Chapter 7TIME 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) = 1,000,000A 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 thatFVIFA (20%, 6 years) = 9.930FVIFA (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) = 5,000FVIF (r,10 years) = 5,000 / 1000 = 5

From the tables we find that

FVIF (16%, 10 years) = 4.411FVIF (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 The amount that can be withdrawn annually is:100,000 100,000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.50,000is 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) = 5.019PVIFA (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 xPVIF (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.3,625.2PV (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 theeffective rate and statedrate (%) 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.40,388PVIF(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

From the tables we find thatFVIF (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 isRs.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 thenA x FVIFA (12%, 6 years) = Rs.51,335A x 8.115 = Rs.51,335A = 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.18,854The 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 - 1Rs.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.14,998P x 1.817 = Rs.14,998

Rs.14,998P = ------------ = Rs.8254

1.817

27. Rs.300 x PVIFA(r, 24 months) = Rs.6,000PVIFA (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 interpolation21.244 – 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, thenA x FVIFA (8%, 5 years) = Rs.2.21 millionA x 5.867 = Rs.2.21 millionA = 5.867 = Rs.2.21 millionA = 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.100,000PVIFA (15%, n) = Rs.100,000 / Rs.20,000 = 5.000

From the tables we find thatPVIFA (10%, 7 years) = 4.868PVIFA (10%, 8 years) = 5.335

Thus n is between 7 and 8. Using a linear interpolation we get

5.000 – 4.868n = 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 RemainingYear 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) = 1,500,000PVIFA (13%, n) = 7.500

From the tables or otherwise it can be verified that PVIFA(13,30) = 7.500Hence 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.48,338FVIFA (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

1.12 15

9

1 – 1.08

= 400,000 0.08 – 0.12

= Rs.7,254,962

10

Chapter 8

VALUATION OF BONDS AND STOCKS

1. 5 11 100P = +

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.100t=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.711.60Thus the value of r at which the RHS becomes equal to Rs.750 lies between 18% and 20%.

11

Using linear interpolation in this range, we get

771.44 – 750.00Yield 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 isRs.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 - 80Yield 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:

Bond A Bond B

12

* 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)/10Bond A : Post-tax YTM = --------------------

0.6 x 70 + 0.4 x 97

= 13.73%

7 + (96 – 60)/6Bond 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 – gg = 0.0575 or 5.75%

11. Po = D1/ (r – g) = Do(1+g) / (r – g)Do = Rs.1.50, g = -0.04, Po = Rs.8So8 = 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 yearsB: Present value of the dividend stream for the next 4 yearsC: 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.37.45So

C = Rs.37.45 / (1.14)8 = Rs.13.14

Thus,Po = A + B + C = 5.74 + 4.89 + 13.14

= Rs.23.77

14

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

Terminal value of the proceeds from the bond = 1709.24

15

Define r as the yield to maturity. The value of r can be obtained from the equation

900 (1 + r)4 = 1709.24r = 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 9RISK 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) (R i- R)2 pi (Ri-R)2

--------------------------------------------------------------------------------------------------- 10 0.4 4 -8 64 25.620 0.4 8 2 4 1.630 0.2 6 12 144 28.8---------------------------------------------------------------------------------------------------

R = pi Ri pi (Ri-R)2

= 56σ = 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) ProbabilityHigh Growth 20 x 55 = 1,100 0.3Low Growth 20 x 50 = 1,000 0.3Stagnation 20 x 60 = 1,200 0.2Recession 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 0.3Low growth 20 x 65 = 1,300 0.3Stagnation 20 x 50 = 1,000 0.2Recession 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.1,175Standard 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.84.41d. 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 :

OptionExpected return

(Rs)Standard deviation

(Rs)Expected / Standard return deviation

a 1,150 143 8.04b 1,200 265 4.53c 1,175 84 13.99d 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 equalproportions = 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 equalproportions = 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 equalproportions = 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 0.292 -6 1 -21.09 -14.18 444.79 201.07 299.063 18 14 2.91 -1.18 8.47 1.39 -3.434 30 24 14.91 8.82 222.31 77.79 131.515 12 16 0-3.09 0.82 9.55 0.67 -2.536 25 30 9.91 14.82 98.21 219.63 146.877 2 -3 -13.09 -18.18 171.35 330.51 237.988 20 24 4.91 8.82 24.11 77.79 43.319 18 15 2.91 -0.18 8.47 0.03 -0.5210 24 22 8.91 6.82 79.39 46.51 60.7711 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 = 0.96975.61

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)

0.07i.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 = 0.195or 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 10OPTIONS AND THEIR VALUATION

1. S = 100 u = 1.5 d = 0.8

22

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 = 0.8R = 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

Cd = Max (32 – 45, 0) = 0

23

∆ 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 + B8 = ∆ x 40 + B (2)

Substituting (1) in (2) we get

8 = (-0.034365 x 40) B + B8 = -0.375 Bor 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 = 0u = 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 = t

24

= ln (120 / 110) + 0.14 + 0.4 2 /2 0.4

= 0.08701 + 0.14 + 0.08 0.4

= 0.7675

d2 = d1 - t= 0.7675 – 0.4= 0.3675

N(d1) = N (0.7675) ~ N (0.77) = 0.80785N (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. 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- Stock price ……… (A)

25

The value of the call option gives an exercise price of Rs.85 can be obtained as follows:

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) = 0.81057d2 = d1 - t

= 0.8775 - 0.18= 0.4532 = 0.45

26

N (d2) = N (0.45) = 0.67364So = 6000 x 0.81057 – (5000 x 0.9048 x 0.67364)

= 1816

B0 = V0 – S0

= 60000 – 1816= 4184

Chapter 11TECHNIQUES 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 ----------- ---------- ---------- (1.14)3 (1.14)4 (1.14)5

27

= - 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 yearsb) NPV = 40000 x PVIFA (12,10) – 200 000

= 26000c) IRR (r ) can be obtained by solving the equation:

40000 x PVIFA (r, 10) = 200000i.e., PVIFA (r, 10) = 5.000

From the PVIFA tables we find that PVIFA (15,10) = 5.019PVIFA (16,10) = 4.883

28

Linear interporation in this range yieldsr = 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 thatr = 1.37%

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

Investment C

a) Payback period lies between 2 years and 3 years. Linear interpolation in this range provides an approximate payback period of 2.88 years.

b) NPV = 80.000 x PVIF (12,1) + 60,000 x PVIF (12,2) + 80,000 x PVIF (12,3) + 60,000 x PVIF (12,4)

+ 80,000 x PVIF (12,5) + 60,000 x PVIF (12,6)+ 40,000 x PVIFA (12,4) x PVIF (12.6)- 210,000

= 111,371

29

c) IRR (r) is obtained by solving the equation80,000 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 equation200,000 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

d) BCR 1.13 0.65 1.53 0.88

30

Among the four alternative investments, the investment to be chosen is ‘C’because it has the Lowest payback period

Highest NPVHighest IRRHighest 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) = 500000NCF = 500000 / 5.335

= 93271

6. Define I as the initial investment that is justified in relation to a net annual cashinflow 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) = Ii.e., I = 141256

7. PV of benefits (PVB) = 25000 x PVIF (15,1)+ 40000 x PVIF (15,2)+ 50000 x PVIF (15,3)+ 40000 x PVIF (15,4)+ 30000 x PVIF (15,5)

31

= 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 6005% 223 251 312

10% 69 40 7015% - 66 - 142 - 135

25% - 291 - 435 - 46130% - 386 - 555 - 591

9. NPV profiles for Projects P and Q for selected discount rates are as follows:(a)

ProjectP Q

Discount rate (%) 0 2950 500 5 1876 20810 1075 - 2815 471 - 22220 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'

-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

32

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) = 1075NPV (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)

= 2728TV of cash inflows = 2000 x (1.12) + 4000 = 6240The MIRR of the project P is given by the equation:

2728 = 6240 x PVIF (MIRR,5)(1 + MIRR)5 = 2.2874MIRR = 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

MIRR = 11.62%

33

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) = 100i.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 equation13 x PVIFA (r',6) = 50i.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 millionDifference 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 equation12 x PVIFA (r'', 6) = 50i.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 NThe pay back period lies between 1 and 2 years. Interpolating in this range we get an approximate pay back period of 1.55 years.

(b) Project M

34

Cost of capital = 12% p.aPV of cash flows up to the end of year 2 = 24.97PV of cash flows up to the end of year 3 = 47.75PV of cash flows up to the end of year 4 = 71.26

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

Project NCost of capital = 12% per annumPV of cash flows up to the end of year 1 = 33.93PV of cash flows up to the end of year 2 = 51.47

DPB lies between 1 and 2 years. Interpolating in this range we get an approximate DPB of 1.92 years.

(c ) Project MCost of capital = 12% per annumNPV = - 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 NCost of capital = 12% per annumNPV = Rs.20.63 millionSince 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 MCost of capital = 10% per annumNPV = Rs.25.02 million

Project NCost of capital = 10% per annumNPV = Rs.23.08 million

Since the two projects are mutually exclusive, we need to choose the project with the higher NPV i.e., choose project M.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 MCost of capital = 15% per annumNPV = 16.13 million

35

Project NCost of capital: 15% per annumNPV = Rs.17.23 millionAgain 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: 114.47MIRR of the project is given by the equation

50 (1 + MIRR)4 = 114.47i.e., MIRR = 23.01%

Project NTerminal value of the cash inflows: 115.41MIRR of the project is given by the equation

50 ( 1+ MIRR)4 = 115.41i.e., MIRR = 23.26%

36

Chapter 12ESTIMATION 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)+107.67 x PVIF (r,6) + 205 x PVIF (r,7) = 0

37

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 80 120 160 200 160 120 804. Raw material cost 24 36 48 60 48 36 245. Variable mfg cost. 8 12 16 20 16 12 86. Fixed operating & maint. 10 10 10 10 10 10 10 cost7. Variable selling expenses 8 12 16 20 16 12 88. Incremental overheads 4 6 8 10 8 6 49. Loss of contribution 10 10 10 10 10 10 1010.Bad debt loss 411. Depreciation 30 22.5 16.88 12.66 9.49 7.12 5.3412. Profit before tax -14 11.5 35.12 57.34 42.51 26.88 6.6613. Tax -4.2 3.45 10.54 17.20 12.75 8.06 2.0014. Profit after tax -9.8 8.05 24.58 40.14 29.76 18.82 4.6615. Net salvage value of capital equipments 2516. Recovery of working 16 capital17. 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

3.(a) A. Initial outlay (Time 0)

38

i. Cost of new machine Rs. 3,000,000ii. Salvage value of old machine 900,000iii Incremental working capital requirement 500,000iv. 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 52,207iv. 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. 1,500,000ii. Salvage value of old machine 200,000iii. Recovery of incremental working capital 500,000iv. 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

4. Tax shield (savings) on depreciation (in Rs)

39

Depreciation Tax shield PV of tax shieldYear 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. 400,000ii. Salvage value of the old machine 90,000iii. Net investment 310,000

B. Operating cash flow (years 1 through 5)

Year 1 2 3 4 5i. 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 flow 28700 21210 15656 11540 8494

C. Terminal cash flow (year 5)

40

i. Salvage value of new machine Rs. 25000ii. Salvage value of old machine 10000iii. 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 30 304. Costs (other than depreciation and interest) 20 20 20 20 205. Loss of rental 1 1 1 1 16. Depreciation 3.750 2.813 2.109 1.582 1.1877. Profit before tax 5.250 6.187 6.891 7.418 7.8138. Tax 1.575 1.856 2.067 2.225 2.3449. Profit after tax 3.675 4.331 4.824 5.193 5.46910. Salvage value of fixed assets 5.00011. Net recovery of working capital 8.000 12. Initial outlay (23)13. Operating cash inflow 7.425 7.144 6.933 6.775 6.65614. Terminal cash

41

flow 13.00015. 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 30 303. Costs (other than depreciation and interest) 20 20 20 20 204. Loss of rental 1 1 1 1 15. Depreciation 3.75 2.813 2.109 1.582 1.1876. Interest on working capital advance 0.70 0.70 0.70 0.70 0.707. Interest on term loans 1.20 1.125 0.825 0.525 0.2258. Profit before tax 3.35 4.362 5.366 6.193 6.8889. Tax 1.005 1.309 1.610 1.858 2.06610. Profit after tax 2.345 3.053 3.756 4.335 4.82211. Net salvage value of fixed assets 5.00012. Net salvage value of current assets 10.00013. Repayment of term term loans 2.000 2.000 2.000 2.000 14. Repayment of bank advance 5.00015. Retirement of trade creditors 2.00016. Initial investment (10) 17. Operating cash inflow 6.095 5.866 5.865 5.917 6.00918. Liquidation and retirement cash flows (2.0) (2.0) (2.0) 6.0019. Net cash flow (10) 6.095 3.866 3.865 3.917 12.009

42

Chapter 13RISK 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 200Sales 150 200 275Variable costs 97.5 120 154Fixed costs 30 20 15Depreciation 30 25 20Pretax profit - 7.5 35 86Tax @ 28.57% - 2.14 10 24.57Profit after tax - 5.36 25 61.43Net cash flow 24.64 50 81.43Cost 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.

(c) Accounting break even point (under ‘expected’ scenario)Fixed costs + depreciation = Rs. 45 million

43

Contribution margin ratio = 60 / 200 = 0.3Break 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 levelof sales = 238.74 / 1.1628 = Rs.205.31 million

2.(a) Sensitivity of NPV with respect to quantity manufactured and sold:

(in Rs)Pessimistic Expected Optimistic

Initial investment 30000 30000 30000Sale revenue 24000 42000 54000Variable costs 16000 28000 36000Fixed costs 3000 3000 3000Depreciation 2000 2000 2000Profit before tax 3000 9000 13000Tax 1500 4500 6500Profit after tax 1500 4500 6500Net cash flow 3500 6500 8500NPV at a cost of capital of 10% p.aand useful life of 5 years -16732 - 5360 2222

(b) Sensitivity of NPV with respect to variations in unit price.

Pessimistic Expected Optimistic

Initial investment 30000 30000 30000Sale revenue 28000 42000 70000Variable costs 28000 28000 28000Fixed costs 3000 3000 3000

44

Depreciation 2000 2000 2000Profit before tax -5000 9000 37000Tax -2500 4500 18500Profit after tax -2500 4500 18500Net cash flow - 500 6500 20500NPV - 31895 (-) 5360 47711

(c) Sensitivity of NPV with respect to variations in unit variable cost.

Pessimistic Expected Optimistic

Initial investment 30000 30000 30000Sale revenue 42000 42000 42000Variable costs 56000 28000 21000Fixed costs 3000 3000 3000Depreciation 2000 2000 2000Profit before tax -11000 9000 16000Tax -5500 4500 8000Profit after tax -5500 4500 8000Net cash flow -3500 6500 10000NPV -43268 - 5360 7908

(d) Accounting break-even point

i. Fixed costs + depreciation = Rs.5000ii. Contribution margin ratio = 10 / 30 = 0.3333iii. Break-even level of sales = 5000 / 0.3333

= Rs.15000Financial break-even point

i. Annual cash flow = 0.5 x (0.3333 Sales – 5000) = 2000ii. PV of annual cash flow = (i) x PVIFA (10,5)

= 0.6318 sales – 1896iii. Initial investment = 30000iv. 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= 5.8

45

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

12 = 0.41

22 = 0.56

32 = 0.49

12 2

2 32

2NPV = + + (1.1)2 (1.1)4 (1.1)6

= 1.00 (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 t

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 4 At

= - 10,000 …. (1) t=1 (1.06)t

46

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 2t

2 (NPV) = …….. (2) t=1 (1.06)2t

12 = [(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

22 = [(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

32 = [(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

42 = [(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

Substituting these values in (2) we get490,000 / (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

47

+ 490,000 x 0.705 + 560,000 x 0.627 ]= 1,679,150

NPV = 1,679,150 = Rs.1,296

NPV – NPV 0 - NPVProb (NPV < 0) = Prob. <

NPV 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

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 05

48

NPV + - 30,000t =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

Value

Prob

Cumulative Prob.

Two digit random numbers Valu

ePro

b

Cumulative Prob.

Two digit random numbers Value Pro

b

Cumu-

lative Prob.

Two digit random numbers

800 0.10

0.10 00 to 09 20 0.40

0.40 00 to 39 15 0.30

0.30 00 to 29

1,000

0.10

0.20 10 to 19 30 0.40

0.80 40 to 79 20 0.50

0.80 30 to 79

1,200

0.20

0.40 20 to 39 40 0.10

0.90 80 to 89 40 0.20

1.00 80 to 99

1,400

0.30

0.70 40 to 69 50 0.10

1.00 90 to 99

1,600

0.20

0.90 70 to 89

1,800

0.10

1.00 90 to 99

Exhibit 2Simulation Results

QUANTITY (Q) PRICE (P) VARIABLE COST (V) NPVRu Rando Corres- Random Corres- Rando Corres- 1.8955 Q(P-V)-

49

n m Numbe

r

ponding Value

Number ponding value

m Number

ponding value

31,895.5

1 03 800 38 20 17 15 -24,3142 32 1,200 69 30 24 15 2,2243 61 1,400 30 20 03 15 -18,6274 48 1,400 60 30 83 40 -58,4335 32 1,200 19 20 11 15 -20,5236 31 1,200 88 40 30 20 13,5977 22 1,200 78 30 41 20 -9,1508 46 1,400 11 20 52 20 -31,8969 57 1,400 20 20 15 15 -18,627

QUANTITY (Q) PRICE (P) VARIABLE COST (V) NPVRun

Random

Number

Corres-ponding Value

Random Number

Corres-ponding

value

Random

Number

Corres-ponding value

1.8955 Q(P-V)-31,895.5

10 92 1,800 77 30 38 20 2,22411 25 1,200 65 30 36 20 -9,15012 64 1,400 04 20 83 40 -84,97013 14 1,000 51 30 72 20 -12,94114 05 800 39 20 81 40 -62,22415 07 800 90 50 40 20 13,59716 34 1,200 63 30 67 20 -9,15017 79 1,600 91 50 99 40 -1,56818 55 1,400 54 30 64 20 -5,35919 57 1,400 12 20 19 15 -18,62720 53 1,400 78 30 22 15 7,91021 36 1,200 79 30 96 40 -54,64222 32 1,200 22 20 75 20 -31,89623 49 1,400 93 50 88 40 -5,35924 21 1,200 84 40 35 20 13,59725 08 .800 70 30 27 15 -9,15026 85 1,600 63 30 69 20 -1,56827 61 1,400 68 30 16 15 7,91028 25 1,200 81 40 39 20 13,59729 51 1,400 76 30 38 20 -5,35930 32 1,200 47 30 46 20 -9,15031 52 1,400 61 30 58 20 -5,35932 76 1,600 18 20 41 20 -31,89633 43 1,400 04 20 49 20 -31,89634 70 1,600 11 20 59 20 -31,896

50

35 67 1,400 35 20 26 15 -18,62736 26 1,200 63 30 22 15 2,224

QUANTITY (Q) PRICE (P) VARIABLE COST (V) NPVRun

Random Number

Corres-

ponding

Value

Random Number

Corres-ponding

value

Random

Number

Corres-ponding value

1.8955 Q(P-V)-31,895.5

37 89 1,600 86 40 59 20 28,76138 94 1,800 00 20 25 15 -14,83639 09 .800 15 20 29 15 -24,31440 44 1,400 84 40 21 15 34,44741 98 1,800 23 20 79 20 -31,89642 10 1,000 53 30 77 20 -12,94143 38 1,200 44 30 31 20 -9,15044 83 1,600 30 20 10 15 -16,73245 54 1,400 71 30 52 20 -5,35946 16 1,000 70 30 19 15 -3,46347 20 1,200 65 30 87 40 -54,64248 61 1,400 61 30 70 20 -5,35949 82 1,600 48 30 97 40 -62,22450 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

50Variance of NPV = 1/50 NPVi – NPV)2

i=1

= 1/50 [27,474.047 x 106]= 549.481 x 106

Standard deviation of NPV = 549.481 x 106

= 23,441

51

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.30,000k 10% - 10% 10%F Rs.3,000 – Rs.3,000 Rs.3,000D Rs.2,000 – Rs.2,000 Rs.2,000T 0.5 – 0.5 0.5N 5 – 5 5S 0 – 0 0Q Can assume any one of the values - 1,400*

800, 1,000, 1,200, 1,400, 1,600 and 1,800P Can assume any of the values 20, 30, 30**

40 and 50V 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 0NPV = + - 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:

Q 800 1,000 1,200 1,400 1,600 1,800NPV -16,732 -12,941 -9,150 -5,359 -1,568 2,224

52

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 0NPV = + - 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 50NPV(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

6Expected PI = PI = (PI)j P j

j=1= 1.24

6 Standard deviation of P1 = (PIj - PI) 2 P j

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.

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

53

Project A: NPV = - 10,000 = Rs.2,333t=1 (1.12)t

5 11,000Project 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 1.26IRR 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

t = 1 – 0.06 t

1 1 = 0.942 2 = 0.883 3 = 0.82 4 = 0.76 5 = 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

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

54

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

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

55

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 aircraftIf 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

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 +

56

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

57

Chapter 14THE 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)/10rD = ------------------------ 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)/6rp = --------------------

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. Given0.5 x 14% x (1 – 0.35) + 0.5 x rE = 12%

where rE is the cost of equity capital.

Therefore rE – 14.9%

58

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 valueEquity 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 13Q 0.9 17.2 14R 1.5 22.0 16S 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

59

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) Given13% 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 centThe 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 earningsrE = D1/PO + g

= 1.50 / 20.00 + 0.07 = 14.5%The cost of preference capital, using the approximate formula, is :

11 + (100-75)/10rE = = 15.9%

0.6 x 75 + 0.4 x 100

60

The pre-tax cost of debentures, using the approximate formula, is :

13.5 + (100-80)/6rD = = 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 4.06Preference capital 15.9% 10 0.03 0.48Retained earnings 14.5% 120 0.33 4.79Debentures 9.6% 50 0.14 1.34Term 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 capitaland retained earnings 14.5% 200 0.62 8.99Preference capital 15.9% 7.5 0.02 0.32Debentures 9.6% 40 0.12 1.15Term loans 6.0% 80 0.24 1.44

327.5 Average cost 11.90% capital

12

61

(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 8.5rd = = = 7.93

0.6 x 112 + 0.4 x 100 107.2

rd (1 – 0.3) = 5.55

c. Post-tax cost of preference9 + (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. WACC0.50 x 14.70 + 0.10 x 7.53 + 0.40 x 5.55

62

= 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%

63

Chapter 15CAPITAL 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.

64

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

65

(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

66

Chapter 18 RAISING LONG TERM FINANCE

1 Underwriting Shares Excess/ Credit Netcommitment 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 = 4a. 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 :

67

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 = 5a. 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 isRs.180? 100?

5 x 180 + 180 = Rs.180

5+1

5 x 180 + 100 = Rs.166.7

5+1

68

Chapter 19CAPITAL STRUCTURE AND FIRM VALUE

1. Net operating income (O) : Rs.30 millionInterest on debt (I) : Rs.10 millionEquity earnings (P) : Rs.20 millionCost 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 millionMarket 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 Corporation13.33. 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.6,000,000Interest on debt Rs.3,000,000Equity earnings Rs.3,000,000Cost of equity 15%

69

Cost of debt 10%Market value of equity Rs.20 millionMarket value of debt Rs.30 millionMarket 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

70

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 belongs7. 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 isgiven 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 Optimal8. The tax advantage of one rupee of debt is :

71

1-(1-tc) (1-tpe) (1-0.55) (1-0.05) = 1 - (1-tpd) (1-0.25)

= 0.43 rupee

Chapter 20CAPITAL 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

72

= 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 =

73

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 >

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 EBIT7. a. Interest coverage ratio =

Interest on debt

150 =

40 = 3.75 EBIT + Depreciation b. Cash flow coverage ratio =

Loan repayment instalment

74

Int.on debt + (1 – Tax rate)

= 150 + 30

40 + 50

= 28. 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 duringa 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, = 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 = - 1.645

75

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 21DIVIDEND 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.1000.12 – 0.16(0.50) 8(1.00)

1.0 =Rs.66.7 0.12 – 0.16 (0)

76

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) + 4.8Q

=14% Current price (obtained by solving the preceding equation)

P = Rs.69.23 Q = Rs.68.65

77

Chapter 22DIVIDEND 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 15,000Capital expenditure 8,000 7,000 10,000 8,000Equity investment 4,000 3,500 5,000 4,000Pure residualdividends 6,000 8,500 4,000 11,000Dividends 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

F . External financing

78

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 2,000otherwise

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 tobe between Rs.1.00 (the dividend for the previous year) and Rs.1.60 (80 percent 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 equitybecause of high issue costs ( in the form of underpricing and floatation costs)

Considering the conflicting requirements, it seems to make sense to payRs.1.20 per share by way of dividend. Put differently the pay out ratio may beset at 60 per cent.

3. According to the Lintner modelDt = cr EPSt + (1-c)Dt –1

EPSt =3.00, c= 0.7, r=0.6 , and Dt-1

Hence Dt = 0.7 x 0.6 x 3.00 + (1-0.7)1.20

= Rs.1.62

79

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 millionHence 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 tob ≥ 76/84b ≥ 2

The condition b ≥ 76/84 is more restructive than b≥ 2 So the maximum bonus ratio is 76/84 or 19/21

80

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 bondsGross 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 17,400,0000.4 [42,500,000 + 8,000,000/10]

25,100,000(b) Annual net cash outflow on new bonds

Interest expense 37,500,000- Tax savings on interest expense and amortisation of 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

(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

81

(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). 1,358,5002. (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 120,000,000Issue costs 2,400,000

117,600,000 (c) Tax savings on tax-deductible expenses 3,120,000

Tax rate[Call premium+Unamortised issue costs onthe 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

Interest expense 19,200,000- Tax savings on interest expense and amortisation of 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 Interest expense 18,000,000- 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

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

82

(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

1 120 100.0 0.131 0.131 2 120 83.2 0.109 0.218 3 120 69.5 0.091 0.273

83

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)

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 :

84

13,000 13,000 113,000 99,500 = + +

(1.1236) (1.1236)(1.1394) (1.1236)(1.1394)(1+r3)

Solving this for r3 we get r3 = 13.49%

To get the forward rate for year 4, r4 , the following equation may be set up :

13,500 13,500 13,500100,050 = + +

(1.1236) (1.1236)(1.1394) (1.1236)(1.1394)(1.1349)

113,500 +

(1.1236)(1.1394)(1.1349)(1+r4)

Solving this for r4 we get r4 = 14.54%

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)

Solving this for r5 we get r5 = 15.08%

85

Chapter 25HYBRID FINANCING

1. The product of the standard deviation and square root of time is :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 thetable 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 interpolatebetween 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

Then, interpolation between 1.75 and 2.00 gives

86

1.75 1.856 2.00

0.495 45.23 47.78 51.25

Chapter 24LEASING, HIRE PURCHASE, AND PROJECT FINANCE

1. NPV of the Purchase Option(Rs.in ‘000)

Year 0 1 2 3 4 51.Investment(I) (1,500)2.Revenues(Rt) 1,700 1,700 1,700 1,700 1,7003.Costs(other than (Depreciation)(Ct) 900 900 900 900 9004.Depreciation(Dt) 500 333.3 222.2 148.1 98.85.Profit before tax (Rt-Ct-Dt) 300 466.7 577.8 651.9 701.26.Profit after tax: 5(1-t) 210 326.7 404.5 456.3 490.87.Net salvage value 3008.Net cash flow (1+6+4+7) (1,500) 710 610 626.7 604.4 889.69.Discount factor at 11 percent 1.000 0.901 0.812 0.731 0.659 0.59310.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 51.Revenues(Rt) - 1,700 1,700 1,700 1,700 1,7002.Costs(other than lease rentals)(Ct) 900 900 900 900 9003.Lease rentals(Lt) 420 420 420 420 420 04.Profit before tax (Rt-Ct-Lt) -420 380 380 380 380 8005.Profit after tax (which also reflects the net cash flow)(1-t) -294 266 266 266 266 5606.Discount factor at 13 per cent 1.000 0.885 0.783 0.693 0.613 0.543

87

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

783 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

The lease rental will be as follows :Rs. 560,000 per year for the first 5 yearsRs. 20,000 per year for the next 5 years

88

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) 20,02310 - 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

20,023 215,017 +

(1.10)9 (1.10)10

89

= - 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 inventory1 Inventory period =

Annual cost of goods sold/365

(60+64)/2 = = 62.9 days

360/365

Average accounts receivableAccounts receivable = period Annual sales/365

(80+88)/2 = = 61.3 days

500/365

Average accounts payableAccounts payable =

period Annual cost of goods sold/365

(40+46)/2= = 43.43 days

360/365

Operating cycle = 62.9 + 61.3 = 124.2 daysCash cycle = 124.2 – 43.43 = 80.77 days

(110+120)/22. Inventory period = = 56.0 days

750/365

(140+150)/2Accounts receivable = = 52.9 days

period 1000/365

90

(60+66)/2Accounts payable = = 30.7 days

period 750/365

Operating cycle = 56.0 + 52.9 = 108.9 daysCash 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 2,940,000Debtors x 2 = x 2 = 490,000

12 12

Material cost 900,000Raw material x 1 = x 1 = 75,000 stock 12 12

Cash manufacturing cost 2,580,000Finished goods x 1 = x 1 = 215,000 stock 12 12

Cash balance A predetermined amount = 100,000

Sales promotion expenses 120,000

91

Prepaid sales x 1.5 = x 1.5 = 15,000promotion 12 12expensesCash balance A predetermined amount = 100,000

A : Current Assets = 995,000

B : Current Liabilites Rs.

Material cost 900,000Sundry creditors x 2 = x 2 = 150,000

12 12

Manufacturing One month’s cashexpenses outstanding manufacturing expenses = 80,000

Wages outstanding One month’s wages = 60,000

B : Current liabilities 290,000

Working capital (A – B) 705,000Add 20 % safety margin 141,000Working capital required 846,000

92

Chapter 27CASH 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 2002. Credit sales 84 84 105 105 105 140 140 1403. Cash sales 36 36 45 45 45 60 60 604. 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 84.05. Sale of machine 70.06. Interest on securities 3.07. 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 payable3. Cash purchases 3 3 3 3 3 34. Wage payments 25 25 25 25 25 255. Manufacturing expenses 32 32 32 32 32 326. General, administrative & selling expenses 15 15 15 15 15 157. Dividends 308. Taxes 359. Acquisition of

93

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 282. Receipts 129.0 137.4 150.0 235.0 179.0 203.03. Payments 135.0 135.0 215.0 135.0 155.0 220.04. 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 66.47. Minimum cash balance required 30.0 30.0 30.0 30.0 30.0 30.08. 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 25,000Payment to sundry creditors 22,000 20,000 22,000Rent 5,000 5,000 5,000Drawings 5,000 5,000 5,000Salaries & other expenses 15,000 18,000 20,000Purchase of furniture - 25,000 -

Total outflows(2to6) 47,000 73,000 52,000

94

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 5,0002. Inflows 50,000 55,000 60,0003. Outflows 47,000 73,000 52,0004. Net cash flow (2 - 3) 3,000 (18,000) 8,0005. 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 8,0008. 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 10Books of Datta Co:

Opening Balance

30,000

46,000

62,000

78,000 94,000

1,10,000

1,26,000

1,42,000

1,58,000

1,74,000

Add: Cheque received

20,000

20,000

20,000

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

46,000

62,000

78,000

94,000 1,10,000

1,26,000

1,42,000

1,58,000

1,74,000

1,90,000

Books of the Bank:

Opening Balance

30,000

30,000

30,000

30,000 30,000 30,000 50,000 70,000 90,000

1,06,000

Add: Cheques - - - - - 20,000 20,000 20,000

95

realised 20,000 20,000Less: Cheques debited

- - - - - - - - 4,000

4,000

Closing Balance

30,000

30,000

30,000

30,000 30,000 50,000 70,000 90,000 1,06,000

1,22,000

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 is2bT

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.346,4100.05

5. 3 3 b2

RP = + LL 4I

UL = 3 RP – 2 LL

I = 0.12/360 = .00033, b = Rs.1,500, = Rs.6,000, LL = Rs.100,000

3 3 x 1500 x 6,000 x 6,000RP = + 100,000

4 x .00033

= 49,695 + 100,000 = Rs.149,695

UL = 3RP – 2LL = 3 x 149,695 – 2 x 100,000 = Rs.249,085

96

Chapter 28CREDIT MANAGEMENT

1. Δ RI = [ΔS(1-V)- ΔSbn](1-t)- k ΔIΔ S

Δ I = x ACP x V360

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 ΔSΔ I = (ACPN – ACPo) +V(ACPN)

360 360

ΔS=Rs.1.5 million, V=0.80, bn=0.05, t=0.45, k=0.15, ACPN=60, ACPo=45, So=Rs.15 millionHence ΔRI = [1,500,000(1-0.8) – 1,500,000 x 0.05] (1-.45)

97

-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 ΔSΔ 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= .02Hence

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 IΔBD=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)

Rs.50,000,000 Rs.6,000,000 - 0.15 (40-25) + x 40 x 0.75

360 360

98

= - 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 the25th 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

= Rs.525,333

99

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 onInitial 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.2000Loss 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 Post-tax cost of capital : 12 percent ACP on credit sales : 20 days

100

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

∆Swhere ∆ 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 ∆Swhere ∆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 ∆ Iwhere ∆ I = savings in receivables investment

So ∆S = (ACPo – ACPn) – V x ACPn

101

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 2x250x200b. Economic Order Quantity (EOQ) = =

PC 30 2UF = 58 units (approx)

102

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 400EOQ = = 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

= 30,000 + 2498 – 4600 = Rs.27898

4. U=5000 , F= Rs.300 , PC= Rs.30 x 0.2 = Rs.6

103

2 x 5000 x 300EOQ = = 707 units

6 If 1000 units are ordered the discount is : .05 x Rs.30 = Rs.1.5 Change in profit when 1,000 units are ordered is :

5,000 5,000 Δπ = 5000 x 1.5 + - x 300

707 1,000

1000 x 28.5 x 0.2 707 x 30 x 0.2 - - = 7500 + 622-729 =Rs.7393

2 2

If 2000 units are ordered the discount is : .10 x Rs.30 = Rs.3 Change in profit when 2,000 units are ordered is :

5000 5000 2000x27x0.2 707x30x0.2 Δπ = 5000 x 3.0 + - x 300- -

707 2000 2 2

= 15,000 +1372 – 3279 = Rs.13,093

5. The quantities required for different combinations of daily usage rate(DUR)and lead times(LT) along with their probabilities are given in the following

table

LT (Days)DUR 5(0.6) 10(0.2) 15(0.2)

(Units)

4(0.3) 20*(0.18) 40(0.06) 60(0.06)

6(0.5) 30 (0.30) 60(0.10) 90(0.10) 8(0.2) 40 (0.12) 80(0.04) 120(0.04)

* Note that if the DUR is 4 units with a probability of 0.3 and the LT is 5 days with a probability of 0.6, the requirement for the combination DUR = 4 units and LT =

104

5 days is 20 units with a probability of 0.3x0.6 = 0.18. We have assumed that the probability distributions of DUR and LT are independent. All other entries in the table are derived similarly.

The normal (expected) consumption during the lead time is :20x0.18 + 30x0.30 + 40x0.12 + 40x0.06 + 60x0.10 + 80x0.04 + 60x0.06 + 90x0.10 + 120x0.04 = 46.4 tonnes

a. Costs associated with various levels of safety stock are given below :

Safety Stock Stock out Probability Expected Carrying Total CostStock* outs(in Cost Stock out Cost

tonnes)

1 2 3 4 5 6 7[3x4] [(1)x1,000] [5+6]

Tonnes Rs. Rs. Rs. 73.6 0 0 0 0 73,600 73,600 43.6 30 120,000 0.04 4,800 43,600 48,400

33.6 10 40,000 0.10 40 160,000 0.04 10,400 33,600 44,000

13.6 20 80,000 0.04 30 120,000 0.10 24,800 13,600 38,400 60 240,000 0.04

0 13.6 54,400 0.16 33.6 134,400 0.04 43,296 0 43,296 43.6 174,400 0.10

105

73.6 294,400

* Safety stock = Maximum consumption during lead time – Normal consumption during lead time

So the optimal safety stock= 13.6 tonnes Reorder level = Normal consumption during lead time + safety stock

K= 46.4 + 13.6 = 60 tonnes

b. Probability of stock out at the optimal level of safety stock = Probability(consumption being 80 or 90 or 120 tonnes)

Probability (consumption = 80 tonnes) + Probability (consumption = 90 tonnes) + Probability (consumption = 120 tonnes) = 0.04 +0.10+0.04 = 0.18

6. Reorder point is given by the formula : S(L) + F SR (L)

= 30 x 40 + 2.00 30 x 1,000 x 40 = 3,391 units

7. Item Annual Usage Price per Annual Ranking

(in Units) Unit Usage Value Rs. Rs.

1 400 20.00 8,000 6 2 15 150.00 2,250 10 3 6,000 2.00 12,000 5 4 750 18.00 13,500 4 5 1,200 25.00 30,000 1 6 25 160.00 4,000 9

7 300 2.00 600 14 8 450 1.00 450 15 9 1,500 4.00 6,000 7 10 1,300 20.00 26,000 2 11 900 2.00 1,800 11 12 1,600 15.00 24,000 3 13 600 7.50 4,500 8 14 30 40.00 1,200 12 15 45 20.00 900 13

1,35,200

106

Cumulative Value of Items & Usage

Item Rank Annual Cumulative Cumulative Cumulative No. UsageValue Annual Usage % of Usage % of Items

(Rs.) Value (Rs.) Value

5 1 30,000 30,000 22.2 6.7 10 2 26,000 56,000 41.4 13.3 12 3 24,000 80,000 59.2 20.0 4 4 13,500 93,500 69.2 26.7 3 5 12,000 105,500 78.0 33.3 1 6 8,000 113,500 83.9 40.0 9 7 6,000 119,500 88.4 46.7 13 8 4,500 124,000 91.7 53.3 6 9 4,000 128,000 94.7 60.0 2 10 2,250 130,250 96.3 66.7 11 11 1,800 132,050 97.7 73.3 14 12 1,200 133,250 98.6 80.0 15 13 900 134,150 99.2 86.7 7 14 600 134,750 99.7 93.3

107

8 15 450 135,200 100.0 100.0

Class No. of Items % to the Total Annual Usage % to Total Value Value Rs.

A 4 26.7 93,500 69.2 B 3 20.0 26,000 19.2 C 18 53.3 15,700 11.6

15 135,200

Chapter 30WORKING CAPITAL FINANCING

1. Annual interest cost is given by , Discount % 360

x 1- Discount % Credit period – Discount period

Therefore, the annual per cent interest cost for the given credit terms will be as follows:

a. 0.01 360 x = 0.182 = 18.2%

0.99 20

b. 0.02 360 x = 0.367 = 36.7%

0.98 20

c. 0.03 360 x = 0.318 = 31.8%

0.97 35

d. 0.01 360

108

x = 0.364 = 36.4%0.99 10

2.a. 0.01 360

x = 0.104 = 10.4%0.99 35

b. 0.02 360 x = 0.21 = 21%

0.98 35

c. 0.03 360 x = 0.223 = 22.3%

0.97 50

d. 0.01 360 x = 0.145 = 14.5%

0.99 253. The maximum permissible bank finance under the three methods suggested by

The Tandon Committee are :

Method 1 : 0.75(CA-CL) = 0.75(36-12) = Rs.18 millionMethod 2 : 0.75(CA)-CL = 0.75(36-12 = Rs.15 million

Method 3 : 0.75(CA-CCA)-CL = 0.75(36-18)-12 = Rs.1.5 million

109

Chapter 31WORKING CAPITAL MANAGEMENT :EXTENSIONS

1.(a) The discriminant function is :

Zi = aXi + bYi

where Zi = discriminant score for the ith account Xi = quick ratio for the ith accountYi = EBDIT/Sales ratio for the ith account

The estimates of a and b are : y

2. dx - xy . dy a =

x 2. y 2 - xy . xy

x 2. dy xy . dx

b = x

2 y 2 xy xy

The basic calculations for deriving the estimates of a and b are giventhe accompanying table.

110

Drawing on the information in the accompanying table we find that

Xi = 19.81 Yi= 391 (Xi-X)2 Yi-Y)2 Xi-X)(Yi-Y)

X = 0.7924 Y = 15.64 = 0.8311 =1661.76 = 10.007

Account Xi Yi (Xi-X) (Yi-Y) (Xi-X)2 (Yi-Y)2 (Xi-X)(Yi-Y) Number

1 0.90 15 0.1076 -0.64 0.0116 0.4096 -0.06892 0.75 20 -0.0424 4.36 0.0018 19.0096 -0.18493 1.05 10 -0.2576 -5.64 0.0664 31.8096 -1.45294 0.85 14 0.0576 -1.64 0.0033 2.6896 -0.0945

G 5 0.65 16 -0.1424 0.36 0.0203 0.1296 -0.513R 6 1.20 20 0.4076 4.36 0.1661 19.0096 1.7771O 7 0.90 24 0.1076 8.36 0.0116 69.8896 0.8995U 8 0.84 26 0.0476 10.36 0.0023 107.3296 0.4931P 9 0.93 11 0.1376 -4.64 0.0189 21.5296 -0.6385 10 0.78 18 -0.0124 2.36 0.0002 5.5696 -0.0293I 11 0.96 12 0.1676 -3.64 0.0281 13.2496 -0.6101 12 1.02 25 0.2276 9.36 0.0518 87.6096 2.1303 13 0.81 26 0.0176 10.36 0.0003 107.3296 0.1823 14 0.76 30 -0.0324 14.36 0.0010 206.2096 -0.4653 15 1.02 28 0.2276 12.36 0.0518 152.7696 2.8131

16 0.76 10 -0.0324 -5.64 0.0010 31.8069 0.1827 17 0.68 12 -0.1124 -3.64 0.0126 13.2496 0.4091G 18 0.56 4 -0.2324 -11.64 0.0540 135.4896 2.7051R 19 0.62 18 -0.1724 2.36 0.0297 5.5696 -0.4069O 20 0.92 -4 0.1276 -19.64 0.0163 385.7296 -2.5061U 21 0.58 20 -0.2124 4.36 0.0451 19.0096 -0.9261P 22 0.70 8 -0.0924 - 7.64 0.0085 58.3696 0.7059 23 0.52 15 –0.2724 -0.64 0.0742 0.4096 0.1743II 24 0.45 6 –0.3424 -9.64 0.1172 92.9296 3.3007 25 0.60 7 –0.1924 -8.64 0.0370 74.6496 1.6623

19.81 391 0.8311 1661.76 9.539

Sum of Xi for group 1 13.42X1 = = = 0.8947

15 15

Sum of Xi for group 2 6.39

111

X2 = = = 0.639010 10

Sum of Yi for group 1 295Y1 = = = 19.67

15 15

Sum of Yi for group 2 96Y2 = = = 9.60

10 10

1 0.8311x 2 = Xi –X)2 = = 0.0346

n-1 25-1

1 1661.76 y

2 = Yi – Y)2 = = 69.24n-1 25-1

1 10.0007xy = Xi-X)(Yi-Y) = = 0.4167

n-1 25-1

dx = X1 - X2 = 0.8947 – 0.6390 = 0.2557

dy = Y1 – Y2 = 19.67 – 9.60 = 10.07

Substituting these values in the equations for a and b we get :

69.24 x 0.2557 – 0.4167 x 10.07a = = 6.079 0.0346 x 69.24 – 0.4167 x 0.4167

0.0346 x 10.07 – 0.4167 x 0.2557b = = 0.1089

0.0346 x 69.24 – 0.4167 x 0.4167

Hence , the discriminant function is :Zi = 6.079 Xi + 0.1089 Yi

(b) Choice of the cutoff pointThe Zi score for various accounts are shown below

112

Zi scores for various accounts

Account No. Zi Score

1 7.10462 6.73733 7.47204 6.69185 5.69386 9.47287 8.08478 7.93789 6.851410 6.701811 7.142612 8.923113 7.755414 7.887015 9.249816 5.709017 5.440518 3.839819 5.729220 5.157121 5.703822 5.126523 4.794624 3.389025 4.4097

The Zi scores arranged in an ascending order are shown below

Good(G)Account Number Zi Score or

Bad (B)

24 3.3890 B18 3.8398 B25 4.4097 B23 4.7946 B22 5.1265 B20 5.1571 B17 5.4405 B 5 5.6938 G

113

21 5.7038 B16 5.7090 B19 5.7292 B 4 6.6918 G10 6.7018 G 2 6.7373 G 9 6.8514 G 1 7.1046 G11 7.1426 G 3 7.4720 G13 7.7554 G14 7.8870 G 8 7.9378 G 7 8.0847 G12 8.9231 G15 9.2498 G 6 9.4728 G

From the above table, it is evident that a Zi score which represents the mid-point between the Zi scores of account numbers 19 and 4 results in the minimum number of misclassifications . This Zi

score is :

5.7292 + 6.6918= 6.2105

2Given this cut-off Zi score, there is just one misclassification (Account number 5)

114

Chapter 4ANALYSING FINANCIAL PERFORMANCE

Net profit1. Return on equity =

Equity

= Net profit Net sales Total assets x x

Net sales Total assets Equity

1 = 0.05 x 1.5 x = 0.25 or 25 per cent

0.3

Debt EquityNote : = 0.7 So = 1-0.7 = 0.3

Total assets Total assets

Hence Total assets/Equity = 1/0.3

2. PBT = Rs.40 million PBIT

Times interest covered = = 6 Interest

115

So PBIT = 6 x InterestPBIT – Interest = PBT = Rs.40 million 6 x Interest = Rs.40 millionHence Interest = Rs.8 million

3. Sales = Rs.7,000,000Net profit margin = 6 per centNet profit = Rs.7000000 x 0.06 = 420,000Tax rate = 60 per cent

420,000 So, Profit before tax = = Rs.1,050,000

(1-.6)Interest charge = Rs.150,000

So Profit before interest and taxes = Rs.1,200,000 Hence

1,200,000 Times interest covered ratio = = 8

150,000

4. CA = 1500 CL = 600 Let BB stand for bank borrowingCA+BB

= 1.5CL+BB

1500+BB = 1.5

600+BB

BB = 120

1,000,0005. Average daily credit sales = = 2740

365160000

ACP = = 58.4 2740

If the accounts receivable has to be reduced to 120,000 the ACP must be:120,000

x 58.4 = 43.8days

116

160,000

Current assets6. Current ratio = = 1.5

Current liabilities

Current assets - InventoriesAcid-test ratio = = 1.2

Current liabilities

Current liabilities = 800,000 Sales

Inventory turnover ratio = = 5 InventoriesCurrent assets - Inventories

Acid-test ratio = = 1.2 Current liabilities

Current assets InventoriesThis means - = 1.2

Current liabilities Current liabilities

Inventories1.5 - = 1.2

800,000

Inventories = 0.3

800,000

Inventories = 240,000

Sales = 5 So Sales = 1,200,000

2,40,000

7. Debt/equity = 0.60Equity = 50,000 + 60,000 = 110,000So Debt = 0.6 x 110,000 = 66,000Hence Total assets = 110,000+66,000 = 176,000Total assets turnover ratio = 1.5So Sales = 1.5 x 176,000 = 264,000

117

Gross profit margin = 20 per centSo Cost of goods sold = 0.8 x 264,000 = 211,200Day’s sales outstanding in accounts receivable = 40 days

SalesSo Accounts receivable = x 40

360

264,000 = x 40 = 29,333

360

Cost of goods sold 211,200Inventory turnover ratio = = = 5

Inventory Inventory

So Inventory = 42,240

Assuming that the debt of 66,000 represent current liabilitiesCash + Accounts receivable

Acid-test ratio = Current liabilities

Cash + 29,333 = = 1.2

66,000So Cash = 49867

Plant and equipment = Total assets - Inventories – Accounts receivable – Cash = 176,000 - 42240 - 29333 – 49867 = 54560

Pricing together everything we get

Balance SheetEquity capital 50,000 Plant & equipment 54,560Retained earnings 60,000 Inventories 42,240Debt(Current liabilities) 66,000 Accounts receivable 29,333

Cash 49,867

176,000 176,000

Sales 264,000Cost of goods sold 211,200

118

Cash & bank balances + Receivables + Inventories + Pre-paid expenses8. (i) Current ratio =

Short-term bank borrowings + Trade creditors + Provisions

5,000,000+15,000,000+20,000,000+2,500,000 = 15,000,000+10,000,000+5,000,000

42,500,000 = = 1.42

30,000,000

Current assets – Inventories 22,500,000(ii) Acid-test ratio = = = 0.75

Current liabilities 30,000,000

Long-term debt + Current liabilities (iii) Debt-equity ratio =

Equity capital + Reserves & surplus

12,500,000 + 30,000,000 = = 1.31 10,000,000 + 22,500,000

Profit before interest and tax (iv) Times interest coverage ratio =

Interest

15,100,000 = = 3.02

5,000,000

Cost of goods sold 72,000,000 (v) Inventory turnover period = = = 3.6

Inventory 20,000,000 365

(vi) Average collection period = Net sales/Accounts receivable

365 = = 57.6 days

95,000,000/15,000,000

119

Net sales 95,000,000 (vii) Total assets turnover ratio = = = 1.27

Total assets 75,000,000

Profit after tax 5,100,000 (ix) Net profit margin = = = 5.4%

Net sales 95,000,000

PBIT 15,100,000 (x) Earning power = = = 20.1%

Total assets 75,000,000

Equity earning 5,100,000 (xi) Return on equity = = = 15.7%

Net worth 32,500,000

The comparison of the Omex’s ratios with the standard is given below

Omex StandardCurrent ratio 1.42 1.5Acid-test ratio 0.75 0.80Debt-equity ratio 1.31 1.5Times interest covered ratio 3.02 3.5Inventory turnover ratio 3.6 4.0Average collection period 57.6 days 60 daysTotal assets turnover ratio 1.27 1.0Net profit margin ratio 5.4% 6%Earning power 20.1% 18%Return on equity 15.7% 15%

Note that solutions to problems 10 & 11 are not given

MINICASE

Solution:

(a) Key ratios for 20 X 5 12.4

Current ratio = = 0.93 13.4

8.8 + 6.7

120

Debt-equity ratio = = 0.98 6.5 + 9.3

57.4Total assets turnover ratio = = 1.96

[(34 – 6.6) + (38 – 6.7)] / 2

3.0Net profit margin = = 5.2 percent 57.4

5 Earning power = = 17.0 percent

[(34 – 6.6) + (38 – 6.7)] / 2

3.0Return on equity = = 20.2 percent

(13.9 + 15.8) / 2

(b) Dupont Chart for 20 x 5

–

÷

121

Return on total assets

10.2%

Net profitmargin5.2%

Total asset turnover

1.96

Net profit3.0

Net sales57.4

Net sales57.4

Net sales +/-Non-op. surplus

deficit 57.8

Total costs54.8

Average fixed assets

21.4

÷

+

+

(c) Common size and common base financial statements

Common Size Financial Statements Profit and Loss Account

Regular (in million) Common Size (%)

20 X 4 20 X 5 20 X 4 20 X 5 Net sales 39.0 57.4 100 100 Cost of goods sold 30.5 45.8 78 80 Gross profit 8.5 11.6 22 20 Operating expenses 4.9 7.0 13 12 Operating profit 3.6 4.6 9 8 Non-operating surplus / deficit

0.5 0.4 1 1

PBIT 4.1 5.0 11 9 Interest 1.5 2.0 4 3 PBT 2.6 3.0 7 5 Tax - - - - Profit after tax 2.6 3.0 7 5

Balance Sheet

Regular (in million) Common Size (%)

20 X 4 20 X 5 20 X 4 20 X 5

122

Average total assets29.35

Average net current assets 54.0

Average other assets

2.55

Shareholders’ funds 13.9 15.8 51 50 Loan funds 13.5 15.5 49 50

Total 27.4 31.3 100 100 Net fixed assets 19.6 23.2 72 74 Net current assets 5.1 5.7 19 18 Other assets 2.7 2.4 10 8

Total 27.4 31.3 100 100

Common Base Year Financial Statements Profit and Loss Account

Regular (in million) Common Base Year(%)

20 X 4 20 X 5 20 X 4 20 X 5 Net sales 39.0 57.4 100 147 Cost of goods sold 30.5 45.8 100 150 Gross profit 8.5 11.6 100 136 Operating expenses 4.9 7.0 100 43 Operating profit 3.6 4.6 100 128 Non-operating surplus / deficit

0.5 0.4 100 80

PBIT 4.1 5.0 100 122 Interest 1.5 2.0 100 133 PBT 2.6 3.0 100 115 Tax - - 100 100 Profit after tax 2.6 3.0 100 115

Balance Sheet

Regular (in million) Common Base Year(%)

20 X 4 20 X 5 20 X 4 20 X 5 Shareholders’ funds 13.9 15.8 100 114 Loan funds 13.5 15.5 100 115

Total 27.4 31.3 100 114 Net fixed assets 19.6 23.2 100 118

123

Net current assets 5.1 5.7 100 112 Other assets 2.7 2.4 100 89

Total 27.4 31.3 100 114

(d) The financial strengths of the company are:

Asset productivity appears to be good. Earning power and return on equity are quite satisfactory Revenues have grown impressively over 20 x 4 – 20 x 5

The financial weaknesses of the company are:

Current ratio is unusually low While revenues grew impressively, costs rose even faster: As a result profit margins

declined The company did not have any tax liability in the last two years. If the company has to

bear the burden of regular taxes, its return on equity will be adversely impacted

(e) The following are the problems in financial statement analysis

There is no underlying theory It is difficult to find suitable benchmarks for conglomerate firms Firms may resort to window dressing Financial statements do not reflect price level changes Diversity of accounting policies may vitiate financial statement analysis It is somewhat difficult to judge whether a certain ratio is ‘good’ or ‘bad’

(f) The qualitative factors relevant for evaluating the performance and prospects of a company are as follows:

Are the company’s revenues tied to one key customer? To what extent are the company’s revenues tied to one key product? To what extent does the company rely on a single supplier? What percentage of the company’s business is generated overseas? How will competition impact the company? What are the future prospects of the firm? What could be the effect of the changes in the legal and regulatory environment?

124

Chapter 5BREAK-EVEN ANALYSIS AND LEVERAGES

1. a. EBIT = Q(P-V)-F = 20,000(10-6)-50,000 = Rs.30,000

b. EBIT = 12,000(50-30)-200,000 = Rs.40,000

2. EBIT = Q(P-V)-FEBIT=Rs.30,000 , Q=5,000 , P=Rs.30 , V=Rs.20So, 30,000 = 5,000(30-20)-FSo, F = Rs.20,000.

Q(P-V)3. DOL =

Q(P-V)-F

P=Rs.1,000 ,V=Rs.600, F=Rs.100,000

400(1,000-600)DOL(Q=400) = = 2.67

400(1,000-600)-100,000

600(1,000-600)DOL(Q=600) = = 1.71

600(1,000-600)-1,00,000

4. DOL(Q=15000) = 2.5

125

EBIT(Q=15000) = Rs.3,00,000

Percentage change in EBIT = DOL x Percentage change in Q If the percentage change in Q is –10%

Percentage change in EBIT = 2.5 x –10% = - 25%If the percentage change in Q is + 5%Percentage change in EBIT = 2.5 x 5% = 12.5%

Hence the possible forecast errors of EBIT in percentage terms is –25% to 12.5%The corresponding value range of EBIT is Rs.225,000 to Rs.337,500

5. Break even point in units F 50,000

Q = = =10,000 units P-V 12-7

Break even point in rupees:Q x P = 10,000 x Rs.12 = Rs,120,000

To earn a pre-tax income of Rs.60,000 the number of units to be sold is

F + Target pre-tax incomeQ =

P-V = 50,000 + 60,000

= 22,000 units 12-7

To earn an after-tax income of Rs.60,000 if the tax rate is 40 per cent, thePre-tax income must be Rs.60,000

= Rs.100,000 1-.4

Hence the number of units to be sold to earn an after-tax income of Rs.60,000 is :

50,000 + 100,000Q = = 30,000 units

12-7

6. P-V = 0.30 P-V = Rs.6 F=20,000 P

20000 6

126

Q = = 3,333 P = = Rs.20 6 0.30

Break even point in rupees = Rs.66,666

When net income is Rs.60,00020,000 +60,000

Q = = 13,3336

Sales in rupees = 13,333 x Rs.20 = Rs.266,666

10,0007. (a) P = Rs.30 ,V=Rs.16, F=Rs.10,000 Q = = 714.3 bags

30-16

(b) Profit when the quantity is 3000 bags Profit =3,000(30-16)-10000 = Rs.3200010 per cent increase in production means that the quantity is 3300 bagsAt that productionProfit = 3,300(30-16)-10,000 = Rs.36200So, the percentage change in profit is :

36200-32000 = 13.1%

32000

(c) A 10 per cent increase in selling price means that P= Rs.33Break-even point when P= Rs.33

10,000Q = = 588.2 bags

33-16

(d) A 50 per cent increase in fixed costs means that F=Rs.15,000Break-even point when F= Rs.15,000 15,000Q = = 882.4 bags 33-16

(e) If V= Rs.20, the break-even point is : 10,000

Q = = 1000 bags 30-20

127

8. A B C D Selling price per unit Rs.10 Rs.16.66 Rs.20 Rs.10 Variable cost per unit Rs.6 Rs.8.33 Rs.12 Rs.5 Contribution margin per unit Rs.4 Rs.8.33 Rs.8 Rs.5 Contribution margin ratio 0.4 0.5 0.4 0.5 Total fixed costs Rs.16000 Rs.100000 Rs.160000 Rs.60000 Break-even point in units 4000 12000 20000 12000 Break-even sales(Rs.) Rs.40000 Rs.200000 Rs.400000 Rs.120000 Net income(loss)before tax Rs.30000 Rs.80000 Rs.(40000) Rs.40000 No.of units sold 11500 21600 15000 20000

9. (a) Break-even point for product P 30,000

= 3,000 units 30-20

Break-even point for product Q100,000

= 5,000 units 50-30

Break-even point for product R200,000

= 5,000 units 80-40

(b) The weighted contribution margin is : 5000 8,000 6,000

x Rs.10 + x Rs.20 + x Rs.40 = Rs.23.68 19000 19000 19000

10. EBITDFL =

Dp

EBIT – I -T

at Q = 20000EBIT= 20000(Rs.40-Rs.24)=Rs.320,000

Rs.320,000

128

DFL(Q=20,000) = Rs.10,000

Rs.320,000-Rs.30,000 - (1-.5)

= 1.185

11. (a) EBIT = Q(P-V) – F

Firm A : 20,000(Rs.20-Rs.15) – Rs.40,000 = Rs.60,000 Firm B : 10,000(Rs.50-Rs.30) - Rs.70,000 = Rs.130,000

Firm C : 3,000(Rs.100-Rs.40)- Rs.100,000 = Rs.80,000(EBIT-I) (1-T) - Dp

(b) EPS = n

(Rs.60,000-Rs.10,000)(1-.4)-Rs.5,000 Firm A : = Rs.1.9

10,000

(Rs.130,000-Rs.20,000)(1-.5)-Rs.5,000 Firm B : = Rs.4.17

12,000

(Rs.80,000-Rs.40,000)(1-.6)-Rs.10,000 Firm C : = Rs.0.40

15,000F + I

(c) BEP =P – V

Rs.40,000 + Rs.10,000 Firm A : = 10,000 units

Rs.20 – Rs.15

Rs.70,000 + Rs.20,000Firm B : = 4,500 units

Rs.50 – Rs.30

Rs.100,000 + Rs.40,000Firm C : = 2,333 units

Rs.100 – Rs.40

Q(P-V)

129

(d) DOL = Q(P-V)-F

20,000(Rs.20-Rs.15)Firm A : = 1.67

20,000(Rs.20-Rs.15)- Rs.40,000

10,000(Rs.50-Rs.30)Firm B : = 1.54

10,000(Rs.50-Rs.30)-Rs.70,000

3,000(Rs.100-Rs.40)Firm C : = 2.25

3,000(Rs.100-Rs.40)-Rs.100,000

EBIT (e) DFL = Dp

EBIT – I - (1-T)

Rs.60,000Firm A : = 1.44

Rs.5000Rs.60,000-Rs.10,000 -

(1-.4)

Rs.130,000Firm B : = 1.30

Rs.5,000Rs.130,000-Rs.20,000 -

(1-.5)

Rs.80,000Firm C : = 5.333

Rs.10,000Rs.80,000-Rs.40,000-

(1-.6) (f) DTL = DOL x DFL

Firm A : 1.67 x 1.44 = 2.40Firm B : 1.54 x 1.30 = 2.00Firm C : 2.25 x 5.333 = 12.00

130

Chapter 6FINANCIAL PLANNING AND BUDGETING

1. The proforma income statement of Modern Electronics Ltd for year 3 based on the per cent of sales method is given below

Average per cent Proforma income statement of sales for year 3 assuming sales of

1020

Net sales 100.0 1020.0Cost of goods sold 76.33 778.57Gross profit 23.67 241.43Selling expenses 7.40 75.48General & administration expenses 6.63 67.63Depreciation 6.75 68.85Operating profit 2.90 29.58Non-operating surplus/deficit 1.07 10.91Earnings before interest and taxes 3.96 40.39Interest 1.24 12.65Earnings before tax 2.72 27.74Tax 1.00 10.20Earnings after tax 1.72 17.54Dividends (given) 8.00Retained earnings 9.54

131

2. The proforma income statement of Modern Electronics for year 3 using the the combination method is given below :

Average per cent Proforma income statementof sales for year 3

Net sales 100.0 1020.0Cost of goods sold 76.33 778.57Gross profit 23.67 241.43Selling expenses 7.40 75.48General & administration expenses Budgeted 55.00Depreciation Budgeted 60.00Operating profit 50.95Non-operating surplus/deficit 1.07 10.91Earnings before interest and taxes 61.86 Interest Budgeted 12.0Earnings before tax 49.86 Tax 1.00 10.20Earnings after tax 39.66Dividends (given) Budgeted 8.00Retained earnings 31.66

132

3. The proforma balance sheet of Modern Electronics Ltd for year 3 is given below

Average of percent Projections for year 3 of sales or some based on a forecast other basis sales of 1400

Net sales 100.0 1020.0

ASSETSFixed assets (net) 40.23 410.35Investments No change 20.00

Current assets, loans & advances :Cash and bank 1.54 15.71Receivables 22.49 229.40Inventories 21.60 220.32

Prepaid expenses 5.09 51.92Miscellaneous expenditure & losses No change 14.00

961.70

LIABILITIES :

Share capital :Equity No change 150.00Reserves & surplus Proforma income 160.66

statement

Secured loans:Term loans No change 175.00Bank borrowings No change 199.00

133

Current liabilities :Trade creditors 17.33 176.77Provisions 5.03 51.31

External funds requirement Balancing figure 48.96

961.7

A L4. EFR = - S – m S1 (1-d)

S S

800 190 = - 300 – 0.06 x 1,300 (1-0.5)

1000 1000

= (0.61 x 300) – (0.06) x 1,300 x (0.5)

= 183 – 39 = Rs.144.

Projected Income Statement for Year Ending 31st December , 2001

Sales 1,300Profits before tax 195Taxes 117Profit after tax (6% on sales) 78Dividends 39Retained earnings 39

Projected Balance Sheet as at 31.12 2001

Liabilities Assets

Share capital 150 Fixed assets 520Retained earnings 219 Inventories 260Term loans (80+72) 152 Receivables 195Short-term bank borrowings 272 Cash 65(200 + 72)Accounts payable 182

134

Provisions 65

1,040 1,040

A L5. (a) EFR = - S – m S1 (1 –d)

S S

150 30 = - x 80 – (0.625) x 240 x (0.5)

160 160

= (60 – 7.5) = 52.5

(b) Projected Balance Sheet as on 31.12.20X1

Liabilities Assets

Share capital 56.25 Net fixed assets 90Retained earnings 47.50 Inventories 75(40 + 7.5)Term loans 46.25 Debtors 45Short-term bank 30.00 Cash 15borrowingsTrade creditors 37.50Provisions 7.50

225.00 225.00

(c) 20X0 20X1 i) Current ratio 1.50 1.80 ii) Debt to total assets ratio 0.53 0.54 iii) Return on equity 14.3% 14.5%

(d) A L

EFR 20X1= - S – mS1 (1 – d) S S

150 30

135

= - 20 – 0.0625 x 180 x 0.5160 160

= 9.38

150 x (1.125) 30 x 1.125EFR 20X2 = - x 20 – 0.0625 x 200 x 0.5

180 180

168.75 33.75 = - x 20 –0.0625 x 220 x 0.5

180 180

= 8.75

168.75 x (1.11) 33.75 x (1.11)EFR 20X3 = - 20 – 0.0625 x 220 x 0.5

200 200

187.31 37.46= - x 20 – 6.88

200 200

= 8.11

187.31 x (1.1) 37.46 x (1.1) EFR 20X4 = - x 20 – 0.0625 x 240 x 0.5

220 220

= 7.49

Balance Sheet as on 31st December, 20X4

Liabilities Rs. Assets Rs.

Share capital 46.87 Net fixed assets 90.00(30+16.87) (60 x 240/160)Retained earnings Inventories(40.00+5.63+6.25+6.88+7.50) 66.26 (50x240/160) 75.00Term loans(20+16.87) 36.87 Debtors (30x240/160) 45.00Short-term bank borrowings 30.00 Cash (10x240/160) 15.00

136

Trade creditors 37.50Provisions 7.50

225.00 225.00

6. EFR A L m (1+g) (1-d)= - -

S S S gGiven A/S= 0.8 , L/S= 0.5 , m= 0.05 , d= 0.6 and EFR = 0 we have,

(0.05)(1+g)(0.4)(0.8-0.5) - = 0

g

(0.05)(1+g)(0.4)i.e. 0.3 - = 0

g

Solving the above equation we get g = 7.14%

A L7. (a) EFR = - S – mS1 (1-d)

S S

320 70= - x 100 – (0.05) (500) (0.5)

400 400

= Rs.50

(b) Let CA = denote Current assetsCL = Current liabilities

SCL = Spontaneous current liabilities STL = Short-term bank borrowings FA = Fixed assets

and LTL = Long-term loans

i. Current ratio CA

i.e greater than or equal to 1.25 or CL

137

CA

STL +SCL

As at the end of 20X1, CA = 20x0 x 1.25 = 237.50SCL = 70 x 1.25 = 87.50Substituting these values, we get1.25 (STL + 87.5) 237.50or 1.25 STL x

or STL =

1.25i.e STL Rs.102.50

ii. Ratio of fixed assets to long term loans 1.25FA

LTL

At the end of 20X1 FA = 130 x 1.25 = 162.5 162.5

LTL or LTL = Rs.130 1.25

If STL and LTL denote the maximum increase in ST borrowings & LT

borrowings , we have : STL = STL (20X1) – STL (20X1) = 102.50 – 60.00 = 42.50LTL = LTL (20X1)- LTL (20X1) = 130.00 – 80.00 = 50.00Hence, the suggested mix for raising external funds will be :

Short-term borrowings 42.50 Long-term loans 7.50 Additional equity issue --

50.00

A L8. EFR = - S – m S1 (1-d)

S S A S

Therefore, mS1(1-d) – - S represents surplus funds S S

Given m= 0.06, S1 =11,000, d= 0.6 , L= 3,000 S= 10,000 and surplus funds = 150 we have

138

A 3,000(0.06) 11,000 (1-0.6) - - 1,000 = 150

10,000 10,000

A – 3,000= (0.06) (0.4) (11,000) – 150 = 114

10

or A = (1,140 + 3,000) = 4,140

The total assets of Videosonics must be 4,140

9. m= .05 , d = 0.6 , A/E = 2.5 , A/S = 1.4

m (1-d)A/E .05 (1-0.6) 2.5 (a) g = = = 3.70 per cent

A/S –m(1-d)A/E 1.4 -.05 (1-0.6) 2.5

.05 (1-0.6) x A/E(b) 0.5 = A/E = 3.33

2.4 - .05 (1-0.6) A/E

d = 0.466The dividend payout ratio must be reduced from 60 per cent to 46.6 per cent

.05 (1-0.6) x A/E(c) .05 = A/E = 3.33

1.4 -.05 (1-0.6) A/E

The A/E ratio must increase from 2.5 to 3.33

m (1-0.6) 2.5(d) .06 = m = 7.92 per cent

1.4 – m (1-0.6) x 2.5

The net profit margin must increase from 5 per cent to 7.92 per cent

.05 (1-0.6) 2.5(e) .06 = A/S = .883

A/S - .05 (1-0.6) 2.5

The asset to sales ratio must decrease from 1.4 to 0.883

139

Chapter 32 CORPORATE VALUATION

1. (a) The calculations for Hitech Limited are shown below :Year 2 Year3

EBIT PBT 86 102+ Interest expense 24 28- Interest income (10) (15)- Non-operating income (5) (10) EBIT 95 105

Tax on EBIT Tax provision on income statement 26 32+ Tax shield on interest expense 9.6 11.2- Tax on interest income (4) (6)- Tax on non-operating income (2) (4) Tax on EBIT 29.6 33.2

NOPLAT 65.4 71.8Net investment (50) (50)Non-operating cash flow (post-tax) 3 6FCFF 18.4 27.8

(b) The financing flow for years 2 and 3 is as follows :Year 2 Year 3

After-tax interest expense 14.4 16.8 Cash dividend 30 40- Net borrowings (30) (30)+ Excess marketable securities 30 10- After-tax income on excess (6) (9) marketable securities- Share issue (20) -

18.4 27.8

140

(c) Year 2 Year 3Invested capital (Beginning) 310 360Invested capital (Ending) 360 410NOPLAT 65.4 71.8Turnover 400 460Net investment 50 50

Post-tax operating margin 16.35% 15.61%Capital turnover 1.29 1.28ROIC 21.1% 19.9%Growth rate 16.1% 13.9%FCF 15.4 21.8

2. Televista Corporation

0 1 2 3 4 5 Base year

1. Revenues 1600 1920 2304 2765 3318 36502. EBIT 240 288 346 415 498 5473. EBIT (1-t) 156 187 225 270 323 3564. Cap. exp. 200 240 288 346 415 -

- Depreciation 120 144 173 207 2495. Working capital 400 480 576 691 829 9126. Working capital 80 96 115 138 83 7. FCFF 11 13 16 19 273

(3-4-6)

Discount factor 0.876 0.767 0.672 .589Present value 9.64 9.97 10.76 11.19

Cost of capital for the high growth period

0.4 [12% + 1.25 x 7%] + 0.6 [15% (1 - .35)]8.3% + 5.85%

= 14.15%

Cost of capital for the stable growth period0.5 [12% + 1.00 x 6%] + 0.5 [14% (1 - .35)]

9% + 4.55% = 13.55%

141

Present value of FCFF during the explicit forecast period= 9.64 + 9.97 + 10.76 + 11.19 = 41.56

273 273Horizon value = = = 7690

0.1355 – 0.10 0.0355

Present value of horizon value = 4529.5

Value of the firm = 41.56 + 4529.50 = Rs.4571.06 million

3. The WACC for different periods may be calculated :

WACC in the high growth period

Year kd(1-t) = 15% (1-t) ke = Rf + x Market risk premium ka = wd kd (1-t)+ we ke

1 15 (0.94) = 14.1% 12 + 1.3 x 7 = 21.1% 0.5 x 14.1 + 0.5 x 21.1 = 17.6%2 15 (0.88) = 13.2% 21.1% 0.5 x 13.2 + 0.5 x 21.1 = 17.2%3 15 (0.82) = 12.3% 21.1% 0.5 x 12.3 + 0.5 x 21.1 = 16.7%4 15 (0.76) = 11.4% 21.1% 0.5 x 11.4 + 0.5 x 21.1 = 16.3%5 15 (0.70) = 10.5% 21.1% 0.5 x 10.5 + 0.5 x 21.1 = 15.8%

WACC in the transition periodkd(1-t) = 14 (1 – 0.3) = 9.8%ke = 11 + 1.1 x 6 = 17.6%ka = 0.44 x 9.8 + 0.56 x 17.6 = 14.2%

WACC for the stable growth periodkd(1-t) = 13 (1 – 0.3) = 9.1%ke = 11 + 1.0 x 5 = 16%ka = 1/3 x 9.1 + 2/3 x 16 = 13.7%

The FCFF for years 1 to 11 is calculated below. The present value of the FCFF for the years 1 to 10 is also calculated below.

Multisoft Limited

Period Growth rate (%)

EBIT Tax rate (%)

EBIT (1-t)

Cap. exp.

Dep. WC FCFF D/E Beta WACC %

PV Factor

Present value

0 90 100 601 40 126 6 118 140 84 26 36 1:1 1.3 17.6 .850 30.6

142

2 40 176 12 155 196 118 39 38 1:1 1.3 17.2 .726 27.63 40 247 18 203 274 165 50 44 1:1 1.3 16.7 .622 27.44 40 346 24 263 384 230 70 39 1:1 1.3 16.3 .535 20.85 40 484 30 339 538 323 98 26 1:1 1.3 15.8 .462 12.06 34 649 30 454 721 432 132 33 0.8:1 1.1 14.2 .405 13.47 28 830 30 581 922 553 169 43 0.8:1 1.1 14.2 .354 15.48 22 1013 30 709 1125 675 206 53 0.8:1 1.1 14.2 .310 16.79 16 1175 30 822 1305 783 239 61 0.8:1 1.1 14.2 .272 16.910 10 1292 30 905 1436 862 263 68 0.8:1 1.1 14.2 .238 16.611 10 1421 30 995 1580 948 289 74 0.5:

1.01.1 13.7 476

673.4The present value of continuing value is :

FCF11 74 x PV factor 10 years = x 0.238 = 476

k – g 0.137 – 0.100

This is shown in the present value cell against year 11.

The value of the firm is equal to :Present value of FCFF during + Present value of continuingThe explicit forecast period of 10 years value

This adds up to Rs.685.4 million as shown below

MINI CASE

Solution:Solution:

143

1 2 3 4 5 61. Revenues 950 1,000 1,200 1,450 1,660 1,7702. PBIT 140 115 130 222 245 2873. NOPAT = PBIT (1 – .35)

91 74.8 84.5 144.3 159.3 186.6

4. Depreciation 55 85 80 83 85 875. Gross cash flow 146 159.8 164.5 227.3 244.3 273.76. Gross investment in fixed assets

100 250 85 100 105 120

7. Investment in net current assets

10 15 70 70 70 54

8. Total investment 110 265 155 170 175 1749. FCFF (5) – (8) 36 (105.2) 9.5 57.3 69.3 99.6

0.4 1.0 WACC = x 12 x (1 – 0.35) + {8 + 1.06 (8)} 1.4 1.4

= 14%

99.6 (1.10)Continuing Value = = 2739.00

0.14 – 0.10

2739Present value of continuing value = = 1249 (1.14)6

PV of the FCFF during the explicit forecast period 3.6 105.2 9.5 57.3 69.3 99.6= – + + + + (1.14) (1.14)2

(1.14)3 (1.14)4 (1.14)5 (1.14)6

= 72.4 Firm value = 72.4 + 1249 = 1321.4

Value of equity = 1321.4 – 200 = 1121.4 million

Chapter 33VALUE BASED MANAGEMENT

1. The value created by the new strategy is calculated below :

Current Income Statement ProjectionValues (Year 0) 1 2 3 4 5

Sales 2000 2240 2509 2810 3147 3147Gross margin (20%) 400 448 502 562 629 629Selling and general 160 179 201 225 252 252 administration (8%)Profit before tax 240 269 301 337 378 378Tax 72 81 90 101 113 113 Profit after tax 168 188 211 236 264 264

144

Balance Sheet ProjectionsFixed assets 600 672 753 843 944 944Current assets 600 672 753 843 944 944Total assets 1200 1344 1505 1696 1888 1888Equity 1200 1344 1505 1686 1888 1888

Cash Flow ProjectionsProfit after tax 188 211 236 264 264Depreciation 60 67 75 84 94Capital expenditure 132 148 166 185 94Increase in current assets 72 81 90 101 -Operating cash flow 44 49 55 62 264

Present value of the operating cash flow = 147Residual value = 264 / 0.15 = 1760Present value of residual value = 1760 / (1.15)4 = 1007Total shareholder value = 147 + 1007 = 1154Pre-strategy value = 168/0.15 = 1120Value of the strategy = 1154 – 1120 = 34

2. According to the Marakon approachM r – g =B k – g

r - .102 =

k - .10r - .10 = 2k - .20r = 2k - .10r/k = 2 - (.10/k)

Thus r/k is a function of k. Unless k is specified r/k cannot be determined.

3. (a) NOPAT for 20X1PBIT (1 – T) = 24 (0.65) = 15.6

(b) Return on capital for 20X1 NOPAT 15.6

= = 15.6%Capital employed 120 – 20 (Non-interest bearing liabilities)

145

(c) Cost of equity6% + 0.9 (6%) = 1.4%

(d) Average cost of capital0.5 x 8% (1 - .35) + 0.5 x 11.4% = 8.3%

(e) EVA for 20X1NOPAT - Average cost of capital x Capital employed15.6 - .083 x 100 = 7.3

4.I = Rs.200 millionr = 0.40c* = 0.20T = 5 years

200 (0.40 – 0.20) 5Value of forward plan =

0.20 (1.20)

= Rs.833.3 million

5. Cost of capital = 0.5 x 0.10 + 0.5 x 0.18 = 0.14 or 14 per cent

1. Revenues 2,000 2,000 2,000 2,000 2,0002. Costs 1,400 1,400 1,400 1,400 1,4003. PBDIT 600 600 600 600 6004. Depreciation 200 200 200 200 2005. PBIT 400 400 400 400 4006. NOPAT 240 240 240 240 2407. Cash flow (4+6) 440 440 440 440 4408. Capital at charge 1,000 800 600 400 2009. Capital charge (8x0.14) 140 112 84 56 2810. EVA (6-9) 100 128 156 184 212

5 440NPV = - 1000 = 440 x 3.433 – 1000 = 510.5

t=1 (1.14)t

EVAt

NPV = = 100 x 0.877 + 128 x 0.769 + 156 x 0.675 + 184 x 0.592 + (1.14)t 212 x 0.519

= 510.3

6. Equipment cost = 1,000,000

146

Economic life = 4 years Salvage value = Rs.200,000 Cost of capital = 14 per cent

Present value of salvage value = 200,000 x 0.592 = 118,400

Present value of the annuity = 1,000,000 – 118,400= 881,600

881,600 881,600Annuity amount = =

PVIFA14%, 4yrs 2.914

= Rs.302,540

Depreciation charge under sinking fund method1 2 3 4

Capital 1,000,000 837,460 652,164 440,927Depreciation 162,540 185,296 212,237 240,810Capital charge 140,000 117,244 91,303 61,730Sum 302,540 302,540 302,540 302,540

7. Investment : Rs.2,000,000Life : 10 yearsCost of capital : 15 per centSalvage value : 0

2,000,000Economic depreciation =

FVIFA(10yrs, 15%)

2,000,000 = = 98,503

20.304

8. Investment : Rs.5,000,000Life : 5 yearsCost of capital : 12 per centSalvage value : Nil

PVIFA(5yrs,12%) = 3.605 ; Annuity amount = 5,000,000 / 3.605 = 1,386,963

147

Depreciation charge under sinking fund method1 2 3 4 5

Capital 5,000,000 4,213,037 3,331,638 2,344,472 1,238,846Depreciation 786,963 881,399 987,166 1,105,626 1,238,301Capital charge 600,000 505,564 399,797 281,336 148,662Sum 1,386,963 1,386,963 1,386,963 1,386,963 1,386,963

5,000,000Economic depreciation =

FVIFA(5yrs, 12%)

5,000,000 = = Rs.787,030

6.353

9. Investment = Rs.100 millionNet working capital = Rs.20 millionLife = 8 yrsSalvage value = Rs.20 million (Net working capital)Annual cash flow = Rs.21.618 millionCost of capital = 15%Straight line depreciation = Rs.10 million per year

80 80Economic depreciation = = = Rs.5.828 million

FVIFA(8, 15%) 13.727

Year 1 Year 4 Profit after tax 11.618 11.618 Depreciation 10.000 10.000 Cash flow 21.618 21.618 Book capital100 70 (Beginning) ROCE 11.62% 16.59% ROGI 21.62% 21.62% CFROI 15.79% 15.79%

148

Chapter 34 MERGERS, ACQUISITIONS AND RESTRUCTURING

149

1. The pre-amalgamation balance sheets of Cox Company and Box Company and the post-amalgamation balance sheet of the combined entity, Cox and Box Company, under the ‘pooling’ method as well as the ‘purchase’ method are shown below :

Before Amalgamation After Amalgamation Cox & Box Company

Cox Box Pooling method Purchase method

Fixed assets 25 10 35 45Current assets Goodwill

20 7.5 27.5 302.5

Total assets 45 17.5 62.5 77.5

Share capital(face value @ Rs.10)

20 5 25 20

Reserves & surplus 10 10 20 10Share premium 15 2.5 17.5 17.5Debt 45 17.5 42.5 77.5

2. Post-merger EPS of International Corporation will be

2 x 100,000 + 2 x100,000

100,000 + ER x 100,000

Setting this equal to Rs.2.5 and solving for ER givesER = 0.6

3. PVA = Rs.25 million, PVB = Rs.10 millionBenefit = Rs.4 million, Cash compensation = Rs.11 millionCost = Cash compensation – PVB = Rs.1 millionNPV to Alpha = Benefit – Cost = Rs.3 millionNPV to Beta = Cash Compensation – PVB = Rs.1 million

4. Let A stand for Ajeet and J for JeetPVA = Rs.60 x 300,000 = Rs.18 millionPVJ = Rs.25 x 200,000 = Rs.5 millionBenefit = Rs.4 millionPVAJ = 18 + 5 + 4 = Rs.23 millionExchange ratio = 0.5The share of Jeet in the combined entity will be :

100,000= = 0.25

150

300,000 + 100,000

a) True cost to Ajeet Company for acquiring Jeet CompanyCost = PVAB - PVB

= 0.25 x 27 - 5 = Rs.1.75 million

b) NPV to Ajeet= Benefit - Cost= 4 - 1.75 = Rs.2.25 million

c) NPV to Jeet = Cost = Rs.1.75 million

5. a) PVB = Rs.12 x 2,000,000 = Rs.24 millionThe required return on the equity of Unibex Company is the value of k in the equation.

Rs.1.20 (1.05)Rs.12 =

k - .05

k = 0.155 or 15.5 per cent.

If the growth rate of Unibex rises to 7 per cent as a sequel to merger, the intrinsic value per share would become :

1.20 (1.07)= Rs.15.11

0.155 - .07

Thus the value per share increases by Rs.3.11 Hence the benefit of the acquisition is

2 million x Rs.3.11 = Rs.6.22 million

(b) (i) If Multibex pays Rs.15 per share cash compensation, the cost of the merger is 2 million x (Rs.15 – Rs.12) = Rs.6 million.

(ii) If Multibex offers 1 share for every 3 shares it has to issue 2/3 millionshares to shareholders of Unibex.

So shareholders of Unibex will end up with

0.667 = 0.1177 or 11.77 per cent

5+0.667

151

shareholding of the combined entity,The present value of the combined entity will be

PVAB = PVA + PVB + Benefit= Rs.225 million + Rs.24 million + Rs.6.2 million = Rs.255.2 million

So the cost of the merger is :Cost = PVAB - PVB

= .1177 x 255.2 - 24 = Rs.6.04 million

6. The expected profile of the combined entity A&B after the merger is shown in the last column below.

A B A&BNumber of shares 5000 2000 6333Aggregate earnings Rs.45000 Rs.4000 Rs.49000Market value Rs.90000 Rs.24000 Rs.114000P/E 2 6 2.33

7. (a) The maximum exchange ratio acceptable to shareholders of Vijay Limited is :

S1 (E1+E2) PE12

ER1 = - + S2 P1S2

12 (36+12) 8= - + = 0.1

8 30 x 8

(b) The minimum exchange ratio acceptable to shareholders of Ajay Limited is : P2 S1

ER2 = (PE12) (E1+E2) - P2 S2

9 x 12 = = 0.3

9 (36+12) - 9 x 8

(c) 12 (48) PE12

ER1 = - + 8 240

152

9 x 12 ER2 =

PE12 (48) - 72

Equating ER1 and ER2 and solving for PE12 gives, PE12 = 9 When PE12 = 9 ER1 = ER2 = 0.3Thus ER1 and ER2 intersect at 0.3

8. The present value of FCF for first seven years is 16.00 14.30 9.7 0

PV(FCF) = - - - + (1.15) (1.15)2 (1.15)3 (1.15)4

0 10.2 16.7 + + +

(1.15)5 (1.15)6 (1.15)7

= - Rs.20.4 millionThe horizon value at the end of seven years, applying the constant growth model is

FCF8 18 V4 = = = Rs.257.1 million

0.15-0.08 0.15 – 0.08

1 PV (VH) = 257.1 x = Rs.96.7 million

(1.15)7

The value of the division is :- 20.4 + 96.7 = Rs.76.3 million

MINICASE

Solution:

153

(a)

Modern Pharma Magnum Drugs Exchange Ratio

Book value per share 2300 650 = Rs.115 = Rs.65 20 10

65

115Earnings per share 450 95

= Rs.22.5 = Rs.9.5 20 10

9.5

22.5Market price per share Rs.320 Rs.102 102

320

Exchange ratio that gives equal weightage to book value per share, earnings per share, and market price per share

65 9.5 102 + + 115 22.5 320 0.57 + 0.42 + 0.32 = = 0.44 3 3

(b) An exchange ratio based on earnings per share fails to take into account the following:

(i) The difference in the growth rate of earnings of the two companies.(ii) The gains in earnings arising out of merger.(iii) The differential risk associated with the earnings of the two companies.

(c) Current EPS of Modern Pharma 450= = Rs.22.5

20

If there is a synergy gain of 5 percent, the post-merger EPS of Modern Pharma is

(450 + 95) (1.05)

20 + ER X 10Equating this with Rs.22.5, we get

(450 + 95) (1.05) = 22.5

154

20 + 10ERThis gives ER = 0.54

Thus the maximum exchange ratio Modern Pharma should accept to avoid initial dilution of EPS is 0.54

(d) Post-merger EPS of Modern Pharma if the exchange ratio is 1:4, assuming no synergy gain:

450 + 95 = Rs.24.2 20 + 0.25 x 10

(e) The maximum exchange ratio acceptable to the shareholders of Modern Pharma if the P/E ratio of the combined entity is 13 and there is no synergy gain

-S1 (E1 + E2) P/E12

ER1 = + S2 P1 S2

- 20 (450 + 95) 13 = + = 0.21

10 320 x 10

(f) The minimum exchange ratio acceptable to the shareholders of Magnum Drugs if the P/E ratio of the combined entity is 12 and the synergy benefit is 2 percent

P2S1

ER2 = (P/E12) (E1 + E2) (1 + S) – P2S2

102 x 20 =

12 (450 + 95) (1.02) – 102 X 10 = 0.36

(g) The level of P/E ratio where the lines ER1 and ER2 intersect.

To get this, solve the following for P/E12

- S1 (E1 + E2) P/E12 P2S1

+ = S2 P1S2 P/E12 (E1 + E2) – P2S2

155

- 20 (450 +95) P/E12 102 x 20 + = 10 320 x 10 P/E12 (450 +95) – 1020

- 6400 + 545 P/E12 2040 = 3200 545 P/E12 – 1020

(545 P/E12 – 1020) (545 P/E12 – 6400) = 2040 x 3200

297025 P/E212 – 3488000 P/E12 – 555900 P/E12

+6528000 = 6528000297025 P/E2

12 = 4043900 P/E297025 P/E12 = 4043900

P/E12 = 13.61

156

Chapter 37INTERNATIONAL FINANCIAL MANAGEMENT

1. The annualised premium is :

Forward rate – Spot rate 12x

Spot rate Forward contract length in months

46.50 – 46.00 12 = x = 4.3%

46.00 3

2. 100100 (1.06) = x 1.07 x F

1.553

106 x 1.553F = = 1.538

107 A forward exchange rate of 1.538 dollars per sterling pound will mean indifference between

investing in the U.S and in the U.K.

3. (a) The annual percentage premium of the dollar on the yen may be calculated with reference to 30-days futures

105.5 – 105 12 x = 5.7%

105 1

(b) The most likely spot rate 6 months hence will be : 107 yen / dollar

(c) Futures rate 1 + domestic interest rate =

Spot rate 1 + foreign interest rate

107 1 + domestic interest rate in Japan=

106 1.03

Domestic interest rate in Japan = .0397 = 3.97 per cent

4. S0 = Rs.46 , rh = 11 per cent , rf = 6 per cent

157

Hence the forecasted spot rates are :Year Forecasted spot exchange rate 1 Rs.46 (1.11 / 1.06)1 = Rs.48.17 2 Rs.46 (1.11 / 1.06)2 = Rs.50.44 3 Rs.46 (1.11 / 1.06)3 = Rs.52.82 4 Rs.46 (1.11 / 1.06)4 = Rs.55.31 5 Rs.46 (1.11 / 1.06)5 = Rs.57.92

The expected rupee cash flows for the project

Year Cash flow in dollars Expected exchange Cash flow in rupees (million) rate (million)

0 -200 46 -9200 1 50 48.17 2408.5 2 70 50.44 3530.8 3 90 52.82 4753.8 4 105 55.31 5807.6 5 80 57.92 4633.6

Given a rupee discount rate of 20 per cent, the NPV in rupees is :

2408.5 3530.8 4753.8NPV = -9200 + + +

(1.18)2 (1.18)3 (1.18)4

5807.6 4633.6 + +

(1.18)5 (1.18)6

= Rs.3406.2 million

The dollar NPV is : 3406.2 / 46 = 74.05 million dollars

5. Forward rate 1 + domestic interest rate =

Spot rate 1 + foreign interest rate

F 1 + .015 =

1.60 1 + .020F = $ 1.592 / £

158

6. Expected spot rate a year from now 1 + expected inflation in home country=

Current spot rate 1 + expected inflation in foreign country

Expected spot rate a year from now 1.06 =

Rs.70 1.03

So, the expected spot rate a year from now is : 72 x (1.06 / 1.03) = Rs.72.04

7. (a) The spot exchange rate of one US dollar should be :12000

= Rs.48 250

(b) One year forward rate of one US dollar should be :13000

= Rs.50 260

8. (1 + expected inflation in Japan)2

Expected spot rate = Current spot rate x2 years from now (1 + expected inflation in UK)2

(1.01)2

= 170 x = 163.46 yen / £ (1.03)2

9. (i) Determine the present value of the foreign currency liability (£100,000) by using 90-day money market lending rate applicable to the foreign country. This works out to :

£100,000 = £ 98522

(1.015)(ii) Obtain £98522 on today’s spot market(iii) Invest £98522 in the UK money market. This investment will grow to

£100,000 after 90 days

10. (i) Determine the present value of the foreign currency asset (£100,000) by using the 90-day money market borrowing rate of 2 per cent.

100,000 = £98039

(1.02)

159

(ii) Borrow £98039 in the UK money market and convert them to dollars in the spot market.

(iii) Repay the borrowing of £98039 which will compound to £100000 after 90 days with the collection of the receivable

11. A lower interest rate in the Swiss market will be offset by the depreciation of the US dollar vis-à-vis the Swiss franc. So Mr.Sehgal’s argument is not tenable.

160

Chapter 40CORPORATE RISK MANAGEMENT

1. (a) The investor must short sell Rs.1.43 million (Rs.1 million / 0.70) of B(b) His hedge ratio is 0.70(c) To create a zero value hedge he must deposit Rs.0.43 million

2. Futures price Spot price x Dividend yield = Spot price -

(1+Risk-free rate)0.5 (1+Risk-free rate)0.5

4200 4000 x Dividend yield = 4000 -

(1.145) 0.5 (1.145) 0.5

The dividend yield on a six months basis is 2 per cent. On an annual basis it is approximately 4 per cent.

3. Futures price = Spot price + Present value of – Present value

(1+Risk-free rate)1 storagecosts of convenience yield

5400 = 5000 + 250 – Present value of convenience yield

(1.15)1

Hence the present value of convenience yield is Rs.554.3 per ton.

161

162

163