Answer to PTP_Final_Syllabus 2012_Dec2015_Set 1

PAPER-14: ADVANCED FINANCIAL MANAGEMENT

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 Answer to PTP_Final_Syllabus 2012_Dec2015_Set 1

The following table lists the learning objectives and the verbs that appear in the syllabus learning
aims and examination questions:

Learning objectives Verbs used Definition

KNOWLEDGE List Make a list of
State Express, fully or clearly, the details/facts
What you are expected to
know Define Give the exact meaning of
Describe Communicate the key features of
Distinguish Highlight the differences between
COMPREHENSION Explain Make clear or intelligible/ state the
meaning or purpose of
What you are expected to Identity Recognize, establish or select after
understand consideration
Illustrate Use an example to describe or explain
something
Apply Put to practical use
Calculate Ascertain or reckon mathematically
APPLICATION Demonstrate Prove with certainty or exhibit by practical
means
How you are expected to
Prepare Make or get ready for use
apply
your knowledge Reconcile Make or prove consistent/ compatible
Solve Find an answer to
LEVEL C

Tabulate Arrange in a table

Analyse Examine in detail the structure of
Categorise Place into a defined class or division
ANALYSIS Compare Show the similarities and/or differences
and contrast between
How you are expected to
Construct Build up or compile
analyse the detail of what you
have learned Prioritise Place in order of priority or sequence for
action
Produce Create or bring into existence

SYNTHESIS Discuss Examine in detail by argument

How you are expected to
utilize the information
gathered to reach an Interpret Translate into intelligible or familiar terms
optimum
conclusion by a process of Decide To solve or conclude
reasoning
Advise Counsel, inform or notify
EVALUATION
How you are expected to use Evaluate Appraise or asses the value of
your learning to evaluate,
make decisions or Recommend Propose a course of action
recommendations

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 Answer to PTP_Final_Syllabus 2012_Dec2015_Set 1

PAPER-14: Advanced Financial Management

Time Allowed: 3 hours Full Marks: 100

This paper contains 5 questions. All questions are compulsory, subject to instruction provided
against each question. All workings must form part of your answer.
Assumptions, if any, must be clearly indicated.

Question No. 1. (Answer all questions. Each question carries 2 marks)

(a) 15% debentures of `1,000 (face value) to be redeemed after 10 years. Net proceeds are after
5% floatation costs and 5% discount. The tax rate is 50%. Calculate the cost of debt. [2]

Answer to (a):

Year Cash flows

0 1,000 – 5% of 1,000 (floatation) – 5% of discount = 900 C. Inflow
1 – 10 `15% of 1,000 ( 1 – 0.5) = `75 C. outflow
10 `1,000 (repayment) C. outflow

So, 900= 10 = ∑ 75/(1 + kd)n + 1,000/(1 + kd)10

n=1
By trial and error; kd = 9% approx.
Note: As the first method is simple to calculate, and second one is bit lengthy, the first
method is preferred in general.

Alternative:

RV  SV
I 1 t  
Kd  n
RV  SV
2
1000  900
150 1 0.50  
Kd  10 Kd
1000  900
2
75  10
Kd   9%  approx 
950

(b) Ms. Vasuda is considering an investment in a Mutual Fund with a 2% load. As another
alternative, she can also invest in a Bank deposit paying 10% interest. Her investment
planning period is 3 years. What should be the annual rate of return on Mutual fund so that
she prefers the investment in the fund to the investment in Bank Deposit? [2]

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 Answer to PTP_Final_Syllabus 2012_Dec2015_Set 1

Answer to (b):

(1 – 0.02) × (1+r)3 ≥ (1.10)3

Or, 0.98 × (1+r)3 ≥ 1.331 or (1+r)3 ≥ (1.331 ÷ 0.98) or, (1+r)3 ≥ 1.358163
Or, (1+r) ≥ (1.107433) or, r = (1.107433 – 1) or r = 0.107433 i.e. r = 10.743%
The annual rate of return on mutual fund = 10.743%

(c) The characteristics of two securities A and B are as follows:

Particulars Security A Security B
Expected Return (%) 12 13
Standard deviation of return (%) 21 29
Beta (β) 1.10 1.20

The correlation co-efficient between the return on Securities A and B is 0.94. If variance of
returns on the market index is 400%, calculate the systematic risk of a portfolio consisting
of two securities in equal proportion. [2]

Answer to (c):

The Beta of portfolio consisting of two securities given that money is allotted equally
between two assets.
= 1.10 × 0.5 + 1.20 × 0.5
= 1.15

The Systematic Risk of a portfolio = β2 σm2

= (1.15)2 × 400
= 529%

(d) The Sterling is trading at $ 1.6100 today. Inflation in U. K. is 4% and that in U. S.A. is 3%. What
could be the spot rate ($/£) after 2 years? [2]

Answer to (d):

S ($ /£) = F ($ /£) × (1 + r$)2 /(1 + r£)2

= 1.61 × (1+ 0.03)2/(1+ 0.04)2
= 1.5792.

(e) Immense Regional Disparities is a key reason to invest in infrastructure in India- Justify. [2]

Answer to (e):

Inter-state disparity in per capita income among Indian states has been rising over the
last couple of decades. In addition, the inter-state disparities in economic and social
infrastructure facilities too have remained at alarmingly high levels. Hence, investment in
infrastructure is required in order to boost inter- state level of development.

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 Answer to PTP_Final_Syllabus 2012_Dec2015_Set 1

(f) An investor buys a call option contract for a premium of `200. The exercise price is `20 and
the current market price of the share is `17. If the share price after three months reaches `25,
what is the profit made by the option holder on exercising the option? Contract is for 100
shares. Ignore the transaction charges. [2]

Answer to (f):

Assuming in call option, the total outgo Premium + Exercise Price = `200 + (`20 × 100)
= `2,200.

After 3 months, if the share price is `2,500, the net profit = `2,500 – `2,200 = `300.

(g) State the term ―Commission house‖ and ―Consumption Commodity‖ in commodity market.
[1+1]
Answer to (g):

Commission House: A concern that buys and sells actual commodities or futures contract
for the accounts of customers.

Consumption Commodity: - Consumption commodities are held mainly for consumption

purpose. Example: Oil, Steel

(h) Your customer requests you to book a sale forward exchange contract for US $ 2 million
delivery 3rd month. The quotes are:
Spot US$ 1 = `48.050/60
1 month margin = 0.0850/0900
2 month margin = 0.2650/2700
3 month margin = 0.5300/5350

You are required to make an exchange profit of 0.125%. Ignore telex charges and
brokerage. What will be your profit? [2]

Answer to (h):

3 month interbank rate (ask) with margin = `(48.0600 + 0.5350)

= `48,5950
With exchange profit @ 0.125%, the quote will be `48.5950 × 1.00125 = `48.66
Profit = `(48.66 – 48.60) × 2m USD = `1,20,000.

(i) The capital structure of a company is as under:

3,00,000 Equity Shares of `10 each.
32,000, 12% Preference Shares of `100 each
General Reserve `15,00,000
Securities Premium Account ` 5,00,000
25,000, 14% Fully Secured Debentures of `100 each,
Term Loan of `13,00,000.
Based on these, calculate the leverage of the company. [2]

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 Answer to PTP_Final_Syllabus 2012_Dec2015_Set 1

Answer to (i):

(a) Fixed income Funds = `(32,00,000 + 25,00,000 + 13,00, 000)

(b) Equity Funds = `(30,00,000 + 15,00,000 + 5,00,000)
a `70,00,000
Leverage = = = 58.33%
a + b 1,20,00,000

(j) The standard deviation of Greaves Ltd. stock is 24% and its correlation coefficient with
market portfolio is 0.5. The expected return on the market is 16% with the standard deviation
of 20%. If the risk-free return is 6%, calculate the required rate of return on Greaves Ltd.
script. [2]

Answer to (j):

Rf (risk free return) as 6%

Rm (Market return) as 16%
σm (standard deviation of market return) as 20%.
σg (standard deviation of Greaves stock) as 24%,
And Pgm (correlation coefficient of Greaves stock) and then use the CAPM formula for
the required return on Greaves stock.

Pgm  g  m 0.5  0.24  0.20

Beta of Greaves stock =  = 0.6
2
(m) (0.20)2
The required return = Rf + βg (Rm – Rf) = 6% + 0.6 (16 – 6) = 12%

Question No. 2. (Answer any three questions. Each question carries 8 marks)

2(a)(i). A mutual fund has a NAV of `8.50 at the beginning of the year. At the end of the year
NAV increases to `9.10. Meanwhile fund distributes `0.90 as dividend and `0.75 as capital
gains.
I. Calculate the fund's return during the year.
II. Assuming that the investor had 200 units and also assuming that the distributions been
re-invested at an average NAV of `8.75, find out the return. [2+4]

Answer to 2(a)(i):

I. Return for the year (all changes on a per unit basis):

Change in price (`9.10 – `8.50) = `0.60

Dividends received 0.90
Capital gains distributions 0.75
Total return `2.25
Holding period return = ` 2.25
 100  26.47%
` 8.50

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 Answer to PTP_Final_Syllabus 2012_Dec2015_Set 1

II. When all dividends and capital gains distributions are reinvested into additional units
of the fund (`8.75/unit):

Dividends and capital gains per unit: `0.90 + `0.75 = `1.65

Total received from 200 units: `1.65 × 200 = `330.00

Additional units acquired: `330/`8.75 = 37.7 unit

Value of 237.7 units held at end of year = 237.7unit × `9.10 = `2,163

Price paid for 200 units at beginning of year 200 units × `8.50 = `1,700

Thus, the holding period return would be: = (2,163 – 1,700)/1,700 = 27.24%

2(a) (ii). State the Forward Market Commission of India. [2]

Answer to 2(a)(ii):

The Forward Markets Commission is a regulatory body for commodity markets in India.
The forward contracts in commodities are regulated as per F.C.(R) Act, 1952 by this
body. Inherent objective is to achieve price stability by means of price discovery and
risk management. The Commission also collects information regarding the trading
conditions in respect of goods to which any of provisions of Act is made applicable. It
also advises Central Government regarding recognition of associations .

2(b)(i). From the following particulars, calculate the effective rate of interest p.a. as well as the
total cost of funds to Bhaskar Ltd., which is planning a CP issue: [2+2]

Issue Price of CP : `97,550

Face Value : `1,00,000
Maturity Period : 3 Months
Issue Expenses :
Brokerage : 0.15% for 3 months
Rating Charges : 0.50% p. a.
stamp Duty : 0.175% for 3 months

Answer to 2(b)(i):

 F  P  12
Effective interest =    100
 P  M

Substituting the given values of F, P and M we get,

 1,00,000  97,550  12
Effective Interest = 
97,550   3 100 = 10.05%
 

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 Answer to PTP_Final_Syllabus 2012_Dec2015_Set 1

Cost of funds to the company

Effective interest rate =10.05%
Brokerage (0.15 × 4) = 0.60%
Rating charges = 0.50%
Stamp Duty (0.175 × 4) = 0.70%
Total cost of Funds to Bhaskar Ltd. = 11.85% p.a.

2(b) (ii). List the key elements of a well – functioning Financial System. [4]

Answer to 2(b)(ii):

Key elements of a well-functioning financial system are:

(i) A strong legal and regulatory environment;
(ii) Stable money;
(iii) Sound public finances and public debt management;
(iv) a central bank;
(v) a sound banking system;
(vi) an information system; and
(vii) well functioning securities market.

2(c)(i). Suppose a bank offers a 6-month CD at an annual percentage rate of 11.5%

compounded monthly and a 1-year CD with an annual percentage rate of 11.3%
compound weekly. You are required to find out which of them offers a higher rate of
interest. Assume a face value of `1000. [4]

Answer to 2(c)(i):

Effective annual interest rate on the 6 month CD – 11.5% compounded monthly:

A CD paying 11.5% p.a. would pay monthly 11.5%/12 = 0.958%

This when compounded 12 times (corresponding to monthly compounding), we get:
Amount = 1,000 × (1+ 0.00958)12 = `1121.214
i.e. 12.12% on an investment of `1,000.

Effective annual interest rate on the a one year CD -11.3% compounded weekly:
A CD paying 11.3% p.a. would pay weekly 11.3%/52 = 0.217%
This when compounded 52 times (corresponding to weekly compounding), we get:
Amount = 1000 × (1+ 0.00217)52 = `1119.315
i.e. 11.93% on an investment of `1,000.

Comment: The effective annual interest rate of 1st CD is higher than that of the 2nd CD.

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2(c)(ii).Explain two main distinguishing features of Project Finance compared to Corporate

Finance. [4]

Answer to 2(c)(ii):

Two main distinguishing features of Project Finance compared to Corporate Finance are:
(a) Enhanced verifiability of cash flows: Due to contractual agreements possible
because of a single, discrete project in legal isolation from the sponsor and
the resultant absence of future growth opportunities in the Project Financed
Company. Since Corporate Finance involves a multitude of future and current
projects the same contractual agreements cannot be effected in Corporate
Finance Company, and
(b) Lack of sponsors‘ assets and cash flows: In case of Corporate Finance the lender
has a potentially larger pool of cash flows from which to get paid as compared
to Project Finance where the cash flows from the project only are used to pay
the investors.
According to some empirical researches, Project Finance is more likely than
Corporate Finance in countries where the investor protection against managerial
self-dealing is weaker and investor protection is low. This can be better understood
in terms of comparison between the neighboring countries: India and China.
India used predominantly Project Financing for Infrastructure Projects while China
has started using Capital Finance for its huge infrastructure projects.

2 (d). Two funds are available for investment. Fund A is being launched today i.e. 30/9/2005
and available for investment at `10 per unit. A similar fund B (same risk profile like
Fund A) is also available for investment at `19.45 per unit. The information of quarterly
NAV for the next three quarters are available as given below.

Closing NAV Fund A Fund B

30/09/2015 10 19.45
31/12/2015 11.1567 21.50
31/03/2016 14.768 27.15
30/06/2016 12.8554 23.69

Assuming that investor X prefers fund A and investor Y prefers Fund B for investment
through SIP (Systematic Investment Plan) each installment entailing `2,000 for the four
quarters including the initial investment, which investor (X or Y) would clock a higher
return on investment, as on 30/6/2006? (Ignore time value of money). Is the difference
in return because of one investor chose to invest at `10 and the other at `19.45? [8]

Answer to 2(d):

Amount in ` Fund A Fund B

Installment = 2000 NAV Units NAV Units
30/09/2015 10.0000 200.0000 19.4500 102.8278
31/12/2015 11.1567 179.2645 21.5000 93.0233

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31/3/2016 14.7680 135.4280 27.1500 73.6648

30/6/2016 12.8554 155.5766 23.6900 84.4238
670.2691 353.9397
Value 670.2691 ×12.8554 8616.577 353.9397 × 23.69 8384.830
Investment 8000 8000
Return 616.577/8000 7.71% 384.83 / 8000 4.81%

X has fetched a higher return from Fund A. The difference in performance is not due to
investing at the `10 or `19.45. It is due to comparative poor performance of Fund B during
the period.

Question No. 3. (Answer any two questions. Each question carries 10 marks)

3(a)(i).The Price of Infosys Stock of a Face Value of `10 on 31st December was `350 and the
Futures Price on the same stock on the same date i.e. 31 st December for March (next
year) was `370.
Other features of the contract are as –
 Time to expiration 3 months (0.25 year)
 Annual dividend on the stock of 30% payable before 31 st March.
 Borrowing rate is 20% p. a.
Based on the above information, calculate Future Price for Infosys stock on 31 st Dec.
Also explain whether any arbitrage opportunity exists. [5+3]

Answer to 3(a)(i):

Securities of Infosys
Spot price [Sx] `350
Expected rate of Dividend [y] 30% or 0.30
Borrowing rate 20%
Tenor/Time Period [t] in years 3 Months or 0.25 Year

Theoretical Forward Price [TFP x] = `350 × e 0.20×0.25 – (30% × 10)

TFPx = (ASx × ert) – Dividend at T 3 = `350 × e 0.05 – 3

= (`350 ×1.0513) – 3 = `364.96

3 – Months Futures Contract rate [AFP x] `370
TFPx Vs. AFPx AFPx is Higher
Inference AFPx is overvalued
Recommended action Buy spot, Sell Future.

Note: Since the dividend is payable at t 3, no discounting is required.

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 Answer to PTP_Final_Syllabus 2012_Dec2015_Set 1

Cash Flows arising out of the Activities to gain on the Arbitrage.

`
(a) Borrow for a period of 3 months and Buy Stock at T 0 ` 350
(b) Receive the dividend at the end of 3 months 3
(c) Sell the Futures at the Forward price at the end of 3 months 370
(d) Repay the amount of borrowing together with interest = (350 ×e0.20×0.25 ) 367.96
(e) Net Cash Inflow [(b) + (c) – (d) ] ` 5.04

3. (a) (ii) Describe the two main types of commodity swaps. [2]

Answer to 3(a)(ii):

Two main types of commodity swaps are:

 Fixed-floating commodity swaps are similar to the interest rate fixed-floating
swaps except that both legs are commodity based. These are used by
commodity producers and consumers to lock in commodity prices.
 Commodity for interest swaps are similar to equity swaps, in which a total return
on the commodity is exchanged for some money market rate (plus or minus a
spread).

3(b)(i). M/s Parker & Company is contemplating to borrow an amount of `60 Crores for a
period of 3 months in the coming 6 month‘s time from now. The current rate of Interest
is 9% p.a. but it may go up in 6 months‘ time. The Company wants to hedge itself
against the likely increase in Interest Rate. The Company ‗Bankers quoted an FRA
(Forward Rate Agreement) at 9.30% p.a.

What will be the effect of FRA and actual rate of Interest Cost to the company, if the
actual arte of Interest after 6 months happens to be (i) 9.60% p.a. and (ii) 8.80% p.a.?
[3+3]
Answer to 3(b)(i):

Particulars If Actual rate is 9.60% If Actual rate is 8.80%

Forward Rate 9.30% 9.30%
quoted by bank
Profit/(Loss) Since the Actual rate is higher Since the actual rate is lower
than the FRA, the profit is 9.60 – than the FRA, the Loss is 8.80
9.30 = 0.30 – 9.30 = (0.50)
Profit/(Loss) on  3   3 
(0.096  0.093)   (0.088  0.093)  
Settlement (See
60Crores   12  60Crores   12 
Note Below)  3   3 
1 0.096   1 0.080  
 12   12 
= 60 Crores × (0.00075 ÷ 1.024) = = 60 Crores × (0.00125 ÷ 1.02)
4,39,453 = (7,35,294)

Note: Profit/ (Loss) on settlement is identified using the following –

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 Answer to PTP_Final_Syllabus 2012_Dec2015_Set 1

 Actual Rate Forward Rate    Period

 

 12 
Profit/(Loss) = Principal ×
 Period 
1 ActualRate  
 12 

3(b)(ii). MNC rolls over a $25 million loan priced at LIBOR on a three-month basis. The
company feels that interest rates are rising and that rates will be higher at the next
roll-over date in three months. Suppose the current LIBOR is 5.4375%. Explain how
MNC can use FRA at 6% offered by a bank to reduce its interest rate risk on this loan.
In three months, if interest rates have risen to 6.25%, how much will MNC receive/pay
on its FRA? Assume the three month period as 90 days. [4]

Answer to 3(b)(ii):
MNC can use 3 × 6 FRA, if it expects that the rates would be higher at the next roll-over
of three months, starting three months from today. In other words MNC would buy 3 ×6
FRA @ 6%, clearly with a view that higher rate would prevail on the settlement date i.e. 3
months from now.

Now if on the settlement date, the rate is 6.25%, then MNC’s decision to buy 3 × 6 FRA
has been proved right and it would receive the present value of the interest differentials
on the loan amount i.e. it would receive:

Payoff = Notional Amount ×

Reference Rate  Fixed rate ×( is the day count function)
1 Reference Rate  α

= $2,50,00,000 ×
 0.0625  0.0600   90 / 360 = $15,385
1 0.0625  90 / 360

3 (c). Given the following:

Strike price `200

Current stock price `185
Risk free rate of interest 5 % p.a

I. Calculate the theoretical minimum price of a European put option after 6 months.
II. If European put option price is ` 5 , then how can an arbitrageur make profit. [4+6]

Answer to 3(c):

I. Computation of theoretical Minimum price

Particulars Value
Exercise price `200
Current Stock Price `185
Risk Free Rate of Return (r) 5% or 0.05

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 Answer to PTP_Final_Syllabus 2012_Dec2015_Set 1

Time (in years) 6 ÷ 12 = 0.5

Theoretical Minimum Price = Present Value of Exercise Price - Current Stock Price
–rt
= 200 × e – 185
0.05×0.5
= 200 + e – 185 = (200 ÷ 1.02532) – 185
= 195.0611 – 185 = 10.0611

Inference: Since the Value of Put Option is more than the price of the Put Option, it is under
priced and the recommended action will be to buy the Put Option.
II. Cash Flows to make Profit for the Arbitrageur Activity Flow:
1. Arbitrageur can borrow the amount required to buy the Put Option and Stock at the
rate of 5% p.a. for 6 months.
2. Buy Put Option.
3. Take the opposite position and buy stock at spot price.
4. At the end of six months, exercise the Put option and realise the receipts.
5. Pay the amount of Borrowing together with Interest.

Particulars Time `
1. Borrow at the rate of 5% for 6 months [185 + 5] T0 190
2. Buy Put Option T0 (5)
3. Buy Stock at Spot Price T0 (185)
4. Exercise the Put Option and realise the Sale Proceeds T1 200
5. Repay the amount of Borrowing together with Interest [190 e
0.05×0.5
] = [190 T1 194.81
× 1.02532]
6. Net Gain made [(4) - (5)] T1 5.19

Note: the amount of gain is the minimum amount and will increase with every increase in
Spot Price as on the Exercise Date.

Question No. 4. (Answer any two questions. Each question carries 8 marks)

4(a)(i). Suppose that all stocks have a rate of return with a standard deviation of 40% and
that the correlation between rates of returns for all pairs of stocks is 0.6.
I. Consider forming an equally-weighted portfolio of 10 stocks. Calculate the standard
deviation of this port-folio's return?
II. How many stocks would be required in an equally-weighted portfolio in order to have a
portfolio standard deviation of 31%? [4+2]

Answer to 4(a)(i):
I. The variance of N = 10 stock portfolios would comprise of 10 variance terms + 10(10-
1) covariance/correlation terms.

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 Answer to PTP_Final_Syllabus 2012_Dec2015_Set 1

1/2
 N N 
= N  w12 σi2    wiw jσ iσ jρ ij
 1111 

Since weights, standard deviation and correlation coefficient are same for all the ten
stocks,
1
 10  wi 2i2  10 10  1 wi 2 i 2ij  2

= [10 × (1/10) 2 (0.4)2 +10(10 – 1)(1/10)2 (0.40)2 (0.6)] 1/2

= 32%

II. Now we are given the portfolio risk, and we are asked to find N. Therefore we have the
1

   0.4    0.40   0.6
2 2 2
LHS = 0.31 and RHS = N  1  NN  1 1
2 2

 N N 
Solving we get N = 640 stocks.

4(a)(ii). State gross national product analysis. [2]

Answer 4(a)(ii):

Gross National Product Analysis: Gross National Product (GNP) as a measure national
income reflects the growth rate in economic activities and is regarded as a forecasting
tool for analyzing the overall economy along with its various components during a
particular period.

4 (b). Currently the risk-free rate equals 5% and the expected return on the market portfolio
equals 11%. We also have the following information:
Stock Beta Expected Return
A 1.33 12%
B 0.70 10%
C 1.50 14%
D 0.66 9%

I. Which stock has the highest reward to risk ratio and which has the lowest?
II. Show how an investor could construct a portfolio of stocks C and D that would
outperform stock A.
III. Construct a portfolio consisting of some combination of the market portfolio and the
risk-free asset such that the portfolio's expected return equals 9%. What is the beta of
this portfolio? What does this say about stock D? [4+2+2]

Answer to 4(b):

I. The reward to risk ratio can be found as: (R s - Rf) / βs. We calculate for each of these
stocks below:

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 Answer to PTP_Final_Syllabus 2012_Dec2015_Set 1

A: (12- 5)/1.33 = 5.26

B: (10- 5)/0.7 = 7.14

C: (14 - 5)/1.5 = 6

D: (9- 5)/0.66 = 6.06

We have market risk premium =11- 5 = 6%. C, the fairly priced stock, has a ratio exactly
equal to the market risk premium of 6%. The overvalued stock has a ratio less than the
market risk premium and the under priced stocks have ratios greater than the market risk
premium.

II. A portfolio of C and D that would equal the return of A can be found, by assuming
proportion of investment in C as X and solving the equation X × 14 + (1- X) × 9 =12.
Solving for X, we get X = 0.60. Any portfolio with more than 60% of stock C will have a
return greater than the return of stock A.

III. A portfolio with a return of 9% combining the risk free rate and market can be found,
by assuming proportion of investment in risk free rate as X and solving the equation X ×
5 + (1 - X) × 11 = 9. Solving for X, we get X = 0.33. Therefore the portfolio beta =1/3 × 0 +
2/3 ×1= 0.66. This is same as stock D's risk & return.

4(c)(i).Century is an Indian conglomerate, with holdings in Cement & Textiles. The beta
estimated for the firm, relative to the Indian stock exchange is 1.15, and the long term
government borrowing rate in India is 11.5% and market risk premium is 12%.
I. Estimate the expected return on the stock.
II. If you are an international investor, what concerns if any, would you have about using
the beta estimated relative to the Indian Index? If you have concerns, how would you
modify the beta? [2+3]

Answer to 4(c)(i):

I. The expected return on this Indian stock is given by the CAPM that shows the
minimum return on the stock expected by investors. The CAPM gives k e = 0.115 +
(1.15)(0.12) = 0.25 or 25%

II. The beta estimated relative to the Indian index may be a good estimate of risk for a
Indian investor. However, an international investor would be better off using a beta
for that stock that has been estimated relative to an international index, such as the
Morgan Stanley Capital Index. This index captures better the returns of the market
portfolio that an internationally diversified investor holds.

4(c)(ii).A fund manager knows that her fund currently is well diversified and that it has a
CAPM beta of 1.0. The risk-free rate is 8 percent and the CAPM risk premium is 6.2
percent. She has been learning about APT measures of risk and knows that there are

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 Answer to PTP_Final_Syllabus 2012_Dec2015_Set 1

(at least) two factors: changes in the industrial production index, d1, and unexpected
inflation, d2. The APT equation is E (Ri) = 0.08 + 0.05 b i1 + 0.11b i2.
I. If her portfolio currently has a sensitivity to the first factor of bp1= - 0.5, calculate its
sensitivity to unexpected inflation.
II. If the fund manager rebalances her portfolio to keep the same expected return but to
reduce the exposure to inflation to zero, calculate the portfolio's sensitivity to the first
factor. [2+1]

Answer:
I. The general APT equation is given by:
E (R) = 0.08 + 0.05bi1 + 0.11 bi2
The sensitivity to the first factor if - 0.5; Using the expected return (as arrived at from
CAPM), we can calculate bi2:
As per CAPM,
E (Ri) = 8 + 1 × (6.2) = 14.2%
Substituting in the APT equation,
0.142 = 0.08 + 0.05 × (-0.5) + 0.11 × bi2
We get, bi2 = 0.79

II. By keeping E (Ri) = 14.2% & substituting bi2 = 0,, we can use the same equation to find b i1
and we get:
 0.142 = 0.08 + 0.05 bi1 + 0
 bi1 = 1.24

Question No. 5. (Answer any two questions. Each question carries 10 marks)

5 (a) JKL Ltd. has the following book-value capital structure as on March 31, 2015.
Amount in (`)
Equity Share capital (2,000 shares) 40,00,000
11.5% preference shares 10,00,000
10% Debentures 30,00,000
80,00,000

The equity share of the company sells for `20. It is expected that the company will pay
next year a dividend of `2 per equity share, which is expected to grow at 5% p.a. forever.
Assume a 35% corporate tax rate. Required:
I. Compute weighted average cost of capital (WACC) of the company based on the
existing capital structure.
II. Compute the new WACC, if the company raises an additional `20 lakhs debt by
issuing 12% debentures. This would result in increasing the expected equity dividend
to `2.40 and leave the growth rate unchanged, but the price of equity share will fall to
`16 per share.
III. Comment on the use of weights in the computation of weighted average cost of
capital. [3+3+(2+2)]

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 Answer to PTP_Final_Syllabus 2012_Dec2015_Set 1

Answer to 5(a):

I. Computation of weighted Average cost of capital of the company

Capital Structure Amount Cost of Capital Weights WACC
Equity Share Capital 40,00,000 15% 0.500 7.50%
11.5% Preference Shares 10,00,000 11.5% 0.125 1.4375%
10% Debentures 30,00,000 6.5% 0.375 2.4375%
80,00,000 1.000 11.375%

Working Notes:
D1 `2
1. Cost of Equity Capital (Ke) = +g = + 5% = 15%
Po ` 20
D `11.5
2. Cost of Preference Share Capital (Kp) = = = 11.5%
P `100
I 1- t  `10(1- 0.35)
3. Cost of New Debentures (Kd) = = = 6.5%
P `100

II. Computation of New weighted Average cost of Capital of the company

Capital Structure Amount (`) Cost of Capital Weights WACC
Equity Share Capital 40,00,000 20% 0.40 8.00%
11.5% Preference Shares 10,00,000 11.5% 0.10 1.15%
10% Debentures 30,00,000 6.5% 0.30 1.95%
12% Debentures 20,00,000 7.8% 0.20 1.56%
1,00,00,000 1.00 12.66%

D1 ` 2.40
Working notes: Cost of Equity Capital (Ke) = +g= + 5% = 20%
Po `16
III. Comment:
(a) Book Value Weights: The weights are said to be book value weights if the proportions
of different sources are ascertained on the basis of the face value i.e., the
accounting values. The book value weights can be easily calculated by taking the
relevant information from the capital structure as given in the balance sheet of the
firm. Based on the value proportions in the company's Balance Sheet, this represents
the proportion a particular source of financing has in the Balance Sheet total.
(b) Market Value Weights: The weights may also be calculated on the basis of the market
value of different sources i. e„ the proportion of each source at its market value. In
order to calculate the market value weights, the firm has to find out the current
market price of the securities in each category. However, a problem may arise if
there is no market value available for a particular type of security.

5 (b). Nine Gems Ltd. has just installed Machine R at a cost of `2,00,000. The machine has a
five-year life with no residual value. The annual volume of production is estimated at
1,50,000 units, which can be sold at `6 per unit. Annual operating costs are estimated at
`2,00,000 (excluding depreciation) at this output level. Fixed costs are estimated at `3
per unit for the same level of production.

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 Answer to PTP_Final_Syllabus 2012_Dec2015_Set 1

Nine Gems Ltd. has just come across another model called Machine — S capable of
giving the same output at an annual operating cost of `1,80,000 (exclusive of
depreciation). There will be no change in fixed costs. Capital cost of this machine is
`2,50,000 and the estimated life is for five-years with nil residual value.

The company has an offer for sale of Machine — R at `1,00,000. But the cost of
dismantling and removal will amount to `30,000. As the company has not yet
commenced operations, it wants to sell Machine — R and purchase Machine — S. Nine
Gems Ltd. will be a zero-tax company for seven years in view of several incentives and
allowances available. The cost of capital may be assumed at 14%.
P. V. factors for five years are as follows:
Year 1 2 3 4 5
PVF 0.877 0.769 0.675 0.592 0.519

I. Advise whether the company should opt for the replacement.

II. Will there be any change in your view, if Machine — R has not been installed but the
company, is in the process of selecting one or the other machine?

Support your view with necessary workings. [6+4]

Answer to 5 (b):

I. Statement showing evaluation of Replacement Proposal

Particulars Time P.V. Factor Amount in (`) PV in (`)
Cash Outflows:
Cost of machine 2,50,000
Less: Scrap value (70,000)
Sale Proceeds `1,00,000
Less: Dismantling & removal costs `(30.000)
Net Cost of Replacement 0 1 1,80,000 1,80,000
PVCO (A) 1,80,000
Cash Inflows:
Incremental CFAT 1-5 3.432 20,000 68,640
[2,00,000 - 1,80,000]
PVCI (B) 68,640
NPV (B) - (A) (1,11,360)
Advise: No, the company should not opt the replacement.

II. Statement showing Evaluation of Proposal:

Time PV Factor Machine R Machine S
Amount in PV in (`) Amount in PV in (`)
(`) (`)
Cash Outflows:
Cost of machine 0 1 2,00,000 2,00,000 2,50,000 2,50,000
Annual Operating Costs 1-5 3.432 2, 00,000 6,86,400 1,80,000 6,17,760
PVCO 8,86,400 8,67,760
Advise: Machine S should be installed as it has lower PVCO.

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 Answer to PTP_Final_Syllabus 2012_Dec2015_Set 1

5 (c). A company is engaged in evaluating an investment project, which requires on initial cash
outlay of `2,50,000 on equipment. The project's economic life is 10 years and its salvage
value `30,000. It would require current assets of `50,000. An additional investment of
`60,000 would also be necessary at the end of five years to restore the efficiency of the
equipment. This would be written off completely over the last five years. The project is
expected to yield Annual (before tax) Cash Inflow of `1,00,000. The company follows sum
of year's digit method of depreciation. Income tax is assumed to be 40%. Should be
project be accepted if the minimum required rate of return is 20%? [10]
Note: PVs of `1at 20% discount rate are as follows:
Year 1 2 3 4 5 6 7 8 9 10
PVF 0.833 0.694 0.579 0.482 0.402 0.335 0.279 0.233 0.194 0.162

Answer to 5 (c):

Statement showing computation of PVCO:

Particulars Time PVF Amount PVF
Cash outflows:
Initial Cash outlay of equipment 0 1 2,50,000 2,50,000
Working capital/Current Assets 0 1 50,000 50,000
Additional investment to restore efficiency of equipment 5 0.402 60,000 24,120
PVCO (A) 3,24,120

Statement showing computation of PVCI:

Particulars 1 2 3 4 5 6 7 8 9 10
CFBT (1) 1,00,000 1,00,000 1,00,000 1,00,000 1,00,000 1,00,000 1,00,000 1,00,000 1,00,000 1,00,000
Less: Depreciation (40,000) (36,000) (32,000) (28,000) (24,000) (20,000) (16,00) (12,000) (8,000) (4,000)
Less: Additional
Depreciation (20,000) (16,000) (12,000) (8,000) (4,000)
PBT 60,000 64,000 68,000 72,000 76,000 60,000 68,000 76,000 84,000 92,000
Tax Liability (2)
(40%) 24,000 25,600 27,200 28,800 30,400 24,000 27,200 30,400 33,600 36,800
CFAT (1) – (2) 76,000 74,400 72,800 71,200 69,600 76,000 72,800 69,600 66,400 63,200
Add: Terminal
Value 80,000
76,000 74,400 72,800 71,200 69,600 76,000 72,800 69,600 66,400 1,43,200
PV Factor 0.833 0.694 0.579 0.482 0.402 0.335 0.279 0.233 0.194 0.162
PVCI (B) 63,308 51,634 42,151 34,318 27,979 25,460 20,311 16,217 12,882 23,198

Particulars Amount in (`)

Total PVCI 3,17,458
Less: PVCO (3,24,120)
NPV (6,662)

Advise: reject the proposal

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