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Chapter 8 of 'Fundamentals of Financial Management' covers the time value of money, including calculations for present and future values, loan amortization schedules, and the impact of interest rates on investments. It explains concepts such as the Rule of 72 and Rule of 69 for estimating doubling periods, and provides various examples and formulas for financial calculations. The chapter emphasizes the importance of understanding these principles for effective financial decision-making.

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0% found this document useful (0 votes)
42 views20 pages

Solutions To Problem

Chapter 8 of 'Fundamentals of Financial Management' covers the time value of money, including calculations for present and future values, loan amortization schedules, and the impact of interest rates on investments. It explains concepts such as the Rule of 72 and Rule of 69 for estimating doubling periods, and provides various examples and formulas for financial calculations. The chapter emphasizes the importance of understanding these principles for effective financial decision-making.

Uploaded by

Sidhi Rawal
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOC, PDF, TXT or read online on Scribd
You are on page 1/ 20

Prasanna Chandra: Fundamentals of Financial Management, 6 th Edition

Copyright © 2014 by McGraw Hill Education (India) Private Limited

Chapter 8
TIME VALUE OF MONEY

1.
(i)
A x PVIFA (12%, 5) = 15,000,000

A x 3.605 = 15,000,000

15,000,000
A = = 4,160,888
3.605

(ii)

Year Principal Installment Interest Principal


(beginning) repayment
1 15,000,000 4,160,888 1,800,000 2,360,888
2 12,639,112 4,160,888 1,516,693 2,644,195
3 9,994,917 4,160,888 1,199,390 2,961,498
4 7,033,419 4,160,888 844,010 3,316,878

2,961,498
 The required proportion = = 0.71
4,160,888

2.

The doubling period as per the rule of 69 is :

69
0.35 +
r

69
= 0.35 + = 5.66 years
13

3.

1,000,000
Annual installment = = 298,329
3.352

1
Prasanna Chandra: Fundamentals of Financial Management, 6 th Edition
Copyright © 2014 by McGraw Hill Education (India) Private Limited

Loan Amortisation Schedule

Year Beg. Instalment Interest Principal Balance


repayment
1 1,000,000 298,329 150,000 148,329 851,671
2 851,671 298,329 127,751 170,578 681,093

170,578 / 298,329 = 0.572 or 57.2%

4. Value 10 years hence of a deposit of Rs.20,000 at various interest rates is as


follows:

r = 4% FV5 = 20,000 x FVIF (4%, 10 years)


= 20,000 x1.480 = Rs.29, 600

r = 6% FV5 = 20,000 x FVIF (6 %, 10 years)


= 20,000 x 1.791 =Rs.35, 820

r = 8% FV5 = 20,000 x FVIF (8 %, 10 years)


= 20,000 x 2.159 =Rs.43, 180

r = 9% FV5 = 20,000 x FVIF (9 %, 10 years)


= 20,000 x 2.367 =Rs. 47,340

5.
Rs.32,000 / Rs. 2,000 = 16 = 24

According to the Rule of 72 at 6 percent interest rate doubling takes place


approximately in 72 / 6 = 12 years

So Rs.2, 000 will grow to Rs.32, 000 in approximately 4 x 12 years = 48 years

6.
In 14 years Rs.5, 000 grows to Rs.20, 000 or 4 times. This is 2 2 times the initial
deposit. Hence doubling takes place in 14 / 2 = 7 years.

According to the Rule of 69, the doubling period is .35 + 69 / Interest rate
We therefore have
0.35 + 69 / Interest rate = 7
Interest rate = 69/(7-0.35) = 10.38 %

2
Prasanna Chandra: Fundamentals of Financial Management, 6 th Edition
Copyright © 2014 by McGraw Hill Education (India) Private Limited

7.
In 18 years Rs.10, 000 grows to Rs.80, 000 or 8 times. This is 2 3 times the initial
deposit. Hence doubling takes place in 18 / 3 = 6 years.

According to the Rule of 69, the doubling period is 0.35 + 69 / Interest rate. We
therefore have
0.35 + 69 / Interest rate = 6

Interest rate = 69/(6-0.35) = 12.21 %

8.

Saving Rs.5000 a year for 3 years and Rs.7000 a year for 7 years thereafter is
equivalent to saving Rs.5000 a year for 10 years and Rs.2000 a year for the years 4
through 10.
Hence the savings will cumulate to:
5000 x FVIFA (8%, 10 years) + 2000 x FVIFA (8%, 7 years)
= 5000 x 14.487 + 2000 x 8.923 = Rs.90281

9.
Let A be the annual savings.

A x FVIFA (10%, 5years) = 2,000,000


A x 6.105 = 2,000,000

So, A = 2,000,000 / 6.105 = Rs. 327,600

10.
The present value of an annual pension of Rs.120, 000 for 20 years when r =
10% is:
120,000 x PVIFA (10%, 20 years)
= 120,000 x 8.514 = Rs.1, 021,680

The alternative is to receive a lumpsum of Rs 1,000,000

Rahul will be better off with the annual pension amount of Rs.120,000.

11.
The present value of an annual payment of Rs.10,000 for 10 years when r = 9%
is:
10,000 x PVIFA ( 9 %, 10 years)
= 10,000 x 6.418 = Rs.64, 180

The annual payment option would be the better alternative

3
Prasanna Chandra: Fundamentals of Financial Management, 6 th Edition
Copyright © 2014 by McGraw Hill Education (India) Private Limited

12.
The present value of the income stream is:
30,000 x PVIF (9%, 1 year) + 50,000 x PVIF (9%, 3 years)
+ 100,000 x PVIFA (9 %, 7 years) x PVIF (9%, 3 years)
= 30,000 x 0.917 + 50,000 x 0.772 + 100,000 x 5.033 x 0.772 =
Rs.454, 658...352 x 0.658 = Rs.152, 395.

13.
The present value of the income stream is:
1,000 x PVIFA (12%, 3 years) + (5,000/ 0.12) x PVIF (12%, 3 years)
= 1,000 x 2.402 + (5000/0.12) x 0.712
= Rs.32,069

14.
To earn an annual income of Rs.240,000 forever , beginning from the end of 6
years from now, if the deposit earns 12% per year a sum of Rs.240,000 / 0.12 =
Rs.2,000,000 is required at the end of 5 years. The amount that must be
deposited to get this sum is:
Rs.2, 000,000 PVIF (12%, 5 years) = Rs.2, 000,000 x 0.567
= Rs. 1,134,000

15.

PV( Stream X) = 500 PV( 18%, 1yr) +550 PV( 18%, 2yrs) + 600 PV( 18%,
3yrs) + 650 PV( 18%, 4yrs) + 700 PV( 18%, 5yrs) + 750 PV( 18%, 6yrs)
= 500 x 0.847 +550 x 0.718 + 600 x 0.609 + 650 x 0.516 + 700 x 0.437 + 750 x
0.370 = 2102.6

PV( Stream Y) = 750 PV( 18%, 1yr) +700 PV( 18%, 2yrs) + 650 PV( 18%,
3yrs) + 600 PV( 18%, 4yrs) + 550 PV( 18%, 5yrs) + 500 PV( 18%, 6yrs)
= 750 x 0.847 +700 x 0.718 + 650 x 0.609 + 600 x 0.516 + 550 x 0.437 + 500 x
0.370 = 2268.65

PV (Stream Z) = 600 PVIFA (18%, 6yrs) = 600 x 3.498 = 2098.8

16.
FV10 = Rs.200,000 [1 + (0.12 / 6)]10x6
= Rs.200,000 (1.02)60
= Rs.200,000 x 3.281
= Rs.656,200

4
Prasanna Chandra: Fundamentals of Financial Management, 6 th Edition
Copyright © 2014 by McGraw Hill Education (India) Private Limited

17.

A B C

Stated rate (%) 8 10 12

Frequency of compounding 6 times 4 times 12 times

Effective rate (%) (1 + 0.08/6)6- 1 1+0.10/4)4 –1 (1 + 0.12/12)12-1

= 8.27 = 10.38 = 12.68

Difference between the


effective rate and stated
rate (%) 0.27 0.38 0.68

18. The interest rate implicit in the offer of Rs.600,000 after 8 years in lieu of
Rs.200,000 now is the value of r in the following equation:
Rs.200,000 x FVIF (r,8 years) = Rs.600,000

Rs.600,000
FVIF (r,8 years) = = 3.000
Rs.200,000

From the tables we find that


FVIF (15%, 8years) = 3.059

This means that the implied interest rate is nearly 15%.


I would choose Rs.600,000 after 8 years from now because I find a return of
15% quite attractive.

19.
FV5 = Rs.500,000 [1 + (0.09 / 4)]5x4
= Rs.500,000 (1.0225)20
= Rs.500,000 x 1.5605
= Rs.780,250

If the inflation rate is 3 % per year, the value of Rs.780,250, 5 years from
now, in terms of the current rupees is:
Rs.780,250 x PVIF (3%, 5 years)
= Rs.780,250 x 0. 863 = Rs.673,356

5
Prasanna Chandra: Fundamentals of Financial Management, 6 th Edition
Copyright © 2014 by McGraw Hill Education (India) Private Limited

20.
The discounted value of Rs.100,000 receivable at the beginning of each year
from 2015 to 2019, evaluated as at the beginning of 2014 (or end of 2013)
is:
= Rs.100,000 x PVIFA (10%, 5 years)
= Rs.100,000 x 3.791= Rs.379,100

The discounted value of Rs.379,100 evaluated at the end of 2011 is

= Rs.379,100 x PVIF (10 %, 2 years)


= Rs.379,100 x 0.826= Rs.313,137

If A is the amount deposited at the end of each year from 2007 to 2011 then
A x FVIFA (10%, 5 years) = Rs.313,137
A x 6.105 = Rs.313,137
A = Rs.313,137/ 6.105 = Rs.51,292

21.
The discounted value of the annuity of Rs.120,000 receivable for 20 years,
evaluated as at the end of 7th year is:

Rs.120,000 x PVIFA (12%, 20 years) = Rs.120,000 x 7.469 = Rs.896,280

The present value of Rs. 896,280 is:

= Rs. 896,280 x PVIF (12%, 7 years)


= Rs. 896,280 x 0.452
= Rs.405,119

22.
40 per cent of the pension amount is
0.40 x Rs.10,000 = Rs.4,000

Assuming that the monthly interest rate corresponding to an annual interest rate
of 12% is 1%, the discounted value of an annuity of Rs.4,000 receivable at the
end of each month for 240 months (20 years) is:

Rs.4,000 x PVIFA (1%, 240)

(1.01)240 - 1
Rs.4,000 x = Rs.363,278
.01 (1.01)240
If Mr. Tiwari borrows Rs.P today on which the monthly interest rate is 1%

P x (1.01)96 = Rs. 363,278


P x 2.60 = Rs. 363,278

6
Prasanna Chandra: Fundamentals of Financial Management, 6 th Edition
Copyright © 2014 by McGraw Hill Education (India) Private Limited

Rs. 363,278
P = = Rs.139,722
2.60

23.
The discounted value of the debentures to be redeemed between 6 to 8 years
evaluated at the end of the 5th year is:

Rs.20 million x PVIFA (10%, 3 years) = Rs.20 million x 2.487


= Rs.49.74million

If A is the annual deposit to be made in the sinking fund for the years 1 to 5,
then
A x FVIFA (10%, 5 years) = Rs.49.74 million
A x 6.105 = Rs.49.74 million
A = Rs.8,147,420

24.
Equated annual installment = 2,000,000 / PVIFA(12%,5)
= 2,000,000 / 3.605
= Rs.554,785

Loan Amortisation Schedule

Beginning Annual Principal Remaining


Year amount installment Interest repaid balance

1 2,000,000 554,785 240,000 314,785 1,685,215


2 1,685,215 554,785 202,226 352,559 1, 332,656
3 1,332,656 554,785 159.919 394,866 937,790
4 937,790 554,785 112,535 442,250 495,540
5 495,540 554,785 59,465 495320 220*
(*) rounding off error

7
Prasanna Chandra: Fundamentals of Financial Management, 6 th Edition
Copyright © 2014 by McGraw Hill Education (India) Private Limited

Chapter 9
VALUATION OF SECURITIES

1.
(i)
Value = 60 x PVIFA (8%, 10) + 1000 x PVIF (8%, 10)
= 60 x 6.710 + 1000 x 0. 463
= 402.60 + 463 = 865.60

(ii)
60 + (1000 – 965) /10
YTM = = 0.0649 % per semi annum or 12.98 p.a
0.4 x 1000 + 0.6 x 965

2.
D1
g = r -
P0

20
= 0.25 - = 17.86%
280

3.
D1
g = r -
P0

10
= 0.20 - = 17.85 %
465

4.
Approximate YTM

C + (M - P) /n
=
0.4 M + 0.6 P

120 + (1000 - 1050)/5


= = 10.68%

8
Prasanna Chandra: Fundamentals of Financial Management, 6 th Edition
Copyright © 2014 by McGraw Hill Education (India) Private Limited

0.4 x 1000 + 0.6 x 1050


5.

The approximate YTM is:

90 + (1000 – 1050) / 5
= 7.77%
0.6 x 1,050 + 0.4 x 1,000

6.
D1 8 (1.12)
P0 = = = Rs.149.33
r–g 0.18 – 0.12

7.
(i)
Value = 70 x PVIFA (10%, 3) + 1000 x PVIF (10% , 3)
= 70 x 2.487 + 1000 x 0.751
= 174 + 751 = 925

(ii)
70 + (1000 – 985) / 3
YTM = = 7.57%
0.4 x 1000 + 0.6 x 985

8.
(i)
9 + (100 – 108)/6
= 7.32%
0.6 x 108 + 0.4 x 100
(ii)
D0 (1 + g) 2.40 (1.10)
rE = +g= + 0.10
P0 60

= 14.4%

9.
Po = D1/ (r – g) = Do (1+g) / (r – g)
Do = Rs.2.00, g = -0.05, Po = Rs.10
So
10 = 2.00 (1- .05) / (r-(-.05)) = 1.90 / (r + .05)
r +0.05 =1.90/10 = 0.19
r = 0.19 – 0.05 = 0.14

9
Prasanna Chandra: Fundamentals of Financial Management, 6 th Edition
Copyright © 2014 by McGraw Hill Education (India) Private Limited

Chapter 11
TECHNIQUES OF CAPITAL BUDGETING

1.
(i)

Cash flow PVIF PV


–530,000 1.000 –530,000
150,000 0.870 130,500
180,000 0.756 136,080
240,000 0.658 157,920
250,000 0.572 143,000
37,500
(ii)

18% 19%
PVIF PV PVIF PV
150,000 0.847 127,050 0.840 126,000
180,000 0.718 129,240 0.706 127,080
240,000 0.609 146,160 0.593 142,320
250,000 0.516 129,000 0.499 124,750
531,450 520,150

531,450 – 530,000
18% + x 1%
531,450 – 520,150

= 18.13%

(iii)
PVB
BCR =
I

567,500
= = 1.071
530,000

10
Prasanna Chandra: Fundamentals of Financial Management, 6 th Edition
Copyright © 2014 by McGraw Hill Education (India) Private Limited

2.
(i)
100,000 200,000
NPV = - 500 000 + +
(1.10) (1.10)2

300,000 100,000
+ +
(1.10)3 (1.10)4

= - 500000 + 90909 + 165289 + 225394 + 68301


= 49893

(ii)

14 % 15 %
100,000 .877 87,700 .870 87,000
200,000 .769 153,800 .756 151,200
300,000 .675 202,500 .658 197,400
100,000 .529 59,200 .572 57,200

503,200 492,800

3200
14 % + = 14.31 %
10,400
(iii)
Depends on the COC
If the COC is 10 %

549893
= 1.0998
500000

3. (All amounts in Rupees thousands)


200 300 400
PVB = + +
(1.10) (1.10) (1.12) (1.10) (1.12) (1.14)

500
+
(1.10) (1.12) (1.14) (1.16)

11
Prasanna Chandra: Fundamentals of Financial Management, 6 th Edition
Copyright © 2014 by McGraw Hill Education (India) Private Limited

= 181.82 + 243.51 + 284.80 + 306.90


= 1017.03; NPV = 1017.03 - 1000 = 17.03
4.
Project M
Cost of capital =
15 % p.a

Year Cash flow PV of cash flow Cumulative PV


of
cash flow
1 85 73.91 73.91
2 120 90.74 164.65
3 180 118.35 283
4 100

Discounted pay back period (DPB) lies between 2 and 3 years. Interpolating
in this range we get an approximate DPB of 2.64 years.

Project N
Cost of capital =
15 % p.a

Year Cash flow PV of cash flow Cumulative PV


of
cash flow
1 100 86.96 86.96
2 110 83.18 170.14
3 120 78.90 249.04
4 90

Discounted pay back period (DPB) lies between 2 and 3 years. Interpolating
in this range we get an approximate DPB of 2.89 years.

5 Project N
Cost of capital =
15 % p.a

Year Cash flow PV of cash flow Cumulative PV


of
cash flow
1 100 86.96 86.96
2 110 83.18 170.14
3 120 78.90 249.04
4 90

12
Prasanna Chandra: Fundamentals of Financial Management, 6 th Edition
Copyright © 2014 by McGraw Hill Education (India) Private Limited

Discounted pay back period (DPB) lies between 2 and 3 years. Interpolating
in this range we get an approximate DPB of 2.89 years.

5.
The details for the two alternatives are shown below:

Gunning plow Coulter plow

1. Initial outlay Rs.2,500,000 Rs.1,500,000


2. Economic life 12 years 9 years
3. Annual operating and maintenance costs Rs.250,000 Rs.320,000
4. Present value of the stream of operating Rs.1,548,500 Rs.1,704,960
and maintenance costs at 12% discount rate
5. Salvage value Rs.800,000 Rs.500,000
6. Present value of salvage value Rs.205,600 Rs.180,500
7. Present value of total costs (1+4-6) Rs.3,842,900 Rs.3,024,460
8. Equivalent annual cost of 7 Rs.3,842,900 Rs.3,024,460
PVIFA (12%,12) PVIFA (12%,9)
= 3,842,900 = 3,024,460
6.194 5.328
= Rs.620,423 = Rs.567,654

The Coulter plow is the cheaper alternative

6.

(i) NPV of the project at a discount rate of 14%.

= - 1,000,000 + 100,000 + 200,000

(1.14) (1.14)2

+ 300,000 + 600,000 + 300,000

(1.14)3 (1.14)4 (1.14)5

= - 44837

(ii)
NPV of the project at time varying discount rates

= - 1,000,000

+ 100,000

13
Prasanna Chandra: Fundamentals of Financial Management, 6 th Edition
Copyright © 2014 by McGraw Hill Education (India) Private Limited

(1.12)

+ 200,000

(1.12) (1.13)

+ 300,000

(1.12) (1.13) (1.14)

+ 600,000

(1.12) (1.13) (1.14) (1.15)

+ 300,000

(1.12) (1.13) (1.14) (1.15) (1.16)

= - 1,000,000 + 89286 + 158028 + 207931 + 361620 + 155871


= - 27264

7.
Investment A

a) Payback period = 5 years


b) NPV = 40000 x PVIFA (12, 10) – 200 000
= 26000
c) IRR (r) can be obtained by solving the equation:
40000 x PVIFA (r, 10) = 200000
i.e., PVIFA (r, 10) = 5.000

From the PVIFA tables we find that


PVIFA (15,10) = 5.019
PVIFA (16,10) = 4.833

Linear interporation in this range yields


r= 15 + 1 x (0.019 / 0.186)
= 15.10%

d) BCR = Benefit Cost Ratio


= PVB / I
= 226,000 / 200,000 = 1.13

Investment B

a) Payback period = 9 years

14
Prasanna Chandra: Fundamentals of Financial Management, 6 th Edition
Copyright © 2014 by McGraw Hill Education (India) Private Limited

b) NP V = 40,000 x PVIFA (12, 5)


+ 30,000 x PVIFA (12, 2) x PVIF (12, 5)
+ 20,000 x PVIFA (12, 3) x PVIF (12, 7)
- 300,000

= (40,000 x 3.605) + (30,000 x 1.690 x 0.567)


+ (20,000 x 2.402 x 0.452) – 300,000
= - 105339

c) IRR (r ) can be obtained by solving the equation


40,000 x PVIFA (r, 5) + 30,000 x PVIFA (r, 2) x PVIF (r,5) +
20,000 x PVIFA (r, 3) x PVIF (r, 7) = 300,000

Through the process of trial and error we find that


r = 1.37%

d) BCR = PVB / I
= 194,661 / 300,000 = 0.65

Investment C

a) Payback period lies between 2 years and 3 years. Linear interpolation


in this Range provides an approximate payback period of 2.88 years.

b) NPV = 80.000 x PVIF (12, 1) + 60,000 x PVIF (12, 2)


+ 80,000 x PVIF (12, 3) + 60,000 x PVIF (12, 4)

+ 80,000 x PVIF (12, 5) + 60,000 x PVIF (12, 6)


+ 40,000 x PVIFA (12,4) x PVIF (12.6)
- 210,000
= 141,750

c) IRR (r) is obtained by solving the equation


80,000 x PVIF (r, 1) + 60,000 x PVIF (r, 2) + 80,000 x PVIF (r, 3)
+ 60,000 x PVIF (r, 4) + 80,000 x PVIF (r, 5) + 60,000 x PVIF (r, 6)
+ 40000 x PVIFA (r, 4) x PVIF (r,6) = 210000

Through the process of trial and error we get


r = 29.29%

d) BCR = PVB / I = 351,750 / 210,000 = 1.67

Investment D

15
Prasanna Chandra: Fundamentals of Financial Management, 6 th Edition
Copyright © 2014 by McGraw Hill Education (India) Private Limited

a) Payback period lies between 8 years and 9 years. A linear


interpolation in this range provides an approximate payback period of
8.5 years.

8 + (1 x 100,000 / 200,000)

b) NPV = 200,000 x PVIF (12, 1)


+ 20,000 x PVIF (12, 2) + 200,000 x PVIF (12, 9)
+ 50,000 x PVIF (12, 10)
- 320,000
= - 37,160

c) IRR (r ) can be obtained by solving the equation


200,000 x PVIF (r,1) + 20,000 x PVIF (r,2)
+ 200,000 x PVIF (r,9) + 50,000 x PVIF (r,10)
= 320000

Through the process of trial and error we get r = 8.45%

d) BCR = PVB / I = 282,840 / 320,000 = 0.88

Comparative Table

Investment A B C D

a) Payback period
(in years) 5 9 2.88 8.5

b) NPV @ 12% pa 26000 -105339 141750 -37160

c) IRR (%) 15.10 1.37 29.29 8.45

d) BCR 1.13 0.65 1.67 0.88

Among the four alternative investments, the investment to be chosen is ‘C’


because it has the lowest payback period:

 Highest NPV
 Highest IRR
 Highest BCR

8.

IRR (r) can be calculated by solving the following equations for the value of r.

60000 x PVIFA (r,7) = 300,000

16
Prasanna Chandra: Fundamentals of Financial Management, 6 th Edition
Copyright © 2014 by McGraw Hill Education (India) Private Limited

i.e., PVIFA (r,7) = 5.000

Through a process of trial and error it can be verified that r = 9.20% pa.

9.
Define NCF as the minimum constant annual net cashflow that justifies the purchase
of the given equipment. The value of NCF can be obtained from the equation

NCF x PVIFA (10,8) = 500000


NCF = 500000 / 5.335
= 93,721

10.
. a) (i) The IRR (r ) of project P can be obtained by solving the following
equation for `r’.

-1000 -1200 x PVIF (r,1) – 600 x PVIF (r,2) – 250 x PVIF (r,3)
+ 2000 x PVIF (r,4) + 4000 x PVIF (r,5) = 0

Through a process of trial and error we find that r = 20.13%


(ii) The IRR (r') of project Q can be obtained by solving the following
equation for r'

-1600 + 200 x PVIF (r',1) + 400 x PVIF (r',2) + 600 x PVIF (r',3)
+ 800 x PVIF (r',4) + 100 x PVIF (r',5) = 0

Through a process of trial and error we find that r' = 9.3 %.

11.

(a) Project A

NPV at a cost of capital of 12%


= - 100 + 25 x PVIFA (12, 6)
= Rs.2.78 million

IRR (r ) can be obtained by solving the following equation for r.


25 x PVIFA (r,6) = 100
i.e., r = 12 .98%

Project B

NPV at a cost of capital of 12%


= - 50 + 13 x PVIFA (12,6)
= Rs.3.44 million

17
Prasanna Chandra: Fundamentals of Financial Management, 6 th Edition
Copyright © 2014 by McGraw Hill Education (India) Private Limited

IRR (r') can be obtained by solving the equation


13 x PVIFA (r',6) = 50
i.e., r' = 14.40% [determined through a process of trial and error]

(b) Difference in capital outlays between projects A and B is Rs.50 million


Difference in net annual cash flow between projects A and B is Rs.12 million.
NPV of the differential project at 12%

= -50 + 12 x PVIFA (12,6)


= - Rs. 0.668 million

IRR (r'') of the differential project can be obtained from the equation
12 x PVIFA (r'', 6) = 50
i.e., r'' = 11.53%

12.
(i) Project M
The pay back period of the project lies between 2 and 3 years. Interpolating in
this range we get an approximate pay back period of 2.63 years/
Project N
The pay back period lies between 1 and 2 years. Interpolating in this range we
get an approximate pay back period of 1.55 years.

(ii) Project M
Cost of capital =
12% p.a

Year Cash flow Discounted cash flow Cumulative


discounted
Cash flow
1 11 9.82 9.82
2 19 15.15 24.97
3 32 22.78 47.75
4 37 23.51 71.26

Discounted pay back period (DPB) lies between 3 and 4 years. Interpolating
in this range we get an approximate DPB of 3.1 years.

Project N
Cost of capital =
12% per annum

Year Cash flow Discounted cash flow Cumulative


discounted
cash flow
1 38 33.93 33.93

18
Prasanna Chandra: Fundamentals of Financial Management, 6 th Edition
Copyright © 2014 by McGraw Hill Education (India) Private Limited

2 22 17.54 51.47

DPB lies between 1 and 2 years. Interpolating in this range we get an


approximate DPB of 1.92 years.

(iii) Project M
Cost of capital = 12% per annum
NPV = - 50 + 11 x PVIFA (12,1)
+ 19 x PVIF (12,2) + 32 x PVIF (12,3)
+ 37 x PVIF (12,4)
= Rs.21.26 million
Project N
Cost of capital = 12% per annum
NPV = Rs.20.63 million

Since the two projects are independent and the NPV of each project is (+) ve,
both the projects can be accepted. This assumes that there is no capital
constraint.

(iv) Project M
Cost of capital = 10% per annum
NPV = Rs.25.02 million
Project N
Cost of capital = 10% per annum
NPV = Rs.23.08 million

Since the two projects are mutually exclusive, we need to choose the project
with the higher NPV i.e., choose project M.

(v) Project M
Cost of capital = 15% per annum
NPV = 16.13 million
Project N
Cost of capital: 15% per annum
NPV = Rs.17.23 million

Again the two projects are mutually exclusive. So we choose the project with
the higher NPV, i.e., choose project N.

19
Prasanna Chandra: Fundamentals of Financial Management, 6 th Edition
Copyright © 2014 by McGraw Hill Education (India) Private Limited

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