exercise 38-8

E (R )
i
= R +
f
β i
(R
m
- R)
f

Security X = 7 + 1.8 (15.3 - 7) = 21.94%

The required rate of return 21.94% of Security X is less than its expected rate of return 22%. Therefore, Security X

is not correctly priced.

Security Y = 7 + 1.6 (15.3 - 7) = 20.28%

The required rate of return 20.28% of Security Y is less than its expected rate of return 20.40%. Therefore, Security

Y is not correctly priced.

Calculation of risk-free rate of return, if the Security X and Security Y are correctly priced

0.22 - R 0.204 - R
f f
=
1.8 1.6

1.6 (0.22 - R ) = 1.8 (0.204 - R )

f f

0.352 - 1.6 R = 0.3672 - 1.8 R

f f

1.8 R - 1.6 R = 0.3672 - 0.352

f f
 0.2 R = 0.0152
f

R = 0.0152/0.2 = 0.076 or 7.6%

f

Therefore, both securities would be correctly priced when the risk free rate of return is 7.6%.

Exercise 38-9

Calculation of Beta coefficient ( β)

i

Standard deviation ( σ) i
= 5% Market standard deviation ( σ m
) = 4%

Correlation coefficient (r )= 0.75

im

σ 
β =
J
S JN = ×  = 0.9375
i
σ N


Calculation of required rate of return [E(R )]

i

E(R )
i
= R +
f
β i
(R
m
- R )
f
= 6 + 0.9375(11 - 6) = 6 + 4.69 = 10.69%

Exercise 38-10

N
R - R 0.095 - 0.025
m ƒ
(i) Market’s Return-Risk Trade-off = = = 2
σ 0.035

N
σ 0.07
(ii) Security Beta ( β) =
i
× r = × 0.75 = 1.5
i
σ im
0.035

A
m

(iii) Calculation of Equilibrium Required for Expected Rate of Return on the Security

M
E(R ) = R + (R - R) = 8 + 1.5 (6) = 17%
i f i m f

X
Exercise 38-11

Calculation of Expected Return on Market Portfolio

A
Investment Cost Dividends Capital gains

T
Equity shares:

Company X 8,000 800 200

Company Y 10,000 800 500

Company Z 16,000 800 6,000

PSU Bonds 34,000 3,400 -1,700

Total 68,000 5,800 5,000

  +  
Expected Return on Market Portfolio (R
m
) = ×  = 15.88%
 

Calculation of Expected rate of return on Individual security

Share X = 15 + 0.8 (15.88 - 15) = 15.7% Share Z = 15 + 0.5 (15.88 - 15) = 15.44%

Share Y = 15 + 0.7 (15.88 - 15) = 15.62% PSU Bonds = 15 + 1.0 (15.88 - 15) = 15.88%

Calculation of Average Return on Portfolio = (15.7 + 15.62 + 15.44 + 15.88)/4 = 15.66%

Exercise 38-12

(i) Calculation of Expected Rate of Return of market portfolio using CAPM `

( )

Particulars Investment Dividend Capital gain

(A) Equity shares of

Cement Ltd. 25 2 25

Steel Ltd. 35 2 25

Liquor Ltd. 45 2 90

(B) GOI Bonds 1,000 140 5

1,105 146 145

%JWJEFOE FBSOFE + $BQJUBM BQQSFDJBUJPO

*OJUJBM JOWFTUNFOU
Expected rate of return on market portfolio =

C  + C 
= ×  = 26.33%
C  

N
Now, we can calculate the expected rate of return on individual portfolio, by applying the formula of CAPM

β (R

N
R = R + - R )
i f i m f

Cement Ltd. = 14 + 0.80 (26.33 - 14) = 23.86% Liquor Ltd. = 14 + 0.50 (26.33 - 14) = 20.17%

A
Steel Ltd. = 14 + 0.70 (26.33 - 14) = 22.63% GOI Bonds = 14 + 0.99 (26.33 - 14) = 26.21%

+  +  + 

M
 
(ii) Average Return of Portfolio = = = 23.22%
 

X
Alternatively,

 +  +  +  

A
Average beta = = = 0.7475
 

T
Average return of portfolio = 14 + 0.7475(26.33 - 14) = 14 + 9.22 = 23.22

Exercise 38-13

Calculation of Beta of individual securities

σ $PS
β
J JN
=
i
σ N

Where, β i
= Beta of individual security

σ i
= Standard deviation of returns of individual security

σ m
= Standard deviation of returns of market portfolio i.e. 13%

Cor = Correlation coefficient between the returns of individual security and the market portfolio
im

 ×   × 
Alpha = = 0.635 Beta = = 1.154
 

 ×   × 
Gamma = = 0.905 Delta = = 0.858
 

Calculation of overall Beta = (0.635 × 0.28) + (1.154 ×0.17) + (0.905 × 0.31) + (0.858 × 0.24)

= 0.178 + 0.196 + 0.280 + 0.206 = 0.860

Calculation of required rate of return using CAPM

= R +
f
β i
(R
m
- R )
f
= 5% + 0.860(14% - 5%) = 12.74%
Calculation of average 5 years historical rate of return

= (0.10 × 0.28) + (0.18 × 0.17) + (0.15 × 0.31) + (0.13 × 0.24)

= 0.028 + 0.031 + 0.046 + 0.03 = 0.135 or 13.5%

Analysis - The average 5 years historical rate of return (13.5%) is higher than the required rate of return (12.74%).

Therefore, the share price of Tara Ltd. is undervalued.

Exercise 38-14

(i) Estimation of return based on CAPM

E(r )
i
= R +
f
β i
(R
m
- R )
f

E(r ) = 8 + 1.4 (14 - 8) = 16.4% E(r ) = 8 + 1.0 (14 - 8) = 14%

A C

E(r ) = 8 + 1.2 (14 - 8) = 15.2% E(r ) = 8 + 0.5 (14 - 8) = 11%

B D

(ii) Calculation of predicted return from each security

 
+   
+ 
P(r ) = ×  = 19.8% P(r ) = ×  = 15%

N
A B
 

 
+   
+ 

N
P(r )
C
= ×  = 13.15% P(r
D
) = ×  = 6.81%
 

A
Analysis

Security Predicted CAPM Under valued/

M
return return over valued

X
A 19.8% 16.4% Under valued

B 15% 15.2% Over valued

A
C 13.15% 14% Over valued

T
D 6.81% 11% Over valued
 Key to Short Answer Questions

True or False Statements

1. False - Systematic risk refers to that part of total risk which causes the movement in individual stock prices

due to changes in general stock market index. Systematic risk arises out of external and uncontrollable

factors. This movement is generally due to the response to economic, social and political changes. The

systematic risk cannot be avoided by portfolio diversification.

2. True - In real world, assumptions of CAPM will not hold good. In practice it is difficult to estimate risk free

return, market rate of return and risk premium. CAPM is a single period model while most projects

are often available only as large indivisible projects. It is therefore more difficult to adjust.

3. True - Systematic risk refers to that part of total risk which causes the movement in individual stock price

due to changes in general stock market index. Systematic risk arises out of external and uncontrollable

N
factors. The systematic risk cannot be eliminated by diversification, it being common to all firms.

N
Choose Correct Word

1. capital asset pricing

A
2. unsystematic

3. greater

M
4. systematic

X
5. non-systematic

A
6. systematic

7. systematic

T
8. average

9. systematic

10. market rate

11. expected

12. beta

13. beta

14. aggressive

15. zero

16. four

Choose Correct Answer

1. (C) systematic risk

2. (B) unsystematic

3. (B) systematic risk

4. (B) non-systematic risk

5. (B) Systematic risk

6. (C) dividend payout ratio is nil

7. (B) β>1
 8. (B) required rate

9. (D) rate of return on market portfolio

10. (D) systematic risk of a project

11. (B) Non-systematic risk

12. (D) all of (A), (B) and (C) above

13. (C) systematic risk

14. (C) identify the equilibrium asset price

15. (B) A security

16. (D) all of the above

17. (D) all of the above

18. (D) all of the above

19. (C) security is over priced

20. (A) total risk of the portfolio

N
21. (D) 19%

22. (A) 15%

N
23. (C) 18.8%

A
24. (B) 13%

25. (A) 0.11

M
26. (C) 18%

27. (C) 11.20%

X
28. (B) + 25%

A
29. (D) The expected return on Stock A will be greater than that on Stock B

T
30. (C) whose return has no correlation with the market return

31. (C) increase in import duty on materials used by the firm

32. (C) the weighted average of the individual security betas

33. (D) all of the above

34. (A) there is a relationship between security returns and a limited number of factors
 Practical Exercises

Exercise 40-1 Which accounting ratio will be useful in indicating the following symptoms:

(1) Low capacity utilization.

(2) Falling demand for the product in the market.

(3) Inability to pay interest.

(4) Borrowing for short-term and investing in long-term assets.

(5) Large inventory accumulation in anticipation of price rise in future.

(6) Inefficient collection of debtors.

(7) Inability to pay dues to financial institutions.

(8) Return of shareholders’ funds being much higher than the overall return on investment.

N
(9) Liquidity crisis.

(10) Increase in average credit period to maintain sales in view of falling demand.

N
Exercise 40-2 Given below are the abridged Balance Sheet and Profit and Loss Account of AB Spinning Mills Ltd.

A
Balance Sheet (` lakhs)

Particulars 2015-16 2014-15 2013-14

M
Share capital 245 245 245

X
Reserves and surplus 726 1,077 1,313

Long-term borrowings 287 180 160

A
Working capital loans 1,639 451 672

T
Sundry creditors 1,616 1,255 1,015

Other provisions 389 315 305

Total 4,902 3,523 3,710

Net block 1,009 541 612

Investment 19 19 19

Current assets

Inventories 1,160 1,521 1,641

Book debts 11 114 172

Loans and advances 2,641 1,286 1,231

Cash and bank balances 62 42 35

Total 4,902 3,523 3,710

Profit and Loss Account

Particulars 2015-16 2014-15 2013-14

Sales 5,091 3,938 4,215

Other Income 446 365 342

Total 5,537 4,303 4,557

Raw materials, Stores and Spares consumed 3,728 2,775 2,964

Factory wages 162 215 206

Salaries 377 322 275

Power and Fuel 826 673 710

Repairs and Maintenance

Particulars 2015-16 2014-15 2013-14

Building 7 18 15

Plant and machineries 38 54 48

Vehicles 43 33 24

Depreciation

Building 11 14 16

Plant and machineries 57 43 48

Vehicles 66 26 30

Interest 277 130 152

Other Overheads (excluding salaries & depreciation):

Factory overheads 138 94 82

Administrative overheads 71 59 61

Selling and Distribution overheads 87 83 80

Loss for the year (-)351 (-)236 (-)154

Total 5,537 4,303 4,557

N
Sale for the year (Kgs.) 43,50,890 34,36,921 37,25,405

N
The banker to the company has appointed you as a consultant for identifying the factors which have contributed to

the continuing losses. Prepare a short note highlighting the factors which have, prima facie, led the company to

A
sickness.

X M
T A
 Key to Practical Exercises

Exercise 40-1

Symptoms Accounting Ratio to be used

1. Low capacity utilization 1. Actual hours/budgeted hours or Fixed assets

turnover ratio.

2. Falling demand for the product in the market. 2. Finished goods turnover ratio.

3. Inability to pay interest. 3. Interest coverage ratio.

4. Borrowing for short-term and investing in 4. Current ratio or Fixed assets to Long-term loans

long-term assets. ratio.

5. Large inventory accumulation in anticipation. 5. Inventory turnover ratio of price rise in future.

N
6. Inefficient collection of debtors. 6. Debtors turnover ratio.

N
7. Inability to pay dues to financial institutions. 7. Debt service coverage ratio

8. Return of shareholders’ funds being much 8. Debt-equity ratio, Return on investment and

A
higher than the overall return on investment. Return on equity compared.

9. Liquidity crisis 9. Current ratio, Quick assets or Acid test ratio.

M
10. Increase in average credit period to maintain sales 10. Average collection period or Debtors turnover

in view of falling demand. ratio.

X
Exercise 40-2

A
Particulars 2015-16 2014-15 2013-14

T
Sales - Quantity (kgs.) 43,50,890 34,36,921 37,25,405

Sales value ( ` lakhs) 5,091 3,938 4,215

Average sales realization (per kg./ ) ` 117 115 113

Raw materials, stores & Spares consumed ( ` lakhs) 3,728 2,775 2,964

Material cost as % of sales value (%) 73.2 70.5 70.3

Direct wages cost % of sales value (%) 3.2 5.4 4.9

Observations - From the above figures, it is apparent that the company’s declining profitability is not due to market

conditions, as revealed by the following factors:

(i) The sales price has been marginally increasing year to year.

(ii) The very small increase in material cost is also in step with the increase in sales realization.

(iii) The company has been able to control direct labour cost effectively.

(iv) The level of production has been maintained and has in fact improved in the latest year.

(v) Inventory and book debt levels has been brought down considerably.

On the other hand, the following factors present a disturbing picture and lead to the inference that the Financial

Management is either incompetent or the management has diverted the borrowed working capital funds to some

other activity or invested in unproductive assets like vehicles.

 `
( lakhs)

Particulars 2015-16 2014-15 2013-14

Long-term borrowings 287 180 160

Working capital loans 1,639 451 672

Net block 1,009 541 1,231

Loans & advances 2,641 1,286 612

Depreciation, Repairs & maintenance of vehicle 109 59 54

Interest 277 130 152

The increase in working capital borrowings and the consequent interest thereon were not warranted, especially

when the funds blocked in inventory and book debt have come down. The additional interest burden and the

additional expenses on vehicles amount to ` 197 lakhs, whereas the increase in loss, as compared to the previous year
is only ` 115 lakhs.

Preliminary conclusions:

(i) Prima facie, it appears that the unit has become sick, due to diversion of funds by the management to other

N
activities, which are unproductive, or the management had invested in unproductive assets like vehicles or the

funds have been misused for personal expenditure.

N
(ii) The fixed assets have doubted. But there is no profit accruing by the increased assets.

M A
A X
T
 Practical Exercises

Exercise 41-1 Gentry Motor Ltd. a producer of turbine generators, is in this situation:

EBIT ` 40 lakh K
e
15%

Tax rate (t) 35% Shares of stock outstanding (Nos.) 6,00,000

Debt outstanding (D) ` 20 lakhs Book value per share ` 10

K 10%
d

Since Gentry’s product market is stable and the company expects no growth, all earnings are paid out as dividends.

The debt consists of perpetual bonds.

(i) What are the Gentry’s earning per share (EPS) and its price per share (P ) ?
o
(ii) What is Gentry’s weighted average cost of capital (K ) ?
o

N
(iii) Gentry can increase its debt by ` 80 lakhs, to a total of ` 1 crore, using the new debt to buy back and retire some

N
of its shares at the current price. Its interest rate on debt will be 12% (it will have to call and refund the old debt),

and its cost of equity will rise from 15% to 17%. EBIT will remain constant. Should Gentry change its capital

A
structure ?

Exercise 41-2 The following information relating to Fortune India Ltd. having two divisions, viz ., Pharma Division

M
and Fast Moving Consumer Goods Division (FMCG Division). Paid up share capital of Fortune India Ltd. is

consisting of 3,000 lakhs equity shares of ` 1 each. Fortune India Ltd. decided to de-merge Pharma Division as

X
Fortune Pharma Ltd. w.e.f. 1-4-2016. Details of Fortune India Ltd. as on 31-3-2016 and of Fortune Pharma Ltd. as

on 1-4-2016 are given below: ( ` lakhs)

A
Particulars Fortune Pharma Ltd. Fortune India Ltd.

T
Outside Liabilities:

Secured loans 400 3,000

Unsecured loans 2,400 800

Current liabilities and provisions 1,300 21,200

Assets:

Fixed assets 7,740 20,400

Investments 7,600 12,300

Current assets 8,800 30,200

Loans and advances 900 7,300

Deferred tax/Miscellaneous expenses 60 (200)

Board of Directors of the Company have decided to issue necessary equity shares of Fortune Pharma Ltd. of ` 1 each,
without any considerations to the shareholders of Fortune India Ltd. For that purpose following points are to be

considered:

(1) Transfer of liabilities and assets at book value.

(2) Estimated profit for the year 2016-17 is ` 11,400 lakhs for Fortune India Ltd. and ` 1,470 lakhs for Fortune

Pharma Ltd.

(3) Estimated market price of Fortune Pharma Ltd. is ` 24.50 per share.

(4) Average P/E ratio of FMCG sector is 42 & Pharma sector is 25, which is to be expected for both the companies.

Calculate:

(1) The ratio in which shares of Fortune Pharma are to be issued to the shareholders of Fortune India Ltd.
 (2) Expected market price of Fortune India Ltd.

(3) Book value per share of both the companies immediately after Demerger.

Exercise 41-3 Abhishek Ltd. has a surplus cash of ` 90 lakhs and wants to distribute 30% of it to the shareholders.
The Company decides to buyback shares. The Finance Manager of the Company estimates that its share price after

repurchase is likely to be 10% above the buyback price, if the buyback route is taken. The number of shares

outstanding at present is 10 lakhs and the current EPS is ` 3. You are required to determine:

(a) The price at which the shares can be repurchased, if the market capitalization of the company should be ` 200
lakhs after buyback.

(b) The number of shares that can be repurchased.

(c) The impact of share repurchase on the EPS, assuming the net income is same.

Exercise 41-4 Trust Ltd. is deciding whether to payout ` 4,80,000 in excess cash in the form of an extra dividend
or go for a share repurchase. Current earnings are ` 2.40 per share and the stock sells for ` 24. The market value

balance sheet currently is as follows:

Balance Sheet ( ` ’000)

N
Equity 2,400 Assets other than cash 2,560

N
Debt 640 Cash 480

3,040 3,040

A
Evaluate the two alternatives in terms of the effect on the price per share of the stock, the EPS and the P/E ratio. Which

M
alternative do you recommend ? Give reasons.

X
Exercise 41-5 Nibus Ltd. has 1,000 shares of ` 10 each raised at a premium of ` 15 per share. The company’s retained
earnings are ` 5,52,500. The company’s stock sells for ` 20 per share.

A
(a) If a 10% stock dividend is declared how many new shares would be issued ? What would be the market price

T
after the stock dividend? How would the equity account change ?

(b) If the company instead declares a 5 : 1 stock split, how many shares will be outstanding? What would be new

par value ? What would be the new market price ?

(c) Suppose if the company declares a 1 : 4 reverse split, how many shares will be outstanding? What would be the

new par value ? What would be the new market value?

 Key to Practical Exercises

Exercise 41-1

K = I (1 - t)
d
10% = I (1 - 0.35) ∴ Interest (I) = 15.3846%
(i) Calculation of Earning per share and Price per share `
( )

EBIT 40,00,000

Interest (20,00,000 × 15.3846/100) 3,07,692

Net income before tax 36,92,308

Less: Taxes (35%) 12,92,308

Net income after taxes 24,00,000

EPS = ` 24,00,000/6,00,000 = ` 4.00

N
E 4
K = 0.15 = = 26.67

N
e
P P
0 0

(ii) Calculation of Weighted Average Cost of Capital (K ) `

( )

A
o

Equity (6,00,000 × ` 10) 60,00,000

M
Debt 20,00,000

Total capital 80,00,000

X
K = (K × W ) + (K × W ) = (0.15 × 0.75) + (0.10 × 0.25) = 0.1375 or 13.75%
o e 1 d 2

A
(iii) `
( )

T
EBIT 40,00,000

Interest (1,00,00,000 × 0.12) 12,00,000

Net income before taxes 28,00,000

Less: Taxes (35%) 9,80,000

Net income after taxes 18,20,000

Shares Bought and Retired ( ∆N) = Debt/P

0
= ` 80,00,000/26.67 = 2,99,963 shares

New Outstanding Shares (N) = N -

0
∆N = 6,00,000 - 2,99,963 = 3,00,037

New EPS = 18,20,000/3,00,037 = ` 6.07

New Price Per Share (P )
0
= 6.07/0.17 = ` 35.71
Results

(a) New EPS ` 6.07 as against existing EPS of ` 4.00

(b) New price per share ` 35.71 as against existing price per share of ` 26.67

Therefore, Gentry should change its capital structure.

Exercise 41-2

(1) Calculation of number of shares in Fortune Pharma Ltd. to be issued to shareholders of Fortune India Ltd.

Fortune Pharma Ltd.:

Estimated profit for 2016-17 ` 1,470 lakhs

Estimated market price per share ` 24.50

 Estimated P/E ratio 25

Market price ` 24.50

= P/E ratio = 25 ∴ EPS = ` 24.50/25 = ` 0.98
Earnings EPS

Estimated profit ` 14,70,00,000

Total Number of Shares = = = 15,00,00,000 or 1,500 lakhs shares
EPS ` 0.98
Hence, for every 2 shares in Fortune India Ltd., one share in Fortune Pharma Ltd. are to be issued.

(2) Calculation of Expected Market Price of Fortune India Ltd.

Estimated profit = ` 11400 lakhs

No. of equity shares = 3000 lakhs

Estimated EPS = ` 11,400 lakhs/3,000 lakh shares = ` 3.80

Estimated P/E ratio = 42

Estimated market price Estimated market price

= 42 = 42
Estimated EPS ` 3.80

` 3.80 `

N
Estimated market price = 42 × = 159.60

(3) Calculation of Book value per share of both the companies immediately after demerger ( ` lakhs)

N
Before demerger After demerger

A
Particulars Fortune India Ltd. Fortune Pharma Ltd. Fortune India Ltd.

Assets 70,000 25,100 44,900

M
Less: Outside liabilities 25,000 4,100 20,900

X
Net worth 45,000 21,000 24,000

No. of shares outstanding (lakhs) 1500 3000

A
Book value per share ` 14 ` 8

T
Exercise 41-3

(a) Calculation of Buyback Price if Market Capitalization should be ` 200 lakhs

Surplus cash available = ` 90 lakhs

Estimated share price after repurchase = 10% above the buyback price

Let market price of share after buyback be ‘P’

`
( )
30% of 90,00,000
Market capitalization = 1.10 P 10,00,000 - = 11,00,000 P - 29,70,000
P

Market capitalization rate after buyback is ` 2,00,00,000. Then,

11,00,000 P - 29,70,000 = 2,00,00,000

11,00,000 P = 2,00,00,000 + 29,70,000

P = 2,29,70,000/11,00,000 = 20.88

∴ Buyback price is to be fixed at ` 20.88.

(b) Number of shares to be bought back = ` 27,00,000/` 20.88 = 1,29,310 shares

(c) Impact on EPS due to buyback

No. of equity shares outstanding after bought-back = 10,00,000 - 1,29,310 = 8,70,690 shares

10,00,000 × ` 3
EPS = = ` 3.45
8,70,690

The EPS has increased from ` 3 to ` 3.45 after the shares are bought-back.
Exercise 41-4

Current Earnings Per Share = ` 2.40

Current Market price of share = ` 24

Number of shares outstanding = ` 24,00,000/ ` 24 = 1,00,000 shares

(i) Calculation of New Price per share if excess cash paid in the form of extra dividend

Dividend per share = ` 4,80,000/1,00,000 shares = ` 4.80

P/E ratio = ` 24/ ` 2.40 = 10

Since the share price depends on company’s earning power, the market price remains at ` 24 and it is unaffected
by any dividend payment.

(ii) Calculation of New Price per share if excess cash is used for share repurchase.

Number of shares repurchased = ` 4,80,000/` 24 = 20,000 shares

Number of shares outstanding after repurchase = 1,00,000 - 20,000 = 80,000 shares

1,00,000
` `

N
New EPS = 2.40 × = 3
80,000

3
` 24 × `

N
New Share Price After Share Repurchase = = 30
2.4

A
Assumption - It is assumed that the P/E ratio remains unaltered in both the alternatives.

Exercise 41-5

M
(a) Number of new shares to be issued = 1,000 × 10/100 = 100 shares

X
4 × 1   ×C 

Market price after stock dividend =

4+/ =
+ 
= ` 18.18

A
 

Change in equity Account: An amount of ` 1,000 would be transferred from Retained earnings to Equity Share

T
Capital A/c

(b) Stock split proposed is 5 : 1

No. of new shares to be issued replacing old shares = 1,000 shares × 5/1 = 5,000 shares

New face value per share after split = ` 10/ ` 5 = ` 2

  ×C 

New market price of one share after the split = = ` 4

 

(c) Company declares reverse split in the ratio 1 : 4

 
No. of shares outstanding = × = 250 shares


New market price will be = ` 20 × 4 = ` 80

 Key to Short Answer Questions

True or False Statements

1. False - A Management buy-in occurs when a manager or a management team from outside the company

raises the necessary finance, buys it, and becomes the company’s new management.

2. False - The statement refers to the situation of ‘management buy-in’.

3. False - In a leveraged buyout, a company is acquired by a specialized investment firm using a relatively small

portion of equity and a relatively large portion of outside debt financing.

4. False - A company can utilize its reserves to buyback equity shares for the purpose of extinguishing these or

for treasury operations. The former option results in reduction of the paid up capital. In the latter

option, companies buy their shares from open market and keep these as ‘treasury stock’.

5. False - With repurchase of shares, few shares remaining outstanding which will result in increased earnings

N
per share and increase in the market price of share and reduction in amounts required in the form of

dividends. Therefore, valuation of shares on the basis of dividend payout ratio will not over estimate

N
the value of equity in firms, when stock buy back take place.

True

A
6. - In divestitures, the company who has acquired assets and divisions will make an examination to

determine whether the assets or divisions fit into overall corporate strategy in value maximization.

If it does not serve the purpose, such assets or divisions are hived-off.

M
7. True - The term ‘divestment’ denotes getting rid of something.

X
8. True - If a company is profit making, its accumulated profits and reserves will go on increasing. To avoid

A
abnormality in capital structure, part of free reserves can be distributed among the existing sharehold-

ers by issue of bonus shares. The intrinsic value of a share decreases after bonus issue, due to the

T
increased volume of stock in the stock market.

9. True - The issue of bonus shares and splitting of shares into smaller denominations may increase the share

price but it will not have any effect on the value of the firm since there is no cash inflow or cash outflow

of the transactions. The assets of the balance of the firm is unaffected. On the liabilities side of the

balance sheet, there will be change in the quantum of shares.

10. False - The post bonus issue will increase number of shares in the market and increase number of

shareholders. The bonus issue increases the voting power of promoters marginally. The reason being

that the small shareholders position and representation gets diluted and spreads across the nation due

to increased volume of stock in hand. Promoters are in a better position to trade and speculate well

in the market without risk of being voted out.

11. True - Corporate restructuring is the process of significantly changing a company’s business model,

management team or financial structure to address challenges and increase shareholder value.

12. False - BPR is a continuous process of rethinking, reassessment, redesign, evaluation of each element of

business process and consequent improvement in structure and work place.

13. True - The financial reorganization is resorted to bring balance in debt and equity funds, short-term and

long-term financing, to achieve reduction in finance charges, to reduce cost of capital, to increase EPS,

to improve market value of share, to reduce the control of financiers on the management of the

company etc.

Choose Correct Word

1. franchise

2. bonus
 3. scrip

4. stock split

5. MBO

6. tax benefits

7. sell-off

8. slump sale

9. strategic alliance

10. equity carveout

11. demerger

12. LBO

Choose Correct Answer

1. (B) a share split

2. (B) open market purchase

N
3. (A) increase on divestiture

N
4. (A) liquidation

5. (C) equity carveout

A
6. (B) book value

M
7. (D) shark repellants

8. (D) equity carveout

X
9. (B) exchange rates

A
10. (A) diversification

T
11. (C) strategic alliances

12. (D) product advantages

13. (A) organizational learning

14. (B) Divestitures

15. (D) consolidation

16. (D) all of the above

17. (C) bustup takeover

18. (A) decrease in number of firms

19. (C) open market share repurchase

20. (B) share repurchase

21. (B) unrelated type of business activity

22. (A) proxy contest

23. (D) leveraged cashout

24. (D) management buyout

25. (B) golden parachute

26. (D) all of the above

27. (B) 25% of total paid-up equity capital of the company

28. (B) increasing the par value of shares by consolidation of shares

29. (B) Liquidate when liquidation value > continuing value

30. (B) the parent company continues to exist in a spin-off while it leases to exist in a split-up

31. (B) There is no change in stockholding, but more shares available for trading

32. (D) stake holding remains the same with more shares available for trading

33. (B) distribution of shares to a portion of shareholders in a subsidiary in exchange for parent company

stock

34. (B) when foreign economy is imperfectly correlated with the domestic economy

35. (C) sale of a portion of the firm to an outside third party in consideration of cash or equivalent thereof

36. (B) as a way of learning about prospective merger partners for a full merger or acquisition at a later date

N N
M A
A X
T
 Practical Exercises

Exercise 42-1 Kangan Ltd. is considering merger with Payal Ltd. Kangan Ltd.’s shares are currently traded at ` 25
per share. It has 2,00,000 shares outstanding and its earnings after taxes (EAT) amount to ` 4,00,000. Payal Ltd. has
1,00,000 shares outstanding; its current market price is ` 12.50 per share and its EAT is ` 1,00,000. The merger will
be effected by means of a stock-swap (exchange). Payal Ltd. has agreed to a plan under which Kangan Ltd. will offer

the current market value of Payal Ltd.’s shares.

(i) What are the pre-merger earnings per share (EPS) and P/E ratios of both the companies ?

(ii) What must the exchange ratio be for Kangan Ltd.’s pre-merger and post-merger EPS to be the same ?

(iii) If Payal Ltd.’s P/E ratio is 8, what will be its current market price ? What will be the exchange ratio? What will

Kangan Ltd.’s post-merger EPS be ?

Exercise 42-2 Lara Dutta Ltd. is a highly successful company and wishes to expand by acquiring other firms. Its

N
expected high growth in earnings and dividends is reflected in its price-earnings (P/E) ratio of 17. The Board of

directors of Lara Dutta Ltd. has been advised that if it were to takeover firms with a lower P/E ratio than its own,

N
using a share-for-share exchange, it could increase its reported earnings per share. Priyanka Chopra Ltd. has been

suggested as a possible target for takeover, which has a P/E ratio of 10 and 10,00,000 shares in issue with a share price

A
of ` 15 each, Lara Dutta Ltd. has 50,00,000 shares in issue with a share price of ` 12 each.

Calculate the change in earnings per share of Lara Dutta Ltd., if it acquires Priyanka Chopra Ltd. shares for ` 15 per

M
share, assuming that the price of Lara Dutta Ltd. shares remains constant.

X
Exercise 42-3 Allen Ltd., a listed company, is considering merger of Ben Ltd. which is also a listed company, with

itself through allotment of shares in the proportion of the market value per share. Explain the impact of the above

A
decision on the wealth of the shareholders of both the companies after merger based on P/E ratio and EPS analysis.

T
The following are the financial data of the two companies:

Particulars Allen Ltd. Ben Ltd.

Profit after tax ( ) ` 12,00,000 8,00,000

Number of shares 50,000 10,000

Market value ( ` per share) 50 25

Exercise 42-4 A Ltd. is considering takeover of B Ltd. and C Ltd. The financial data for three companies are as

follows:

Particulars A Ltd. B Ltd. C Ltd.

Equity share capital of ` 10 each ( ` millions) 450 180 90

Earnings ( ` millions) 90 18 18

Market price of each share ( ) ` 60 37 46

Calculate: (i) Price earnings ratios, (ii) Earning per share of A Ltd. after the acquisition of B Ltd. and C Ltd. separately.

Will you recommend the merger of either/both of the companies? Justify your answer.
Exercise 42-5 Small Co. Ltd. is being acquired by Large Co. Ltd. on a share exchange basis, their selected data are:

Particulars Large Co. Ltd. Small Co. Ltd.

Profit after tax ( ` in lakhs) 56.0 21.0

Number of share (in lakhs) 10.0 8.4

Earnings per share ( ) ` 5.6 2.5

Price-earnings ratio 12.5 7.5

Calculate: (i) the market value per share (per-merger), and (ii) the maximum exchange ratio Large Co. Ltd. should

offer without the dilution of the EPS, and the market value per share.

Exercise 42-6 Firm A is planning to acquire Firm B. The relevant financial details of the two firms prior to merger

announcement are as follows:

Particulars Firm A Firm B

Market price per share `

( ) 75 30

Number of shares 10,00,000 5,00,000

N
Market value of the firm `
( ) 7,50,00,000 1,50,00,000

The merger is expected to bring gains which have present value of ` 1.50 crore. Firm A offers 2,50,000 shares in

N
exchange for ` 5 lakh shares to the shareholders of Firm B. You are required to calculate : (i) True cost of Firm A

A
for acquiring Firm B, and (ii) Net present value of the merger to Firm B. You may state your assumptions, if any.

Exercise 42-7 Smart Ltd. wants to acquire Dull Ltd. The balance sheet of Dull Ltd. as on 31.03.2016 is as follows:

M
Liabilities ` Assets `

X
Equity share capital (60,000 shares) 6,00,000 Cash 20,000

Retained earnings 2,00,000 Debtors 30,000

A
12% Debentures 2,00,000 Inventories 1,70,000

T
Creditors and other liabilities 3,20,000 Plant and equipments 11,00,000

13,20,000 13,20,000

Additional information:

(i) Shareholders of Dull Ltd. will get one share in Smart Ltd. for every two shares. External liabilities are expected

to be settled at ` 3,00,000. Shares of Smart Ltd. would be issued at its current price of ` 15 per share.

Debentureholders will get 13% convertible debentures in the purchasing company for the same amount.

Debtors and inventories are expected to realize ` 1,80,000.

(ii) Smart Ltd. has decided to operate the business of Dull Ltd. as a separate division. The division is likely to give

` 3,00,000 per year for 6 years. Smart Ltd. has planned that, after 6 years,
cash flows (after tax) to the extent of

this division would be demerged and disposed of for ` 1,00,000.

(iii) Company’s cost of capital is 14%.

Make a report to the Managing Director advising him about the financial feasibility of the acquisition.

Note: Present value of ` 1 for six years @ 14%: 0.8772, 0.7695, 0.6750, 0.5921, 0.5194 and 0.4556.

Exercise 42-8 Adroit Ltd. is run and managed by an effective team that insists on reinvesting 60% of its earnings

in projects that provide a return on equity (ROE) of 10% despite the fact that the firm’s capitalization rate (k) is 15%.

The firm’s current year’s earnings is ` 10 per share.

(i) At what price will the share of Adroit Ltd. sell ?

(ii) What is the present value of growth opportunities ?

(iii) Why would such a firm be a takeover target ?

 Key to Practical Exercises

Exercise 42-1

Calculation of pre-merger EPS

Kangan Ltd. = ` 4,00,000/2,00,000 shares = ` 2.00

Payal Ltd. = ` 1,00,000/1,00,000 shares = ` 1.00

Calculation of Price-Earning ratio

Kangan Ltd. = ` 25/` 2 = 12.5 Payal Ltd. = ` 12.50/` 1 = 12.5

C 
Share exchange ratio based on market value of shares = = 0.5 : 1
C 

For every two shares in Payal Ltd. one share of Kangan Ltd. will be issued.

N
No. of new shares to be issued = 1,00,000/2 = 50,000 shares

C    + C   

N
Post-merger EPS of Kangan Ltd. = = ` 2
   TIBSFT +   TIBSFT

A
If Payal Ltd.’s P/E ratio is 8, what will be its current market price

Current market price = EPS × P/E ratio = `1×8 = ` 8

M
C

X
Share exchange ratio = = 0.32 : 1
C 

A
For every 100 shares in Payal Ltd. 32 shares in Kangan Ltd. will be issued.

  
× 

T
No. of new shares to be issued = = 32,000 shares


C    + C   
Post-merger EPS of Kangan Ltd. = = ` 2.16
   TIBSFT +   TIBSFT

Exercise 42-2

Particulars Lara Dutta Ltd. Priyanka Chopra Ltd.

P/E ratio 17 10

Number of shares 50,00,000 10,00,000

`
MPS ( ) 12 15

EPS = (MPS ÷ P/E) `

( ) 0.706 0.667

Earnings ( )` 35,30,000 6,67,000

Total earnings after takeover = ` 35,30,000 + ` 6,67,000 = ` 41,97,000

Number of Shares offered by Lara Dutta Ltd. to Priyanka Chopra Ltd.

= 10,00,000 × 15/12 = 12,50,000 shares

(50,00,000 × 12) + (10,00,000 × 15) ` 7,50,00,000

MPS of Lara Dutta Ltd. after takeover = = = ` 12
50,00,000 + 12,50,000 62,50,000

EPS of Lara Dutta Ltd. after takeovers = ` 41,96,000/62,50,000 shares = ` 0.6715

Decrease in earning per share = 0.706 - 0.667 = ` 0.039
Exercise 42-3

Calculation of EPS before acquisition

Allen Ltd. = ` 12,00,000/50,000 shares = ` 24 Ben Ltd. = ` 8,00,000/10,000 shares = ` 80

Market value per share: Allen Ltd. = ` 50 Ben Ltd. = ` 25

C 
Share exchange ratio based on market value per share = = 0.5 : 1
C 

For every 2 shares in Ben Ltd. one share of Allen Ltd. will be issued.

No. of new shares to be issued = 10,000/2 = 5,000 shares

Price-earning ratio: Allen Ltd. = ` 50/` 24 = 2.08 Ben Ltd. = ` 25/` 80 = 0.31

C    + C   
EPS after merger = = ` 36.36
  TIBSFT +   TIBSFT

         
Post-merger weighted PE ratio =   ×  +   ×  = 1.25 + 0.12 = 1.37
         

N
1SJDF 1SJDF

N
Price-Earning ratio = 1.37 = Price = 1.37 × 36.36 = ` 49.81
&14 

A
Analysis - The shareholders of Allen Ltd. lose in their wealth as P/E ratio for them has comedown from 2.08 to 1.37

and the shareholders of Ben Ltd. stand to gain as P/E ratio for them has gone up from 0.31 to 1.37.

M
Exercise 42-4

X
Calculation of P/E Ratios

A
Particulars A Ltd. B Ltd. C. Ltd.

Earnings ( ` Millions) 90 18 18

T
Number of equity shares (millions) 45 18 9

EPS ( ) ` 2 1 2

Market price per share ( ) ` 60 37 46

P/E Ratio (Market price/EPS) 30 37 23

Calculation of EPS of A Ltd. after acquisition of B Ltd. and C Ltd.

Exchange ratio or rate = Buyer’s P/E ratio / Seller’s P/E ratio

Particulars A Ltd. B Ltd. C. Ltd.

Exchange ratio in A Ltd. - 0.81 1.30

Value of shares ( ` millions) 2,700 666 414

Number of A Ltd.’s shares to be given (millions) - 666/60 414/60

EPS ( ) ` - 11.11 6.9

Total earning after acquisition ( ` million) - 108 108

Total number of shares (millions) - 56.1 51.9

EPS after acquisition ( ) ` - 1.93 2.08

Analysis - After merger of C Ltd. with A Ltd., C Ltd.’s. EPS is higher than A Ltd. ( ` 2.08). Hence merger with only
with C Ltd. is suggested to increase the value to the shareholders of A Ltd.
Exercise 42-5

(i) Pre-merger market value per share = P/E ratio × EPS

Large Co. Ltd. = 12.5 × ` 5.6 = ` 70 Small Co. Ltd. = 7.5 × ` 2.5 = ` 18.75

(ii) Maximum Exchange Ratio without dilution of EPS of Large Co. Ltd.

Particulars Large Co. Ltd. Small Co. Ltd.

Profit after tax `

( ) 56,00,000 21,00,000

Number of shares 10,00,000 8,40,000

EPS `
( ) 5.6 2.5

56,00,000 + 21,00,000
= 5.6
10,00,000 + x

77,00,000 = 56,00,000 + 5.6x

5.6x = 77,00,000 - 56,00,000

x = 21,00,000/5.6 = 3,75,000 shares

N
Large Co. Ltd. can issue 3,75,000 shares for acquiring Small Co. Ltd.

Share exchange ratio = 8,40,000/3,75,000 = 2.24

N
Against 2.24 shares in Small Co. Ltd., Large Co. Ltd. can issue 1 share.

A
(iii) Maximum Exchange Ratio Large Co. Ltd. should offer without dilution of its market value per share

Particulars Large Co. Ltd. Small Co. Ltd.

M
Profit after tax `
( ) 56,00,000 21,00,000

X
Number of shares 10,00,000 8,40,000

EPS `
( ) 5.6 2.5

A
Market value `
( ) 70 18.75

T
Market capitalization 7,00,00,000 1,57,50,000

7,00,00,000 + 1,57,50,000
= 70
10,00,000 + x

8,57,50,000 = 7,00,00,000 + 70x

70x = 8,57,50,000 - 7,00,00,000

x = 1,57,50,000/70 = 2,25,000 shares

Large Co. Ltd. can issue 2,25,000 shares for acquiring Small Co. Ltd.

= 8,40,000/2,25,000 = 3.733 shares

For every 3.733 shares in Small Co. Ltd., Large Co. Ltd. can issue 1 share.

Exercise 42-6

(i) True Cost of Firm A for Acquiring Firm B

True cost = α PVAB - PVB

Where,

α PVAB = The value of what Firm B’s shareholders get in Firm A

PV
B = The value of what Firm B gives up

No. of shares offered to Firm B 2,50,000

α = = = 0.2
Total number of shares in Firm A 10,00,000 + 2,50,000

On assumption of Firm A’s and Firm B’s total market value before the proposal for merger is equal to the

present values of both the firms and the total value is calculated below:
 PV
AB = PV
A+ PV
B = 7,50,00,000 + 1,50,00,000 + 1,50,00,000 = ` 10,50,00,000

True Cost = α PVAB - PVB = (0.2 × 10,50,00,000) - 1,50,00,000 = ` 60,00,000

(ii) Net Present Value of the Merger to Firm B is calculated as below:

(a) Net present value of Firm A = 1,50,00,000 - 60,00,000 = ` 90,00,000

(b) Net present value of Firm B = 1,50,00,000 - 90,00,000 = ` 60,00,000
∴ NPV of merger to Firm B = ` 60,00,000

Exercise 42-7

Cost of Acquisition `
( )

60,000
Equity share capital × ` 15 4,50,000
2

13% Convertible debentures 2,00,000

Cash (Payment for external liabilities - Realization of cash from debtors and

inventories - Cash of Dull Ltd.) (i.e. 3,00,000 - 1,80,000 - 20,000) 1,00,000

N
Total Consideration 7,50,000

N
Calculation of NPV `
( )

A
Year Cash inflow P.V. factor @ 14% Present values

1 3,00,000 0.8772 2,63,160

M
2 3,00,000 0.7695 2,30,850

3 3,00,000 0.6750 2,02,500

X
4 3,00,000 0.5921 1,77,630

5 3,00,000 0.5194 1,55,820

A
6 3,00,000 0.4556 1,36,680

T
6 (Salvage value) 1,00,000 0.4556 45,560

Total P.V. of cash inflow 12,12,200

Less: Cost of acquisition 7,50,000

NPV 4,62,200

Suggestion - Since the NPV is positive it is suggested to acquire Dull Ltd. to maximize the value of shareholders of

both the companies.

Exercise 42-8

(i) Calculation of Market price of share

&  − C

P =
,F − CS
Where, E = Earnings per share i.e. ` 10

b = Retention ratio i.e. 60%

r = Capitalization rate or Cost of equity i.e. 15%

g = Dividend growth rate or Growth rate of firm

= Return on equity (r) × Retention ratio (b) = 0.10 × 0.60 = 0.06 or 6%

By substituting,

  − 

P = = = ` 44.44
 −  
(ii) Calculation present value of growth opportunities (PVGO)

= Market price per share when the firm retention ratio is 60% - Market price

per share when the payout ratio is 100% or retention ratio is 0%

= ` 66.67 - ` 44.44 = (-) ` 22.23 (negative)

%JWJEFOE C 
Note: P =
, F
=

= ` 66.67

The company has negative PVGO since the company’s capitalization rate (15%) is higher than its rate of return

on equity (10%).

(iii) Reasons to be a takeover target

The negative PVGO implies that the NPV of the firm’s projects is negative. It means the rate of return on the

projects is less its opportunity cost of capital. Another firm will try to takeover such firm with negative PVGO

at a lesser market price, turn it around and improve its own EPS after restructuring by utilizing its managerial

capabilities and competitive advantages over the firm with negative NPVs. Therefore, decision relating to

retention of profits is to be done strategically instead satisfying the immediate demands of the investors.

N N
M A
A X
T
 Practical Exercises
Exercise 44-1 In September, 2015, the Multinational Industries Inc. assessed the March, 2016 spot rate for pound
sterling at the following rates:

$/Pound 1.30 1.35 1.40 1.45 1.50

Probability 0.15 0.20 0.25 0.20 0.20

(i) What is the expected spot rate for March, 2016 ?

(ii) If six-month forward rate is $1.40, should the firm sell forward its pound receivables due in March, 2016 ?

Exercise 44-2 On the same date that the DM spot rate was quoted at $0.40 in New York, the price of the Pound
Sterling was quoted at $1.80:

(i) What would you expect the price of the Pound to be in Germany?

(ii) If the Pound was quoted in Frankfurt at DM 4.40/Pound, what would you do to profit from the situation?

Exercise 44-3 The following rates appear in the foreign exchange market:

N
Spot rate 2 Month Forward

N
`/US$ ` 45.80/46.05 ` 46.50/47.00
(i) How many dollars should a firm sell to get ` 5 crore after 2 months?

A
(ii) How many rupees is the firm required to pay to obtain US$ 2,00,000 in the spot market?

M
(iii) Assume the firm has US$ 50,000. How many rupees does the firm obtain in exchange of US$?

X
Exercise 44-4 Calculate the arbitrage gains possible on ` 10,00,000 from the middle rates given below. Assume there
are no transaction costs:

A
` 76.200 = £ 1 in London ` 46.600 = $ 1 in Delhi $ 1.5820 = £ 1 in New York

Exercise 44-5

T
The following direct quotes have been observed from the forex market:

(i) `/US $ = 43.70 (ii) `/UK £ = 77.02

Forward rate (60 days) for the Euro = ` 54.50/Euro

(iii) `/Euro = 53.50

DM/Dollar = 1.578 (overseas)

Find: (1) Indirect quotes in respect of (i) to (iii). (2) Forward discount on the Indian Rupee. (3) Cross rates for
Rupee/DM.

Exercise 44-6 Sunshine Ltd. is engaged in the production of synthetic yarn and planning to expand its operations.
In this context, the company is planning to import a multipurpose machine from Japan at a cost of ¥ 2,460 lakh. The
company is in a position to borrow funds to finance import at 12% interest per annum with quarterly rests. India
based Tokyo branch has also offered to extend credit of 90 days at 2% per annum against opening of an irrevocable
letter of credit. Other information are as under:

Present exchange rate ` 100 = ¥ 246 90 days forward rate ` 100 = ¥ 250

Commission charges for letter of credit at 4% per 12 months.

Advise whether the offer from the foreign branch should be accepted.

Exercise 44-7 Management of an Indian company is contemplating to import a machine from USA at a cost of
US $15,000 at today’s spot rate of $0.0227272 per Rupee.

Finance Manager opines that in the present foreign exchange market scenario, the exchange rate may shoot up by
10% after two months and accordingly he proposes to defer import of machine. Management thinks that deferring
import of machine will cause a loss of ` 50,000 to the company in the coming two months.
As the Financial Advisor, you are asked to express your views, giving reasons, as to whether the company should go
in for purchase of machine right now or defer purchase for two months.

Exercise 44-8 A company operating in a country having the dollar as its unit of currency has today invoiced sales
to an Indian company, the payment being due three months from the date of invoice. The invoice amount is $ 13,750
and at today’s spot rate of $ 0.0275 per ` 1, is equivalent to ` 5,00,000.

It is anticipated that the exchange rate will decline by 5% over the three months period and in order to protect the
dollar proceeds, the importer proposes to take appropriate action through foreign exchange market. The three
months forward rate is quoted as $ 0.0273 per ` 1. You are required to calculate the expected loss and to show, how
it can be hedged by forward contract.

Exercise 44-9 An Indian telecom company had approached Punjab National Bank for forward contract of
£5,00,000 delivery on 31st May, 2016. The bank had quoted a rate of ` 61.60/£ for the purchase of pound sterling
from the customer. But on 31st May, 2016, the customer informed the bank that it was not able to deliver the pound
sterling as anticipated receivable from London has not materialized and requested the bank to extend the contract
for delivery by 31st July, 2016. The following are the market quotes available on 31st May, 2016:

Spot (`/£) 62.60/65 2-month forward premium 42/46

N
1-month forward premium 20/25 3-month forward premium 62/68

Flat charges for cancellation of forward contract is ` 500.

N
You are required to find out the extension charges payable by the telecom company.

A
Exercise 44-10 Excel Exporters are holding an export bill in United States Dollar (USD) 1,00,000 due 60 days hence.
They are worried about the falling USD value which is currently at ` 45.60 per USD. The concerned export

M
consignment has been priced on an exchange rate of ` 45.50 per USD. The firm’s bankers have quoted a 60-day
forward rate of ` 45.20. Calculate: (i) Rate of discount quoted by the Bank. (ii) The probable loss of operating profit

X
if the forward sale is agreed to.

A
Exercise 44-11 The United States Dollar is selling in India at ` 45.50. If the interest rate for a 6-months borrowing

T
in India is 8% per annum and the corresponding rate in USA is 2%.

(i) Do you expect United States Dollar to be at a premium or at discount in the Indian forward market?

(ii) What is the expected 6-months forward rate for United States Dollar in India?

(iii) What is the rate of forward premium or discount?

Exercise 44-12 The following table shows interest rates for the United States Dollar and French Francs. The spot
exchange rate is 7.05 Francs per dollar. Complete the missing entries:

Particulars 3 Months 6 Months 1 Year

Dollar interest rate (annually compounded) 11½% 12¼% ?

Franc interest rate (annually compounded) 19½% ? 20%

Forward Franc per Dollar ? ? 7.5200

Forward discount on Franc per cent per year ? -6.3% ?

Exercise 44-13 On 1st April, 3 months interest rate in the US and Germany are 6.5 per cent and 4.5 per cent per
annum respectively. The $/DM spot rate is 0.6560. What would be the forward rate for DM for delivery on 30th June?
 Key to Practical Exercises

Exercise 44-1

Calculation of expected spot rate for March, 2016

$ spot rate for £ Probability $

(1) (2) (1) × (2) = (3)

1.30 0.15 0.195

1.35 0.20 0.270

1.40 0.25 0.350

1.45 0.20 0.290

1.50 0.20 0.300

1.00 Ev = 1.405

N
Therefore, the expected spot value of $ for £ for March, 2016 would be $1.405.

N
(ii) If the six-month forward rate is $1.40, the expected profits of the firm can be maximized by retaining its pounds

A
receivable and sell the proceeds in the spot market.

Exercise 44-2

M
The New York, DM1 = $0.40, and £1 = $1.80

X
(i) To find price of Pound in Germany, i.e., DM/£ we need to find the product of DM/£ and $/£

i.e. DM/$ × $/£ = 1/0.4 × 1.80/1 = 2.5 × 1.80

A
or DM/£ = 4.5

T
Thus, DM 4.5 = £1

(ii) In Frankfurt DM 4.40 = £1

New York DM 4.5 = £1

Then to profit from the situation, we will buy Pounds in Frankfurt and sell them in New York.

Exercise 44-3

(i) Calculation of number of dollars obtained after 2 months, by selling ` 5 crores.

2 month forward rate for selling of dollars

1 $ = ` 46.50
` 5,00,00,000
= US $ 10,75,268.82
` 46.50

(ii) Calculation of rupees required to purchase US $ 2,00,000 in the spot market

1 $ = ` 46.05
US $ 2,00,000 × ` 46.05 = ` 92,10,000
(iii) Calculation of rupees that can be obtained by selling US $ 50,000 in the spot market

1 $ = ` 45.80
US $ 50,000 × ` 45.80 = ` 22,90,000
Exercise 44-4

Currency rates prevailing in different cities

In London 1 £ = ` 76.20 In Delhi 1 $ = ` 46.60 In New York 1 £ = $ 1.5820

An arbitrager uses the cross currency rates for making arbitrage gains by taking the advantage of currency rate

differentials in different markets. To make arbitrage gains, the following sequence of transactions is entered:

Step 1 Buy US dollars in Delhi using ` 10,00,000 = ` 10,00,000/ ` 46.6 = US $ 21,459.23

Step 2 Sell US $ 21,459.23 in New York and purchase £ = $ 21,459.23/$ 1.5820 = £ 13,564.62

Step 3 Sell £ 13,564.62 in London to get Rupees = £ 13,564.62 × ` 76.20 = ` 10,33,624

Arbitrage gain = ` 10,33,624 - ` 10,00,000 = ` 33,624

Exercise 44-5

(1) Indirect Quotes US $ UK £ EURO

= 1/43.70 = 1/77.02 = 1/53.50

= 0.0229 = 0.01298 = 0.01869

N
(2) Forward Discount on the Indian Rupee vis-a-vis Euro

Premium/Discount p.a.

N
Forward rate - Spot rate 365 54.50 - 53.50 365
= × × 100 = × × 100 = 11.37% discount
Spot rate 60 53.50 60

A
(3) Cross rates for Rupee/DM = 43.70/1.578 = 27.69 `/DM

M
Exercise 44-6

X
Alternative I : Purchase of multipurpose machine by availing loan @ 12% interest p.a. ( lakhs)

Cost of machine ¥ 2,460 lakhs (Conversion rate ` 100 = ¥ 246) 1,000.00

A
Add: Ist quarter interest ( ` 1,000 lakhs × 12/100 × 3/12) 30.00

T
Total outflow 1,030.00

Alternative II : Extension of 90 days credit by Tokyo branch of an India-based bank ( ` lakhs)

Commission for establishment of letter of credit ( ` 1,000 lakhs × 4/100 × 3/12) 10.00

Interest for quarter ( ` 10 lakhs × 12/100 × 3/12) 0.30

10.30

Amount payable at the end of 90 days (lakh yen)

Cost of machine 2,460.00

Interest (2,460 × 2/100 × 90/365) 12.13

2,472.13

Conversion cost (at ` 100 = ¥ 250) = 2,472.13 × 100/250 = ` 988.85 lakhs

Total cost = ` 10.30 lakhs + ` 988.85 lakhs = ` 999.15 lakhs

Recommendation - The total cash outflow is lesser in case of alternative II by ` 41.15 lakhs. Therefore, import of

machine by establishing letter of credit is suggested.

Exercise 44-7

Spot rate ` = US$ 0.0227272

Two month forward rate ` 1 = US $ 0.0227272 × 1.10 = $ 0.02499992

Current cost of machine = $ 15,000

Current cost of machine in Rupees = $ 15,000/0.0227272 = ` 6,60,002

Cost of machine after two months = $ 15,000/$0.02499992 = ` 6,00,002

Saving due to foreign exchange rate fluctuations = ` 6,60,002 - ` 6,00,002 = ` 60,000

Increase in cost of machine if purchased after two months = ` 50,000

Net savings = ` 60,000 - ` 50,000 = ` 10,000

Suggestion - It is suggested to purchase the machine after two months to get net savings in cost of ` 10,000.

Exercise 44-8

Calculation of Spot Rate after 3 months

There is an anticipated decline in exchange rate by 5% over the 3 months period. The exchange rate after 3 months

would be: = $ 0.0275 × 95/100 = $ 0.026125

Calculation of Expected Loss due to Foreign Exchange Rate Fluctuation `

( )

Present cost ($ 13,750/$0.0275 per ` 1) 5,00,000

Cost after 3 months ($13,750/$0.026125 per ` 1) 5,26,316

Expected loss due to exchange rate fluctuation 26,316

N
Evaluation Taking Forward Cover

N
Forward cover for 3 months 1 = $0.0273

= $13750/$0.0273 = ` 5,03,663

A
Analysis - By taking a forward cover, the expected loss will reduce by ` 22,653 (i.e., ` 5,26,316 - ` 5,03,663). Hence
it is suggested to take a forward cover.

M
Exercise 44-9

X
Calculation of charges for cancellation of forward contract

A
The forward contract required for delivery on 31st May, 2016 should be cancelled and charges for such cancellation

will be booked to the Indian Telecom Company. `

( )

T
£ bought from customer under original contract 61.60

£ sold to customer under cancellation contract 62.65

1.05

Exchange difference (£ 5,00,000 × ` 1.05) 5,25,000

Add: Flat Charges 500

Total charges for cancellation of forward contract 5,25,500

The bank will again book a forward contract for delivery by 31st July, 2016 at `
( )

Spot rate for £ on 31.5.2016 62.60

Add: Two months forward premium 0.42

Forward contract will be booked at 63.02

Exercise 44-10

Spot rate US $ 1 = ` 45.60 60 day forward rate US $ 1 = ` 45.20

(i) Rate of discount quoted by Bank

Forward rate - Spot rate 365 45.20 - 45.60 365

× × 100 = × × 100 = 5.336%
Spot rate n 45.60 60

(ii) Probable loss of operating profit if the forward sale is agreed

= US $ 1,00,000 × (45.20 - 45.50) = ` 30,000

Exercise 44-11

(i) Under Interest Rate Parity Theorem, when all things being equal, the currency with highest interest rate will

at a discount in the forward market against the currency with lower interest rate. In view of the above

statement, US dollars are expected to quote at a premium over Indian rupees. Since interest rate of US is lower

than that of India.

(ii) Calculation 6-month Forward Rate for US dollar

The Interest Rate Parity relationship can be expressed as follows:

F 1 + i
h
=
S 1 + i
0 f

Where, F = Forward rate i = Interest rate of home country

h

S = Spot rate i = Interest rate of foreign country

0 f

F 1 + 0.04
=
45.50 1 + 0.01

F + 0.01 F = 45.50 + 1.82

N
1.01 F = 47.32

F = 47.32/1.01 = 46.85

N
∴ 6 month forward rate of US dollar against Rupee is ` 46.85

A
(iii) Rate of Forward Premium

Forward rate - Spot rate 12 46.85 - 45.50 12

× × 100 = × × 100 = 5.934%

M
Spot rate n 45.50 6

X
Exercise 44-12

A
(a) Calculation of 3 months forward discount on Franc per cent per year and 3 months forward Franc per Dollar

T
3 months Dollar interest rate = 11.5% or 0.115

3 months Franc interest rate = 19.5% or 0.195

As per Interest Rate Parity Theorem:

Interest rate differential = Exchange rate differential

1 + r S
d f/d
=
1 + r F
f f/d

where, r = Rate of interest of country with Francs as currency

f

r = Rate of interest of country with Dollar as currency

d

S = Spot rate between Franc and Dollar

f/d

F = Forward rate between Franc and Dollar

f/d

Interest rate differential = Exchange rate differential

1 + 0.115
= Exchange rate differential (differential between forward rate and spot rate)
1 + 0.195

Differential between forward and spot rate = 93.3%

∴Forward discount on Franc per cent per year = 93.3% - 100% = - 6.7%

Forward discount on Franc per cent for 3 months = - 6.7%/4 = - 1.675%

Spot rate of Franc against Dollar = 1/7.05 = 0.141844

Forward Franc = Today’s spot rate (difference between forward and spot rate)

= 0.141844 dollar (100% - 1.675%) = 0.1394681 dollar

Forward Franc per Dollar = 1/0.1394681 = 7.17

 (b) Calculation of 6 months Franc interest rate and 6 months forward Franc per Dollar

6 months Dollar interest rate = 12 1/4% or 12.25%

Forward discount on franc % per year = –6.3% or - 3.15% for 6 months

Hence 6 months Forward rate = 0.141844 dollar (spot rate) (100% - 3.15%) = 0.13737 dollars

Forward francs per dollar = 1/0.13737 = 7.28 francs

Differential in interest rate between two countries

= Differential between Forward and Spot rate

1 + Dollar interest rate

= Differential between Forward and Spot rate
1 + Franc interest rate

1 + .1225
= (100% - 6.3%)
1 + Franc interest rate

1.1225
= 93.7%
1 + Franc interest rate

1.1225
1 + Franc interest rate =

N
93.7%

Franc interest rate = 1.19797 - 1 = 0.19797 or 19.8%

N
(c) Calculation of one year Dollar interest rate and one year forward discount on Franc

A
One year Franc interest rate = 20%

Forward Franc per dollar = 7.5200

M
($)

X
Today’s spot rate is 7.05 (given) Francs per Dollar i.e., 1 Franc 0.141844

Forward Francs is 7.52 Francs per Dollar i.e., 1 Franc 0.132978

A
Difference 0.008866

T
Forward discount on Francs per cent per year

0.008866
= × 100 = - 6.25% or - 6.3% (rounded off)
0.141844

Differential in interest rates between two countries = Differential between forward rate and spot rate

1 + Dollar interest rate 7.05

=
1 + 0.20 7.52

Dollar interest rate = 1.20 × 0.9374 - 1 = 1.125 - 1 = 0.125 or 12.5%

Exercise 44-13

Interest Rate Parity Theorem - The theorem states that in equilibrium the difference in interest rates between two

countries is equal to the difference between the forward and spot rates of exchange. The mathematical formula

representing the theorem is given below:

i - i F - S
A B 0 0
=
1 + i S
B 0

where, i = Interest rate of US 6.5% or 0.065 F = Forward rate at the end of one year
A 0

i = Interest rate of Germany 4.5% or 0.045 S = Spot rate 1 $ = 0.6560 DM

B 0

0.065 - 0.045 F - 0.6560

0
= 1.045 F = 0.68552 + 0.01312
0
1 + 0.045 0.6560
 0.02 F - 0.6560
0
= 1.045 F = 0.69864
0
1.045 0.6560

0.02 × 0.6560 = (1.045 × F ) - (1.045 × 0.6560) F = 0.69864/1.045 = 0.66855

0 0

0.01312 = 1.045 F
0
- 0.68552 ∴ Forward rate after 12 months = 0.66855

Forward premium p.a. = Forward rate - Spot rate = 0.66855 - 0.6560 = 0.01255

Forward premium for 3 months = 0.01255/4 = 0.003137

Forward rate for 3 months for delivery on 30th June = Spot rate + 3 months forward premium

= 0.6560 + 0.003137 = 0.6591

Alternatively,

USD DM

Spot 0.6560 1.000

Interest rate p.a. 6.5% 4.5%

Interest for 91 days 0.0106 0.0112

Amount after 91 days 0.6666 1.0112

N
∴ Forward rate 0.6666 0.6592

N
(0.6666/0.6592) 1.0112

Alternatively,

A
[ ( )]
91
0.6560 × 1 + 0.065 ×
365
Forward rate = = 0.6592

M
( )
91
1 + 0.045 ×

X
365

T A
 Key to Short Answer Questions

True or False Statements

1. True - The international fisher effect asserts that countries with higher rates of inflation will have higher

nominal interest rates to provide adequate return to investors to combat inflation.

2. False - The model suggests that the difference in interest rates between two countries is equal to the expected

difference in inflation rates between these countries.

3. True - Under PPP theorem, it is assumed that the expected difference in inflation rates between two

countries equals, in equilibrium, the expected movements in spot rates.

4. True - The currency with higher interest rate will sell at a discount in the forward market against the currency

with lower interest rate. The relative interest rates and expected change in interest rates will influence

the exchange rates.

N
5. False - The difference between bid price and offer price is called ‘spread’.

False

N
6. - Continuous adverse balance of payments position will lead to depreciation in country’s currency

exchange rate due to demand for foreign currencies increases.

A
7. False - Under closing rate method, assets and liabilities denominated in foreign currencies are translated

using the closing rate. Revenue items are translated using either an average or the closing rate of

M
exchange for the period.

True

X
8. - Financial stability enables the economy to withstand shocks and crises, without disturbing either the

intermediation role of banks or the payment processing and settlement systems.

A
9. True - Full convertibility is also known as ‘floating rupee’ which means the removal of all controls on the

T
cross-border movement of capital.

10. False - ACU is having its headquarters in Tehran.

Choose Correct Word

1. full

2. financial system

3. dirty float

4. vostro

5. swap rate

6. higher

7. law of one price

8. interest rate

9. purchasing power

10. spot

11. fisher effect

12. default risk

Choose Correct Answer

1. (B) The Central Board of Directors of the RBI

2. (C) Capital Account

 3. (B) managed float

4. (B) factor influencing at national level

5. (D) depreciating currencies

6. (A) offer price

7. (D) all of the above

8. (B) replacement and market price method

9. (A) country’s political stability

10. (D) investment risk

11. (D) all of the above

12. (D) all of the above

13. (B) Inflation rates differing in the two concerned countries

N N
M A
A X
T
 Practical Exercises

Exercise 45-1 An American multinational corporation has subsidiaries whose cash positions for the month of

September, 2016 are given below:

Swiss subsidiary Cash surplus of SF 1,50,00,000

Canadian subsidiary Cash deficit of Can $ 2,50,00,000

UK subsidiary Cash deficit of 30,00,000 (UK pound)

What are the cash requirements, if:

(i) Decentralized cash management is adopted?

(ii) Centralized cash management is adopted?

(Exchange rate : SF 1.48/$, Can $ 1.58/$, $1.57/£)

N
Exercise 45-2 Following are the spot exchange rates quoted at three different forex markets:

USD/INR 48.30 in Mumbai GBP/INR 77.52 in London GBP/USD 1.6231 in New York

N
The arbitraguer has USD 1,00,00,000. Assuming that there are no transaction costs, explain whether there is any

arbitrage gain possible from the quoted spot exchange rates.

A
Exercise 45-3 Given the following information:

M
Exchange rate Canadian dollar 0.665 per DM (spot)

X
Canadian dollar 0.670 per DM (3 months)

Interest rates DM 7% p.a.

A
Canadian Dollar 9% p.a.

T
What operations would be carried out to take the possible arbitrage gains?

Exercise 45-4 Spot rate (1 US $) = ` 48.0123

180 days Forward rate for 1 US $ = ` 48.8190

Annualized interest rate for 6 months - Rupee = 12%

Annualized interest rate for 6 months - US $ = 8%

Is there any arbitrage possibility? If yes how an arbitrageur can take advantage of the situation, if he is willing to

borrow ` 40,00,000 or US $ 83,312?

Exercise 45-5 Following are the details of cash inflows and outflows in foreign currency denominations of MNP

Co. an Indian export firm, which have no foreign subsidiaries:

Currency Inflow Outflow Spot rate Forward rate

US $ 4,00,00,000 2,00,00,000 48.01 48.82

French Franc (FFr) 2,00,00,000 80,00,000 7.45 8.12

U.K. £ 3,00,00,000 2,00,00,000 75.57 75.98

Japanese Yen 1,50,00,000 2,50,00,000 3.20 2.40

(i) Determine the net exposure of each foreign currency in terms of Rupees.

(ii) Are any of the exposure positions offsetting to some extent?

Exercise 45-6 AMK Ltd. an Indian based company has subsidiaries in U.S. and U.K.

Forecasts of surplus funds for the next 30 days from two subsidiaries are as below:

U.S. $ 12.5 million U.K. £ 6 million

Following exchange rate informations are obtained:

$/ ` £/ `

Spot 0.0215 0.0149

30 days forward 0.0217 0.0150

Annual borrowing/deposit rates (simple) are available.

` 6.4%/6.2% $ 1.6%/1.5% £ 3.9%/3.7%

The Indian operation is forecasting a cash deficit of ` 500 million.

It is assumed that interest rates are based on a year of 360 days.

(i) Calculate the cash balance at the end of 30 days period in ` for each company under each of the following

scenarios ignoring transaction costs and taxes:

N
(a) Each company invests/finances its own cash balances/deficits in local currency independently.

(b) Cash balances are pooled immediately in India and the net balances are invested/borrowed for 30 days

N
period.

(ii) Which method do you think is preferable from the parent company’s point of view?

A
Exercise 45-7 Following information relates to AKC Ltd. which manufactures some parts of an electronic device

M
which are exported to USA, Japan and Europe on 90 days credit terms.

Cost and Sales information:

X
Japan USA Europe

A
Variable cost per unit ` 225 ` 395 ` 510

T
Export sale price per unit Yen 650 US $ 10.23 Euro 11.99

Receipts from sale due in 90 days Yen 78,00,000 US $ 1,02,300 Euro 95,920

Foreign exchange rate information:

Yen/ ` US $/ ` Euro/ `
Spot market 2.417 - 2.437 0.0214 - 0.0217 0.0177 - 0.0180

3 months forward 2.397 - 2.427 0.0213 - 0.0216 0.0176 - 0.0178

3 months spot 2.423 - 2.459 0.02144 - 0.02156 0.0177 - 0.0179

Advice AKC Ltd. by calculating average contribution to sales ratio whether it should hedge it’s foreign currency risk

or not.

Exercise 45-8 Zenith Ltd.(ZL) places an order to buy machinery with an American company. As per the agreement

Zenith Ltd. will be paying $ 2,00,000 after 180 days. The company (ZL) considers to use (1) a forward hedge ; (2) a

money market hedge; (3) an option hedge; or (4) no hedge. The consultant of Zenith Ltd. collects and develops the

following data/information as desired by the company. which can be used to assess the alternative approaches for

hedging.

(i) Spot rate of dollar as of today is ` 47/$.

(ii) 180 days forward rate of dollar as of today is ` 47.50/$.

(iii) Interest rates are as follows:

 India US

180 day deposit (per annum) 7.5% 3%

180 day borrowing rate (per annum) 8.0% 4%

(Assume 360 days in a year)

(iv) Future Spot rate in 180 days as estimated by the Consultant is ` 47.75/$.

(v) A call option on the dollar, which expires in 180 days has an exercise price of ` 47/$ and premium ` 0.52/$.
(vi) A put option on the dollar, which expires in 180 days has an exercise price of ` 47.50 and premium ` 0.40/$.
Required: Carry out a comparative analysis of various outcomes (rupee cost of import)/alternatives and decide

which of the alternatives is the most attractive to Zenith Ltd.

Exercise 45-9 The finance director of Molson Ltd. has been studying exchange rates and interest rates relevant in

India and USA. Molson Ltd. has purchased goods from the US Co. at a cost of $ 40.50 lakhs payable in $ in 3 months

time. In order to maintain profit margins the Finance Director wishes to adopt, if possible a risk-free strategy that

will ensure that the cost of goods to Molson Ltd. is no more than ` 18 crores:

N
`/$ spot 41/43 `/$(1 month forward) 42/44 `/$(3 months forward) 43/46

Interest rates available of Molson Ltd.

N
India (Rates in %) USA (Rates in %)

A
Deposit Borrowing Deposit Borrowing

1 month 9.00 12.00 4.00 7.00

M
3 months 9.00 13.00 5.00 8.00

X
Calculate whether it is possible for Molson Ltd. to achieve a cost directly associated with transaction not more than

A
` 18 crores, by means of a forward market hedge or money market hedge. Ignore transaction costs.

T
 Key to Practical Exercises

Exercise 45-1

(i) Cash requirement under decentralized cash management system (US $)

Canadian subsidiary - cash deficit (Can $ 2,50,00,000/1.58 US $) 1,58,22,785

U.K. Subsidiary - cash deficit (U.K. £ 30,00,000 × 1.57 US $) 47,10,000

Total cash requirement 2,05,32,785

(ii) Cash requirement under centralized cash management system (US $)

Cash requirement as per table (i) 2,05,32,785

Less: Cash surplus with Swiss subsidiary (SF 1,50,00,000/1.48 US $) 1,01,35,135

Net cash requirement 1,03,97,650

Exercise 45-2

N N
The following steps will be followed by the arbitraguer who is having USD 1,00,00,000:

A
Step I Convert US dollars in Indian rupees at spot rate of ` 48.30 in Mumbai

= US $ 1,00,00,000 × ` 48.30 = ` 48,30,00,000

M
Step II Convert again rupees into GBP at London = ` 48,30,00,000/ ` 77.52 = GBP 62,30,650.155

X
Step III Convert GBP to USD at New York = GBP 62,30,650.155 × US $1.6231 = US $1,01,12,968.26

A
Net gain from arbitrage operations = US $1,01,12,968.26 - US $1,00,00,000 = US $1,12,968.26

T
Exercise 45-3

Spot rate 1 DM = 0.665 Can $

DM is at premium against Can $

0.670 - 0.665 12
Forward premium = × × 100 = 3.01%
0.665 3

Interest rate differential = 9% - 7% = 2%

The interest differential (2%) is smaller than the forward premium (3.01%). Then, it will be profitable to place money

in DM to make arbitrage gain.

The following operations are suggested to take possible arbitrage gains:

Operation 1 Borrow Can $ 1000 at 9% rate of interest for 3 months.

Operation 2 Convert those Can $ 1000 into DM 1503.7 in spot (i.e . 1,000/0.665).

Operation 3 Place DM 1503.7 in the money market for 3 months. This will fetch DM 1530 as follows: (DM )

Principal 1503.70

Add: Interest @ 7% for 3 months 26.30

1530.00

Operation 4 Sell DM 1530 at 3 month forward to obtain Can $ 1025 (i.e . DM 1530 × 0.670).
Operation 5 Repay the Can $ 1000 debt with interest as follows: (Can $ )

Principal 1000.00

Add: Interest @ 9% for 3 months 22.50

1022.50

∴ Net Arbitrage Gain = 1025.1 - 1022.5 = Can $ 2.6

Exercise 45-4

Spot rate = ` 40,00,000/$ 83,312 = ` 48.0123

48.8190 - 48.0123 12
ForwardPremium = × × 100 = 3.36%
48.0123 6

Annualized interest rate for 6 months - Rupee = 12%

Annualized interest rate for 6 months - US $ = 8%

Interest rate differential = 12% - 8% = 4%

N
Since the interest rate differential is negative and is greater than forward premium , there is a possibility of arbitrage

inflow into India.

N
The advantage by using arbitrage possibility can be analyzed as follows:

A
Option I - Borrow $ 83,312 for 6 months

Amount repayable after 6 months along with interest = $ 83,312 + ($ 83,312 × 8/100 × 6/12) = $ 86,644.48

M
Option 2 - Convert $ 83,312 into Rupees and get the principal amount of ` 40,00,000

` 40,00,000 × 6/100 `

X
Interest on investments for 6 months = = 2,40,000

Total amount at the end of 6 months = ` 40,00,000 + ` 2,40,000 = ` 2,40,000

A
Converting the total amount at forward rate = ` 42,40,000/ ` 48.8190 = $ 86,851.43

T
Net gain by selecting Option II = ($ 86,851.43 - $ 86,644.48) × ` 48.8190 = ` 10,103

Exercise 45-5

(i) Determination of Net Exposure of each Foreign Currency in terms of Rupees (in millions)

Currency Inflow Outflow Net flow Spread Net exposure

US $ 40 20 20 0.81 16.20

FFr 20 8 12 0.67 8.04

UK £ 30 20 10 0.41 4.10

Japan Yen 15 25 -10 - 0.80 8.00

(ii) The exposure of Japanese Yen position is being offset by a better forward rate.

Exercise 45-6

Cash Balances if Subsidiaries acting independently (in 000’s)

Segment Capital Interest ` in 30 days

India - 5,00,000 - 2,666.67 - 5,02,667

U.S 12,500 15.63 5,76,757

U.K. 6,000 18.50 4,01,233

4,75,323
Cash Balances on immediate cash pooling from U.S. and U.K. subsidiaries (in 000’s)

India - 5,00,000

U.S. (12,500/0.0215) 5,81,395

U.K. (6,000/0.0149) 4,02,685

4,84,080

Suggestion - The company can maximize its interest earnings by immediate cash pooling and investing the pooled

amount of ` 4,84,080 @ 6.2% p.a. for 30 days, which will earn interest amount of ` 2,501.

Exercise 45-7

Calculation of No. of Units sold

Japan = Yen 78,00,000/Yen 650 = 12,000 units

USA = $ 1,02,300/$ 10.23 = 10,000 units

Europe = Euro 95,920/Euro 11.99 = 8,000 units

(i) Calculation of Average Contribution to Sales ratio when foreign currency risk is hedged

N
Particulars Japan USA Europe Total

N
No. of units sold 12,000 10,000 8,000

A
Receipts from sales Yen 78,00,000 US $ 1,02,300 Euro 95,920

3 month forward rate for selling 2.427 0.0216 0.0178

M
Receipt from sales In ` (a) 32,13,844 47,36,111 53,88,764 1,33,38,719

`)

X
Variable cost p.u. ( 225 395 510

Variable cost (b) 27,00,000 39,50,000 40,80,000 1,07,30,000

A
Contribution (a) - (b) 5,13,844 7,86,111 13,08,764 26,08,719

T
Average Contribution to Sales Ratio 19.56%

(ii) Calculation of Average Contribution to Sales ratio when foreign currency risk is not hedged

Particulars Japan USA Europe Total

No. of units sold 12,000 10,000 8,000

Receipts from sales Yen 78,00,000 US $ 1,02,300 Euro 95,920

3 month spot rate for selling 2.459 0.02156 0.0179

Receipt from sales In ` (a) 31,72,021 47,44,898 53,58,659 1,32,75,578

Variable cost p.u. ( `) 225 395 510

Variable cost (b) 27,00,000 39,50,000 40,80,000 1,07,30,000

Contribution (a) - (b) 4,72,021 7,94,898 12,78,659 25,45,578

Average Contribution to Sales Ratio 19.17%

Suggestion - The average contribution to sales ratio is more when the foreign currency risk is hedged. Hence it is

suggested to hedge the foreign currency risk.

Exercise 45-8

(i) Forward Hedge: Purchase dollars 180 days forward Rupees needed in 180 days

= Payable in $ × Forward Rate of dollar = $ 2,00,000 × ` 47.50 = ` 95,00,000

 (ii) Money Market Hedge

Borrow Rupee, Convert to US dollar, Invest US dollar, Repay rupee loan in 180 days.

Amount in US dollar to be invested:

           

= = = = $ 1,97,044
 +  × 
 +  
Amount in rupees needed to convert into $ for deposit = $ 1,97,044 × ` 47 = ` 92,61,068

Interest and principal owed on rupees loan to be returned after 180 days.

C    C    C   

= = = = ` 96,31,511
 +  × 
 +  

(iii) Option hedge

Purchase Call option (assuming that the option to be exercised on the day the US dollar are needed) exercise

price is ` 47/$; and Premium is ` 0.52/$.

At the expected future spot rate of ` 47.75/$ which is higher than the exercise price of ` 47/$, the company

N
will exercise its call option and buy $ 2,00,000 for ` 95,04,000 which is the sum of exercise value and premium
[2,00,000 × ( ` 47 + ` 0.52)]

N
So, total price to be paid for $ 2,00,000 is ` 95,04,000.

A
(iv) Remain unhedged

Zenith Ltd. will need to purchase US $ 2,00,000 to fulfill its import obligation. It will do so by making a purchase

M
in the spot market after 180 days. Zenith Ltd. rupee outgo in this case will be:

Expected spot rate in 180 days × Purchase of US dollars

X
= $ 2,00,000 × ` 47.75= ` 95,50,000

A
Suggestion - On making comparative analysis of the above alternatives it is observed that hedging through forward

T
market is the cheapest. Hence, this is the most attractive to Zenith Ltd.

Exercise 45-9

Alternative I - Choose Forward Market Hedge

Amount payable in 3 months time = $ 40.50 lakhs

Amount payable by taking 3 month forward rate = $ 40.50 lakhs × ` 46 = ` 18.63 crores

Alternative II - Choose Money Market Hedge

Amount payable in $ after 3 months = $ 40.50 lakhs

First borrow rupees @ 13%, convert to $ in spot, deposit the same @ 5% and use the maturity $ amount to pay the

purchase cost of goods.

Amount deposited + Interest should equal to $ 40.50 lakh after 3 months.

   
The amount to be deposited = = $ 40,00,000 or $ 40 lakhs
 + 
Now to get $ 40 lakhs from rupee proceeds, it would borrow $ 40 lakhs × ` 43 = ` 17.20 crores.

Total commitment = `17.20 crores + Interest @ 13% p.a. for 3 months

= ` 17.20 crores + ( ` 17.20 crores × 13/100 × 3/12)

= ` 17.20 crores + ` 0.559 crores = ` 17.759 crores

Suggestion - Since cash outflow is less in case of alternative II, it is suggested to choose money market hedge.
 Key to Short Answer Questions

True or False Statements

1. True - Lead means when a company may make payment earlier than when the amount is due for payment.

In netting, a company having overseas subsidiaries, settles the net amounts of its subsidiaries

periodically. A currency swap is a legal agreement between two parties to exchange the principal and

interest rate obligations. Therefore, leading and netting are internal hedging techniques where as

swap is an external hedging technique.

2. True - In the situation of depreciating rupee against foreign currency, it is preferable to accept invoices in

home currency. The exchange risk is not eliminated in this case, but transferred to the supplier.

3. False - The person off-loading the risk is the hedger and the person taking the risk is the speculator or trader.

4. False - An aggressive firm seeks to maximize profit in foreign exchange markets.

N
5. True - The exposure management copes with the possibility of loss arising from uncovered (open) position

when the related exchange rate rises or falls or the currency involved is devalued or revalued.

N
6. True - The increased linkages between financial markets speed up the transmission of turbulence from one

A
market to another.

7. True - Market risk of derivative products is the risk of adverse price, interest rate, index level volatility and

M
other fluctuations, typically in the underlying instruments.

False

X
8. - Market liquidity risk arises when an entity is unable to unwind or offset a derivative transaction in a

timely manner. On the other hand, funding liquidity risk is the risk that an entity cannot meet its

A
payment obligations on settlement date.

True

T
9. - Hedging refers to process, whereby one can protect the price of financial instrument at a date in future

by taking an opposite position in the present by using derivatives.

10. False - A foreign exchange risk impacting the balance sheet would stem from import of fixed assets, obtaining

foreign exchange loans.

Choose Correct Word

1. operating

2. exposure

3. foreign exchange exposure

4. transaction risk

5. defensive firm

6. transfer

7. leads

8. geographical

9. covered interest arbitrage

10. derivative

11. operational risk

12. variation

13. exchange rate

14. increases
Choose Correct Answer

1. (B) operating risk

2. (D) economic exposure

3. (B) currency option contract

4. (D) default risk

5. (C) credit risk

6. (C) marketability risk

7. (C) to know with certainty the quantum of future cash flows

8. (C) relying on past trends or events as a predictor of future events

N N
M A
A X
T
 Practical Exercises

Exercise 47-1 The 6-month forward price of a security is ` 208.18. The borrowing rate is 8% per annum payable
with monthly rests. What should be the spot price ?

Exercise 47-2

BSE index 500 Risk free interest rate 9% p.a.

Value of portfolio ` 10,10,000 Dividend yield on Index 6% p.a.

Beta of portfolio 1.5

We assume that a futures contract on the BSE index with four months maturity is used to hedge the value of portfolio

over next three months. One future contract is for delivery of 50 times the index.

Based on the above information calculate:

(i) Price of future contract.

N
(ii) The gain on short futures position if index turns out to be 4,500 in three months.

N
Exercise 47-3 Calculate the price of 3 months PQR futures, if PQR (FV ` 10) quotes ` 220 on NSE and the three

months future price quotes at ` 230 and the one month borrowing rate is given as 15 percent and the expected annual

A
dividend yield is 25 percent per annum payable before expiry. Also examine arbitrage opportunities.

Exercise 47-4

M
A company operating in a country having the dollar as its unit of currency has today invoiced sales

to an Indian company, the payment being due three months from the date of invoice. The invoice amount is $ 13,750

X
and at today’s spot rate of $ 0.0275 per ` 1, is equivalent to ` 5,00,000.

It is anticipated that the exchange rate will decline by 5% over the three months period and in order to protect the

A
dollar proceeds, the importer proposes to take appropriate action through foreign exchange market. The three

` 1. You are required to calculate the expected loss and to show, how

T
months forward rate is quoted as $ 0.0273 per

it can be hedged by forward contract.

Exercise 47-5

(i) Interest rates for 3 months in US and Canada are as follows:

Currency Borrow Invest

US $ 4% 2.5%

Can. $ 4.5% 3.5%

(ii) Can. $/US $ spot 1.235 - 1.240

3 month forward 1.255 - 1.260

Advise the currency in which borrowing and lending for 3 months needs to be done for a US company. Take

3 months = 90/360 fraction of a year.

Exercise 47-6 MN, a UK company, has a substantial portfolio of its trade with American and German companies.

It has recently invoiced a US customer the sum of $ 5,000,000, receivable in one year’s time. MN finance director

is considering two methods of hedging the exchange risk:

Method 1 Borrowing present value of $ 5 million now for one year, converting the amount into sterling, and

repaying the loan out of eventual receipts.

Method 2 Entering into a 12 month forward exchange contract with the company’s bank to sell the $ 5 million.

The spot rate of exchange is £ 1 = US $ 1.6355 The 12 month forward rate of exchange is £ 1 = US $ 1.6125

Interest rates for 12 months are USA 3.5%; UK 4%.

You are required to calculate the net proceeds in sterling under both methods and advise the company.

(Ignore bank commissions)

Exercise 47-7 For imports from UK, Philadelphia Ltd. of USA owes £ 6,50,000 to London Ltd., payable on May,

2016. It is now 12 February, 2016. The following future contracts (contract size £ 62,500) are available on the

Philadelphia exchange:

Expiry March June

Current futures rate 1.4900 $/£ 1 1.4960 $/£ 1

(a) Illustrate how Philadelphia Ltd. can use future contracts to reduce the transaction risk if, on 20 May the spot

rate is 1.5030 $/£ 1 and June futures are trading at 1.5120 $/£. The spot rate on 12 February is 1.4850 $/£ 1.

(b) Calculate the “hedge efficiency” and comment on it.

N N
M A
A X
T
 Key to Practical Exercises

Exercise 47-1

Calculation of Spot Price

6 month forward price of security = ` 208.18

Borrowing rate is 8% p.a. payable with monthly rests.

Forward Price

A = P(1 + r/n) raised to nt

Where, A = Forward price P = Spot price t = Time

r = Rate of interest n = Number of compoundings

208.18 = P(1+ 0.08/12) raised to 6

208.18 = P × 1.0409

N
P = 208.18/1.0409 = 200

N
Hence, the spot price should be 200.

Exercise 47-2

A
(i) Calculation of Price of Future Contract = 5,000 + 5,000 (0.09 - 0.06) 4/12 = 5,000 + 50 = 5,050

` 50 × 5050 ` 2,52,500

M
Price of Future Contract = =

(ii) Calculation of Gain on Short Futures Contract position

X
` 10,10,000
Hedge ratio = × 1.5 = 6 contracts

A
` 2,52,500
Index after 3 months turns out to be 4500.

T
Then, Future price is = 4,500 + 4,500 (0.09 - 0.06)1/3 = 4,500 + 45 = 4,545

Gain on Short Futures Position = 60 × (505 - 4,545) × 50 = -1,21,20,000

Exercise 47-3

Futures price = Spot + Cost of carry - Dividend

= 220 + (220 × 0.15 × 0.25) - (10 × 0.25) = 220 + 8.25 - 2.50 = ` 225.75

The futures price is ` 225.75 which is now quoted at ` 230 in the exchange. The fair value of Futures is less than the
actual Futures price. Because of over valuation of Futures in the market, arbitrage opportunities exist.

Step I - Buy PQR stock at ` 220 by borrowing at 15% for 3 months. Its outflows are as follows `
( )

Cost of stock 220.00

Add: Interest ( ` 220 × 15/100 × 3/12) 8.25

Total outflows 228.25

Step II - Sell March 2000 Futures at ` 230. Meanwhile he would receive dividend for his stock. Total inflows are as

follows `
( )

Sale proceeds of March 2000 futures 230.00

Receipt of dividend 2.50

Total inflows 232.50

Profit earned by Arbitraguer = 232.50 - 228.25 = ` 4.25

Exercise 47-4

Calculation of Spot Rate after 3 months

There is an anticipated decline in exchange rate by 5% over the 3 months period. The exchange rate after 3 months

would be: = $ 0.0275 × 95/100 = $ 0.026125

Calculation of Expected Loss due to Foreign Exchange Rate Fluctuation ( `)

Present cost ($ 13,750/$0.0275 per ` 1) 5,00,000

Cost after 3 months ($13,750/$0.026125 per ` 1) 5,26,316

Expected loss due to exchange rate fluctuation 26,316

Evaluation Taking Forward Cover

Forward cover for 3 months ` 1 = $0.0273 = $13750/$0.0273 = ` 5,03,663

Analysis - By taking a forward cover, the expected loss will reduce by ` 22,653 (i.e., ` 5,26,316 - ` 5,03,663). Hence
it is suggested to take a forward cover.

Exercise 47-5

N
Borrow US $

 
Amount to be paid =  +  × ×  = 1.01

N
   
Borrow Can.$

A
+   × × 
  

    
Amount to be paid = = = 0.999163

M
 

Now, borrow in Can.$ and take 3 month forward in Can.$ to repay the obligation.

X
Invest in US $

+  × × 

A
 
Amount to be received =  = 1.00625
   

T
+   × × 
 

    
Invest Can.$ = = = 0.988735
 

Analysis - It is suggested to invest in US $.

Exercise 47-6

Amount receivable in one year time = $ 50,00,000

Spot exchange rate £ 1 = US $ 1.6355 12-month forward rate £ 1 = US $ 1.6125

Alternative I Borrow present value of $ 5 million now for one year, converting the amount into sterling, and

repaying the loan out of eventual receipts.

   
Borrow now present value US $ 50,00,000 = = $ 48,30,918

   
Convert $48,30,918 into sterling = = £ 29,53,787


Deposit sterling at 4% interest = b    × = £ 30,71,938


Alternative II Enter into a 12-month forward exchange contract with the company’s bank to sell the

$ 5 million. Take a forward cover at 1.6125

MN company gets = $ 50,00,000/1.6125 = £ 31,00,775

Analysis - Since the £ inflow is highest in alternative II, it is suggested to take forward cover to maximize £ value of

the invoice $ 5 million.

Exercise 47-7

(a) For Philadelphia Ltd. the appropriate futures contract will be the one that will expire soonest after the end of

the exposure period i.e. the June contract.

Number of contracts needed = £6,50,000/£62,500 = 10.4 (say 10 contracts)

P Ltd. will buy 10 June contracts now (12 Feb.) at $1.4960/£1 and sell 10 contracts on 20 May for $1.5120/£1,

thus making a profit from the futures trading that will largely but not totally, negate the ‘loss’ from the spot

market (since sterling has strengthened between 12 February and 20 May).

We now calculate the profit/loss from the futures contracts trade:

i) The ‘tick’ movement is (1.5120 - 1.4960) = 0.0160 i.e., 160 ticks (for one tick = 0.0001)

ii) ‘Tick’ value per contract = £ 62,500 × 0.0001 = $ 6.25

iii) Profit = 10 contracts × 160 × $ 6.25 = $ 10,000

iv) Overall cost on 20 May when P Ltd. will exchange $ for £ on the spot market :

£ 6,50,000 × 1.5030 = $ 9,76,950 [Conversion at the prevailing spot rate]

v) The net ‘cost’ to P Ltd. = $ 9,76,950 - $ 10,000 = $ 9,66,950

N
(b) Hedge Efficiency

The spot on February 12 was 1.4850 $/£1. So, £650.000 would have cost $ 9,65,250 and the loss on the ‘spot

N
market’ is $ (9,76,950 - 9,65,250) = $ 11,700.

The hedge efficiency is therefore the futures contract profit divided by the spot market loss

A
  
= ×  = 85.5%
  

M
The inefficiency is due to: (i) rounding the contracts to 10 from 10.4, and (ii) basis risk - the fact that the

X
movement on the futures price has not exactly equalled the movement on the spot rate.

T A
 Key to Short Answer Questions

True or False Statements

1. False - Hedgers and investors provide the economic substance to any financial market. Speculators provide

liquidity and depth to the market.

2. True - Arbitraguers bring price uniformity and help price discovery.

3. True - Speculators are those class of investors who willingly take price risks to profit from price changes in

the underlying.

4. False - Buy a future to agree to take delivery of a commodity will protect against a rise in price in the spot

market as it produces a gain if spot prices rise. Buying a future is said to be going long.

5. False - Only futures contracts are freely traded in primary and secondary market.

N
6. False - The difference between bid price and offer price is called ‘spread’. This represents the margin of

foreign exchange dealer. The size of spread for a given currency has no relation to period of maturity

N
of a forward exchange rate contract.

True

A
7. - Futures contracts are standardized, exchange traded and subject to rules and regulations of the

exchange. In futures trading, the margin is to be deposited by both the parties to the contract.

M
Choose Correct Word

1. spot

X
2. forward

A
3. counterparty

T
4. futures

5. profit

6. backwardation

7. futures

8. forward

9. forward

10. contango

11. long

12. rise

13. increases

Choose Correct Answer

1. (D) all of the above

2. (A) 45.29

3. (B) clearing agency

4. (A) basis

5. (B) future price > forward price

6. (A) = 0

7. (C) offsetting
 8. (C) in contango

9. (C) equal to spot rate

10. (B) contango

11. (C) black pepper futures

12. (C) futures price < current spot price

13. (D) long put option + short call option

14. (B) they are biased predictors of future spot rates

15. (A) futures are exchange products whereas forwards are not

16. (C) the difference between the delivery price and the spot price on the date of settlement

N N
M A
A X
T
 Practical Exercises

Exercise 49-1 NBA Bank Ltd. transacted on August 19, 2016 the following:

(i) Sold $10,00,000 two months forward to Alpha Manufacturing Co. Ltd. at ` 44.50.

(ii) Purchase Euro 10,00,000 two months forward from Beta Trading Co. Ltd. at ` 47.20.

On October 19, 2016, both the customers approached the bank. Alpha Manufacturing Co. wants the forward

contract to be cancelled while Beta Trading Co. wants the contract to be extended by one month. The following

exchange rates prevailed on that day:

`/$ `/Euro
Spot 44.60/65 47.75/85

One month forward 44.75/85 48.00/48.20

Based on the above information (ignores interest etc.), you are required to:

N
(i) Calculate the amount to be paid to or recovered from Alpha Manufacturing Co. due to the cancellation of the

forward contract.

N
(ii) Calculate the amount to be paid to or recovered from Beta Trading Co. due to the extension of the forward

A
contract.

Exercise 49-2 Carlhams Corporation Ltd. in U.K. will need to make a payment of $2,50,000 in six months time. It

M
is currently 1st January. The company is considering the various choices it has, in order to hedge its transaction

X
exposure. Following market information is available:

Exchange rates

A
£ Spot rate $1.5617 - 1.5773

T
Six month £ Forward rate $1.5455 - 1.5609

Country Money market rates

Borrow (%) Deposit (%)

US $ 6 4.5

UK £ 7 5.5

Foreign currency option prices:

Exercise price $1.70 Call option (June) 0.037 Put option (June) $0.096

Evaluate the following hedging alternatives with necessary calculations and decide which of the same is the most

attractive to Carlhams Corporation Ltd.

Exercise 49-3 Fresno Corporation Ltd., a US company will need £ 2,00,000 in 180 days. It considers using

(1) a forward hedge, (2) a money market hedge, (3) and option hedge, or (4) no hedge. Its analysts develop the

following information, which can be used to assess the alternative approaches to hedging:

n Spot rate of pound as of today = $ 1.50

n 180-days forward rate of pound as of today = $ 1.47

n Interest rates per annum are as follows:

UK US

180-days deposit rate 4.5% 4.5%

180-days borrowing rate 5.0% 5.0%

 n A call option on pounds that expires in 180 days has an exercise price of $ 1.48 and a premium of $ 0.03.

n Fresno Corporation forecasted the future spot rate in 180 days as follows:

Possible outcome $ 1.43 1.46 1.52

Probability 20% 70% 10%

Evaluate each alternative with necessary calculation and give your recommendations. (Assume 360 days in a year).

Ignore transaction cost or taxes.

Exercise 49-4 Sunshine Ltd., an Indian based Company has subsidiaries in U.S and U.K whole forecast surplus

funds for the next 30 days (June 2016) are given below:

U.S subsidiary $ 12.00 million U.K subsidiary $ 6.00 million

The following informations pertaining to exchange rates are obtained:

$/ ` £/ `
Spot 0.0243 0.0148

30 days forward 0.0245 0.0150

N
The borrowing/deposit rates per annum (simple) are available:

` 8.4%/7.5% $ 1.6%/1.5% £ 4.0%/3.8%

N
The Indian operation is forecasting a cash deficit of ` 400 million. It is assumed that interest rates over based on a

A
year of 360 days.

Required:

M
(i) Calculate the cash balance in Rupees at the end of 30 days period (at the end of June, 2016) for each company

under each of the following scenarios ignoring transaction costs and taxes:

X
(a) Each company invests/finances its own cash balances/deficits in local currency independently.

A
(b) Cash balances are pooled immediately in India and the net balances are invested/borrowed for the

30 days period.

T
(ii) Which method do you think preferable from the parent company’s (Sunshine Ltd.) point of view?

Exercise 49-5 A company, operating in Japan, has today effected sales to an Indian company, the payment being

due 3-month from the date of invoice. The invoice amount is 108 lakh yen. At today’s spot rate, it is equivalent to

` 30 lakhs. It is anticipated that the exchange rate will decline by 10% over the 3-month period and in order to protect

the yen payments, the importer decides to take appropriate action in the foreign exchange market. The 3-month

forward rate is presently quoted as 3.3 yen per rupee.

You are required to calculate the expected loss and to show how it can be hedged by a forward contract.

Exercise 49-6 Unilever’s subsidiary in India, Hindustan Lever, procures most of its soaps from a Japanese

company. Because of the shortage of working capital in India, payments terms for the Indian importers are typically

180 days or more. Hindustan Lever wishes to hedge a 8.5 million Japanese Yen payable. Although options are not

available on the Indian Rupee ( ` ), forward rates are available against the Yen. Additionally, a common practice in
India is, for companies like Hindustan Lever, to work with a currency agent who will, in this case, lock in the current

spot exchange for a 4.85% fee. Using the following data, recommend a hedging strategy.

Spot rate, USD/JPYYen 120.60/$ 180-day Yen investment rate 1.5%

Spot rate, USD/INR ` 47.75/$ 180-day rupee investment rate 8.0%

180-day forward rate, JPY/INR ` 0.4166/Yen Cost of Capital 12.0%

Expected spot exchange rate in 180 days ` 0.3846/Yen

 Key to Practical Exercises

Exercise 49-1

(i) Alpha manufacturing co. bought $ 2 month forward from NBA Bank at 44.50 value August 19, 2016. Now he

request cancellation. Thus the bank has to square of the purchase of $ made for Alpha manufacturing co. Thus

the Bank will sell $ at spot at ` 44.60/$. The difference between the two is paid (collected) to (from) the

customer.

Rate of original contract ` 44.50

Rate for cancellation ` 44.60

Difference between the two ` 0.10

Amount to be paid to the customer = ` 0.10 × 10,00,000 = ` 1,00,000

(ii) Now Beta Trading Company wants the contract to be extended by one month. Earlier the bank had purchased

N
EURO from Beta i.e. Beta sold EURO. Now Beta requests bank to extend by one month.

The Bank will square of the existing position (nullify it) and would sell EURO a fresh value 1 month forward.

N
The difference between the two is paid (collected) to (from) the customer.

A
SWAP Charges:

Purchase EURO at ` 47.85

Sold one month forward at ` 48.00

M
Amount payable to Beta Trading Co. = (48.00 - 47.85) × EURO 10,00,000 = ` 1,50,000

X
Inflow/Outflow charges:

A
Rate of original contract 47.20 (sold)

Rate of cancellation ` 47.85 (bought)

T
Difference between the two ` 0.65

Amount to be collected from the customer = ` 0.65 × 10,00,000 = ` 6,50,000

Net amount to be collected from the customer = ` 6,50,000 - ` 1,50,000 = ` 5,00,000

Exercise 49-2

Amount payable in six months time = $ 2,50,000

Alternative I - Hedge the transaction exposure through Forward market

Carlhans Corporation Ltd. is a UK based company having a $ liability to pay in 6 months.

To meet the commitment, it needs to buy dollars in forward market.

Cost of Forward cover = $ 2,50,000/£ 1.5455 = £ 1,61,759.95

Alternative II - Hedge the transaction exposure through Money Market

Borrow in UK £ and deposit in US $ to repay 6 months later.

       
Amount to be borrowed in terms of dollars = = = $ 2,44,498.78
 + 

Convert this into £ to find the amount to be borrowed in UK at spot rate

   
= = £ 1,56,559.38
b 
At the end of 6 months, $ liability will be settled with the maturity proceeds in US $.

Principal amount of loan is £ 1,56,559.38

 Principal and interest at the end of 6 months = £ 1,56,559.38 + (£ 1,56,559.38 × 7/100 × 6/12)

= £ 1,56,559.38 + £ 5,479.58 = £ 1,62,038.96

∴ Total cost of hedging through money market is £ 1,62,038.96

Alternative III - Hedge the transaction exposure through currency options

The UK company need to pay in US $ in 6 months. It has to buy US dollars and has to sell UK pounds. Therefore,

the company should use £ put option.

Now each contract = £ 12,500 × $ 1.70 = $ 21,250

   
Maximum number of contracts that can be purchased = = 11.76 say 12 contracts
  
∴ Exposure covered = $ 12,500 × 12 = $ 1,50,000

Premium to be paid for the exposure = 12 × 0.096 × 12,500 = $ 14,400

b  
Cost of put option in Pounds = = £ 9,220.72
 

N
Calculation of £ Cost of Put Option Hedge (Pounds)

Exercise price $ 1.70 1,50,000.00

N
Premium 9,220.72

A
1,59,220.72

Less : Excess $ covered

M
$ per one option contract 21,250

$ for 12 contracts (12 × 12,500 × 1.70) 2,55,000

X
$ liability to be met 2,50,000

A
Excess $ 5,000

Equivalent in pounds at forward rate of 1.5455

T
(treated as future spot rate) 3,235.20

Net cost 1,55,985.52

Therefore, the total cash flow if currency option is chosen as hedging the transaction exposure is £ 1,55,985.52.

Suggestion - Since the cash outflow is lowest in case of alternative (III), it is suggested to hedge the transaction

exposure through currency options.

Exercise 49-3

(a) Forward Hedge

Purchase pounds 180 days forward

Dollars needed in 180 days = £ 2,00,000 × $1.47 = $2,94,000

(b) Money Market Hedge

Borrow $, convert to £, invest £, repay $ loan in 180 days

b   
Amount in £ to be invested = = £1,95,599
 + 
Amount in $ needed = £1,95,599 × $1.50 = $2,93,398

Convert into £ for deposit = $ 2,93,398

Interest and principal owed on $ loan after 180 days = $2,93,398 × 1.025 = $3,00,733
 (c) Call Option Hedge

Exercise = $1.48 premium = $0.03

Expected Premium Exercise Total price Total price Proba- Expected

spot rate per unit paid option (incl. premium paid for bility amount

in 180 days for option paid p.u.) £2,00,000

$1.43 $0.03 No $1.46 $2,92,000 0.20 $58,400

1.46 0.03 No 1.49 2,98,000 0.70 2,08,600

1.52 0.03 Yes 1.51 3,02,000 0.10 30,200

$2,97,200

(d) No Hedge

Future spot Dollars needed Probability Expected

rate expected to purchase amount

in 180 days £2,00,000

$1.43 $2,86,000 0.20 $57,200

N
1.46 2,92,000 0.70 2,04,400

N
1.52 3,04,000 0.10 30,400

$2,92,000

A
Suggestion - The probability distribution outcomes for no hedge strategy appears to be minimum. Hence, it is

suggested to remain un-hedge.

M
Exercise 49-4

X
Alternative I - Each company invests/finances its own cash balances/deficits in local currency independently.

A
India

Forecast cash deficit = ` 400 million

T
Interest on borrowing (@ 8.4%) = 400 × 8.4/100 × 1/12 = ` 2.8 million

Total deficit in rupee terms = 400 + 2.8 = ` 402.8 million

U.S. Subsidiary

Forecast cash surplus = $ 12 million

Interest on investment (@ 1.5%) = 12 × 1.5/100 × 1/12 = $ 0.015 million

Total surplus in US $ = 12 + 0.015 = $ 12.015 million

Total surplus in Indian ` = $ 12.015/0.0245 = ` 490.408 million

US subsidiary

Forecast cash surplus = £ 6 million

Interest on investment (@ 3.8%) = 6 × 3.8/100 × 1/12 = £ 0.019 million

Total surplus in U.K. £ = 6 + 0.019 = £ 6.019 million

Total surplus in Indian ` = £ 6.019/0.0150 = ` 401.267 million

Net surplus in Indian ` = (402.8) + 490.408 + 401.267 = ` 488.875 million

Alternative II - Cash balances are pooled immediately in India and the net balances are invested/borrowed for the

30 days period
 (` million)

India - Deficit (400.00)

U.S. Subsidiary - Surplus ($ 12/0.0243) 493.827

U.K. Subsidiary - Surplus (£ 6/0.0148) 405.405

Immediate cash balance 499.232

Interest for one month (499.232 × 7.5/100 × 1/12) 3.120

502.352

Suggestion - From the above calculation it is observed that Alternative II is beneficial for the company by immediate

pooling of cash balances.

Exercise 49-5

 MBLI ZFO

Spot rate of ` 1 against yen = = 3.6 yen
 MBLI C
3-month forward rate of ` 1 against yen = 3.3 yen

N
Anticipated decline in exchange rate = 10%

Expected spot rate after 3 months = 3.6 yen - 10% of 3.6 yen = 3.6 yen - 0.36 yen = 3.24 yen/ `

N
If Exposure kept open ( ` lakhs)

A
Present cost of 108 lakh yen 30.00

Cost after 3 months (108 lakh yen/3.24 yen) 33.33

M
Expected exchange loss 3.33

X
If Exposure is hedged through forward contract ( ` lakhs)

A
Present cost of 108 lakh yen 30.00

Cost after 3 months if forward contract is taken (108 lakh yen/3.3 yen) 32.73

T
Expected loss 2.73

Suggestion - The loss is lower when the exposure is hedged through forward contract. It is suggested to take forward

cover to minimise loss.

Exercise 49-6

Amount payable in 180 days = ¥ 85,00,000 Expected spot rate in 180 days (¥/ ` ) = ¥ 2.6000

Spot rate (¥/$) = ¥ 120.60 180-day investing rate in Indian ` = 8%

Spot rate ( ` /$) = ` 47.75 180-day investing rate in Japanese ¥ = 1.5%

Spot rate (¥/ `) = ¥ 2.5257 Currency Agent’s exchange rate fee = 4.85%

180-day Forward rate (¥/$) = ¥ 2.4000 Hindustan Lever’s cost of capital = 12%

Option I - Buy Japanese yen forward 180 days

Amount payable on taking forward 180 days = ¥ 85,00,000/2.400 = ` 35,41,667

Option II - Money market hedge

Principal amount payable in 180 days = ¥ 85,00,000

Investing rate for 180 days = 1/1.0075 = 0.99256

Principal required to be invested = ¥ 85,00,000 × 0.99256 = ¥ 84,36,760

Current spot rate (¥/ `) = 2.5257

Indian rupees required currently = ¥ 84,36,760/¥ 2.5257 = ` 33,40,365

 Carry forward factor for 180 days = 1.0600

Future value of money market hedge = ` 33,40,365 × 1.06 = ` 35,40,787

Option III - Indian currency Agent hedge

Principal amount payable = ¥ 85,00,000

Current spot rate (¥/ `) = ¥ 2.5257

Current amount payable = ¥ 85,00,000/¥ 2.5257 = ` 33,65,404

Currency Agent’s fee = ` 33,65,404 × 4.85/100 = ` 1,63,222

Carry forward factor for 180 days on fee = ` 1,63,222 × 1.06 = ` 1,73,015

Total cash outflow = ` 33,65,404 + ` 1,73,015 = ` 35,38,419

Option IV - If exposure uncovered

Spot rate (¥/ `) = ¥ 2.5257

Amount payable in 180 days at spot rate = ¥ 85,00,000/¥ 2.5257 = ` 33,65,404

Suggestion - The cash outflow is lower in case of Option IV. Hence, it is suggested to keep exposure open without

N
hedging the risk if the spot rate is as expected.

A N
X M
T A
 Key to Short Answer Questions

True or False Statements

1. True - A cap provides variable rate borrowers with protection against raising interest rates while also

retaining the advantages of lower or falling interest rate. Floors are used to obtain certainty for

investments and budgeting by setting minimum interest rate on investments.

2. True - A borrower can protect himself against rise in the floating interest rate beyond a particular level. The

lender can protect himself from fall in floating rate of interest below a particular level.

3. False - Unlike overnight interest rate swaps, interest rate futures have to be traded on exchanges rather than

over the counter.

4. True - The purchased options protect against the interest rate rising and pays the premium for purchase of

cap option. He will write the put option to protect against interest rate fall and receives the premium

N
on floor option. The strategy of buy the cap and sell the floor such that the net premium is zero.

5. False - Interest rates change continually which makes these markets extremely volatile. It is one of the

N
responsibilities of the Treasurer to manage the interest rate risk of the firm and should able to identify

the methods available for hedging interest rate risk.

A
6. False - Standard and Poor has launched real time currency index called S&P Indian Rupee Index that provide

M
investors with exposure to emerging economic super power that currently lack a liquid futures

market.

X
7. False - The buyer of a currency option knows his worst position since his downside risk is limited. The buyer

knows the maximum cost at the outset, since he has to pay premium plus funding cost on making

A
upfront payment.

T
8. True - By buying a put option, the party sells the domestic exchange to procure the right amount of foreign

exchange at a specified rate.

Choose Correct Word

1. long

2. interest rate

3. falling below

4. covered interest arbitrage

5. interest rate risk

6. long

7. interest

8. closed-out

9. forward to forward

10. futures

11. cap

12. currency options

Choose Correct Answer

1. (C) floor

2. (D) value at risk

3. (A) 1

4. (D) transfer

5. (D) interest rate floors

6. (C) estimating chances of loss from an exposure

7. (C) a negative 100% return

8. (B) when interest rate falls, long futures position gains

9. (B) short-term gain always and equals the price of the option

10. (C) to reduce the burden of interest contracted at

N N
M A
A X
T
 Practical Exercises

Exercise 50-1 Current stock price is ` 100, strike price of call option `100, option premium ` 5. Find out break-even
price at which there will be no loss no profit for a call buyer. Find out pay off of the call option buyer if stock price

remains subdued at ` 100. Draw profit/loss diagrams of call writer and call buyer.

Exercise 50-2 The current market price of the equity shares of Bharat Bank Ltd. is ` 190 per share. It may be either
` 250 or ` 140 after a year. A call option with a strike price of `180 (time 1 year) is available. The rate of interest

applicable to the investor is 9%. Rahul wants to create a replicating portfolio in order to maintain his pay off on the

call option for 100 shares. Find out: (i) hedge ratio, (ii) amount of borrowing, (iii) fair value of the call, and (iv) his

cash flow position after a year.

Exercise 50-3 The following quotes are available for 3-months options in respect of a share currently traded at ` 31:

Strike price ` 30 Call option ` 3 Put option ` 2

N
An investor devises a strategy of buying a call and selling the share and a put option. Draw his profit/loss profile if

N
it is given that the rate of interest is 10% per annum. What would be the position if the strategy adopted is selling

a call and buying the put and the share?

A
Exercise 50-4 Identify the profit or loss (ignoring dealing cost and interest) in each of the following cases:

` 200 is bought for a premium of ` 89. The price of underlying share is

M
(i) A call option with an exercise price of

` 276 at the expiry date.

X
(ii) A put option with exercise price of ` 250 is bought for a premium of ` 42. The price of underlying share is

` 189 at the expiry date.

A
(iii) A put option with an exercise price of ` 300 is written for a premium of ` 57. The price of the underlying share

T
is ` 314 at the expiry date.

Exercise 50-5 The following information is related to stock of Adarsh Ltd. Adarsh Ltd. has a beta of 0.5 with Nifty.

Each Nifty contract is equal to 100 units. Adarsh Ltd. now quotes at ` 250 and the Nifty future is 4000 index points.
You are long on 1,200 shares of Adarsh Ltd. in the spot market.

(i) How many futures contracts will you have to take?

(ii) Suppose the price in the spot market drops by 10%, how are you protected?

Exercise 50-6 Dravid Investments Ltd. deals in equity derivatives. Their current portfolio comprises of the

following instruments:

Infosys ` 5600 Call Expiry June 2010 2,000 Units bought at ` 197 each (cost)

Infosys ` 5700 Call Expiry June 2010 3,600 Units bought at ` 131 each (cost)

Infosys ` 5400 Put Expiry June 2010 4,000 Units bought at `81 each (cost)

What will the profit or loss to Dravid Investments Ltd. in the following situations ?

(i) Infosys closes on the expiry day at ` 6,041

(ii) Infosys closes on the expiry day at ` 5,812

(iii) Infosys closes on the expiry day at ` 5,085

Exercise 50-7 A portfolio manager purchased 1000 equity shares of Reliance Industries Ltd. @ ` 510 per share. He
wants to hedge the position by writing an April call with a strike price of ` 530 and call premium ` 10. Alternatively,
he wants to hedge by buying put option of strike price ` 510 and premium of ` 10.
(a) Find out his profit or loss if the share price goes up to ` 540.
 (b) Find out his profit or loss if the share price goes up to ` 525 till the date of expiration of the option.

(c) Find out his profit or loss if the share price comes down to ` 490.

(d) Does the strategy of buying a stock and writing a call manage his risk effectively ?

(e) Under which circumstance should the portfolio manager buy a put option ?

(f) Assume that the share price goes down to ` 490, what will be the profit or loss of his portfolio if he buys put
option ?

(g) In case he buys one ` 510 put (premium ` 10) and writes one ` 530 call (premium ` 10) what will be his profit
or loss for the share price of ` 540, ` 530, ` 520 and ` 490 ?

Exercise 50-8 Calculate profits and losses from the following transactions:

(i) Mr. X writes a call option to purchase share at an exercise price of ` 60 for a premium of ` 12 per share. The

share price rises to ` 62 by the time the option expires.

(ii) Mr. Y buys a put option at an exercise price of ` 80 for a premium of ` 8.50 per share. The share price falls to
` 60 by the time the option expires.

(iii) Mr. Z writes a put option at an exercise price of ` 80 for a premium of ` 11 per share. The price of the share

N
rises to ` 96 by the time the option expires.

` 70 for a premium of ` 8 per share. The price falls to ` 48

N
(iv) Mr. XY writes a put option with an exercise price of

by the time the option expires.

A
Exercise 50-9

` 542 and write a ` 580 November

M
(a) An investor purchased Reliance November Future (600 shares Tick size) at

call option at a premium of ` 6 (600 shares Tick size). As on November 20 spot price rises and so the future

X
price and the call premium. Future price rises to ` 575 and call premium rises to `12. Find out profit/loss of
the investor, if he/she settles the transaction on that date and at stated prices. Brokerage is 0.05% for the

A
transaction value of futures and strike price net of call premium for option.

T
(b) Why did the investor write a call ? Why did he/she buy a call subsequently settle the written call he/she needed

to buy a call.

(c) Do you think the strategy taken by investor was logical ?

Exercise 50-10 The settlement price of Sensex futures contract on a particular day was ` 4,600. The initial margin
was set at ` 10,000, while the maintenance margin was fixed at ` 8,000. The multiple of each contract is 50.

The settlement prices on the following four days were as follows:

Day 1 2 3 4 5

Settlement price ( ) ` 4700 4500 4650 4750 4700

Calculate the mark to market cash flows and the daily closing balances in the accounts of (a) an investor who has

gone long, and (b) an investor who has gone short at 4,600.

Calculate net profit (loss) on each of the contracts.

Exercise 50-11 Quickset Company’s equity shares are currently selling at a price of ` 400 each. An investor is

interested in purchasing Quickset’s shares. The investor expects that there is a 70% chance that the price will go up

to ` 550 or a 30% chance that it will go down to ` 350, three months from now. There is a call option on the shares
of Quickset that can be exercised only at the end of three months at an exercise price of ` 450.
(i) If the investor wants a perfect hedge, what combination of the share and option should he select?

(ii) Explain how the investor will be able to maintain identical position regardless of the share price.

(iii) If the risk-free rate of return is 5% for the 3 month period, what is the value of the option at the beginning of

the period ?

(iv) What is the expected return on the option ?

Exercise 50-12 The shares of Bangalore Corporation Limited are selling at ` 105 each. Chandrasekhar wants to chip
in with buying a three months call option at a premium of ` 10 per option. The exercise price is `110. Five possible
prices per share on the expiration date ranging from ` 100 to ` 140, with intervals of ` 10 are taken into consideration

by him. What is Chandrasekhar’s payoff as call option holder on expiration ?

Exercise 50-13 On Aug. 2, Mr. Tandon buys 5 contracts of December Reliance futures at ` 840. Each contract covers

50 shares. Initial margin was set at ` 2,400 per contract while maintenance margin was fixed at ` 2,000 per contract.

Daily settlement prices are as follows:

Aug. 2 - 818 Aug. 3 - 866 Aug. 4 - 830 Aug. 5 - 846

Mr. Tandon meet all margin calls. Whenever he is allowed to withdraw money from the Margin Account, he

withdraws half the maximum amount allowed. Compute for each day: (i) Margin, call; (ii) Profit &(Loss) on the

contract; (iii) The balance in the Account at the end of the day.

Exercise 50-14 An investor purchased Reliance November Futures (600 shares Tick size) at ` 1,150 and write a

` 1,190 November call option at a premium of ` 10 (600 shares Tick size). As on November 25, spot price rises and
so the Future price and the call premium. Future price rises to ` 1,180 and call premium rises to ` 16. Brokerage is

0.045% for the transaction value of Futures and strike price net of call premium for option.

N
Find out the profit/(loss) for the investor, if he/she settles the transaction on that date and at stated prices. (Assuming

N
no transaction taxes and service taxes exist).

A
Exercise 50-15 The market received the rumour about XYZ Corporation tie-up with a multinational company.

This has induced the market price to move up. If the rumour is false, the XYZ Corporation stock price will probably

fall dramatically. To protect from this, an investor has bought the call and put options.

M
He purchased one 3 months call with a striking price of ` 42 for ` 2 premium and paid ` 1 per share premium for

X
a 3 months put with a striking price of ` 40.

(i) Determine the investors ending position, if the tie-up offer bids the price of XYZ Corporation’s stock up to

A
` 43 in 3 months.

T
(ii) Determine the investors ending position, if the tie up program fails and the price of the stock falls to ` 36 in

3 months.

Exercise 50-16 Rax Investments Ltd. deals inequity derivatives. Their current portfolio comprises of the following

investments:

Infosys ` 1,400 Call expire December 2016 200 units bought at ` 50 each (cost)

Infosys ` 1,425 Call expire December 2016 3,000 units bought at ` 33 each (cost)

Infosys ` 1,350 Put expire December 2016 4,000 units bought at ` 22 each (cost)

What will be the profit or loss to Rax Investments Ltd. in the following situations?

(i) Infosys closes on the expiry day at ` 1,550, (ii) Infosys closes on the expiry day at ` 1,460 and (iii) Infosys closes
on the expiry day at ` 1,280. (Ignore transaction cost and taxation).
 Key to Practical Exercises

Exercise 50-1

Pay of Pay of

`
( ) `
( )

0 0

100 105 100 105

-5

Stock Price Stock Price

` `

N
( ) ( )

N
Profit/Loss of Call Buyer Profit/Loss of Call Writer

A
Exercise 50-2

Current market price (S) = ` 190 per share Expected price after a year (high) (S )
1
= ` 250

M
Strike price (K) = ` 180 Expected price after a year (low) (S )
2
= ` 140

X
Difference between Strike price and Expected High price (C ) = 250 - 180
1
= ` 70

A
70 - 0 70
(i) Calculation of Hedge Ratio = = = 0.64
250 - 140 110

T
In order to create a replicating portfolio, the investor should buy 0.64 share for a call option of 1 share. Then,

he should buy 100 × 0.64 = 64 shares at the current price of ` 190.

His outflow would be ` 190 × 64 = ` 12,160

(ii) Calculation of Amount of Borrowing (B)

100
S - C
2 2
1 + r

(0.64 × 140 - 0)100 8,960

S
2
- C
2
= = ` 8,220
1.09 1.09

(iii) Determination of Fair Value of the Call (100 shares)

= 100 × Hedge ratio × S - B = 100 × 0.64 × 190 - 8,220 = ` 3,940

(iv) Cash Flow Position after a year

Particulars Pay off

If share price is ` 250 If share price is ` 140

Buy a call option (K = 180) 100 × (250 - 180) = ` 7,000 Nil

Buy 64 shares and borrow (selling 64 × 250 = 16,000 64 × 140 = ` 8,960

price of 64 shares less borrowings) 16,000 - 8,220 = ` 7,780

By replicating the portfolio, the investor is able to have the same pay off of ` 7,780.
Exercise 50-3

Strategy I Buying a call and selling a put and a share

Initial cash inflow ( ` 31 - ` 3 + ` 2) = ` 30 Interest rate = 10%

Amount grows in 3 months to (30 × e

1 × .25
) = ` 30.76 *
If the share price is greater than ` 30, he would exercise the call option and buy one share for ` 30 and

his net profit is ` 0.76 (i.e. ` 30.76 - 30)

However, if the share price is less than ` 30, the counter-party would exercise the put option and the

investor would buy one share at ` 30. The net profit to the investor is again ` 0.76.

Strategy II Selling a call and buying a put and a share

In case, the investor has to arrange a loan @ 10% of ` 30 ( `` 31 + ` 2 - ` 3).

This amount would be repaid after 3 months. Amount payable (30 × e

1 × .25
) is ` 30.76.

After 3 months, if the market price is more than ` 30, the counter-party would exercise the call option
and the investor would be required to sell the share at ` 30. The loss to the investor would be ` 0.76 (i.e.
` 30.76 - 30).

N
However, if the rate is less than ` 30, the investor would exercise the put option and would get ` 30 from
` 0.76.

N
the rate of share. The loss to the buyer would again be

* Interest can also be calculated on simple interest basis instead of continuous compound interest.

A
Exercise 50-4

M
(i) Profit = - 89 + (276 - 200) = - 13, i.e. a loss of ` 13 per contract purchased.

X
(ii) Profit = - 42 + (250 - 189) = 19, i.e. a profit of 19 per contract purchased.

(iii) Profit = + 57(0) = + 57, i.e. a profit of ` 57 per contract purchased.

A
Exercise 50-5

T
(i) Since you are long on the spot market, you will have to go short in the futures market. Hence you will have to

sell Nifty.

Market value of holding to be hedged = 1,200 × ` 250 × 0.5 = ` 1,50,000

Value of one Nifty contract = 4000 × 100 = ` 4,00,000
No. of contracts to be sold = 1,50,000/4,00,000 = 0.375

(ii) If market price goes down by 10%, then Nifty would go down by 20%

Loss on shares = 1,200 × 250 × 10/100 = ` 30,000

Gain on Nifty = 4000 × 100 × 0.375 × 20/100 = ` 30,000
So, the investor is fully protected.

Exercise 50-6

Payoff/unit at Infosys Closing price

Instrument Units Cost Strike (i) At 6041 (ii) At 5812 (iii) At 5085

5600 Call 2,000 197 5,600 441 212 Nil

5700 Call 3,600 131 5,700 341 112 Nil

5400 Put 4,000 81 5,400 Nil Nil 315

 Profit per unit Profit amount

Infosys Closing Price Infosys Closing Price

Instrument 6,041 5,812 5,085 Instrument 6,041 5,812 5,085

5600 Call 244 15 -197 5600 Call 4,88,000 30,000 -3,94,000

5700 Call 210 -19 -131 5700 Call 7,56,000 -68,400 -4,71,000

5400 Put -81 -81 234 5400 Put -3,24,000 -3,24,000 9,36,000

Total 9,20,000 -3,62,000 70,400

Exercise 50-7

(a) His profit is restricted to ` 10, which is the option premium, as the call buyer will strike when the stock price
is ` 540.

(b) His profit will be ` 25, premium plus profit on sale of stock `15. The call expires worthless.

(c) His loss will be ` 10, loss in stock ` 20 minus premium earned ` 10.

N
(d) No. As writing a call does not protect the value of investment in the downside but it restricts upside profit.

(e) When he thinks that the share price will go down.

N
(f) If the share goes down to ` 490, then he will strike and get price of `510. So his stock value will be neutralized
` ` 10 per share.

A
at 51,000 but his loss will be the amount of put premium paid, i.e.,

(g) Share price ` 540 : Call can be exercised, put expires worthless. Increase in share price is restricted to ` 530. His
premium earning is zero, so he will earn profit from shares `30, i.e. `3,000.

M
net

` 530 : Call can be exercised, put expires worthless. Increase in share price is restricted to ` 530. His
Share price

X
net premium earning is zero, so he will earn profit from shares ` 30, i.e. ` 3,000.

` 520 : Call and put expire worthless. His net premium earning is zero, so he will earn profit from

A
Share price

shares ` ` 1,000.
10, i.e.

T
Share price ` 490, call expires worthless, put can be exercised. So he protects his share price at ` 510, net

premium income being zero, there is no profit no loss.

Exercise 50-8

Calculation of Profits and Losses of different investors for their transactions:

(i) Investor X = 60 - 62 + 12 = `10 (profit)

(ii) Investor Y = 80 - 60 - 8.50 = ` 11.50 (profit)

(iii) Investor Z = ` 11 (profit, since option will not be exercised)

(iv) Investor XY = -70 + 48 + 8 = ` 14 (loss)

Exercise 50-9

Calculation of Profit earned on Derivative Trading `

( )

Buying price of 600 shares in Futures including brokerage 3,25,362.60

Selling price of 600 shares in Futures including brokerage 3,44,827.50

Profit on Futures (a) 19,464.90

Premium earning on call writing (600 × ` 6) 3,600.00

Less : Brokerage 172.20

Profit (b) 3,427.80

Premium paid on call buying (600 × ` 12) 7,200.00

Add : Brokerage 170.40

 `
( )

Loss (c) 7,370.40

Net loss on option trading (c) - (b) = (d) 3,942.60

Profit earned on derivative trading (a) - (d) 15,522.30

Exercise 50-10

(a) Status of Investor who has gone long on the Contract Margin Account `
( )

Day Settlement Opening Mark to Margin Closing

price balance market call balance

1 4,700 10,000 5,000 - 15,000

2 4,500 15,000 (-)10,000 5,000 10,000

3 4,650 10,000 7,500 - 17,500

4 4,750 17,500 5,000 - 22,500

5 4,700 22,500 (-)2,500 - 20,000

N
Net profit (loss) on the contract = 5,000 - 10,000 + 7,500 + 5,000 - 2,500 = ` 5,000

N
Status of the Investor who has gone short on the contract `
( )

Day Settlement Opening Mark Margin Closing

A
price balance to market call balance

M
1 4,700 10,000 (-)5,000 5,000 10,000

2 4,500 10,000 10,000 - 20,000

X
3 4,650 20,000 (-)7,500 - 12,500

4 4,750 12,500 (-)5,000 2,500 10,000

A
5 4,700 10,000 2,500 - 12,500

T
Net profit (loss) on the contract = (-)5,000 + 10,000 - 7,500 - 5,000 + 2,500 = (-) 5,000 loss

Exercise 50-11

(i) If the share price increases to ` 550, the option will be worth ` 100 (` 550 - 450). If the price reduces to ` 350,
it will be worth zero, The hedge ratio, therefore will be:

C  − 

= =
C  − C 

The investor will be required to purchase one share for every two call options.

(ii) Value of Hedge at ` 550 = (1 × ` 550) - (2 × ` 100) = ` 350

Value of Hedge at ` 350 = (1 × ` 350) - (2 × 0) = ` 350

The position is unchanged.

(iii) Value of option at the beginning (Vb) = ( ` 400 - 2vb) (i.05) = ` 350

= > 2.10vb = ` 70

vb = ` 33.33
(iv) Expected option value (EV) = ( ` 550 - ` 450) (0.7) + 0 × 0.3 = ` 70

C  − C 
Expected Return (ER) = = 1.10 = 110%
C 
Exercise 50-12

Chandrasekhar’s payoff as call option holder on expiration `

( )

Market price 100 110 120 130 140

Exercise price 110 110 110 110 110

Action Lapse Lapse Exercise Exercise Exercise

Gross profit 0 0 10 20 30

Premium 10 10 10 10 10

Net payoff (10) (10) 0 10 20

Exercise 50-13

Initial margin to be maintained on 5 contracts = 5 contracts × ` 2,400 = ` 12,000

Maintenance margin fixed for 5 contracts = 5 contracts × ` 2,000 = ` 10,000

Computation of margin call, profit/(loss) on the contract and balance in the account at the end of the day.

N
2nd August `
( )

Opening balance -

N
Add: Initial margin paid (5 × ` 2,400) 12,000

A
12,000

Less: Loss to day [5 × 50 shares × (- ` 22)] 5,500

M
Balance before margin 6,500

Add: Margin call paid* 5,500

X
Closing balance 12,000

A
* Balance fell below maintenance margin. To bring back balance to initial margin it is required to pay margin amount

` 5,500.

T
3rd August `
( )

Opening balance 12,000

Add : Profit today (5 × 50 shares × ` 48) 12,000

Balance before withdrawal 24,000

Less : Profit withdrawn [( ` 24,000 - ` 12,000) × 1/2] 6,000

Closing balance 18,000

4th August `
( )

Opening balance 18,000

Less : Loss today [5 × 50 shares × (- ` 36)] 9,000

Balance before margin call 9,000

Add : Margin call paid* 3,000

Closing balance 12,000

*Since balance fell below maintenance margin, it is required to bring balance back to initial margin by making

payment of ` 3,000.

5th August `
( )

Opening balance 12,000

Add : Profit to day (5 × 50 shares × ` 16) 4,000

Balance before withdrawal 16,000

 `
( )

Less : Profit withdrawn [( ` 16,000 - ` 12,000) × 1/2] 2,000

Closing balance 14,000

Margin call whenever balance goes below = 5 contracts × ` 2,000 = ` 10,000

Withdrawal (half) whenever margin account shows balance above = 5 × ` 2,400 = ` 12,000

Exercise 50-14

Calculation of Profit/(Loss) of the Investor

Buying price of 600 shares in Futures including brokerage

= `
[ 1,150 + ( ` 1,150 × 4.5/100)] × 600 = ` 6,90,310.50
Selling price of 600 shares in Futures including brokerage

= `
[ 1,180 - ( ` 1,180 × 4.5/100)] × 600 = ` 7,07,681.40
Profit on Futures = ` 7,07,681.40 - ` 6,90,310.50 = ` 17,370.90

Premium earning on call writing = 600 shares × ` 10 = ` 6,000

N
Brokerage on call writing = [( ` 1,190 - ` 10) × 4.5/100] × 600 = ` 318.60

Net amount earned on call writing = ` 6,000 - ` 318.60 = ` 5,681.40

N
Premium paid on call buying = 600 shares × ` 16 = ` 9,600

A
Brokerage on call buying = [( ` 1,190 - ` 16) × 4.5/100] × 600 = ` 316.98

Net amount paid on call buying = ` 9,600 + ` 316.98 = ` 9,916.98

M
Net loss in option trading = `9,916.98 - ` 5,681.40 = ` 4,235.58

Profit of the investor in Derivative trading = ` 17,370.90 - ` 4,235.58 = ` 13,135.32

X
Exercise 50-15

A
Assumption : Minimum lot of 100 shares

T
Cost of Call and Put options = ( ` `
2 per share) × (100 share call) + ( 1 per share) × (100 share Put)

= ( ` 2 × 100) + (` 1 × 100) = ` 300

(i) Price increases to ` 43.

Since the market price is higher than the strike price of the put, the investor will exercise it.

Ending position = (- ` 300 cost of option) + (` 1 per share gain on call) × 100 = - ` 300 + ` 100

Net loss = ` 200

(ii) Price increase to ` 36.

Since the market price is lower than the strike price, the investor may not exercise the call option.

Ending position = (- ` 300 cost of 2 option) + (` 4 per stock gain on Put) × 100 = - ` 300 + ` 400
Net gain = ` 100

Exercise 50-16

Rax Investments Ltd.

Pay off/unit at Infosys

closing price ( ) `
Instrument Units Cost ( ) ` Strike price ( ) ` ` 1,550 ` 1,460 ` 1,280
1,400 Call 2,000 50 1,400 150 60 Nil

1,425 Call 3,000 33 1,425 125 35 Nil

1,350 Put 4,000 22 1,350 Nil Nil 70

 `
Profit per unit ( ) Total Profit/(Loss) ( )`
Instrument Infosys Closing Price ( )` Units Infosys Closing Price at

1,550 1,460 1,280 ` 1,550 ` 1,460 ` 1,280

1,400 Call 100 10 (50) 2,000 2,00,000 20,000 (1,00,000)

1,425 Call 92 2 (33) 3,000 2,76,000 6,000 (99,000)

1,350 Put (22) (22) 48 4,000 (88,000) (88,000) 1,92,000

Total 3,88,000 (62,000) (7,000)

N N
M A
A X
T
 Key to Short Answer Questions

True or False Statements

1. True - The current index future price must be equal to the index value plus the difference between the risk

free interest and dividends obtainable over the life of the contract.

2. False - The index based options are operating under European model and options based on individual

securities are operating under American model.

3. False - SEBI has approved derivatives trading on futures and options contracts on both stock index as well

as individual securities.

4. True - Stock index futures offer an effective ‘beta’ control to the portfolio manager for having advantages of

(a) the optimal stock mix, (b) considerable lower transaction costs, and (c) achieving the portfolio

target ‘beta’ through buying targeted futures.

N
5. True - If the investor wants to reduce the loss on his holding of securities due to uncertain price movements

N
in the market, then he can sell futures contracts. In such case if the market comes down then the losses

incurred on individual securities can be compensated by profits made in the futures contract.

A
6. True - Volatility index is a measure of the amount by which an underlying index is expected to fluctuate in

the near term, based on the order book of the underlying index options.

M
7. True - A stock index futures contract does not entitle physical delivery of stocks and the contract is settled

X
in cash on the settlement date.

8. False - Speculators are those who willingly take price risks to profit from price changes in the underlying.

A
Speculators provide liquidity and depth to the market.

T
Choose Correct Word

1. short straddle

2. Chicago

3. Mumbai

4. hedger

5. speculators

6. near future

7. Forward Markets Commission

8. national

9. stock index

10. BSE Sensex

11. L.C. Gupta

12. Cansas City Board of Trade

13. premium

Choose Correct Answer

1. (B) ≥ stock price

2. (A) lock-in its revenues

3. (D) all of the above

 4. (D) all of the above

5. (D) all of the above

6. (C) securities

7. (B) NSE

8. (D) all of the above

9. (C) at-the-money options

10. (C) put option is said to be in the money

11. (D) all of the above

12. (C) increases as the time to expiration increases

13. (D) all of the above

14. (C) a call and a favourable effect on the price of put

15. (A) buying a call and a put with identical strike rate and expiration date

16. (C) limited to the difference between the exercise price and the stock price at the time of exercise

N N
M A
A X
T
 Practical Exercises

Exercise 51-1 Company A has outstanding debt on which it currently pays fixed rate of interest at 9.5%. The

company intends to refinance the debt with a floating rate of interest. The best floating rate it can obtain is LIBOR

+2%. However, it does not want to pay more than LIBOR. Another company B is looking for a loan at a fixed rate

of interest to finance its exports. The best rate it can obtain is 13.5% but it cannot afford to pay more than 12%.

However, one bank has agreed to offer finance at a floating rate of LIBOR+2%.

Citi Bank is in the process of arranging an interest rate swap between these two companies.

(i) With a schematic diagram, show how the swap deal can be structured.

(ii) What are the interest savings by each company ?

(iii) How much would Citi Bank receive ?

Exercise 51-2 Celina Ltd. wishes to borrow US Dollars at a fixed rate of interest. Priyanka Ltd. wishes to borrow

N
Japanese Yen at a fixed rate of interest. The amounts required by the two companies are roughly the same at current

exchange rate. The companies have been quoted the following interest rates:

N
Yen Dollar

A
Celina Ltd. 4.0% 8.6%

Priyanka Ltd. 5.5% 9.0%

M
Design a swap that will net a bank, acting as intermediary, 50 basis points per annum. Make the swap equally

attractive to the two companies and ensure that all foreign exchange risk is assumed by the bank.

X
Exercise 51-3 Soni Ltd. and Toni Ltd. face the following interest rate:

A
Particulars Soni Ltd. Toni Ltd.

T
US Dollar (floating rate) LIBOR + 0.25% LIBOR + 2.25%

Japanese Yen (fixed rate) 1.75% 2%

Toni Ltd. wants to borrow US dollars at a floating rate of interest and Soni Ltd. wants to borrow Japanese yen at a

fixed rate of interest. A financial institution is panning to arrange a swap and requires a 100 basis point spread. If

the swap is equally attractive to Soni Ltd. and Toni Ltd., what rate of interest will they end up paying?

Exercise 51-4 Yorkshire Industries, a British Industries firm with a US subsidiary, seeks to refinance some of its

existing British pound debt to include floating rate obligations. The best floating rate it can obtain in London is

LIBOR + 2.0%. Its current debts are as follows:

(i) $10 million owed to Citibank at 9.5% (fixed annually); and

(ii) £ 5 million owed to Midland Bank at 9.5% (fixed) annually.

Huron River Salt Company wishes to finance exports to Briton with £ 3 million of pound denominated fixed rate

debt for six months. Huron is unable to obtain a fixed interest rate in London for less than 13.5% interest because

of its lack of credit history in the UK.

However, Lloyds Bank is willing to extend a floating rate British pound Loan at LIBOR+2%. Huron, however, cannot

afford to pay more than 12%. How can Yorkshire and Huron help one another via an interest rate swap? Assume
that Yorkshire is in a strong bargaining position and can negotiate the best deal possible, but Huron will not pay over

12%. Assume further that transaction costs are 0.5% and exchange rates do not change. Illustrate the effective post-

swap interest rates of each party with boxes and arrows. What are the interest savings by each party over the six

months period of the swap ?

Exercise 51-5 Mumbai Ltd. is an Indian company, they are in the process of raising a US dollar loan and are

negotiating the rates with City bank. The company has been offered a fixed rate of 7% p.a. with a proviso that should

they opt for a floating rate, the interest rate is likely to be linked to the bench mark rate of 60 basis points over the

10-year US T Bill Rate, with interest refixation on a three monthly basis. The expectations of Mumbai Ltd. are that

the dollar interest rates with fall, and are inclined to have a flexible mechanisms built into their interest rates.

On enquiry they find that they could go for a swap arrangement with Chennai India Ltd. who have been offered a

floating rate of 120 basis points over 10-year US T Bill Rate, as against a fixed rate of 8.20%. Describe the swap on

the assumption that the swap differential is shared between Mumbai Ltd. and Chennai India Ltd. in the proportion

of 2 : 1.

N N
M A
A X
T
 Key to Practical Exercises

Exercise 51-1

(i) Schematic diagram of Swap deal

† 9.5% † 12%

Company A Citibank Company B

† †
LIBOR LIBOR + 12%

Borrows Borrows

@ 9.5%
@ LIBOR + 2%

(ii) Savings: Company A = [(LIBOR + 2) - LIBOR)] = 2%

Company B = 13.5 - 12 = 1.5%

N
(iii) Gain of Citibank = LIBOR - (LIBOR + 2) + 12 - 9.5 = 0.05%

N
Exercise 51-2

Celina Ltd. wishes to borrow US dollars at a fixed rate of interest.

A
Priyanka Ltd. wishes to borrow Japanese Yen at a fixed rate of interest.

Celina Ltd. has comparative advantage to borrow Yen @ 4% p.a. but wants to borrow dollars.

M
Priyanka Ltd. has also comparative advantage to borrow Yen @ 5.5% p.a. and wants to borrow Yen.

X
The differential between Yen rates of two companies is 1.5% p.a.

A
The differential between Dollar rates of two companies is 0.4% p.a.

T
The total gain available to both the companies from swap deal is 1.5 - 0.4 = 1.1% p.a.

The bank will charge 0.5% p.a. as intermediation charges.

Still the benefit available to companies is 1.1 - 0.5 = 0.6% p.a.

Since Priyanka Ltd. is going to get comparative advantage in the swap deal even if it surrenders all the gain to Celina

Ltd. The gain of 0.6% from swap may be transferred to Celina Ltd.

Now Priyanka Ltd. would be able to borrow Yen at 4% whereas Celina Ltd. will be able to borrow Dollars at 8.0%.

Alternatively, the swap may be formulated in such a way that bank’s intermediation charges are also borne by

Priyanka Ltd.

Exercise 51-3

Soni Ltd. has comparative advantage in the US dollar floating rate but wants to borrow Japanese yen at a fixed rate

of interest.

Toni Ltd. wants to borrow US dollars at a floating rate of interest for which Soni Ltd. has comparative advantage over

Toni Ltd.

US dollar floating rate differential is 2% (i.e. 2.5% - 0.25%).

Japanese yen fixed rate differential is 0.25% (i.e. 2% - 1.75%).

Total gain to all parties from swap deal is 1.75% (i.e. 2% - 0.25%).

A swap deal can be entered between Soni Ltd. and Toni Ltd. as follows:

Soni Ltd. will raise in dollar yielding gain of 2%.

Toni Ltd. will borrow Japanese yen causing loss of 0.25%.

The bank gets 1.00% per annum for intermediation of the swap deal.

The remaining 0.75% (i.e. 1.75% - 1.00%) will be divided in between Soni Ltd. and Toni Ltd.

The swap deal enables Soni Ltd. to borrow US dollars at LIBOR + 1.875% p.a.

Exercise 51-4

(a) Yorkshire Industries, a UK firm with US subsidiary

Floating rate it can obtain is LIBOR + 2%

Fixed rate on current debts is 9.5%

(b) Huron River Salt Company wishes to Finance exports to Briton

Floating rate it can obtain is LIBOR + 2%

Fixed rate it can obtain is 13.5%

Transaction cost in swap deal = 0.5%

Schematic diagram

N
9.5% † 12%

Swap Dealer
†

N
LIBOR LIBOR + 2%

M A
†

Yorkshire Huron † LIBOR + 2%

A X
†

T
9.5%

Savings:

Yorkshire (LIBOR + 2% - LIBOR) = 2%

Huron (13.50 - 12.00)% = 1.5%

Margin to Dealer (transaction cost) = 12 - 9.50 - 2 = 0.50%

Exercise 51-5

Mumbai Ltd. expects that interest rate will fall so they should opt for floating interest.

Swap arrangement can be as under:

The rates are identified:

Company Fixed Floating

Mumbai Ltd. 7.00% Bench Mark + 60 basis points

Chennai India Ltd. 8.20% Bench Mark + 120 basis points

The net differential of the two types of interest rates between the two companies are:

Fixed interest differential (8.20 - 7.00) 1.20

Floating interest differential (1.20 - 0.60) 0.06

Net differential 0.60

*This gain as per agreement, will be split between Mumbai Ltd. - strong company, 40 basis points and Chennai India

Ltd., the weak company, 20 basis points.

Mumbai Ltd. Chennai India Ltd.

(Borrowed fixed, move to floating) (Borrow floating, move to fixed)

- Pay bank fixed rate (7%) - Pay floating to Bank (BM + 1.20)

- Receive 40 basis points over fixed 7.40% - Pay fixed rate to Mumbai Ltd.

- Pay floating to Chennai India Ltd. plus its share of gain (7.40)

(BM + 0.60) - Receive floating from Mumbai Ltd.:

- Effective rate : BM + 20 Basis points BM + 0.60

- Effective rate : 8.00%

Mumbai Ltd. Chennai India Ltd.

Effective rate = BM + 0.20 Effective rate = 8.00

Otherwise Payable = BM + 0.60 Otherwise Payable = 8.20

Net gain 0.40 Net gain 0.20

N N
M A
A X
T
 Key to Short Answer Questions

True or False Statements

1. True - A currency swap converts a stream of cash flow from one currency to another without exchange rate

risk. It enable a corporation to lower its borrowing costs in any desired currency.

2. True - A fixed-to-floating interest rate swap changes profile of borrowing from fixed to floating. In a

situation of falling interest rates the borrower who has swapped from fixed to floating interest rate will

gain.

3. True - Interest rate swap is a financial contract between two parties who wish to change interest payments

from one currency to another or from floating to fixed interest payment obligations and vice versa.

4. False - The currency swaps are arrangements whereby currencies are exchanged at a specific exchange rates

and specified intervals, takes care of both, principal-only-swap and interest rate swap, together.

N
5. True - Interest payments in one currency are exchanged for interest payments in another in these swaps.

False

N
6. - Plain vanilla swaps are fixed-to-floating interest rate swaps between two parties. In base rate swaps

both legs are floating rate but are measured against different benchmarks.

A
7. True - These swaps are particularly useful for borrowers who have issued redeemable debt. It enables them

to match interest rate hedging with the redemption profile of the bonds.

M
8. True - Options on swaps, they give the buyer of the swaption the right but not the obligation to enter into

X
a swap agreement where term, notional principal and interest rates are predetermined.

9. False - It is common for a commodity swap to be settled in cash, although physical delivery is becoming

A
increasingly common.

T
10. True - Credit derivatives allow users to isolate, price and trade firm’s specific credit risk by unbundling a debt

instrument or a basket of instruments into its component parts and transferring each risk to those best

suited or most interested in managing it.

11. True - They are usually provided by bank or other financial institutions, and cannot be traded on any

exchange. They are custom-tailored to meet specific needs to counterparties within accepted

guidelines.

Choose Correct Word

1. swap

2. currency swaps

3. currency swap

4. credit

5. liability swap

6. credit default swap

7. credit spread options

8. tranches

9. credit linked notes

10. agricultural product processing

11. increases
Choose Correct Answer

1. (C) Currency swap

2. (A) circus swap

3. (D) par swap

4. (A) notional principle

5. (D) all of the above

6. (A) mismatch risk

7. (C) amortizing swap

8. (B) puttable swap

9. (B) call swaption

10. (D) zero-coupon swap

11. (B) buyout

12. (A) circus swap

N
13. (D) both (a) and (b) above

N
14. (B) hedging against foreign exchange risk

15. (C) (CDD or HDD) cumulative × $ 100

A
16. (A) 15 degrees

17. (A) it involves exchange of 2 floating rates

M
18. (D) all of the above

X
19. (C) in which the swap dealer enters into a swap with one party without having a counterparty for the

transaction

T A