Chapter 7
TIME VALUE OF MONEY
1. Value five years hence of a deposit of Rs.1,000 at various interest rates is as follows:
r = 8% FV5 = Rs.1469
r = 10% FV5 = Rs.1611
r = 12% FV5 = Rs.1762
r = 15% FV5 = Rs.2011
2. 30 years
3. In 12 years Rs.1000 grows to Rs.8000 or 8 times. This is 23
times the initial deposit. Hence
doubling takes place in 12 / 3 = 4 years.
According to the Rule of 69, the doubling period is:
0.35 + 69 / Interest rate
Equating this to 4 and solving for interest rate, we get
Interest rate = 18.9%.
4. Saving Rs.2000 a year for 5 years and Rs.3000 a year for 10 years thereafter is equivalent to
saving Rs.2000 a year for 15 years and Rs.1000 a year for the years 6 through 15.
Hence the savings will cumulate to:
2000 x FVIFA (10%, 15 years) + 1000 x FVIFA (10%, 10 years)
= 2000 x 31.772 + 1000 x 15.937 = Rs.79481.
5. Let A be the annual savings.
A x FVIFA (12%, 10 years) = 1,000,000
A x 17.549 = 1,000,000
So, A = 1,000,000 / 17.549 = Rs.56,983.
6. 1,000 x FVIFA (r, 6 years) = 10,000
FVIFA (r, 6 years) = 10,000 / 1000 = 10
1

From the tables we find that
FVIFA (20%, 6 years) = 9.930
FVIFA (24%, 6 years) = 10.980
Using linear interpolation in the interval, we get:
20% + (10.000 – 9.930)
r = x 4% = 20.3%
(10.980 – 9.930)
7. 1,000 x FVIF (r, 10 years) = 5,000
FVIF (r,10 years) = 5,000 / 1000 = 5
FVIF (16%, 10 years) = 4.411
FVIF (18%, 10 years) = 5.234
Using linear interpolation in the interval, we get:
(5.000 – 4.411) x 2%
r = 16% + = 17.4%
(5.234 – 4.411)
8. The present value of Rs.10,000 receivable after 8 years for various discount rates (r ) are:
r = 10% PV = 10,000 x PVIF(r = 10%, 8 years)
= 10,000 x 0.467 = Rs.4,670
r = 12% PV = 10,000 x PVIF (r = 12%, 8 years)
= 10,000 x 0.404 = Rs.4,040
r = 15% PV = 10,000 x PVIF (r = 15%, 8 years)
= 10,000 x 0.327 = Rs.3,270
9. Assuming that it is an ordinary annuity, the present value is:
2,000 x PVIFA (10%, 5years)
= 2,000 x 3.791 = Rs.7,582
10. The present value of an annual pension of Rs.10,000 for 15 years when r = 15% is:
10,000 x PVIFA (15%, 15 years)
= 10,000 x 5.847 = Rs.58,470
2

The alternative is to receive a lumpsum of Rs.50,000.
Obviously, Mr. Jingo will be better off with the annual pension amount of Rs.10,000.
11. The amount that can be withdrawn annually is:
100,000 100,000
A = ------------------ ------------ = ----------- = Rs.10,608
PVIFA (10%, 30 years) 9.427
12. The present value of the income stream is:
1,000 x PVIF (12%, 1 year) + 2,500 x PVIF (12%, 2 years)
+ 5,000 x PVIFA (12%, 8 years) x PVIF(12%, 2 years)
= 1,000 x 0.893 + 2,500 x 0.797 + 5,000 x 4.968 x 0.797 = Rs.22,683.
13. The present value of the income stream is:
2,000 x PVIFA (10%, 5 years) + 3000/0.10 x PVIF (10%, 5 years)
= 2,000 x 3.791 + 3000/0.10 x 0.621
= Rs.26,212
14. To earn an annual income of Rs.5,000 beginning from the end of 15 years from now, if the
deposit earns 10% per year a sum of
Rs.5,000 / 0.10 = Rs.50,000
is required at the end of 14 years. The amount that must be deposited to get this sum is:
Rs.50,000 / PVIF (10%, 14 years) = Rs.50,000 / 3.797 = Rs.13,165
15. Rs.20,000 =- Rs.4,000 x PVIFA (r, 10 years)
PVIFA (r,10 years) = Rs.20,000 / Rs.4,000 = 5.00
From the tables we find that:
PVIFA (15%, 10 years) = 5.019
PVIFA (18%, 10 years) = 4.494
Using linear interpolation we get:
5.019 – 5.00
r = 15% + ---------------- x 3%
5.019 – 4.494
= 15.1%
16. PV (Stream A) = Rs.100 x PVIF (12%, 1 year) + Rs.200 x
PVIF (12%, 2 years) + Rs.300 x PVIF(12%, 3 years) + Rs.400 x
3

PVIF (12%, 4 years) + Rs.500 x PVIF (12%, 5 years) +
Rs.600 x PVIF (12%, 6 years) + Rs.700 x PVIF (12%, 7 years) +
Rs.800 x PVIF (12%, 8 years) + Rs.900 x PVIF (12%, 9 years) +
Rs.1,000 x PVIF (12%, 10 years)
= Rs.100 x 0.893 + Rs.200 x 0.797 + Rs.300 x 0.712
+ Rs.400 x 0.636 + Rs.500 x 0.567 + Rs.600 x 0.507
+ Rs.700 x 0.452 + Rs.800 x 0.404 + Rs.900 x 0.361
+ Rs.1,000 x 0.322
= Rs.2590.9
Similarly,
PV (Stream B) = Rs.3,625.2
PV (Stream C) = Rs.2,851.1
17. FV5 = Rs.10,000 [1 + (0.16 / 4)]5x4
= Rs.10,000 (1.04)20
= Rs.10,000 x 2.191
= Rs.21,910
18. FV5 = Rs.5,000 [1+( 0.12/4)] 5x4
= Rs.5,000 (1.03)20
= Rs.5,000 x 1.806
= Rs.9,030
19 A B C
Stated rate (%) 12 24 24
Frequency of compounding 6 times 4 times 12 times
Effective rate (%) (1 + 0.12/6)6
- 1 (1+0.24/4)4
–1 (1 + 0.24/12)12
-1
= 12.6 = 26.2 = 26.8
Difference between the
effective rate and stated
rate (%) 0.6 2.2 2.8
20. Investment required at the end of 8th
year to yield an income of Rs.12,000 per year from the
end of 9th
year (beginning of 10th
year) for ever:
Rs.12,000 x PVIFA(12%, ∞ )
4

= Rs.12,000 / 0.12 = Rs.100,000
To have a sum of Rs.100,000 at the end of 8th
year , the amount to be deposited now is:
Rs.100,000 Rs.100,000
= = Rs.40,388
PVIF(12%, 8 years) 2.476
21. The interest rate implicit in the offer of Rs.20,000 after 10 years in lieu of Rs.5,000 now is:
Rs.5,000 x FVIF (r,10 years) = Rs.20,000
Rs.20,000
FVIF (r,10 years) = = 4.000
Rs.5,000
FVIF (15%, 10 years) = 4.046
This means that the implied interest rate is nearly 15%.
I would choose Rs.20,000 for 10 years from now because I find a return of 15% quite
acceptable.
22. FV10 = Rs.10,000 [1 + (0.10 / 2)]10x2
= Rs.10,000 (1.05)20
= Rs.10,000 x 2.653
= Rs.26,530
If the inflation rate is 8% per year, the value of Rs.26,530 10 years from now, in terms of
the current rupees is:
Rs.26,530 x PVIF (8%,10 years)
= Rs.26,530 x 0.463 = Rs.12,283
23. A constant deposit at the beginning of each year represents an annuity due.
PVIFA of an annuity due is equal to : PVIFA of an ordinary annuity x (1 + r)
To provide a sum of Rs.50,000 at the end of 10 years the annual deposit should
be
Rs.50,000
A = FVIFA(12%, 10 years) x (1.12)
Rs.50,000
= = Rs.2544
17.549 x 1.12
5

24. The discounted value of Rs.20,000 receivable at the beginning of each year from 2005 to
2009, evaluated as at the beginning of 2004 (or end of 2003) is:
Rs.20,000 x PVIFA (12%, 5 years)
= Rs.20,000 x 3.605 = Rs.72,100.
The discounted value of Rs.72,100 evaluated at the end of 2000 is
Rs.72,100 x PVIF (12%, 3 years)
= Rs.72,100 x 0.712 = Rs.51,335
If A is the amount deposited at the end of each year from 1995 to 2000 then
A x FVIFA (12%, 6 years) = Rs.51,335
A x 8.115 = Rs.51,335
A = Rs.51,335 / 8.115 = Rs.6326
25. The discounted value of the annuity of Rs.2000 receivable for 30 years, evaluated as at the
end of 9th
year is:
Rs.2,000 x PVIFA (10%, 30 years) = Rs.2,000 x 9.427 = Rs.18,854
The present value of Rs.18,854 is:
Rs.18,854 x PVIF (10%, 9 years)
= Rs.18,854 x 0.424
= Rs.7,994
26. 30 per cent of the pension amount is
0.30 x Rs.600 = Rs.180
Assuming that the monthly interest rate corresponding to an annual interest rate of 12% is
1%, the discounted value of an annuity of Rs.180 receivable at the end of each month for 180
months (15 years) is:
Rs.180 x PVIFA (1%, 180)
(1.01)180
- 1
Rs.180 x ---------------- = Rs.14,998
.01 (1.01)180
If Mr. Ramesh borrows Rs.P today on which the monthly interest rate is 1%
P x (1.01)60
= Rs.14,998
P x 1.817 = Rs.14,998
Rs.14,998
P = ------------ = Rs.8254
1.817
27. Rs.300 x PVIFA(r, 24 months) = Rs.6,000
PVIFA (4%,24) = Rs.6000 / Rs.300 = 20
From the tables we find that:
PVIFA(1%,24) = 21.244
6

PVIFA (2%, 24) = 18.914
Using a linear interpolation
21.244 – 20.000
r = 1% + ---------------------- x 1%
21.244 – 18,914
= 1.53%
Thus, the bank charges an interest rate of 1.53% per month.
The corresponding effective rate of interest per annum is
[ (1.0153)12
– 1 ] x 100 = 20%
28. The discounted value of the debentures to be redeemed between 8 to 10 years evaluated at
the end of the 5th
year is:
Rs.10 million x PVIF (8%, 3 years)
+ Rs.10 million x PVIF (8%, 4 years)
+ Rs.10 million x PVIF (8%, 5 years)
= Rs.10 million (0.794 + 0.735 + 0.681)
= Rs.2.21 million
If A is the annual deposit to be made in the sinking fund for the years 1 to 5,
then
A x FVIFA (8%, 5 years) = Rs.2.21 million
A x 5.867 = Rs.2.21 million
A = 5.867 = Rs.2.21 million
A = Rs.2.21 million / 5.867 = Rs.0.377 million
29. Let `n’ be the number of years for which a sum of Rs.20,000 can be withdrawn annually.
Rs.20,000 x PVIFA (10%, n) = Rs.100,000
PVIFA (15%, n) = Rs.100,000 / Rs.20,000 = 5.000
PVIFA (10%, 7 years) = 4.868
PVIFA (10%, 8 years) = 5.335
Thus n is between 7 and 8. Using a linear interpolation we get
5.000 – 4.868
n = 7 + ----------------- x 1 = 7.3 years
5.335 – 4.868
7

30. Equated annual installment = 500000 / PVIFA(14%,4)
= 500000 / 2.914
= Rs.171,585
Loan Amortisation Schedule
Beginning Annual Principal Remaining
Year amount installment Interest repaid balance
------ ------------- --------------- ----------- ------------- -------------
1 500000 171585 70000 101585 398415
2 398415 171585 55778 115807 282608
3 282608 171585 39565 132020 150588
4 150588 171585 21082 150503 85*
(*) rounding off error
31. Define n as the maturity period of the loan. The value of n can be obtained from the
equation.
200,000 x PVIFA(13%, n) = 1,500,000
PVIFA (13%, n) = 7.500
From the tables or otherwise it can be verified that PVIFA(13,30) = 7.500
Hence the maturity period of the loan is 30 years.
32. Expected value of iron ore mined during year 1 = Rs.300 million
Expected present value of the iron ore that can be mined over the next 15 years assuming a
price escalation of 6% per annum in the price per tonne of iron
1 – (1 + g)n
/ (1 + i)n
= Rs.300 million x ------------------------
i - g
= Rs.300 million x 1 – (1.06)15
/ (1.16)15
0.16 – 0.06
= Rs.300 million x (0.74135 / 0.10)
= Rs.2224 million
8

MINICASE
Solution:
1. How much money would Ramesh need 15 years from now?
500,000 x PVIFA (10%, 15years)
+ 1,000,000 x PVIF (10%, 15years)
= 500,000 x 7.606 + 1,000,000 x 0.239
= 3,803,000 x 239,000
= Rs.4,042,000
2. How much money should Ramesh save each year for the next 15 years to be able to meet his
investment objective?
Ramesh’s current capital of Rs.600,000 will grow to :
600,000 (1.10)15
= 600,000 x 4.177 = Rs 2,506,200
This means that his savings in the next 15 years must grow to :
4,042,000 – 2,506,200 = Rs 1,535,800
So, the annual savings must be :
1,535,800 1,535,800
= = Rs.48,338
FVIFA (10%, 15 years) 31.772
3. How much money would Ramesh need when he reaches the age of 60 to meet his donation
objective?
200,000 x PVIFA (10% , 3yrs) x PVIF (10%, 11yrs)
= 200,000 x 2.487 x 0.317 = 157,676
4. What is the present value of Ramesh’s life time earnings?
400,000 400,000(1.12) 400,000(1.12)14
46
1 2 15
9

1.12 15
1 –
1.08
= 400,000
0.08 – 0.12
= Rs.7,254,962
10

Chapter 8
VALUATION OF BONDS AND STOCKS
1. 5 11 100
P = ∑ +
t=1 (1.15) (1.15)5
= Rs.11 x PVIFA(15%, 5 years) + Rs.100 x PVIF (15%, 5 years)
= Rs.11 x 3.352 + Rs.100 x 0.497
= Rs.86.7
2.(i) When the discount rate is 14%
7 12 100
P = ∑ +
t=1 (1.14) t
(1.14)7
= Rs.12 x PVIFA (14%, 7 years) + Rs.100 x PVIF (14%, 7 years)
= Rs.12 x 4.288 + Rs.100 x 0.4
= Rs.91.46
(ii) When the discount rate is 12%
7 12 100
P = ∑ + = Rs.100
t=1 (1.12) t
(1.12)7
Note that when the discount rate and the coupon rate are the same the value is equal to
par value.
3. The yield to maturity is the value of r that satisfies the following equality.
7 120 1,000
Rs.750 = ∑ + = Rs.100
t=1 (1+r) t
(1+r)7
Try r = 18%. The right hand side (RHS) of the above equation is:
Rs.120 x PVIFA (18%, 7 years) + Rs.1,000 x PVIF (18%, 7 years)
= Rs.120 x 3.812 + Rs.1,000 x 0.314
= Rs.771.44
Try r = 20%. The right hand side (RHS) of the above equation is:
Rs.120 x PVIFA (20%, 7 years) + Rs.1,000 x PVIF (20%, 7 years)
= Rs.120 x 3.605 + Rs.1,000 x 0.279
= Rs.711.60
11

Thus the value of r at which the RHS becomes equal to Rs.750 lies between 18% and 20%.
Using linear interpolation in this range, we get
771.44 – 750.00
Yield to maturity = 18% + 771.44 – 711.60 x 2%
= 18.7%
4.
10 14 100
80 = ∑ +
t=1 (1+r) t
(1+r)10
Try r = 18%. The RHS of the above equation is
Rs.14 x PVIFA (18%, 10 years) + Rs.100 x PVIF (18%, 10 years)
= Rs.14 x 4.494 + Rs.100 x 0.191 = Rs.82
Try r = 20%. The RHS of the above equation is
Rs.14 x PVIFA(20%, 10 years) + Rs.100 x PVIF (20%, 10 years)
= Rs.14 x 4.193 + Rs.100 x 0.162
= Rs.74.9
Using interpolation in the range 18% and 20% we get:
82 - 80
Yield to maturity = 18% + ----------- x 2%
82 – 74.9
= 18.56%
5.
12 6 100
P = ∑ +
t=1 (1.08) t
(1.08)12
= Rs.6 x PVIFA (8%, 12 years) + Rs.100 x PVIF (8%, 12 years)
= Rs.6 x 7.536 + Rs.100 x 0.397
= Rs.84.92
6. The post-tax interest and maturity value are calculated below:
12

Bond A Bond B
* Post-tax interest (C ) 12(1 – 0.3) 10 (1 – 0.3)
=Rs.8.4 =Rs.7
* Post-tax maturity value (M) 100 - 100 -
[ (100-70)x 0.1] [ (100 – 60)x 0.1]
=Rs.97 =Rs.96
The post-tax YTM, using the approximate YTM formula is calculated below
8.4 + (97-70)/10
Bond A : Post-tax YTM = --------------------
0.6 x 70 + 0.4 x 97
= 13.73%
7 + (96 – 60)/6
Bond B : Post-tax YTM = ----------------------
0.6x 60 + 0.4 x 96
= 17. 47%
7.
14 6 100
P = ∑ +
t=1 (1.08) t
(1.08)14
= Rs.6 x PVIFA(8%, 14) + Rs.100 x PVIF (8%, 14)
= Rs.6 x 8.244 + Rs.100 x 0.341
= Rs.83.56
8. Do = Rs.2.00, g = 0.06, r = 0.12
Po = D1 / (r – g) = Do (1 + g) / (r – g)
= Rs.2.00 (1.06) / (0.12 - 0.06)
= Rs.35.33
Since the growth rate of 6% applies to dividends as well as market price, the market
price at the end of the 2nd
year will be:
P2 = Po x (1 + g)2
= Rs.35.33 (1.06)2
= Rs.39.70
13

9. Po = D1 / (r – g) = Do (1 + g) / (r – g)
= Rs.12.00 (1.10) / (0.15 – 0.10) = Rs.264
10. Po = D1 / (r – g)
Rs.32 = Rs.2 / 0.12 – g
g = 0.0575 or 5.75%
11. Po = D1/ (r – g) = Do(1+g) / (r – g)
Do = Rs.1.50, g = -0.04, Po = Rs.8
So
8 = 1.50 (1- .04) / (r-(-.04)) = 1.44 / (r + .04)
Hence r = 0.14 or 14 per cent
12. The market price per share of Commonwealth Corporation will be the sum of three
components:
A: Present value of the dividend stream for the first 4 years
B: Present value of the dividend stream for the next 4 years
C: Present value of the market price expected at the end of 8 years.
A = 1.50 (1.12) / (1.14) + 1.50 (1.12)2
/ (1.14)2
+ 1.50(1.12)3
/ (1.14)3
+
+ 1.50 (1.12)4
/ (1.14)4
= 1.68/(1.14) + 1.88 / (1.14)2
+ 2.11 / (1.14)3
+ 2.36 / (1.14)4
= Rs.5.74
B = 2.36(1.08) / (1.14)5
+ 2.36 (1.08)2
/ (1.14)6
+ 2.36 (1.08)3
/ (1.14)7
+
+ 2.36 (1.08)4
/ (1.14)8
= 2.55 / (1.14)5
+ 2.75 / (1.14)6
+ 2.97 / (1.14)7
+ 3.21 / (1.14)8
= Rs.4.89
C = P8 / (1.14)8
P8 = D9 / (r – g) = 3.21 (1.05)/ (0.14 – 0.05) = Rs.37.45
So
C = Rs.37.45 / (1.14)8
= Rs.13.14
Thus,
Po = A + B + C = 5.74 + 4.89 + 13.14
14

= Rs.23.77
13. The intrinsic value of the equity share will be the sum of three components:
A: Present value of the dividend stream for the first 5 years when the
growth rate expected is 15%.
B: Present value of the dividend stream for the next 5 years when the
growth rate is expected to be 10%.
C: Present value of the market price expected at the end of 10 years.
2.00 (1.15) 2.00 (1.15)2
2.00 (1.15)3
2.00(1.15)4
2.00 (1.15)5
A = ------------- + ------------- +-------------- + ------------- + -------------
(1.12) (1.12)2
(1.1.2)3
(1.1.2)4
(1.12)5
= 2.30 / (1.12) + 2.65 / (1.12)2
+ 3.04 / (1.12)3
+ 3.50 / (1.12)4
+ 4.02/(1.12)5
= Rs.10.84
4.02(1.10) 4.02 (1.10)2
4.02(1.10)3
4.02(1.10)4
4.02 (1.10)5
B = ------------ + ---------------- + ------------- + --------------- + ---------------
(1.12)6
(1.12)7
(1.12)8
(1..12)9
(1.12)10
4.42 4.86 5.35 5.89 6.48
= --------- + -------------- + --------------- + ------------- + -------------
(1.12)6
(1.12)7
(1.12)8
(1.1.2)9
(1.12)10
= Rs.10.81
D11 1 6.48 (1.05)
C = -------- x --------------- = ------------------- x 1/(1.12)10
r – g (1 +r)10
0.12 – 0.05
= Rs.97.20
The intrinsic value of the share = A + B + C
= 10.84 + 10.81 + 97.20 = Rs.118.85
14. Terminal value of the interest proceeds
= 140 x FVIFA (16%,4)
= 140 x 5.066
= 709.24
Redemption value = 1,000
15

Terminal value of the proceeds from the bond = 1709.24
Define r as the yield to maturity. The value of r can be obtained from the equation
900 (1 + r)4
= 1709.24
r = 0.1739 or 17.39%
15. Intrinsic value of the equity share (using the 2-stage growth model)
(1.18)6
2.36 x 1 - ----------- 2.36 x (1.18)5
x (1.12)
(1.16)6
= --------------------------------- + -----------------------------------
0.16 – 0.18 (0.16 – 0.12) x (1.16)6
- 0.10801
= 2.36 x ----------- + 62.05
- 0.02
= Rs.74.80
16. Intrinsic value of the equity share (using the H model)
4.00 (1.20) 4.00 x 4 x (0.10)
= -------------- + ---------------------
0.18 – 0.10 0.18 – 0.10
= 60 + 20
= Rs.80
16

Chapter 9
RISK AND RETURN
1 (a) Expected price per share a year hence will be:
= 0.4 x Rs.10 + 0.4 x Rs.11 + 0.2 x Rs.12 = Rs.10.80
(b) Probability distribution of the rate of return is
Rate of return (Ri) 10% 20% 30%
Probability (pi) 0.4 0.4 0.2
Note that the rate of return is defined as:
Dividend + Terminal price
-------------------------------- - 1
Initial price
(c ) The standard deviation of rate of return is : σ = ∑pi (Ri – R)2
The σ of the rate of return on MVM’s stock is calculated below:
---------------------------------------------------------------------------------------------------
Ri pi pI ri (Ri-R) (Ri- R)2
pi (Ri-R)2
---------------------------------------------------------------------------------------------------
10 0.4 4 -8 64 25.6
20 0.4 8 2 4 1.6
30 0.2 6 12 144 28.8
---------------------------------------------------------------------------------------------------
R = ∑ pi Ri ∑ pi (Ri-R)2
= 56
σ = √56 = 7.48%
2 (a) For Rs.1,000, 20 shares of Alpha’s stock can be acquired. The probability distribution of the
return on 20 shares is
Economic Condition Return (Rs) Probability
High Growth 20 x 55 = 1,100 0.3
Low Growth 20 x 50 = 1,000 0.3
Stagnation 20 x 60 = 1,200 0.2
Recession 20 x 70 = 1,400 0.2
Expected return = (1,100 x 0.3) + (1,000 x 0.3) + (1,200 x 0.2) + (1,400 x 0.2)
17

= 330 + 300 + 240 + 280
= Rs.1,150
Standard deviation of the return = [(1,100 – 1,150)2
x 0.3 + (1,000 – 1,150)2
x
0.3 + (1,200 – 1,150)2
x 0.2 + (1,400 – 1,150)2
x 0.2]1/2
= Rs.143.18
(b) For Rs.1,000, 20 shares of Beta’s stock can be acquired. The probability distribution of the
return on 20 shares is:
Economic condition Return (Rs) Probability
High growth 20 x 75 = 1,500 0.3
Low growth 20 x 65 = 1,300 0.3
Stagnation 20 x 50 = 1,000 0.2
Recession 20 x 40 = 800 0.2
Expected return = (1,500 x 0.3) + (1,300 x 0.3) + (1,000 x 0.2) + (800 x 0.2)
= Rs.1,200
Standard deviation of the return = [(1,500 – 1,200)2
x .3 + (1,300 – 1,200)2
x .3
+ (1,000 – 1,200)2
x .2 + (800 – 1,200)2
x .2]1/2
= Rs.264.58
(c ) For Rs.500, 10 shares of Alpha’s stock can be acquired; likewise for Rs.500, 10
shares of Beta’s stock can be acquired. The probability distribution of this option is:
Return (Rs) Probability
(10 x 55) + (10 x 75) = 1,300 0.3
(10 x 50) + (10 x 65) = 1,150 0.3
(10 x 60) + (10 x 50) = 1,100 0.2
(10 x 70) + (10 x 40) = 1,100 0.2
Expected return = (1,300 x 0.3) + (1,150 x 0.3) + (1,100 x 0.2) +
(1,100 x 0.2)
= Rs.1,175
Standard deviation = [(1,300 –1,175)2
x 0.3 + (1,150 – 1,175)2
x 0.3 +
(1,100 – 1,175)2
x 0.2 + (1,100 – 1,175)2
x 0.2 ]1/2
= Rs.84.41
d. For Rs.700, 14 shares of Alpha’s stock can be acquired; likewise for Rs.300, 6
shares of Beta’s stock can be acquired. The probability distribution of this
option is:
18

Return (Rs) Probability
(14 x 55) + (6 x 75) = 1,220 0.3
(14 x 50) + (6 x 65) = 1,090 0.3
(14 x 60) + (6 x 50) = 1,140 0.2
(14 x 70) + (6 x 40) = 1,220 0.2
Expected return = (1,220 x 0.3) + (1,090 x 0.3) + (1,140 x 0.2) + (1,220 x 0.2)
= Rs.1,165
Standard deviation = [(1,220 – 1,165)2
x 0.3 + (1,090 – 1,165)2
x 0.3 +
(1,140 – 1,165)2
x 0.2 + (1,220 – 1,165)2
x 0.2]1/2
= Rs.57.66
The expected return to standard deviation of various options are as follows :
Option
Expected return
(Rs)
Standard deviation
(Rs)
Expected / Standard
return deviation
a 1,150 143 8.04
b 1,200 265 4.53
c 1,175 84 13.99
d 1,165 58 20.09
Option `d’ is the most preferred option because it has the highest return to risk ratio.
3. Expected rates of returns on equity stock A, B, C and D can be computed as follows:
A: 0.10 + 0.12 + (-0.08) + 0.15 + (-0.02) + 0.20 = 0.0783 = 7.83%
6
B: 0.08 + 0.04 + 0.15 +.12 + 0.10 + 0.06 = 0.0917 = 9.17%
6
C: 0.07 + 0.08 + 0.12 + 0.09 + 0.06 + 0.12 = 0.0900 = 9.00%
6
D: 0.09 + 0.09 + 0.11 + 0.04 + 0.08 + 0.16 = 0.095 = 9.50%
6
(a) Return on portfolio consisting of stock A = 7.83%
(b) Return on portfolio consisting of stock A and B in equal
proportions = 0.5 (0.0783) + 0.5 (0.0917)
= 0.085 = 8.5%
19

(c ) Return on portfolio consisting of stocks A, B and C in equal
proportions = 1/3(0.0783 ) + 1/3(0.0917) + 1/3 (0.090)
= 0.0867 = 8.67%
(d) Return on portfolio consisting of stocks A, B, C and D in equal
proportions = 0.25(0.0783) + 0.25(0.0917) + 0.25(0.0900) +
0.25(0.095)
= 0.08875 = 8.88%
4. Define RA and RM as the returns on the equity stock of Auto Electricals Limited a and Market
portfolio respectively. The calculations relevant for calculating the beta of the stock are
shown below:
Year RA RM RA-RA RM-RM (RA-RA) (RM-RM) RA-RA/RM-RM
1 15 12 -0.09 -3.18 0.01 10.11 0.29
2 -6 1 -21.09 -14.18 444.79 201.07 299.06
3 18 14 2.91 -1.18 8.47 1.39 -3.43
4 30 24 14.91 8.82 222.31 77.79 131.51
5 12 16 0-3.09 0.82 9.55 0.67 -2.53
6 25 30 9.91 14.82 98.21 219.63 146.87
7 2 -3 -13.09 -18.18 171.35 330.51 237.98
8 20 24 4.91 8.82 24.11 77.79 43.31
9 18 15 2.91 -0.18 8.47 0.03 -0.52
10 24 22 8.91 6.82 79.39 46.51 60.77
11 8. 12 -7.09 -3.18 50.27 10.11 22.55
RA = 15.09 RM = 15.18
∑ (RA – RA)2
= 1116.93 ∑ (RM – RM)2
= 975.61 ∑ (RA – RA) (RM – RM) = 935.86
Beta of the equity stock of Auto Electricals
∑ (RA – RA) (RM – RM)
∑ (RM – RM)2
= 935.86 = 0.96
975.61
Alpha = RA – βA RM
= 15.09 – (0.96 x 15.18)= 0.52
20

Equation of the characteristic line is
RA = 0.52 + 0.96 RM
5. The required rate of return on stock A is:
RA = RF + βA (RM – RF)
= 0.10 + 1.5 (0.15 – 0.10)
= 0.175
Intrinsic value of share = D1 / (r- g) = Do (1+g) / ( r – g)
Given Do = Rs.2.00, g = 0.08, r = 0.175
2.00 (1.08)
Intrinsic value per share of stock A =
0.175 – 0.08
= Rs.22.74
6. The SML equation is RA = RF + βA (RM – RF)
Given RA = 15%. RF = 8%, RM = 12%, we have
0.15 = .08 + βA (0.12 – 0.08)
0.07
i.e.βA = = 1.75
0.04
Beta of stock A = 1.75
7. The SML equation is: RX = RF + βX (RM – RF)
We are given 0.15 = 0.09 + 1.5 (RM – 0.09) i.e., 1.5 RM = 0.195
or RM = 0.13%
Therefore return on market portfolio = 13%
8. RM = 12% βX = 2.0 RX =18% g = 5% Po = Rs.30
Po = D1 / (r - g)
Rs.30 = D1 / (0.18 - .05)
21

So D1 = Rs.39 and Do = D1 / (1+g) = 3.9 /(1.05) = Rs.3.71
Rx = Rf + βx (RM – Rf)
0.18 = Rf + 2.0 (0.12 – Rf)
So Rf = 0.06 or 6%.
Original Revised
Rf 6% 8%
RM – Rf 6% 4%
g 5% 4%
βx 2.0 1.8
Revised Rx = 8% + 1.8 (4%) = 15.2%
Price per share of stock X, given the above changes is
3.71 (1.04)
= Rs.34.45
0.152 – 0.04
Chapter 10
OPTIONS AND THEIR VALUATION
22

1. S = 100 u = 1.5 d = 0.8
E = 105 r = 0.12 R = 1.12
The values of ∆ (hedge ratio) and B (amount borrowed) can be obtained as follows:
Cu – Cd
∆ =
(u – d) S
Cu = Max (150 – 105, 0) = 45
Cd = Max (80 – 105, 0) = 0
45 – 0 45 9
∆ = = = = 0.6429
0.7 x 100 70 14
u.Cd – d.Cu
B =
(u-d) R
(1.5 x 0) – (0.8 x 45)
=
0.7 x 1.12
-36
= = - 45.92
0.784
C = ∆ S + B
= 0.6429 x 100 – 45.92
= Rs.18.37
Value of the call option = Rs.18.37
2. S = 40 u = ? d = 0.8
R = 1.10 E = 45 C = 8
We will assume that the current market price of the call is equal to the pair value of the call
as per the Binomial model.
Given the above data
23

Cd = Max (32 – 45, 0) = 0
∆ Cu – Cd R
= x
B u Cd – d Cu S
∆ Cu – 0 1.10
= x
B -0.8Cu 40
= (-) 0.034375
∆ = - 0.34375 B (1)
C = ∆ S + B
8 = ∆ x 40 + B (2)
Substituting (1) in (2) we get
8 = (-0.034365 x 40) B + B
8 = -0.375 B
or B = - 21.33
∆ = - 0.034375 (-21.33) = 0.7332
The portfolio consists of 0.7332 of a share plus a borrowing of Rs.21.33 (entailing a
repayment of Rs.21.33 (1.10) = Rs.23.46 after one year). It follows that when u occurs either u x 40
x 0.7332 – 23.46 = u x 40 – 45
-10.672 u = -21.54
u = 2.02
or
u x 40 x 0.7332 – 23.46 = 0
u = 0.8
Since u > d, it follows that u = 2.02.
Put differently the stock price is expected to rise by 1.02 x 100 = 102%.
3. Using the standard notations of the Black-Scholes model we get the following results:
ln (S/E) + rt + σ2
t/2
d1 =
24

σ √ t
= ln (120 / 110) + 0.14 + 0.42
/2
0.4
= 0.08701 + 0.14 + 0.08
0.4
= 0.7675
d2 = d1 - σ √ t
= 0.7675 – 0.4
= 0.3675
N(d1) = N (0.7675) ~ N (0.77) = 0.80785
N (d2) = N (0.3675) ~ N (0.37) = 0.64431
C = So N(d1) – E. e-rt
. N(d2)
= 120 x 0.80785 – 110 x e-0.14
x 0.64431
= (120 x 0.80785) – (110 x 0.86936 x 0.64431)
= 35.33
Value of the call as per the Black and Scholes model is Rs.35.33.
4. σ √t = 0.2 x √ 1 = 0.2
Ratio of the stock price to the present value of the exercise price
80
= -------------------------
82 x PVIF (15.03,1)
80
= ----------------------
82 x 0.8693
= 1.122
From table A6 we find the percentage relationship between the value of the call option and
stock price to be 14.1 per cent. Hence the value of the call option is
0.141 x 80 = Rs.11,28.
5. Value of put option
= Value of the call option
+ Present value of the exercise price
25

- Stock price ……… (A)
The value of the call option gives an exercise price of Rs.85 can be obtained as follows:
σ √t = 0.2 √ 1 = 0.2
Ratio of the stock price to the present value of the exercise price
80
= ---------------------
85 x PVIF (15.03,1)
= 80 / 73.89 = 1.083
From Table A.6, we find the percentage relationship between the value of the call option and
the stock price to be 11.9%
Hence the value of the call option = 0.119 x 80 = Rs.9.52
Plugging in this value and the other relevant values in (A), we get
Value of put option = 9.52 + 85 x (1.1503)-1
– 80
= Rs.3.41
6. So = Vo N(d1) – B1 e –rt
N (d2)
= 6000 N (d1) – 5000 e – 0.1
N(d2)
ln (6000 / 5000) + (0.1 x 1) + (0.18/2)
d1 = ----------------------------------------------
√ 0.18 x √ 1
ln (1.2) + 0.19
=
0.4243
= 0.8775 = 0.88
N(d1) = N (0.88) = 0.81057
d2 = d1 - t
= 0.8775 - 0.18
26

= 0.4532 = 0.45
N (d2) = N (0.45) = 0.67364
So = 6000 x 0.81057 – (5000 x 0.9048 x 0.67364)
= 1816
B0 = V0 – S0
= 60000 – 1816
= 4184
Chapter 11
TECHNIQUES OF CAPITAL BUDGETING
1.(a) 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
27

----------- ---------- ----------
(1.14)3
(1.14)4
(1.14)5
= - 44837
(b) NPV of the project at time varying discount rates
= - 1,000,000
+ 100,000
(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
2. 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
28

PVIFA (15,10) = 5.019
PVIFA (16,10) = 4.883
Linear interporation in this range yields
r = 15 + 1 x (0.019 / 0.136)
= 15.14%
d) BCR = Benefit Cost Ratio
= PVB / I
= 226,000 / 200,000 = 1.13
Investment B
a) Payback period = 9 years
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)
29

- 210,000
= 111,371
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 = 321,371 / 210,000 = 1.53
Investment D
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) + 200,000 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 111371 -37160
c) IRR (%) 15.14 1.37 29.29 8.45
30

d) BCR 1.13 0.65 1.53 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
3. IRR (r) can be calculated by solving the following equations for the value of r.
60000 x PVIFA (r,7) = 300,000
i.e., PVIFA (r,7) = 5.000
Through a process of trial and error it can be verified that r = 9.20% pa.
4. The IRR (r) for the given cashflow stream can be obtained by solving the following equation
for the value of r.
-3000 + 9000 / (1+r) – 3000 / (1+r) = 0
Simplifying the above equation we get
r = 1.61, -0.61; (or) 161%, (-)61%
NOTE: Given two changes in the signs of cashflow, we get two values for the
IRR of the cashflow stream. In such cases, the IRR rule breaks down.
5. 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
= 93271
6. Define I as the initial investment that is justified in relation to a net annual cash
inflow of 25000 for 10 years at a discount rate of 12% per annum. The value
of I can be obtained from the following equation
25000 x PVIFA (12,10) = I
i.e., I = 141256
7. PV of benefits (PVB) = 25000 x PVIF (15,1)
+ 40000 x PVIF (15,2)
+ 50000 x PVIF (15,3)
31

+ 40000 x PVIF (15,4)
+ 30000 x PVIF (15,5)
= 122646 (A)
Investment = 100,000 (B)
Benefit cost ratio = 1.23 [= (A) / (B)]
8. The NPV’s of the three projects are as follows:
Project
P Q R
Discount rate
0% 400 500 600
5% 223 251 312
10% 69 40 70
15% - 66 - 142 - 135
25% - 291 - 435 - 461
30% - 386 - 555 - 591
9. NPV profiles for Projects P and Q for selected discount rates are as follows:
(a)
Project
P Q
Discount rate (%)
0 2950 500
5 1876 208
10 1075 - 28
15 471 - 222
20 11 - 382
b) (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'
32

-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' = 9.34%.
c) From (a) we find that at a cost of capital of 10%
NPV (P) = 1075
NPV (Q) = - 28
Given that NPV (P) . NPV (Q); and NPV (P) > 0, I would choose project P.
From (a) we find that at a cost of capital of 20%
NPV (P) = 11
NPV (Q) = - 382
Again NPV (P) > NPV (Q); and NPV (P) > 0. I would choose project P.
d) Project P
PV of investment-related costs
= 1000 x PVIF (12,0)
+ 1200 x PVIF (12,1) + 600 x PVIF (12,2)
+ 250 x PVIF (12,3)
= 2728
TV of cash inflows = 2000 x (1.12) + 4000 = 6240
The MIRR of the project P is given by the equation:
2728 = 6240 x PVIF (MIRR,5)
(1 + MIRR)5
= 2.2874
MIRR = 18%
(c) Project Q
PV of investment-related costs = 1600
TV of cash inflows @ 15% p.a. = 2772
The MIRR of project Q is given by the equation:
16000 (1 + MIRR)5
= 2772
33

MIRR = 11.62%
10
(a) Project A
NPV at a cost of capital of 12%
= - 100 + 25 x PVIFA (12,6)
= Rs.2.79 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.3.45 million
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.3.15 million
IRR (r'') of the differential project can be obtained from the equation
12 x PVIFA (r'', 6) = 50
i.e., r'' = 11.53%
11
(a) 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.
34

(b) Project M
Cost of capital = 12% p.a
PV of cash flows up to the end of year 2 = 24.97
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
DPB lies between 1 and 2 years. Interpolating in this range we get an approximate
DPB of 1.92 years.
(c ) Project M
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
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.
(d) Project M
Project N
Since the two projects are mutually exclusive, we need to choose the project with the higher
NPV i.e., choose project M.
NOTE: The MIRR can also be used as a criterion of merit for choosing between the two
projects because their initial outlays are equal.
(e) Project M
35

NPV = 16.13 million
Project N
Cost of capital: 15% per annum
Again the two projects are mutually exclusive. So we choose the project with the
higher NPV, i.e., choose project N.
(f) Project M
Terminal value of the cash inflows: 114.47
MIRR of the project is given by the equation
50 (1 + MIRR)4
= 114.47
i.e., MIRR = 23.01%
Project N
Terminal value of the cash inflows: 115.41
MIRR of the project is given by the equation
50 ( 1+ MIRR)4
= 115.41
i.e., MIRR = 23.26%
36

Chapter 12
ESTIMATION OF PROJECT CASH FLOWS
1.
(a) Project Cash Flows (Rs. in million)
Year 0 1 2 3 4 5 6 7
1. Plant & machinery (150)
2. Working capital (50)
3. Revenues 250 250 250 250 250 250 250
4. Costs (excluding de-
preciation & interest) 100 100 100 100 100 100 100
5. Depreciation 37.5 28.13 21.09 15.82 11.87 8.90 6.67
6. Profit before tax 112.5 121.87 128.91 134.18 138.13 141.1143.33
7. Tax 33.75 36.56 38.67 40.25 41.44 42.33 43.0
8. Profit after tax 78.75 85.31 90.24 93.93 96.69 98.77100.33
9. Net salvage value of
plant & machinery 48
10. Recovery of working 50
capital
11. Initial outlay (=1+2) (200)
12. Operating CF (= 8 + 5) 116.25 113.44 111.33 109.75 108.56 107.6 107.00
13. Terminal CF ( = 9 +10) 98
14. N C F (200) 116.25 113.44 111.33 109.75 108.56 107.67 205
(c) IRR (r) of the project can be obtained by solving the following equation for r
-200 + 116.25 x PVIF (r,1) + 113.44 x PVIF (r,2)
+ 111.33 x PVIF (r,3) + 109.75 x PVIF (r,4) + 108.56 x PVIF (r,5)
37

+107.67 x PVIF (r,6) + 205 x PVIF (r,7) = 0
Through a process of trial and error, we get r = 55.17%. The IRR of the project is 55.17%.
2. Post-tax Incremental Cash Flows (Rs. in million)
Year 0 1 2 3 4 5 6 7
1. Capital equipment (120)
2. Level of working capital 20 30 40 50 40 30 20
(ending)
3. Revenues 80 120 160 200 160 120 80
4. Raw material cost 24 36 48 60 48 36 24
5. Variable mfg cost. 8 12 16 20 16 12 8
6. Fixed operating & maint. 10 10 10 10 10 10 10
cost
7. Variable selling expenses 8 12 16 20 16 12 8
8. Incremental overheads 4 6 8 10 8 6 4
9. Loss of contribution 10 10 10 10 10 10 10
10.Bad debt loss 4
11. Depreciation 30 22.5 16.88 12.66 9.49 7.12 5.34
12. Profit before tax -14 11.5 35.12 57.34 42.51 26.88 6.66
13. Tax -4.2 3.45 10.54 17.20 12.75 8.06 2.00
14. Profit after tax -9.8 8.05 24.58 40.14 29.76 18.82 4.66
15. Net salvage value of
capital equipments 25
16. Recovery of working 16
capital
17. Initial investment (120)
18. Operating cash flow 20.2 30.55 41.46 52.80 39.25 25.94 14.00
(14 + 10+ 11)
19. ∆ Working capital 20 10 10 10 (10) (10) (10)
20. Terminal cash flow 41
21. Net cash flow (140) 10.20 20.55 31.46 62.80 49.25 35.94 55.00
(17+18-19+20)
(b) NPV of the net cash flow stream @ 15% per discount rate
= -140 + 10.20 x PVIF(15,1) + 20.55 x PVIF (15,2)
+ 31.46 x PVIF (15,3) + 62.80 x PVIF (15,4) + 49.25 x PVIF (15,5)
+ 35.94 x PVIF (15,6) + 55 x PVIF (15,7)
= Rs.1.70 million
38

3.
(a) A. Initial outlay (Time 0)
i. Cost of new machine Rs. 3,000,000
ii. Salvage value of old machine 900,000
iii Incremental working capital requirement 500,000
iv. Total net investment (=i – ii + iii) 2,600,000
B. Operating cash flow (years 1 through 5)
Year 1 2 3 4 5
i. Post-tax savings in
manufacturing costs 455,000 455,000 455,000 455,000 455,000
ii. Incremental
depreciation 550,000 412,500 309,375 232,031 174,023
iii. Tax shield on
incremental dep. 165,000 123,750 92,813 69,609 52,207
iv. Operating cash
flow ( i + iii) 620,000 578,750 547,813 524,609 507,207
C. Terminal cash flow (year 5)
i. Salvage value of new machine Rs. 1,500,000
ii. Salvage value of old machine 200,000
iii. Recovery of incremental working capital 500,000
iv. Terminal cash flow ( i – ii + iii) 1,800,000
D. Net cash flows associated with the replacement project (in Rs)
Year 0 1 2 3 4 5
NCF (2,600,000) 620000 578750 547813 524609 2307207
(b) NPV of the replacement project
= - 2600000 + 620000 x PVIF (14,1)
+ 578750 x PVIF (14,2)
+ 547813 x PVIF (14,3)
+ 524609 x PVIF (14,4)
+ 2307207 x PVIF (14,5)
= Rs.267849
39

4. Tax shield (savings) on depreciation (in Rs)
Depreciation Tax shield PV of tax shield
Year charge (DC) =0.4 x DC @ 15% p.a.
1 25000 10000 8696
2 18750 7500 5671
3 14063 5625 3699
4 10547 4219 2412
5 7910 3164 1573
----------
22051
----------
Present value of the tax savings on account of depreciation = Rs.22051
5. A. Initial outlay (at time 0)
i. Cost of new machine Rs. 400,000
ii. Salvage value of the old machine 90,000
iii. Net investment 310,000
B. Operating cash flow (years 1 through 5)
Year 1 2 3 4 5
i. Depreciation
of old machine 18000 14400 11520 9216 7373
ii. Depreciation
of new machine 100000 75000 56250 42188 31641
iii. Incremental
depreciation
( ii – i) 82000 60600 44730 32972 24268
iv. Tax savings on
incremental
depreciation
( 0.35 x (iii)) 28700 21210 15656 11540 8494
v. Operating cash
40

flow 28700 21210 15656 11540 8494
C. Terminal cash flow (year 5)
i. Salvage value of new machine Rs. 25000
ii. Salvage value of old machine 10000
iii. Incremental salvage value of new
machine = Terminal cash flow 15000
D. Net cash flows associated with the replacement proposal.
Year 0 1 2 3 4 5
NCF (310000) 28700 21210 15656 11540 23494
MINICASE
Solution:
a. Cash flows from the point of all investors (which is also called the explicit cost funds point of
view)
Rs.in million
Item 0 1 2 3 4 5
1. Fixed assets (15)
2. Net working
capital (8)
3. Revenues 30 30 30 30 30
4. Costs (other than
depreciation and
interest) 20 20 20 20 20
5. Loss of rental 1 1 1 1 1
6. Depreciation 3.750 2.813 2.109 1.582 1.187
7. Profit before tax 5.250 6.187 6.891 7.418 7.813
8. Tax 1.575 1.856 2.067 2.225 2.344
9. Profit after tax 3.675 4.331 4.824 5.193 5.469
10. Salvage value of
fixed assets 5.000
11. Net recovery of
working capital 8.000
12. Initial outlay (23)
13. Operating cash
41

inflow 7.425 7.144 6.933 6.775 6.656
14. Terminal cash
flow 13.000
15. Net cash flow (23) 7.425 7.144 6.933 6.775 19.656
b. Cash flows form the point of equity investors
Rs.in million
Item 0 1 2 3 4 5
1. Equity funds (10)
2. Revenues 30 30 30 30 30
3. Costs (other than
depreciation and
interest) 20 20 20 20 20
4. Loss of rental 1 1 1 1 1
5. Depreciation 3.75 2.813 2.109 1.582 1.187
6. Interest on working
capital advance 0.70 0.70 0.70 0.70 0.70
7. Interest on term
loans 1.20 1.125 0.825 0.525 0.225
8. Profit before tax 3.35 4.362 5.366 6.193 6.888
9. Tax 1.005 1.309 1.610 1.858 2.066
10. Profit after tax 2.345 3.053 3.756 4.335 4.822
11. Net salvage value
of fixed assets 5.000
12. Net salvage value
of current assets 10.000
13. Repayment of term
term loans 2.000 2.000 2.000 2.000
14. Repayment of bank
advance 5.000
15. Retirement of trade
creditors 2.000
16. Initial investment (10)
17. Operating cash
inflow 6.095 5.866 5.865 5.917 6.009
18. Liquidation and
retirement cash
flows (2.0) (2.0) (2.0) 6.00
19. Net cash flow (10) 6.095 3.866 3.865 3.917 12.009
42

Chapter 13
RISK ANALYSIS IN CAPITAL BUDGETING
1.
(a) NPV of the project = -250 + 50 x PVIFA (13,10)
= Rs.21.31 million
(b) NPVs under alternative scenarios:
(Rs. in million)
Pessimistic Expected Optimistic
Investment 300 250 200
Sales 150 200 275
Variable costs 97.5 120 154
Fixed costs 30 20 15
Depreciation 30 25 20
Pretax profit - 7.5 35 86
Tax @ 28.57% - 2.14 10 24.57
Profit after tax - 5.36 25 61.43
Net cash flow 24.64 50 81.43
Cost of capital 14% 13% 12%
NPV - 171.47 21.31 260.10
Assumptions: (1) The useful life is assumed to be 10 years under all three
scenarios. It is also assumed that the salvage value of the
investment after ten years is zero.
(2) The investment is assumed to be depreciated at 10% per annum; and it
is also assumed that this method and rate of depreciation are
acceptable to the IT (income tax) authorities.
(3) The tax rate has been calculated from the given table i.e. 10 / 35 x 100
= 28.57%.
(4) It is assumed that only loss on this project can be offset against the
taxable profit on other projects of the company; and thus the company
can claim a tax shield on the loss in the same year.
43

(c) Accounting break even point (under ‘expected’ scenario)
Fixed costs + depreciation = Rs. 45 million
Contribution margin ratio = 60 / 200 = 0.3
Break even level of sales = 45 / 0.3 = Rs.150 million
Financial break even point (under ‘xpected’ scenario)
i. Annual net cash flow = 0.7143 [ 0.3 x sales – 45 ] + 25
= 0.2143 sales – 7.14
ii. PV (net cash flows) = [0.2143 sales – 7.14 ] x PVIFA (13,10)
= 1.1628 sales – 38.74
iii. Initial investment = 200
iv. Financial break even level
of sales = 238.74 / 1.1628 = Rs.205.31 million
2.
(a) Sensitivity of NPV with respect to quantity manufactured and sold:
(in Rs)
Initial investment 30000 30000 30000
Sale revenue 24000 42000 54000
Variable costs 16000 28000 36000
Fixed costs 3000 3000 3000
Profit before tax 3000 9000 13000
Tax 1500 4500 6500
Profit after tax 1500 4500 6500
Net cash flow 3500 6500 8500
NPV at a cost of
capital of 10% p.a
and useful life of
5 years -16732 - 5360 2222
(b) Sensitivity of NPV with respect to variations in unit price.
Sale revenue 28000 42000 70000
44

Fixed costs 3000 3000 3000
Profit before tax -5000 9000 37000
Tax -2500 4500 18500
Profit after tax -2500 4500 18500
Net cash flow - 500 6500 20500
NPV - 31895 (-) 5360 47711
(c) Sensitivity of NPV with respect to variations in unit variable cost.
Sale revenue 42000 42000 42000
Fixed costs 3000 3000 3000
Profit before tax -11000 9000 16000
Tax -5500 4500 8000
Profit after tax -5500 4500 8000
Net cash flow -3500 6500 10000
NPV -43268 - 5360 7908
(d) Accounting break-even point
i. Fixed costs + depreciation = Rs.5000
ii. Contribution margin ratio = 10 / 30 = 0.3333
iii. Break-even level of sales = 5000 / 0.3333
= Rs.15000
Financial break-even point
i. Annual cash flow = 0.5 x (0.3333 Sales – 5000) = 2000
ii. PV of annual cash flow = (i) x PVIFA (10,5)
= 0.6318 sales – 1896
iii. Initial investment = 30000
iv. Break-even level of sales = 31896 / 0.6318 = Rs.50484
3. Define At as the random variable denoting net cash flow in year t.
A1 = 4 x 0.4 + 5 x 0.5 + 6 x 0.1
= 4.7
A2 = 5 x 0.4 + 6 x 0.4 + 7 x 0.2
45

= 5.8
A3 = 3 x 0.3 + 4 x 0.5 + 5 x 0.2
= 3.9
NPV = 4.7 / 1.1 +5.8 / (1.1)2
+ 3.9 / (1.1)3
– 10
= Rs.2.00 million
σ1
2
= 0.41
σ2
2
= 0.56
σ3
2
= 0.49
σ1
2
σ2
2
σ3
2
σ2
NPV = + +
(1.1)2
(1.1)4
(1.1)6
= 1.00
σ (NPV) = Rs.1.00 million
4. Expected NPV
4 At
= ∑ - 25,000
t=1 (1.08)t
= 12,000/(1.08) + 10,000 / (1.08)2
+ 9,000 / (1.08)3
+ 8,000 / (1.08)4
– 25,000
= [ 12,000 x .926 + 10,000 x .857 + 9,000 x .794 + 8,000 x .735]
- 25,000
= 7,708
Standard deviation of NPV
4 σt
∑
t=1 (1.08)t
= 5,000 / (1.08) + 6,000 / (1.08)2
+ 5,000 / (1,08)3
+ 6,000 / (1.08)4
= 5,000 x .926 + 6,000 x .857 + 5000 x .794 + 6,000 x .735
= 18,152
5. Expected NPV
46

4 At
= ∑ - 10,000 …. (1)
t=1 (1.06)t
A1 = 2,000 x 0.2 + 3,000 x 0.5 + 4,000 x 0.3
= 3,100
A2 = 3,000 x 0.4 + 4,000 x 0.3 + 5,000 x 0.3
= 3,900
A3 = 4,000 x 0.3 + 5,000 x 0.5 + 6,000 x 0.2
= 4,900
A4 = 2,000 x 0.2 + 3,000 x 0.4 + 4,000 x 0.4
= 3,200
Substituting these values in (1) we get
Expected NPV = NPV
= 3,100 / (1.06)+ 3,900 / 1.06)2
+ 4,900 / (1.06)3
+ 3,200 / (1,06)4
- 10,000 = Rs.3,044
The variance of NPV is given by the expression
4 σ2
t
σ2
(NPV) = ∑ …….. (2)
t=1 (1.06)2t
σ1
2
= [(2,000 – 3,100)2
x 0.2 + (3,000 – 3,100)2
x 0.5
+ (4,000 – 3,100)2
x 0.3]
= 490,000
σ2
2
= [(3,000 – 3,900)2
x 0.4 + (4,000 – 3,900)2
x 0.3
+ (5,000 – 3900)2
x 0.3]
= 690,000
σ3
2
= [(4,000 – 4,900)2
x 0.3 + (5,000 – 4,900)2
x 0.5
+ (6,000 – 4,900)2
x 0.2]
= 490,000
σ4
2
= [(2,000 – 3,200)2
x 0.2 + (3,000 – 3,200)2
x 0.4
+ (4,000 – 3200)2
x 0.4]
= 560,000
47

Substituting these values in (2) we get
490,000 / (1.06)2
+ 690,000 / (1.06)4
+ 490,000 / (1.06)6
+ 560,000 / (1.08)8
[ 490,000 x 0.890 + 690,000 x 0.792
+ 490,000 x 0.705 + 560,000 x 0.627 ]
= 1,679,150
σ NPV= 1,679,150 = Rs.1,296
NPV – NPV 0 - NPV
Prob (NPV < 0) = Prob. <
σ NPV σ NPV
0 – 3044
= Prob Z <
1296
= Prob (Z < -2.35)
The required probability is given by the shaded area in the following normal curve.
P (Z < - 2.35) = 0.5 – P (-2.35 < Z < 0)
= 0.5 – P (0 < Z < 2.35)
= 0.5 – 0.4906
= 0.0094
So the probability of NPV being negative is 0.0094
Prob (P1 > 1.2) Prob (PV / I > 1.2)
Prob (NPV / I > 0.2)
Prob. (NPV > 0.2 x 10,000)
Prob (NPV > 2,000)
Prob (NPV >2,000)= Prob (Z > 2,000- 3,044 / 1,296)
Prob (Z > - 0.81)
The required probability is given by the shaded area of the following normal
curve:
P(Z > - 0.81) = 0.5 + P(-0.81 < Z < 0)
= 0.5 + P(0 < Z < 0.81)
= 0.5 + 0.2910
= 0.7910
So the probability of P1 > 1.2 as 0.7910
48

6. Given values of variables other than Q, P and V, the net present value model of Bidhan
Corporation can be expressed as:
[Q(P – V) – 3,000 – 2,000] (0.5)+ 2,000 0
5
NPV ∑ + - 30,000
t =1 (1.1)t
(1.1)5
0.5 Q (P – V) – 500
5
∑ = ------------------------------------ - 30,000
t=1 (1.1)t
= [ 0.5Q (P – V) – 500] x PVIFA (10,5) – 30,000
= [0.5Q (P – V) – 500] x 3.791 – 30,000
= 1.8955Q (P – V) – 31,895.5
Exhibit 1 presents the correspondence between the values of exogenous variables and the two
digit random number. Exhibit 2 shows the results of the simulation.
Exhibit 1
Correspondence between values of exogenous variables and
two digit random numbers
QUANTITY PRICE VARIABLE COST
Valu
e
Pro
b
Cumulati
ve Prob.
Two digit
random
numbers Valu
e
Pro
b
Cumulati
ve Prob.
Two digit
random
numbers Value Pro
b
Cum
u-
lative
Prob.
Two digit
random
numbers
800 0.1
0
0.10 00 to 09 20 0.4
0
0.40 00 to 39 15 0.3
0
0.30 00 to 29
1,00
0
0.1
0
0.20 10 to 19 30 0.4
0
0.80 40 to 79 20 0.5
0
0.80 30 to 79
1,20
0
0.2
0
0.40 20 to 39 40 0.1
0
0.90 80 to 89 40 0.2
0
1.00 80 to 99
1,40
0
0.3
0
0.70 40 to 69 50 0.1
0
1.00 90 to 99
1,60
0
0.2
0
0.90 70 to 89
1,80
0
0.1
0
1.00 90 to 99
49

Exhibit 2
Simulation Results
QUANTITY (Q) PRICE (P) VARIABLE COST (V) NPV
Ru
n
Rando
m
Numb
er
Corres-
ponding
Value
Random
Number
Corres-
ponding
value
Rando
m
Numbe
r
Corres-
pondin
g value
1.8955 Q(P-V)-
31,895.5
1 03 800 38 20 17 15 -24,314
2 32 1,200 69 30 24 15 2,224
3 61 1,400 30 20 03 15 -18,627
4 48 1,400 60 30 83 40 -58,433
5 32 1,200 19 20 11 15 -20,523
6 31 1,200 88 40 30 20 13,597
7 22 1,200 78 30 41 20 -9,150
8 46 1,400 11 20 52 20 -31,896
9 57 1,400 20 20 15 15 -18,627
Ru
n
Rando
m
Numb
er
Corres-
ponding
Value
Random
Number
Corres-
ponding
value
Rando
m
Numbe
r
Corres-
pondin
g value
1.8955 Q(P-V)-
31,895.5
10 92 1,800 77 30 38 20 2,224
11 25 1,200 65 30 36 20 -9,150
12 64 1,400 04 20 83 40 -84,970
13 14 1,000 51 30 72 20 -12,941
14 05 800 39 20 81 40 -62,224
15 07 800 90 50 40 20 13,597
16 34 1,200 63 30 67 20 -9,150
17 79 1,600 91 50 99 40 -1,568
18 55 1,400 54 30 64 20 -5,359
19 57 1,400 12 20 19 15 -18,627
20 53 1,400 78 30 22 15 7,910
21 36 1,200 79 30 96 40 -54,642
22 32 1,200 22 20 75 20 -31,896
23 49 1,400 93 50 88 40 -5,359
24 21 1,200 84 40 35 20 13,597
25 08 .800 70 30 27 15 -9,150
26 85 1,600 63 30 69 20 -1,568
27 61 1,400 68 30 16 15 7,910
28 25 1,200 81 40 39 20 13,597
29 51 1,400 76 30 38 20 -5,359
30 32 1,200 47 30 46 20 -9,150
50

31 52 1,400 61 30 58 20 -5,359
32 76 1,600 18 20 41 20 -31,896
33 43 1,400 04 20 49 20 -31,896
34 70 1,600 11 20 59 20 -31,896
35 67 1,400 35 20 26 15 -18,627
36 26 1,200 63 30 22 15 2,224
Ru
n
Random
Number
Corre
s-
pondi
ng
Value
Random
Number
Corres-
ponding
value
Rando
m
Numbe
r
Corres-
pondin
g value
1.8955 Q(P-V)-
31,895.5
37 89 1,600 86 40 59 20 28,761
38 94 1,800 00 20 25 15 -14,836
39 09 .800 15 20 29 15 -24,314
40 44 1,400 84 40 21 15 34,447
41 98 1,800 23 20 79 20 -31,896
42 10 1,000 53 30 77 20 -12,941
43 38 1,200 44 30 31 20 -9,150
44 83 1,600 30 20 10 15 -16,732
45 54 1,400 71 30 52 20 -5,359
46 16 1,000 70 30 19 15 -3,463
47 20 1,200 65 30 87 40 -54,642
48 61 1,400 61 30 70 20 -5,359
49 82 1,600 48 30 97 40 -62,224
50 90 1,800 50 30 43 20 2,224
Expected NPV = NPV
50
= 1/ 50 ∑ NPVi
i=1
= 1/50 (-7,20,961)
= 14,419
50
Variance of NPV = 1/50 ∑ (NPVi – NPV)2
i=1
= 1/50 [27,474.047 x 106
]
= 549.481 x 106
51

Standard deviation of NPV = 549.481 x 106
= 23,441
7. To carry out a sensitivity analysis, we have to define the range and the most likely values of
the variables in the NPV Model. These values are defined below
Variable Range Most likely value
I Rs.30,000 – Rs.30,000 Rs.30,000
k 10% - 10% 10%
F Rs.3,000 – Rs.3,000 Rs.3,000
D Rs.2,000 – Rs.2,000 Rs.2,000
T 0.5 – 0.5 0.5
N 5 – 5 5
S 0 – 0 0
Q Can assume any one of the values - 1,400*
800, 1,000, 1,200, 1,400, 1,600 and 1,800
P Can assume any of the values 20, 30, 30**
40 and 50
V Can assume any one of the values 20*
15,20 and 40
----------------------------------------------------------------------------------------
* The most likely values in the case of Q, P and V are the values that have the
highest probability associated with them
** In the case of price, 20 and 30 have the same probability of occurrence viz 0.4. We
have chosen 30 as the most likely value because the expected value of the
distribution is closer to 30
Sensitivity Analysis with Reference to Q
The relationship between Q and NPV given the most likely values of other
variables is given by
5 [Q (30-20) – 3,000 – 2,000] x 0.5 + 2,000 0
NPV = ∑ + - 30,000
t=1 (1.1)t
(1.1)5
5 5Q - 500
= ∑ - 30,000
t=1 (1.1)t
The net present values for various values of Q are given in the following table:
52

Q 800 1,000 1,200 1,400 1,600 1,800
NPV -16,732 -12,941 -9,150 -5,359 -1,568 2,224
Sensitivity analysis with reference to P
The relationship between P and NPV, given the most likely values of other variables is defined as
follows:
5 [1,400 (P-20) – 3,000 – 2,000] x 0.5 + 2,000 0
NPV = ∑ + - 30,0
t=1 (1.1)t
(1.1)5
5 700 P – 14,500
= ∑ - 30,000
t=1 (1.1)t
The net present values for various values of P are given below :
P (Rs) 20 30 - 40 50
NPV(Rs) -31,896 -5,359 21,179 47,716
8. NPV - 5 0 5 10 15 20
(Rs.in lakhs)
PI 0.9 1.00 1.10 1.20 1.30 1.40
Prob. 0.02 0.03 0.10 0.40 0.30 0.15
6
Expected PI = PI = ∑ (PI)j Pj
j=1
= 1.24
6
Standard deviation of P1 = ∑ (PIj - PI) 2
Pj
j=1
= √ .01156
= .1075
The standard deviation of P1 is .1075 for the given investment with an expected PI of 1.24.
The maximum standard deviation of PI acceptable to the company for an investment with an
expected PI of 1.25 is 0.30.
53

Since the risk associated with the investment is much less than the maximum risk acceptable
to the company for the given level of expected PI, the company must should accept the
investment.
9. The NPVs of the two projects calculated at their risk adjusted discount rates are as follows:
6 3,000
Project A: NPV = ∑ - 10,000 = Rs.2,333
t=1 (1.12)t
5 11,000
Project B: NPV = ∑ - 30,000 = Rs.7,763
t=1 (1.14)t
PI and IRR for the two projects are as follows:
Project A B
PI 1.23 1.26
IRR 20% 24.3%
B is superior to A in terms of NPV, PI, and IRR. Hence the company must choose B.
10. The certainty equivalent co-efficients for the five years are as follows
Year Certainty equivalent coefficient
αt = 1 – 0.06 t
1 α1 = 0.94
2 α2 = 0.88
3 α3 = 0.82
4 α4 = 0.76
5 α5 = 0.70
The present value of the project calculated at the risk-free rate of return is :
5 (1 – 0.06 t) At
∑
t=1 (1.08)t
7,000 x 0.94 8,000 x 0.88 9,000 x 0.82 10,000 x 0.76 8,000 x 0.70
+ + + +
(1.08) (1.08)2
(1.08)3
(1.08)4
(1.08)5
54

6,580 7,040 7,380 7,600 5,600
+ + + +
(1.08) (1.08)2
(1.08)3
(1.08)4
(1.08)5
= 27,386
Net present value of the Project = (27,386 – 30,000
= Rs. –2,614
MINICASE
Solution:
1. The expected NPV of the turboprop aircraft
0.65 (5500) + 0.35 (500)
NPV = - 11000 +
(1.12)
0.65 [0.8 (17500) + 0.2 (3000)] + 0.35 [0.4 (17500) + 0.6 (3000)]
+
(1.12)2
= 2369
2. If Southern Airways buys the piston engine aircraft and the demand in year 1 turns out to be
high, a further decision has to be made with respect to capacity expansion. To evaluate the
piston engine aircraft, proceed as follows:
First, calculate the NPV of the two options viz., ‘expand’ and ‘do not expand’ at decision
point D2:
0.8 (15000) + 0.2 (1600)
Expand : NPV = - 4400 +
1.12
= 6600
0.8 (6500) + 0.2 (2400)
Do not expand : NPV =
1.12
= 5071
55

Second, truncate the ‘do not expand’ option as it is inferior to the ‘expand’ option. This
means that the NPV at decision point D2 will be 6600
Third, calculate the NPV of the piston engine aircraft option.
0.65 (2500+6600) + 0.35 (800)
NPV = – 5500 +
1.12
0.35 [0.2 (6500) + 0.8 (2400)]
+
(1.12)2
= – 5500 + 5531 + 898 = 929
3. The value of the option to expand in the case of piston engine aircraft
If Southern Airways does not have the option of expanding capacity at the end of year 1, the
NPV of the piston engine aircraft would be:
0.65 (2500) + 0.35 (800)
NPV = – 5500 +
1.12
0.65 [0.8 (6500) + 0.2 (2400)] + 0.35 [0.2 (6500) + 0.8 (2400)]
+
(1.12)2
= - 5500 + 1701 + 3842 = 43
Thus the option to expand has a value of 929 – 43 = 886
4. Value of the option to abandon if the turboprop aircraft can be sold for 8000 at the end of year
1
If the demand in year 1 turns out to be low, the payoffs for the ‘continuation’ and
‘abandonment’ options as of year 1 are as follows.
0.4 (17500) + 0.6 (3000)
Continuation: = 7857
1.12
56

Abandonment : 8000
Thus it makes sense to sell off the aircraft after year 1, if the demand in year 1 turns out to be
low.
The NPV of the turboprop aircraft with abandonment possibility is
0.65 [5500 +{0.8 (17500) + 0.2 (3000)}/ (1.12)] + 0.35 (500 +8000)
NPV = - 11,000 +
(1.12)
12048 + 2975
= - 11,000 + = 2413
1.12
Since the turboprop aircraft without the abandonment option has a value of 2369, the
value of the abandonment option is : 2413 – 2369 = 44
5. The value of the option to abandon if the piston engine aircraft can be sold for 4400 at the
end of year 1:
If the demand in year 1 turns out to be low, the payoffs for the ‘continuation’ and
‘abandonment’ options as of year 1 are as follows:
0.2 (6500) + 0.8 (2400)
Continuation : = 2875
1.12
Abandonment : 4400
Thus, it makes sense to sell off the aircraft after year 1, if the demand in year 1 turns out to
be low.
The NPV of the piston engine aircraft with abandonment possibility is:
0.65 [2500 + 6600] + 0.35 [800 + 4400]
NPV = - 5500 +
1.12
5915 + 1820
= - 5500 + = 1406
1.12
For the piston engine aircraft the possibility of abandonment increases the NPV
57

from 929 to 1406. Hence the value of the abandonment option is 477.
58

Chapter 14
THE COST OF CAPITAL
1(a) Define rD as the pre-tax cost of debt. Using the approximate yield formula, rD can be
calculated as follows:
14 + (100 – 108)/10
rD = ------------------------ x 100 = 12.60%
0.4 x 100 + 0.6x108
(b) After tax cost = 12.60 x (1 – 0.35) = 8.19%
2. Define rp as the cost of preference capital. Using the approximate yield formula rp can be
calculated as follows:
9 + (100 – 92)/6
rp = --------------------
0.4 x100 + 0.6x92
= 0.1085 (or) 10.85%
3. WACC = 0.4 x 13% x (1 – 0.35)
+ 0.6 x 18%
= 14.18%
4. Cost of equity = 10% + 1.2 x 7% = 18.4%
(using SML equation)
Pre-tax cost of debt = 14%
After-tax cost of debt = 14% x (1 – 0.35) = 9.1%
Debt equity ratio = 2 : 3
WACC = 2/5 x 9.1% + 3/5 x 18.4%
= 14.68%
5. Given
0.5 x 14% x (1 – 0.35) + 0.5 x rE = 12%
where rE is the cost of equity capital.
Therefore rE – 14.9%
59

Using the SML equation we get
11% + 8% x β = 14.9%
where β denotes the beta of Azeez’s equity.
Solving this equation we get β = 0.4875.
6(a) The cost of debt of 12% represents the historical interest rate at the time the debt was
originally issued. But we need to calculate the marginal cost of debt (cost of raising new
debt); and for this purpose we need to calculate the yield to maturity of the debt as on the
balance sheet date. The yield to maturity will not be equal to12% unless the book value of
debt is equal to the market value of debt on the balance sheet date.
(b) The cost of equity has been taken as D1/P0 ( = 6/100) whereas the cost of equity is (D1/P0)
+ g where g represents the expected constant growth rate in dividend per share.
7. The book value and market values of the different sources of finance are
provided in the following table. The book value weights and the market value
weights are provided within parenthesis in the table.
(Rs. in million)
Source Book value Market value
Equity 800 (0.54) 2400 (0.78)
Debentures – first series 300 (0.20) 270 (0.09)
Debentures – second series 200 (0.13) 204 (0.06)
Bank loan 200 (0.13) 200 (0.07)
Total 1500 (1.00) 3074 (1.00)
8. Required return
based on SML Expected
Project Beta equation (%) return (%)
P 0.6 14.8 13
Q 0.9 17.2 14
R 1.5 22.0 16
S 1.5 22.0 20
Given a hurdle rate of 18% (the firm’s cost of capital), projects P, Q and R would have been
rejected because the expected returns on these projects are below 18%. Project S would be
accepted because the expected return on this project exceeds 18%.An appropriate basis for
60

accepting or rejecting the projects would be to compare the expected rate of return and the
required rate of return for each project. Based on this comparison, we find that all the four
projects need to be rejected.
9.
(a) Given
rD x (1 – 0.3) x 4/9 + 20% x 5/9 = 15%
rD = 12.5%,where rD represents the pre-tax cost of debt.
(b) Given
13% x (1 – 0.3) x 4/9 + rE x 5/9 = 15%
rE = 19.72%, where rE represents the cost of equity.
10. Cost of equity = D1/P0 + g
= 3.00 / 30.00 + 0.05
= 15%
(a) The first chunk of financing will comprise of Rs.5 million of retained earnings costing 15
percent and Rs.25 million of debt costing 14 (1-.3) = 9.8 per cent
The second chunk of financing will comprise of Rs.5 million of additional equity costing
15 per cent and Rs.2.5 million of debt costing 15 (1-.3) = 10.5 per cent
(b) The marginal cost of capital in the first chunk will be :
5/7.5 x 15% + 2.5/7.5 x 9.8% = 13.27%
The marginal cost of capital in the second chunk will be:
5/7.5 x 15% + 2.5/7.5 x 10.5% = 13.50%
Note : We have assumed that
(i) The net realisation per share will be Rs.25, after floatation costs, and
(ii) The planned investment of Rs.15 million is inclusive of floatation costs
11. The cost of equity and retained earnings
rE = D1/PO + g
= 1.50 / 20.00 + 0.07 = 14.5%
The cost of preference capital, using the approximate formula, is :
11 + (100-75)/10
rE = = 15.9%
0.6 x 75 + 0.4 x 100
61

The pre-tax cost of debentures, using the approximate formula, is :
13.5 + (100-80)/6
rD = = 19.1%
0.6x80 + 0.4x100
The post-tax cost of debentures is
19.1 (1-tax rate) = 19.1 (1 – 0.5)
= 9.6%
The post-tax cost of term loans is
12 (1-tax rate) = 12 (1 – 0.5)
= 6.0%
The average cost of capital using book value proportions is calculated below :
Source of capital Component Book value Book value Product of
Cost Rs. in million proportion (1) & (3)
(1) (2) (3)
Equity capital 14.5% 100 0.28 4.06
Preference capital 15.9% 10 0.03 0.48
Retained earnings 14.5% 120 0.33 4.79
Debentures 9.6% 50 0.14 1.34
Term loans 6.0% 80 0.22 1.32
360 Average cost11.99%
capital
The average cost of capital using market value proportions is calculated below :
Source of capital Component Market value Market value Product of
cost Rs. in million
(1) (2) (3) (1) & (3)
Equity capital
and retained earnings 14.5% 200 0.62 8.99
Preference capital 15.9% 7.5 0.02 0.32
Debentures 9.6% 40 0.12 1.15
Term loans 6.0% 80 0.24 1.44
327.5 Average cost 11.90%
capital
12
62

(a) WACC = 1/3 x 13% x (1 – 0.3)
+ 2/3 x 20%
= 16.37%
(b) Weighted average floatation cost
= 1/3 x 3% + 2/3 x 12%
= 9%
(c) NPV of the proposal after taking into account the floatation costs
= 130 x PVIFA (16.37, 8) – 500 / (1 - 0.09)
= Rs.8.51 million
MINICASE
Solution:
a. All sources other than non-interest bearing liabilities
b. Pre-tax cost of debt & post-tax cost of debt
10 + (100 – 112) / 8 8.5
rd = = = 7.93
0.6 x 112 + 0.4 x 100 107.2
rd (1 – 0.3) = 5.55
c. Post-tax cost of preference
9 + (100 – 106) / 5 7.8
= = 7.53%
0.6 x 106 + 0.4 x 100 103.6
d. Cost of equity using the DDM
2.80 (1.10)
+ 0.10 = 0.385 + 0.10
80
= 0.1385 = 13.85%
e. Cost of equity using the CAPM
7 + 1.1(7) = 14.70%
f. WACC
0.50 x 14.70 + 0.10 x 7.53 + 0.40 x 5.55
63

= 7.35 + 0.75 + 2.22
= 10.32%
g. Cost of capital for the new business
0.5 [7 + 1.5 (7)] + 0.5 [ 11 (1 – 0.3)]
8.75 + 3.85
= 12.60%
64

Chapter 15
CAPITAL BUDGETING : EXTENSIONS
1. EAC
(Plastic Emulsion) = 300000 / PVIFA (12,7)
= 300000 / 4.564
= Rs.65732
EAC
(Distemper Painting) = 180000 / PVIFA (12,3)
= 180000 / 2.402
= Rs.74938
Since EAC of plastic emulsion is less than that of distemper painting, it is the preferred
alternative.
2. PV of the net costs associated with the internal transportation system
= 1 500 000 + 300 000 x PVIF (13,1) + 360 000 x PVIF (13,2)
+ 400 000 x PVIF (13,3) + 450 000 x PVIF (13,4)
+ 500 000 x PVIF (13,5) - 300 000 x PVIF (13,5)
= 2709185
EAC of the internal transportation system
= 2709185 / PVIFA (13,5)
= 2709185 / 3.517
= Rs.770 311
3. EAC [ Standard overhaul]
= 500 000 / PVIFA (14,6)
= 500 000 / 3.889
= Rs.128568 ……… (A)
EAC [Less costly overhaul]
= 200 000 / PVIFA (14,2)
= 200 000 / 1.647
= Rs.121433 ……… (B)
Since (B) < (A), the less costly overhaul is preferred alternative.
65

4.
(a) Base case NPV
= -12,000,000 + 3,000,000 x PVIFA (20,6)
= -12,000,000 + 997,8000
= (-) Rs.2,022,000
(b) Issue costs = 6,000,000 / 0.88 - 6,000,000
= Rs.818 182
Adjusted NPV after adjusting for issue costs
= - 2,022,000 – 818,182
= - Rs.2,840,182
(c) The present value of interest tax shield is calculated below :
Year Debt outstanding at Interest Tax shield Present value of
the beginning tax shield
1 6,000,000 1,080,000 324,000 274,590
2 6,000,000 1,080,000 324,000 232,697
3 5,250,000 945,000 283,000 172,538
4 4,500,000 810,000 243,000 125,339
5 3,750,000 675,000 202,000 88,513
6 3,000,000 540,000 162,000 60,005
7 2,225,000 400,500 120,000 37,715
8 1,500,000 270,000 81,000 21,546
9 750,000 135,000 40,500 9,133
Present value of tax shield = Rs.1,022,076
5.
(a) Base case BPV
= - 8,000,000 + 2,000,000 x PVIFA (18,6)
= - Rs.1,004,000
(b) Adjusted NPV after adjustment for issue cost of external equity
= Base case NPV – Issue cost
= - 1,004,000 – [ 3,000,000 / 0.9 – 3,000,000]
= - Rs.1,337,333
66

(c) The present value of interest tax shield is calculated below :
Year Debt outstanding at Interest Tax shield Present value of
the beginning tax shield
1 5,000,000 750,000 300,000 260,880
2 5,000,000 750,000 300,000 226,830
3 4,000,000 600,000 240,000 157,800
4 3,000,000 450,000 180,000 102,924
5 2,000,000 300,000 120,000 59,664
6 1,000,000 150,000 60,000 25,938
Present value of tax shield = Rs.834,036
67

Chapter 18
RAISING LONG TERM FINANCE
1 Underwriting Shares Excess/ Credit Net
commitment procured shortfall shortfall
A 70,000 50,000 (20,000) 4919 (15081)
B 50,000 30,000 (20,000) 3514 (16486)
C 40,000 30,000 (10,000) 2811 (7189)
D 25,000 12,000 (13,000) 1757 (11243)
E 15,000 28,000 13,000
2.
Underwriting Shares Excess/ Credit Net
commitment procured Shortfall shortfall
A 50,000 20,000 (30,000) 14286 (15714)
B 20,000 10,000 (10,000) 5714 (4286)
C 30,000 50,000 20,000 - -
3. Po = Rs.220 S = Rs.150 N = 4
a. The theoretical value per share of the cum-rights stock would simply be
Rs.220
b. The theoretical value per share of the ex-rights stock is :
68

NPo+S 4 x 220 +150
= = Rs.206
N+1 4+1
c. The theoretical value of each right is :
Po – S 220 – 150
= = Rs.14
N+1 4+1
The theoretical value of 4 rights which are required to buy 1 share is Rs.14x14=Rs.56.
4. Po = Rs.180 N = 5
a. The theoretical value of a right if the subscription price is Rs.150
Po – S 180 – 150
= = Rs.5
N+1 5+1
b. The ex-rights value per share if the subscription price is Rs.160
NPo + S 5 x 180 + 160
= = Rs.176.7
N+1 5+1
c. The theoretical value per share, ex-rights, if the subscription price is
Rs.180? 100?
5 x 180 + 180
= Rs.180
5+1
5 x 180 + 100
= Rs.166.7
5+1
69

Chapter 19
CAPITAL STRUCTURE AND FIRM VALUE
1. Net operating income (O) : Rs.30 million
Interest on debt (I) : Rs.10 million
Equity earnings (P) : Rs.20 million
Cost of equity (rE) : 15%
Cost of debt (rD) : 10%
Market value of equity (E) : Rs.20 million/0.15 =Rs.133 million
Market value of debt (D) : Rs.10 million/0.10 =Rs.100 million
Market value of the firm (V) : Rs.233 million
2. Box Cox
Market value of equity 2,000,000/0.15 2,000,000/0.15
= Rs.13.33 million = Rs.13.33 million
Market value of debt 0 1,000,000/0.10
=Rs.10 million
Market value of the firm Rs.13.33million =23.33 million
(a) Average cost of capital for Box Corporation
13.33. 0
x 15% + x 10% = 15%
13.33 13.33
Average cost of capital for Cox Corporation
13.33 10.00
x 15% + x 10% = 12.86%
23.33 23.33
(b) If Box Corporation employs Rs.30 million of debt to finance a project that yields
Rs.4 million net operating income, its financials will be as follows.
Net operating income Rs.6,000,000
Interest on debt Rs.3,000,000
Equity earnings Rs.3,000,000
Cost of equity 15%
70

Cost of debt 10%
Market value of equity Rs.20 million
Market value of debt Rs.30 million
Market value of the firm Rs.50 million
Average cost of capital
20 30
15% x + 10% = 12%
50 50
(c) If Cox Corporation sells Rs.10 million of additional equity to retire
Rs.10 million of debt , it will become an all-equity company. So its
average cost of capital will simply be equal to its cost of equity,
which is 15%.
3. rE = rA + (rA-rD)D/E
20 = 12 + (12-8) D/E
So D/E = 2
4. E D E D
rE rD rA = rE + rD
D+E D+E (%) (%) D+E D+E
1.00 0.00 11.0 6.0 11.00
0.90 0.10 11.0 6.5 10.55
0.80 0.20 11.5 7.0 10.60
0.70 0.30 12.5 7.5 11.00
0.60 0.40 13.0 8.5 11.20
0.50 0.50 14.0 9.5 11.75
0.40 0.60 15.0 11.0 12.60
0.30 0.70 16.0 12.0 13.20
0.20 0.80 18.0 13.0 14.00
0.10 0.90 20.0 14.0 14.20
The optimal debt ratio is 0.10 as it minimises the weighted average
cost of capital.
5. (a) If you own Rs.10,000 worth of Bharat Company, the levered company
which is valued more, you would sell shares of Bharat Company, resort
to personal leverage, and buy the shares of Charat Company.
(b) The arbitrage will cease when Charat Company and Bharat Company
are valued alike
71

6. The value of Ashwini Limited according to Modigliani and Miller
hypothesis is
Expected operating income 15
= = Rs.125 million
Discount rate applicable to the 0.12
risk class to which Aswini belongs
7. The average cost of capital(without considering agency and bankruptcy cost)
at various leverage ratios is given below.
D E E D
rD rE rA = rE + rD
D + E D+ E % % D+E D+E
(%)
0 1.00 4.0 12.0 12.0
0.10 0.90 4.0 12.0 11.2
0.20 0.80 4.0 12.5 10.8
0.30 0.70 4.0 13.5 10.36
0.40 0.60 4.0 13.5 9.86
0.50 0.50 4.0 14.0 9.30
0.60 0.40 4.0 14.5 8.68
0.70 0.30 4.0 15.0 8.14
0.80 0.20 4.0 15.5 7.90
0.90 0.10 4.0 16.0 7.72 Optimal
b. The average cost of capital considering agency and bankruptcy costs is
given below
.
D E E D
rD rE rA = rE + rD
D + E D+ E % % D+E D+E
(%)
0 1.00 4.0 12.0 12.0
0.10 0.90 4.0 12.0 11.2
0.20 0.80 4.0 13.0 11.2
0.30 0.70 4.2 14.0 11.06
0.40 0.60 4.4 15.0 10.76
0.50 0.50 4.6 16.0 10.30
0.60 0.40 4.8 17.0 9.68
0.70 0.30 5.2 18.0 9.04
0.80 0.20 6.0 19.0 8.60
0.90 0.10 6.8 20.0 8.12 Optimal
8. The tax advantage of one rupee of debt is :
72

1-(1-tc) (1-tpe) (1-0.55) (1-0.05)
= 1 -
(1-tpd) (1-0.25)
= 0.43 rupee
Chapter 20
CAPITAL STRUCTURE DECISION
1.(a) Currently
No. of shares = 1,500,000
EBIT = Rs 7.2 million
Interest = 0
Preference dividend = Rs.12 x 50,000 = Rs.0.6 million
EPS = Rs.2
(EBIT – Interest) (1-t) – Preference dividend
EPS =
No. of shares
(7,200,000 – 0 ) (1-t) – 600,000
Rs.2 =
1,500,000
Hence t = 0.5 or 50 per cent
The EPS under the two financing plans is :
Financing Plan A : Issue of 1,000,000 shares
(EBIT - 0 ) ( 1 – 0.5) - 600,000
EPSA =
2,500,000
Financing Plan B : Issue of Rs.10 million debentures carrying 15 per cent
interest
(EBIT – 1,500,000) (1-0.5) – 600,000
EPSB =
1,500,000
The EPS – EBIT indifference point can be obtained by equating EPSA and EPSB
(EBIT – 0 ) (1 – 0.5) – 600,000 (EBIT – 1,500,000) (1 – 0.5) – 600,000
73

=
2,500,000 1,500,000
Solving the above we get EBIT = Rs.4,950,000 and at that EBIT, EPS is Rs.0.75
under both the plans
(b) As long as EBIT is less than Rs.4,950,000 equity financing maximixes EPS.
When EBIT exceeds Rs.4,950,000 debt financing maximises EPS.
2.
(a) EPS – EBIT equation for alternative A
EBIT ( 1 – 0.5)
EPSA =
2,000,000
(b) EPS – EBIT equation for alternative B
EBIT ( 1 – 0.5 ) – 440,000
EPSB =
1,600,000
(c) EPS – EBIT equation for alternative C
(EBIT – 1,200,000) (1- 0.5)
EPSC =
1,200,000
(d) The three alternative plans of financing ranked in terms of EPS over varying
Levels of EBIT are given the following table
Ranking of Alternatives
EBIT EPSA EPSB EPSC
(Rs.) (Rs.) (Rs.) (Rs.)
2,000,000 0.50(I) 0.35(II) 0.33(III)
2,160,000 0.54(I) 0.40(II) 0.40(II)
3,000,000 0.75(I) 0.66(II) 0.75(I)
4,000,000 1.00(II) 0.98(III) 1.17(I)
4,400,000 1.10(II) 1.10(II) 1.33(I)
More than 4,400,000 (III) (II) (I)
3. Plan A : Issue 0.8 million equity shares at Rs. 12.5 per share.
Plan B : Issue Rs.10 million of debt carrying interest rate of 15 per cent.
(EBIT – 0 ) (1 – 0.6)
EPSA =
74

1,800,000
(EBIT – 1,500,000) (1 – 0.6)
EPSB =
1,000,000
Equating EPSA and EPSB , we get
(EBIT – 0 ) (1 – 0.6) (EBIT – 1,500,000) (1 – 0.6)
=
1,800,000 1,000,000
Solving this we get EBIT = 3,375,000 or 3.375 million
Thus the debt alternative is better than the equity alternative when
EBIT > 3.375 million
EBIT – EBIT 3.375 – 7.000
Prob(EBIT>3,375,000) = Prob >
σ EBIT 3.000
= Prob [z > - 1.21]
= 0.8869
4. ROE = [ ROI + ( ROI – r ) D/E ] (1 – t )
15 = [ 14 + ( 14 – 8 ) D/E ] ( 1- 0.5 )
D/E = 2.67
5. ROE = [12 + (12 – 9 ) 0.6 ] (1 – 0.6)
= 5.52 per cent
6. 18 = [ ROI + ( ROI – 8 ) 0.7 ] ( 1 – 0.5)
ROI = 24.47 per cent
EBIT
7. a. Interest coverage ratio =
Interest on debt
150
=
40
= 3.75
EBIT + Depreciation
b. Cash flow coverage ratio =
Loan repayment instalment
75

Int.on debt +
(1 – Tax rate)
= 150 + 30
40 + 50
= 2
8. The debt service coverage ratio for Pioneer Automobiles Limited is given by :
5
∑ ( PAT i + Depi + Inti)
i=1
DSCR = 5
∑ (Inti + LRIi)
i=1
= 133.00 + 49.14 +95.80
95.80 + 72.00
= 277.94
167.80
= 1.66
9. (a) If the entire outlay of Rs. 300 million is raised by way of debt carrying 15 per cent
interest, the interest burden will be Rs. 45 million.
Considering the interest burden the net cash flows of the firm during
a recessionary year will have an expected value of Rs. 35 million (Rs.80 million - Rs. 45
million ) and a standard deviation of Rs. 40 million .
Since the net cash flow (X) is distributed normally
X – 35
40
has a standard normal deviation
Cash flow inadequacy means that X is less than 0.
0.35
Prob(X<0) = Prob (z< ) = Prob (z<- 0.875)
40
= 0.1909
(b) Since µ = Rs.80 million, σ= Rs.40 million , and the Z value corresponding to the risk
tolerance limit of 5 per cent is – 1.645, the cash available from the operations to service the
debt is equal to X which is defined as :
X – 80
76

= - 1.645
40
X = Rs.14.2 million
Given 15 per cent interest rate, the debt than be serviced is
14.2
= Rs. 94.67 million
0.15
Chapter 21
DIVIDEND POLICY AND FIRM VALUE
1. Payout ratio Price per share
3(0.5)+3(0.5) 0.15
0.5
0.12
= Rs. 28.13
0.12
3(0.7 5)+3(0.25) 0.15
0.12
0.75 = Rs. 26.56
0.12
3(1.00)
1.00 = Rs. 25.00
0.12
2. Payout ratio Price per share
8(0.25)
0.25 = undefined
0.12 – 0.16(0.75)
8(0.50)
0.50 = Rs.100
0.12 – 0.16(0.50)
8(1.00)
1.0 =Rs.66.7
0.12 – 0.16 (0)
77

3.
P Q
• Next year’s price 80 74
• Dividend 0 6
• Current price P Q
• Capital appreciation (80-P) (74-Q)
• Post-tax capital appreciation 0.9(80-P) 0.9 (74-Q)
• Post-tax dividend income 0 0.8 x 6
• Total return 0.9 (80-P)
P
= 14%
0.9 (74-Q) + 4.8
Q
=14%
• Current price (obtained by solving
the preceding equation)
P = Rs.69.23 Q = Rs.68.65
78

Chapter 22
DIVIDEND DECISION
1. a. Under a pure residual dividend policy, the dividend per share over the 4 year
period will be as follows:
DPS Under Pure Residual Dividend Policy
( in Rs.)
Year 1 2 3 4
Earnings 10,000 12,000 9,000 15,000
Capital expenditure 8,000 7,000 10,000 8,000
Equity investment 4,000 3,500 5,000 4,000
Pure residual
dividends 6,000 8,500 4,000 11,000
Dividends per share 1.20 1.70 0.80 2.20
b. The external financing required over the 4 year period (under the assumption that the
company plans to raise dividends by 10 percents every two years) is given below :
Required Level of External Financing
(in Rs.)
Year 1 2 3 4
A . Net income 10,000 12,000 9,000 15,000
B . Targeted DPS 1.00 1.10 1.10 1.21
C . Total dividends 5,000 5,500 5,500 6,050
D . Retained earnings(A-C) 5,000 6,500 3,500 8,950
E . Capital expenditure 8,000 7,000 10,000 8,000
79

F . External financing
requirement 3,000 500 6,500 Nil
(E-D)if E > D or 0 otherwise
c. Given that the company follows a constant 60 per cent payout ratio, the dividend per share
and external financing requirement over the 4 year period are given below
Dividend Per Share and External Financing Requirement
(in Rs.)
Year 1 2 3 4
A. Net income 10,000 12,000 9,000 15,00
B. Dividends 6,000 7,200 5,400 9,000
C. Retained earnings 4,000 4,800 3,600 6,000
D. Capital expenditure 8,000 7,000 10,000 8,000
E. External financing
(D-C)if D>C, or 0 4,000 2,200 6,400 2,000
otherwise
F. Dividends per share 1.20 1.44 1.08 1.80
2. Given the constraints imposed by the management, the dividend per share has to
be between Rs.1.00 (the dividend for the previous year) and Rs.1.60 (80 per
cent of earnings per share)
Since share holders have a preference for dividend, the dividend should be
raised over the previous dividend of Rs.1.00 . However, the firm has substantial
investment requirements and it would be reluctant to issue additional equity
because of high issue costs ( in the form of underpricing and floatation costs)
Considering the conflicting requirements, it seems to make sense to pay
Rs.1.20 per share by way of dividend. Put differently the pay out ratio may be
set at 60 per cent.
3. According to the Lintner model
Dt = cr EPSt + (1-c)Dt –1
EPSt =3.00, c= 0.7, r=0.6 , and Dt-1
80

Hence
Dt = 0.7 x 0.6 x 3.00 + (1-0.7)1.20
= Rs.1.62
4. The bonus ratio (b) must satisfy the following constraints :
(R-Sb)≥0.4S (1+b) (1)
0.3 PBT ≥0.1 S(1+b) (2)
R = Rs.100 million, S= Rs.60 million, PBT = Rs.60 million
Hence the constraints are
(100-60 b) ≥ 0.4 x 60 (1+b) (1a)
0.3 x 60≥0.1 x 60 (1+b) (2a)
These simplify to
b ≥ 76/84
b ≥ 2
The condition b ≥ 76/84 is more restructive than b≥ 2
So the maximum bonus ratio is 76/84 or 19/21
81

Chapter 23
Debt Analysis and Management
1. (i) Initial Outlay
(a) Cost of calling the old bonds
Face value of the old bonds 250,000,000
Call premium 15,000,000
265,000,000
(b) Net proceeds of the new bonds
Gross proceeds 250,000,000
Issue costs 10,000,000
240,000,000
(c) Tax savings on tax-deductible expenses
Tax rate[Call premium+Unamortised issue cost on
the old bonds] 9,200,000
0.4 [ 15,000,000 + 8,000,000]
Initial outlay i(a) – i(b) – i(c) 15,800,000
(ii) Annual Net Cash Savings
(a) Annual net cash outflow on old bonds
Interest expense 42,500,000
- Tax savings on interest expense and amortisation of
issue expenses 17,400,000
0.4 [42,500,000 + 8,000,000/10]
25,100,000
(b) Annual net cash outflow on new bonds
issue cost 15,500,000
0.4 [ 37,500,000 – 10,000,000/8]
22,000,000
Annual net cash savings : ii(a) – ii(b) 3,100,000
82

(iii) Present Value of the Annual Cash Savings
Present value of an 8-year annuity of 3,100,000 at a
discount rate of 9 per cent which is the post –tax cost
of new bonds 3,100,000 x 5.535 17,158,500
(iv) Net Present Value of Refunding the Bonds
(a) Present value of annual cash savings 17,158,500
(b) Net initial outlay 15,800,000
(c) Net present value of refunding the bonds :
iv(a) – iv(b). 1,358,500
2. (i) Initial Outlay
(a) Cost of calling the old bonds
Face value of the old bonds 120,000,000
Call premium 4,800,000
124,800,000
(b) Net proceeds of the new issue
Gross proceeds 120,000,000
Issue costs 2,400,000
117,600,000
(c) Tax savings on tax-deductible expenses 3,120,000
Tax rate[Call premium+Unamortised issue costs on
the old bond issue]
0.4 [ 4,800,000 + 3,000,000]
Initial outlay i(a) – i(b) – i(c) 4,080,000
(ii) Annual Net Cash Savings
(a) Annual net cash out flow on old bonds
issue costs 7,920,000
0.4[19,200,000 + 3,000,000/5]
11,280,000
(b) Annual net cash outflow on new bonds
- Tax savings on interest expense and amortistion of issue
costs 7,392,000
0.4[18,000,000 + 2,400,000/5]
10,608,000
Annual net cash savings : ii(a) – ii(b) 672,000
(iii) Present Value of the Annual Net Cash Savings
83

Present value of a 5 year annuity of 672,000 at
as discount rate of 9 per cent, which is the post-tax 2,614,080 cost of
new bonds
(iv) Net Present Value of Refunding the Bonds
(a) Present value of annual net cash savings 2,614,080
(b) Initial outlay 4,080,000
(c) Net present value of refunding the bonds : - 1,466,000
iv(a) – iv(b)
3. Yield to maturity of bond P
8 160 1000
918.50 =∑ +
t=1 (1+r)t
(1+r)8
r or yield to maturity is 18 percent
Yield to maturity of bond Q
5 120 1000
761 = ∑ +
t=1 (1+r)t
(1+r)5
r or yield to maturity is 20 per cent
Duration of bond P is calculated below
Year Cash flow Present Value Proportion of Proportion of bond’s
at 18% bond’s value Value x Time
1 160 135.5 0.148 0.148
2 160 114.9 0.125 0.250
3 160 97.4 0.106 0.318
4 160 82.6 0.090 0.360
5 160 69.9 0.076 0.380
6 160 59.2 0.064 0.384
7 160 50.2 0.055 0.385
8 160 308.6 0.336 2.688
4.913
Duration of bond Q is calculated below
Year Cash flow Present Value Proportion of Proportion of bond’s
at 20% bond’s value Value x Time
84

1 120 100.0 0.131 0.131
2 120 83.2 0.109 0.218
3 120 69.5 0.091 0.273
4 120 57.8 0.076 0.304
5 1120 450.2 0.592 2.960
3.886
Volatility of bond P Volatility of bond Q
4.913 3.886
= 4.16 = 3.24
1.18 1.20
4. The YTM for bonds of various maturities is
Maturity YTM(%)
1 12.36
2 13.10
3 13.21
4 13.48
5 13.72
Graphing these YTMs against the maturities will give the yield curve
The one year treasury bill rate , r1, is
1,00,000
- 1 = 12.36 %
89,000
To get the forward rate for year 2, r2, the following equation may be set up :
12500 112500
99000 = +
(1.1236) (1.1236)(1+r2)
85

Solving this for r2 we get r2 = 13.94%
To get the forward rate for year 3, r3, the following equation may be set up :
13,000 13,000 113,000
99,500 = + +
(1.1236) (1.1236)(1.1394) (1.1236)(1.1394)(1+r3)
To get the forward rate for year 4, r4 , the following equation may be set up :
13,500 13,500 13,500
100,050 = + +
(1.1236) (1.1236)(1.1394) (1.1236)(1.1394)(1.1349)
113,500
+
(1.1236)(1.1394)(1.1349)(1+r4)
To get the forward rate for year 5, r5 , the following equation may be set up :
13,750 13,750 13,750
100,100 = + +
(1.1236) (1.1236)(1.1394) (1.1236)(1.1394)(1.1349)
13,750
+
(1.1236)(1.1394)(1.1349)(1.1454)
113,750
+
(1.1236)(1.1394)(1.1349)(1.1454)(1+r5)
86

Chapter 25
HYBRID FINANCING
1. The product of the standard deviation and square root of time is :
σ t = 0.35 2 = 0.495
The ratio of the stock price to the present value of the exercise price is :
Stock price 40
= = 1.856
PV (Exercise price) 25/(1.16)
The ratio of the value of call option to stock price corresponding to numbers
0.495 and 1.856 can be found out from Table A.6 by interpolation. Note the
table gives values for the following combinations
1.75 2.00
0.45 44.6 50.8
0.50 45.3 51.3
Since we are interested in the combination 0.495 and 1.856 we first interpolate
between 0.450 and 0.500 and then interpolate between 1.75 and 2.00
Interpolation between 0.450 and 0.500 gives
1.75 2.00
0.450 44.6 50.8
0.495 45.23 51.25
0.500 45.3 51.3
87

Then, interpolation between 1.75 and 2.00 gives
1.75 1.856 2.00
0.495 45.23 47.78 51.25
Chapter 24
LEASING, HIRE PURCHASE, AND PROJECT FINANCE
1. NPV of the Purchase Option
(Rs.in ‘000)
Year 0 1 2 3 4 5
1.Investment(I) (1,500)
2.Revenues(Rt) 1,700 1,700 1,700 1,700 1,700
3.Costs(other than
(Depreciation)(Ct) 900 900 900 900 900
4.Depreciation(Dt) 500 333.3 222.2 148.1 98.8
5.Profit before tax
(Rt-Ct-Dt) 300 466.7 577.8 651.9 701.2
6.Profit after tax: 5(1-t) 210 326.7 404.5 456.3 490.8
7.Net salvage value 300
8.Net cash flow
(1+6+4+7) (1,500) 710 610 626.7 604.4 889.6
9.Discount factor
at 11 percent 1.000 0.901 0.812 0.731 0.659 0.593
10.Present value (8x9) (1,500) 639.7 495.3 458.1 398.3 527.5
NPV(Purchases)= - 1500+639.7+495.3+458.1+398.3+527.5 = 1018.9
NPV of the Leasing Option
(Rs. in ‘000)
Year 0 1 2 3 4 5
1.Revenues(Rt) - 1,700 1,700 1,700 1,700 1,700
2.Costs(other than
lease rentals)(Ct) 900 900 900 900 900
3.Lease rentals(Lt) 420 420 420 420 420 0
4.Profit before tax
(Rt-Ct-Lt) -420 380 380 380 380 800
5.Profit after tax (which
88

also reflects the net
cash flow)(1-t) -294 266 266 266 266 560
6.Discount factor at
13 per cent 1.000 0.885 0.783 0.693 0.613 0.543
7.Present value(5x6) -294 -235.4 208.3 184.3 163.1 304.1
NPV(Leasing) = -294+235.4+208.3+184.3+163.1+304.1 = 801.2
2. Under the hire purchase proposal the total interest payment is
2,000,000 x 0.12 x 3 = Rs. 720,000
The interest payment of Rs. 720,000 is allocated over the 3 years period using
the sum of the years digits method as follows:
Year Interest allocation
366
1 x Rs.720,000 = Rs.395,676
666
222
2 x Rs.720,000 = Rs.240,000
666
78
3 x Rs.720,000 = Rs.84,324
666
The annual hire purchase instalments will be :
Rs.2,000,000 + Rs.720,000
= Rs.906,667
3
The annual hire purchase instalments would be split as follows
Year Hire purchase instalment Interest Principal repayment
1 Rs.906,667 Rs.395,676 Rs. 510,991
2 Rs.906,667 Rs.240,000 Rs. 666,667
3 Rs.906,667 Rs. 84,324 Rs. 822,343
89

The lease rental will be as follows :
Rs. 560,000 per year for the first 5 years
Rs. 20,000 per year for the next 5 years
The cash flows of the leasing and hire purchse options are shown below
Year Leasing High Purchase -It(1-tc)-PRt+
- LRt (1-tc) -It(1-tc) -PRt Dt(tc) NSVt Dt(tc)+NSVt
1 -560,000(1-.4)=-336,000 -395,676(1-.4) -510,991 500,000(0.4) -548,397
2 -560,000(1-.4)=-336,000 -240,000(1-.4) -666,667 375,000(0.4) -660,667
3 -560,000(1-.4)=-336,000 - 84,324(1-.4) -822,343 281,250(0.4) -760,437
4 -560,000(1-.4)=-336,000 210,938(0.4) 84,375
5 -560,000(1-.4)=-336,000 158,203(0.4) 63,281
6 - 20,000(1-.4)= - 12,000 118,652(0.4) 47,461
7 - 20,000(1-.4)= - 12,000 88,989(0.4) 35,596
8 - 20,000(1-.4)= - 12,000 66,742(0.4) 26,697
9 - 20,000(1-.4)= - 12,000 50,056(0.4) 20,023
10 - 20,000(1-.4)= - 12,000 37,542(0.4) 200,000 215,017
Present value of the leasing option
5 336,000 10 12,000
= - ∑ − ∑ = - 1,302,207
t=1 (1.10)t
t=6 (1.10)t
Present value of the hire purchase option
548,397 660,667 760,437 84,375
= - - - -
(1.10) (1.10)2
(1.10)3
(1.10)4
63,281 47,461 35,596 26,697
+ + +
(1.10)5
(1.10)6
(1.10)7
(1.10)8
90

20,023 215,017
+
(1.10.9 (1.10)10
= - 1,369,383
Since the leasing option costs less than the hire purchase option , Apex should choose the
leasing option.
Chapter 26
WORKING CAPITAL POLICY
Average inventory
1 Inventory period =
Annual cost of goods sold/365
(60+64)/2
= = 62.9 days
360/365
Average accounts receivable
Accounts receivable =
period Annual sales/365
(80+88)/2
= = 61.3 days
500/365
Average accounts payable
Accounts payable =
period Annual cost of goods sold/365
(40+46)/2
= = 43.43 days
360/365
Operating cycle = 62.9 + 61.3 = 124.2 days
Cash cycle = 124.2 – 43.43 = 80.77 days
(110+120)/2
2. Inventory period = = 56.0 days
750/365
91

(140+150)/2
Accounts receivable = = 52.9 days
period 1000/365
(60+66)/2
Accounts payable = = 30.7 days
period 750/365
Operating cycle = 56.0 + 52.9 = 108.9 days
Cash cycle = 108.9 – 30.7 = 78.2 days
Rs.
3. 1. Sales 3,600,000
Less : Gross profit (25 per cent) 900,000
Total manufacturing cost 2,700,000
Less : Materials 900,000
Wages 720,000 1,620,000
Manufacturing expenses 1,080,000
2. Cash manufacturing expenses 960,000
(80,000 x 12)
3. Depreciation : (1) – (2) 120,000
4. Total cash cost
Total manufacturing cost 2,700,000
Less: Depreciation 120,000
Cash manufacturing cost 2,580,000
Add: Administration and sales
promotion expenses 360,000
2,940,000
A : Current Assets Rs.
Total cash cost 2,940,000
Debtors x 2 = x 2 = 490,000
12 12
Material cost 900,000
Raw material x 1 = x 1 = 75,000
stock 12 12
Cash manufacturing cost 2,580,000
Finished goods x 1 = x 1 = 215,000
stock 12 12
92

Cash balance A predetermined amount = 100,000
Sales promotion expenses 120,000
Prepaid sales x 1.5 = x 1.5 = 15,000
promotion 12 12
expenses
Cash balance A predetermined amount = 100,000
A : Current Assets = 995,000
B : Current Liabilites Rs.
Material cost 900,000
Sundry creditors x 2 = x 2 = 150,000
12 12
Manufacturing One month’s cash
expenses outstanding manufacturing expenses = 80,000
Wages outstanding One month’s wages = 60,000
B : Current liabilities 290,000
Working capital (A – B) 705,000
Add 20 % safety margin 141,000
Working capital required 846,000
93

Chapter 27
CASH AND LIQUIDITY MANAGEMENT
1. The forecast of cash receipts, cash payments, and cash position is prepared in the
statements given below
Forecast of Cash Receipts (Rs. in 000’s)
November December January February March April May June
1. Sales 120 120 150 150 150 200 200 200
2. Credit sales 84 84 105 105 105 140 140 140
3. Cash sales 36 36 45 45 45 60 60 60
4. Collection of receivables
(a) Previous month 33.6 33.6 42.0 42.0 42.0 56.0 56.0
(b) Two months earlier 50.4 50.4 63.0 63.0 63.0 84.0
5. Sale of machine 70.0
6. Interest on securities 3.0
7. Total receipts 129.0 137.4 150.0 235.0 179.0 203.0
(3+4+5+6)
Forecast of Cash Payments (Rs. in 000’s)
December January February March April May June
1. Purchases 60 60 60 60 80 80 80
2. Payment of accounts 60 60 60 60 80 80
payable
3. Cash purchases 3 3 3 3 3 3
4. Wage payments 25 25 25 25 25 25
5. Manufacturing
expenses 32 32 32 32 32 32
6. General, administrative
94

& selling expenses 15 15 15 15 15 15
7. Dividends 30
8. Taxes 35
9. Acquisition of
machinery 80
Total payments(2to9) 135 135 215 135 155 220
Summary of Cash Forecast (Rs.in 000’s)
January February March April May June
1. Opening balance 28
2. Receipts 129.0 137.4 150.0 235.0 179.0 203.0
3. Payments 135.0 135.0 215.0 135.0 155.0 220.0
4. Net cash flow(2-3) (6.0) 2.4 (65.0) 100.0 24.0 (17.0)
5. Cumulative net cash flow (6.0) (3.6) (68.6) 31.4 55.4 (38.4)
6. Opening balance +
Cumulative net cash flow 22.0 24.4 (40.6) 59.4 83.4 66.4
7. Minimum cash balance
required 30.0 30.0 30.0 30.0 30.0 30.0
8. Surplus/(Deficit) (8.0) (5.6) (70.6) 29.4 53.0 36.4
2. The projected cash inflows and outflows for the quarter, January through March, is shown below
.
Month December January February March
(Rs.) (Rs.) (Rs.) (Rs.)
Inflows :
Sales collection 50,000 55,000 60,000
Outflows :
Purchases 22,000 20,000 22,000 25,000
Payment to sundry creditors 22,000 20,000 22,000
Rent 5,000 5,000 5,000
Drawings 5,000 5,000 5,000
Salaries & other expenses 15,000 18,000 20,000
Purchase of furniture - 25,000 -
95

Total outflows(2to6) 47,000 73,000 52,000
Given an opening cash balance of Rs.5000 and a target cash balance of Rs.8000, the
surplus/deficit in relation to the target cash balance is worked out below :
January February March
(Rs.) (Rs.) (Rs.)
1. Opening balance 5,000
2. Inflows 50,000 55,000 60,000
3. Outflows 47,000 73,000 52,000
4. Net cash flow (2 - 3) 3,000 (18,000) 8,000
5. Cumulative net cash flow 3,000 (15,000) (7,000)
6. Opening balance + Cumulative
net cash flow 8,000 (10,000) (2,000)
7. Minimum cash balance required 8,000 8,000 8,000
8. Surplus/(Deficit) - (18,000) (10,000)
3. The balances in the books of Datta co and the books of the bank are shown below:
(Rs.)
1 2 3 4 5 6 7 8 9 10
Books of Datta
Co:
Opening
Balance
30,00
0
46,00
0
62,00
0
78,000
94,000
1,10,00
0
1,26,0
00
1,42,0
00
1,58,0
00
1,74,0
00
Add: Cheque
received
20,00
0
20,00
0
20,00
0
20,000
20,000 20,000 20,000 20,000 20,000 20,000
Less: Cheque
issued 4,000 4,000 4,000
4,000
4,000 4,000 4,000 4,000 4,000 4,000
Closing
Balance
46,00
0
62,00
0
78,00
0
94,000 1,10,0
00
1,26,00
0
1,42,0
00
1,58,0
00
1,74,0
00
1,90,0
00
Books of the
Bank:
96

Opening
Balance
30,00
0
30,00
0
30,00
0
30,000 30,000 30,000 50,000 70,000
90,000
1,06,0
00
Add: Cheques
realised
- - - - - 20,000 20,000 20,000
20,000 20,000
Less: Cheques
debited
- - - - - - - -
4,000 4,000
Closing
Balance
30,00
0
30,00
0
30,00
0
30,000 30,000 50,000 70,000 90,000 1,06,0
00
1,22,0
00
From day 9 we find that the balance as per the bank’s books is less than the balance as per Datta
Company’s books by a constant sum of Rs.68,000. Hence in the steady situation Datta Company has
a negative net float of Rs.68,000.
4. Optimal conversion size is
2bT
C =
I
b = Rs.1200, T= Rs.2,500,000, I = 5% (10% dividend by two)
So,
2 x 1200 x 2,500,000
C = = Rs.346,410
0.05
5.
3 3 bσ2
RP = + LL
4I
UL = 3 RP – 2 LL
I = 0.12/360 = .00033, b = Rs.1,500, σ = Rs.6,000, LL = Rs.100,000
3 3 x 1500 x 6,000 x 6,000
RP = + 100,000
4 x .00033
= 49,695 + 100,000 = Rs.149,695
97

UL = 3RP – 2LL = 3 x 149,695 – 2 x 100,000
= Rs.249,085
Chapter 28
CREDIT MANAGEMENT
1. Δ RI = [ΔS(1-V)- ΔSbn](1-t)- k ΔI
Δ S
Δ I = x ACP x V
360
Δ S = Rs.10 million, V=0.85, bn =0.08, ACP= 60 days, k=0.15, t = 0.40
Hence, ΔRI = [ 10,000,000(1-0.85)- 10,000,000 x 0.08 ] (1-0.4)
-0.15 x 10,000,000 x 60 x 0.85
360
= Rs. 207,500
2. Δ RI = [ΔS(1-V)- ΔSbn] (1-t) – k Δ I
So ΔS
Δ I = (ACPN – ACPo) +V(ACPN)
360 360
98

ΔS=Rs.1.5 million, V=0.80, bn=0.05, t=0.45, k=0.15, ACPN=60, ACPo=45, So=Rs.15 million
Hence ΔRI = [1,500,000(1-0.8) – 1,500,000 x 0.05] (1-.45)
-0.15 (60-45) 15,000,000 + 0.8 x 60 x 1,500,000
360 360
= 123750 – 123750 = Rs. 0
3. Δ RI = [ΔS(1-V) –Δ DIS ] (1-t) + k Δ I
Δ DIS = pn(So+ΔS)dn – poSodo
So ΔS
Δ I = (ACPo-ACPN) - x ACPN x V
360 360
So =Rs.12 million, ACPo=24, V=0.80, t= 0.50, r=0.15, po=0.3, pn=0.7,
ACPN=16, ΔS=Rs.1.2 million, do=.01, dn= .02
Hence
ΔRI = [ 1,200,000(1-0.80)-{0.7(12,000,000+1,200,000).02-
0.3(12,000,000).01}](1-0.5)
12,000,000 1,200,000
+ 0.15 (24-16) - x 16 x 0.80
360 360
= Rs.79,200
4. Δ RI = [ΔS(1-V)- ΔBD](1-t) –kΔ I
ΔBD=bn(So+ΔS) –boSo
So ΔS
ΔI = (ACPN –ACPo) + x ACPN x V
360 360
So=Rs.50 million, ACPo=25, V=0.75, k=0.15, bo=0.04, ΔS=Rs.6 million,
ACPN=40 , bn= 0.06 , t = 0.3
ΔRI = [ Rs.6,000,000(1-.75) –{.06(Rs.56,000,000)-.04(Rs.50,000,000)](1-0.3)
99

Rs.50,000,000 Rs.6,000,000
- 0.15 (40-25) + x 40 x 0.75
360 360
= - Rs.289.495
5. 30% of sales will be collected on the 10th
day
70% of sales will be collected on the 50th
day
ACP = 0.3 x 10 + 0.7 x 50 = 38 days
Rs.40,000,000
Value of receivables = x 38
360
= Rs.4,222,222
Assuming that V is the proportion of variable costs to sales, the investment in
receivables is :
Rs.4,222,222 x V
6. 30% of sales are collected on the 5th
day and 70% of sales are collected on the
25th
day. So,
ACP = 0.3 x 5 + 0.7 x 25 = 19 days
Rs.10,000,000
Value of receivables = x 19
360
= Rs.527,778
Investment in receivables = 0.7 x 527,778
= Rs.395,833
7. Since the change in credit terms increases the investment in receivables,
ΔRI = [ΔS(1-V)- ΔDIS](1-t) – kΔI
So=Rs.50 million, ΔS=Rs.10 million, do=0.02, po=0.70, dn=0.03,pn=0.60,
ACPo=20 days, ACPN=24 days, V=0.85, k=0.12 , and t = 0.40
ΔDIS = 0.60 x 60 x 0.03 – 0.70 x 50 x 0.2
= Rs.0.38 million
50 10
Δ I = (24-20) + x 24 x 0.85
360 360
= Rs.1.2222 million
Δ RI = [ 10,000,000 (1-.85) – 380,000 ] (1-.4) – 0.12 x 1,222,222
100

= Rs.525,333
8. The decision tree for granting credit is as follows :
Customer pays(0.95)
Grant credit Profit 1500
Customer pays(0.85)
Grant credit Customer defaults(0.05)
Profit 1500 Refuse credit
Loss 8500
Customer defaults(0.15)
Loss 8500
Refuse credit
The expected profit from granting credit, ignoring the time value of money, is :
Expected profit on + Probability of payment x Expected profit on
Initial order and repeat order repeat order
{ 0.85(1500)-0.15(8500)} + 0.85 {0.95(1500)-.05(8500)}
= 0 + 850 = Rs.850
9. Profit when the customer pays = Rs.10,000 - Rs.8,000 = Rs.2000
Loss when the customer does not pay = Rs.8000
Expected profit = p1 x 2000 –(1-p1)8000
Setting expected profit equal to zero and solving for p1 gives :
p1 x 2000 – (1- p1)8000 = 0 p1 = 0.80
Hence the minimum probability that the customer must pay is 0.80
MINICASE
Solution:
Present Data
• Sales : Rs.800 million
• Credit period : 30 days to those deemed eligible
• Cash discount : 1/10, net 30
• Proportion of credit sales and cash sales are 0.7 and 0.3. 50 percent of the credit customers
avail of cash discount
• Contribution margin ratio : 0.20
• Tax rate : 30 percent
101

• Post-tax cost of capital : 12 percent
• ACP on credit sales : 20 days
Effect of Relaxing the Credit Standards on Residual Income
Incremental sales : Rs.50 million
Bad debt losses on incremental sales: 12 percent
ACP remains unchanged at 20 days
∆RI = [∆S(1 – V) - ∆Sbn] (1 – t) – R ∆ I
∆S
where ∆ I = x ACP x V
360
∆ RI = [50,000,000 (1-0.8) – 50,000,000 x 0.12] (1 – 0.3)
50,000,000
- 0.12 x x 20 x 0.8
360
= 2,800,000 – 266,667 = 2,533,333
Effect of Extending the Credit Period on Residual Income
∆ RI = [∆S(1 – V) - ∆Sbn] (1 – t) – R ∆ I
So ∆S
where ∆I = (ACPn – ACPo) + V (ACPn)
360 360
∆RI = [50,000,000 (1 – 0.8) – 50,000,000 x 0] (1 – 0.3)
800,000,000 50,000,000
- 0.12 (50 – 20) x + 0.8 x 50 x
360 360
= 7,000,000 – 8,666,667
= - Rs.1,666,667
Effect of Relaxing the Cash Discount Policy on Residual Income
∆RI = [∆S (1 – V) - ∆ DIS] (1 – t) + R ∆ I
102

where ∆ I = savings in receivables investment
So ∆S
= (ACPo – ACPn) – V x ACPn
360 360
800,000,000 20,000,000
= (20 – 16) – 0.8 x x 16
360 360
= 8,888,889 – 711,111 = 8,177,778
∆ DIS = increase in discount cost
= pn (So + ∆S) dn – po So do
= 0.7 (800,000,000 + 20,000,000) x 0.02 – 0.5 x 800,000,000 x 0.01
= 11,480,000 – 4,000,000 = 7,480,000
So, ∆RI = [20,000,000 (1 – 0.8) – 7,480,000] (1 – 0.3) + 0.12 x 8,177,778
= - 2,436,000 + 981,333
= - 1,454,667
Chapter 29
INVENTORY MANAGEMENT
1.
a. No. of Order Ordering Cost Carrying Cost Total Cost
Orders Per Quantity (U/Q x F) Q/2xPxC of Ordering
Year (Q) (where and Carrying
(U/Q) PxC=Rs.30)
Units Rs. Rs. Rs.
1 250 200 3,750 3,950
2 125 400 1,875 2,275
5 50 1,000 750 1,750
10 25 2,000 375 2,375
2 UF 2x250x200
103

b. Economic Order Quantity (EOQ) = =
PC 30
2UF = 58 units (approx)
2. a EOQ =
PC
U=10,000 , F=Rs.300, PC= Rs.25 x 0.25 =Rs.6.25
2 x 10,000 x 300
EOQ = = 980
6.25
10000
b. Number of orders that will be placed is = 10.20
980
Note that though fractional orders cannot be placed, the number of orders
relevant for the year will be 10.2 . In practice 11 orders will be placed during the year. However,
the 11th
order will serve partly(to the extent of 20 percent) the present year and partly(to the
extent of 80 per cent) the following year. So only 20 per cent of the ordering cost of the 11th
order relates to the present year. Hence the ordering cost for the present year will be 10.2 x
Rs.300
c. Total cost of carrying and ordering inventories
980
= [ 10.2 x 300 + x 6.25 ] = Rs.6122.5
2
3. U=6,000, F=Rs.400 , PC =Rs.100 x 0.2 =Rs.20
2 x 6,000 x 400
EOQ = = 490 units
20
U U Q’(P-D)C Q* PC
Δπ = UD + - F- -
Q* Q’ 2 2
6,000 6,000
= 6000 x .5 + - x 400
490 1,000
1,000 (95)0.2 490 x 100 x 0.2
- -
2 2
104

Here are the key steps to solve this problem:* Ramesh wants to receive Rs. 500,000 annually for 15 years starting 15 years from now* To calculate the amount needed 15 years from now, we use the present value of an annuity formula:PV = Annual Payment x Present Value of Annuity Factor * The annual payment is Rs. 500,000* The interest rate is 10% per year* The time period is 15 years * Looking up the present value of annuity factor for 10% interest and 15 years in the tables, we get:PVIFA(10%, 15 years) = 9.427* Plugging into the formula:PV

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