Prasanna Chandra

Chapter 7 TIME VALUE OF MONEY 1.

Value five years hence of a deposit of Rs.1,000 at various interest rates is as follows: r

=

8%

FV5

=

Rs.1469

r

=

10%

FV5

=

Rs.1611

r

=

12%

FV5

=

Rs.1762

r

=

15%

FV5

=

Rs.2011

2.

30 years

3.

In 12 years Rs.1000 grows to Rs.8000 or 8 times. This is 23 times the initial deposit. Hence doubling takes place in 12 / 3 = 4 years. According to the Rule of 69, the doubling period is: 0.35 + 69 / Interest rate Equating this to 4 and solving for interest rate, we get Interest rate = 18.9%.

4.

Saving Rs.2000 a year for 5 years and Rs.3000 a year for 10 years thereafter is equivalent to saving Rs.2000 a year for 15 years and Rs.1000 a year for the years 6 through 15. Hence the savings will cumulate to: 2000 x FVIFA (10%, 15 years) + 1000 x FVIFA (10%, 10 years) = 2000 x 31.772 + 1000 x 15.937 = Rs.79481.

5.

Let A be the annual savings.

6.

A x FVIFA (12%, 10 years) = A x 17.549 =

1,000,000 1,000,000

So, A = 1,000,000 / 17.549 =

Rs.56,983.

1,000 x FVIFA (r, 6 years)

=

10,000

FVIFA (r, 6 years)

=

10,000 / 1000 = 10 1

From the tables we find that FVIFA (20%, 6 years) = FVIFA (24%, 6 years) =

9.930 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) FVIF (r,10 years)

= =

5,000 5,000 / 1000 = 5

From the tables we find that FVIF (16%, 10 years) = FVIF (18%, 10 years) =

4.411 5.234

Using linear interpolation in the interval, we get: (5.000 – 4.411) x 2% r = 16% +

= 17.4% (5.234 – 4.411)

8.

The present value of Rs.10,000 receivable after 8 years for various discount rates (r ) are: r = 10% PV = 10,000 x PVIF(r = 10%, 8 years) = 10,000 x 0.467 = Rs.4,670 r = 12%

PV

= 10,000 x PVIF (r = 12%, 8 years) = 10,000 x 0.404 = Rs.4,040

r = 15%

PV

= 10,000 x PVIF (r = 15%, 8 years) = 10,000 x 0.327 = Rs.3,270

9.

Assuming that it is an ordinary annuity, the present value is: 2,000 x PVIFA (10%, 5years) = 2,000 x 3.791 = Rs.7,582

10.

The present value of an annual pension of Rs.10,000 for 15 years when r = 15% is: 10,000 x PVIFA (15%, 15 years) = 10,000 x 5.847 = Rs.58,470

2

The alternative is to receive a lumpsum of Rs.50,000. Obviously, Mr. Jingo will be better off with the annual pension amount of Rs.10,000. 11.

The amount that can be withdrawn annually is: 100,000 100,000 A = ------------------ ------------ = ----------- = Rs.10,608 PVIFA (10%, 30 years) 9.427

12.

The present value of the income stream is: 1,000 x PVIF (12%, 1 year) + 2,500 x PVIF (12%, 2 years) + 5,000 x PVIFA (12%, 8 years) x PVIF(12%, 2 years) = 1,000 x 0.893 + 2,500 x 0.797 + 5,000 x 4.968 x 0.797 = Rs.22,683.

13.

The present value of the income stream is: 2,000 x PVIFA (10%, 5 years) + 3000/0.10 x PVIF (10%, 5 years) = 2,000 x 3.791 + 3000/0.10 x 0.621 = Rs.26,212

14.

To earn an annual income of Rs.5,000 beginning from the end of 15 years from now, if the deposit earns 10% per year a sum of Rs.5,000 / 0.10 = Rs.50,000 is required at the end of 14 years. The amount that must be deposited to get this sum is: Rs.50,000 / PVIF (10%, 14 years) = Rs.50,000 / 3.797 = Rs.13,165

15.

Rs.20,000 =- Rs.4,000 x PVIFA (r, 10 years) PVIFA (r,10 years) = Rs.20,000 / Rs.4,000 = 5.00 From the tables we find that: PVIFA (15%, 10 years) PVIFA (18%, 10 years) Using linear interpolation we get: 5.019 – 5.00 r = 15% + ---------------5.019 – 4.494

= =

5.019 4.494

x 3%

= 15.1% 16.

PV (Stream A) = Rs.100 x PVIF (12%, 1 year) + Rs.200 x PVIF (12%, 2 years) + Rs.300 x PVIF(12%, 3 years) + Rs.400 x 3

PVIF (12%, 4 years) + Rs.500 x PVIF (12%, 5 years) + Rs.600 x PVIF (12%, 6 years) + Rs.700 x PVIF (12%, 7 years) + Rs.800 x PVIF (12%, 8 years) + Rs.900 x PVIF (12%, 9 years) + Rs.1,000 x PVIF (12%, 10 years) = Rs.100 x 0.893 + Rs.200 x 0.797 + Rs.300 x 0.712 + Rs.400 x 0.636 + Rs.500 x 0.567 + Rs.600 x 0.507 + Rs.700 x 0.452 + Rs.800 x 0.404 + Rs.900 x 0.361 + Rs.1,000 x 0.322 = Rs.2590.9 Similarly, PV (Stream B) = Rs.3,625.2 PV (Stream C) = Rs.2,851.1 17.

FV5

= = = =

Rs.10,000 [1 + (0.16 / 4)]5x4 Rs.10,000 (1.04)20 Rs.10,000 x 2.191 Rs.21,910

18.

FV5

= = = =

Rs.5,000 [1+( 0.12/4)] 5x4 Rs.5,000 (1.03)20 Rs.5,000 x 1.806 Rs.9,030

19 Stated rate (%)

A

B

C

12

24

24

4 times

12 times

Frequency of compounding 6 times Effective rate (%)

Difference between the effective rate and stated rate (%) 20.

(1 + 0.12/6)6- 1 (1+0.24/4)4 –1 (1 + 0.24/12)12-1 = 12.6

= 26.2

= 26.8

0.6

2.2

2.8

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 Rs.100,000 Rs.100,000 = = Rs.40,388 PVIF(12%, 8 years) 2.476

21.

now is:

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 that FVIF (15%, 10 years) = 4.046 This means that the implied interest rate is nearly 15%. I would choose Rs.20,000 for 10 years from now because I find a return of 15% quite acceptable. 22.

FV10

= Rs.10,000 [1 + (0.10 / 2)]10x2 = Rs.10,000 (1.05)20 = Rs.10,000 x 2.653 = Rs.26,530

If the inflation rate is 8% per year, the value of Rs.26,530 10 years from now, in terms of the current rupees is: Rs.26,530 x PVIF (8%,10 years) = Rs.26,530 x 0.463 = Rs.12,283 23.

A constant deposit at the beginning of each year represents an annuity due. PVIFA of an annuity due is equal to : PVIFA of an ordinary annuity x (1 + r) To provide a sum of Rs.50,000 at the end of 10 years the annual deposit should be

A

=

Rs.50,000 FVIFA(12%, 10 years) x (1.12) Rs.50,000

=

= Rs.2544 17.549 x 1.12

5

24.

The discounted value of Rs.20,000 receivable at the beginning of each year from 2005 to 2009, evaluated as at the beginning of 2004 (or end of 2003) is: Rs.20,000 x PVIFA (12%, 5 years) = Rs.20,000 x 3.605 = Rs.72,100. The discounted value of Rs.72,100 evaluated at the end of 2000 is Rs.72,100 x PVIF (12%, 3 years) = Rs.72,100 x 0.712 = Rs.51,335 If A is the amount deposited at the end of each year from 1995 to 2000 then A x FVIFA (12%, 6 years) = Rs.51,335 A x 8.115 = Rs.51,335 A = Rs.51,335 / 8.115 = Rs.6326

25.

The discounted value of the annuity of Rs.2000 receivable for 30 years, evaluated as at the end of 9th year is: Rs.2,000 x PVIFA (10%, 30 years) = Rs.2,000 x 9.427 = Rs.18,854 The present value of Rs.18,854 is: Rs.18,854 x PVIF (10%, 9 years) = Rs.18,854 x 0.424 = Rs.7,994 26. 30 per cent of the pension amount is 0.30 x Rs.600 = Rs.180 Assuming that the monthly interest rate corresponding to an annual interest rate of 12% is 1%, the discounted value of an annuity of Rs.180 receivable at the end of each month for 180 months (15 years) is: Rs.180 x PVIFA (1%, 180) (1.01)180 - 1 Rs.180 x ---------------- = Rs.14,998 .01 (1.01)180 If Mr. Ramesh borrows Rs.P today on which the monthly interest rate is 1% P x (1.01)60 = P x 1.817 = P

27.

=

Rs.14,998 Rs.14,998 Rs.14,998 ------------ = Rs.8254 1.817

Rs.300 x PVIFA(r, 24 months) = Rs.6,000 PVIFA (4%,24) = Rs.6000 / Rs.300 From the tables we find that: PVIFA(1%,24) =

21.244 6

= 20

PVIFA (2%, 24)

=

18.914

Using a linear interpolation 21.244 – 20.000 r = 1% + ---------------------21.244 – 18,914

x 1%

= 1.53% Thus, the bank charges an interest rate of 1.53% per month. The corresponding effective rate of interest per annum is [ (1.0153)12 – 1 ] x 100 = 20% 28.

The discounted value of the debentures to be redeemed between 8 to 10 years evaluated at the end of the 5th year is: Rs.10 million x PVIF (8%, 3 years) + Rs.10 million x PVIF (8%, 4 years) + Rs.10 million x PVIF (8%, 5 years) = Rs.10 million (0.794 + 0.735 + 0.681) = Rs.2.21 million If A is the annual deposit to be made in the sinking fund for the years 1 to 5, then A x FVIFA (8%, 5 years) = Rs.2.21 million A x 5.867 = Rs.2.21 million A = 5.867 = Rs.2.21 million A = Rs.2.21 million / 5.867 = Rs.0.377 million

29.

Let `n’ be the number of years for which a sum of Rs.20,000 can be withdrawn annually. Rs.20,000 x PVIFA (10%, n) = Rs.100,000 PVIFA (15%, n) = Rs.100,000 / Rs.20,000 = 5.000 From the tables we find that PVIFA (10%, 7 years) = PVIFA (10%, 8 years) =

4.868 5.335

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

n=7+

5.000 – 4.868 ----------------5.335 – 4.868

x 1 = 7.3 years

7

30.

Equated annual installment

= 500000 / PVIFA(14%,4) = 500000 / 2.914 = Rs.171,585 Loan Amortisation Schedule

Year -----1 2 3 4

Beginning amount ------------500000 398415 282608 150588

Annual installment --------------171585 171585 171585 171585

Interest ----------70000 55778 39565 21082

Principal repaid ------------101585 115807 132020 150503

Remaining balance ------------398415 282608 150588 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) PVIFA (13%, n)

= =

1,500,000 7.500

From the tables or otherwise it can be verified that PVIFA(13,30) = 7.500 Hence the maturity period of the loan is 30 years. 32.

Expected value of iron ore mined during year 1

=

Rs.300 million

Expected present value of the iron ore that can be mined over the next 15 years price escalation of 6% per annum in the price per tonne of iron

= Rs.300 million x

1 – (1 + g)n / (1 + i)n -----------------------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

assuming a

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 =

FVIFA (10%, 15 years)

= Rs.48,338 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 46 1

400,000(1.12)14

400,000(1.12)

2

15

9

1.12

15

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

10

Chapter 8 VALUATION OF BONDS AND STOCKS 1. P =

5  t=1

11

100 +

(1.15)

(1.15)5

= Rs.11 x PVIFA(15%, 5 years) + Rs.100 x PVIF (15%, 5 years) = Rs.11 x 3.352 + Rs.100 x 0.497 = Rs.86.7 2.(i)

When the discount rate is 14% 7 12 100 P =  + t=1 (1.14) t (1.14)7 = Rs.12 x PVIFA (14%, 7 years) + Rs.100 x PVIF (14%, 7 years) = Rs.12 x 4.288 + Rs.100 x 0.4 = Rs.91.46

(ii)

When the discount rate is 12% 7 12 100 P =  + = Rs.100 t 7 t=1 (1.12) (1.12)

Note that when the discount rate and the coupon rate are the same the value is par value. 3.

equal to

The yield to maturity is the value of r that satisfies the following equality. 7 120 1,000 Rs.750 =  + = Rs.100 t 7 t=1 (1+r) (1+r) Try r = 18%. The right hand side (RHS) of the above equation is: Rs.120 x PVIFA (18%, 7 years) + Rs.1,000 x PVIF (18%, 7 years) = Rs.120 x 3.812 + Rs.1,000 x 0.314 = Rs.771.44 Try r = 20%. The right hand side (RHS) of the above equation is: Rs.120 x PVIFA (20%, 7 years) + Rs.1,000 x PVIF (20%, 7 years) = Rs.120 x 3.605 + Rs.1,000 x 0.279 = Rs.711.60 Thus 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 – 750.00 Yield to maturity = 18% + 771.44 – 711.60

x 2%

= 18.7% 4. 80 =

10 14 100  + t=1 (1+r) t (1+r)10

Try r = 18%. The RHS of the above equation is Rs.14 x PVIFA (18%, 10 years) + Rs.100 x PVIF (18%, 10 years) = Rs.14 x 4.494 + Rs.100 x 0.191 = Rs.82 Try r = 20%. The RHS of the above equation is Rs.14 x PVIFA(20%, 10 years) + Rs.100 x PVIF (20%, 10 years) = Rs.14 x 4.193 + Rs.100 x 0.162 = Rs.74.9 Using interpolation in the range 18% and 20% we get: 82 - 80 = 18% + ----------- x 2% 82 – 74.9

Yield to maturity

= 18.56% 5. P =

12  t=1

6

100 +

(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 12

Bond B

12(1 – 0.3) =Rs.8.4

*

Post-tax interest (C )

*

Post-tax maturity value (M) 100 [ (100-70)x 0.1] =Rs.97

10 (1 – 0.3) =Rs.7 100 [ (100 – 60)x 0.1] =Rs.96

The post-tax YTM, using the approximate YTM formula is calculated below

Bond A :

Post-tax YTM =

=

Bond B :

Post-tax YTM =

=

8.4 + (97-70)/10 -------------------0.6 x 70 + 0.4 x 97 13.73% 7 + (96 – 60)/6 ---------------------0.6x 60 + 0.4 x 96 17. 47%

7. P =

14  t=1

6

100 +

(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 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

market

9.

10.

11.

Po Po

= =

D1 / (r – g) = Do (1 + g) / (r – g) Rs.12.00 (1.10) / (0.15 – 0.10) =

=

D1 / (r – g)

Rs.32 = g =

Rs.2 / 0.12 – g 0.0575 or 5.75%

Po Do So 8

D1/ (r – g) = Do(1+g) / (r – g) Rs.1.50, g = -0.04, Po = Rs.8

= =

Rs.264

= 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: B: C:

Present value of the dividend stream for the first 4 years Present value of the dividend stream for the next 4 years 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 = =

B=

C

1.68/(1.14) + 1.88 / (1.14)2 + 2.11 / (1.14)3 + 2.36 / (1.14)4 Rs.5.74

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

=

P8 / (1.14)8 P8 = D9 / (r – g) =

3.21 (1.05)/ (0.14 – 0.05) = Rs.37.45

So C

=

Thus, Po = =

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

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.

A=

2.00 (1.15) 2.00 (1.15)2 2.00 (1.15)3 2.00(1.15)4 2.00 (1.15)5 ------------- + ------------- +-------------- + ------------- + ------------(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

B=

4.02(1.10) 4.02 (1.10)2 4.02(1.10)3 4.02(1.10)4 4.02 (1.10)5 ------------ + ---------------- + ------------- + --------------- + --------------(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

C=

=

D11 1 6.48 (1.05) -------- x --------------- = ------------------- x 1/(1.12)10 r–g (1 +r)10 0.12 – 0.05 Rs.97.20

The intrinsic value of the share = A + B + C = 10.84 + 10.81 + 97.20 = Rs.118.85 14.

Terminal value of the interest proceeds = 140 x FVIFA (16%,4) = 140 x 5.066 = 709.24 Redemption value = 1,000

15

Terminal value of the proceeds from the bond = 1709.24 Define r as the yield to maturity. The value of r can be obtained from the 900 (1 + r)4 r 15.

= 1709.24 = 0.1739 or 17.39%

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

16.

=

2.36 x

=

Rs.74.80

- 0.10801 ----------- + 62.05 - 0.02

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

equation

Chapter 9 RISK AND RETURN 1 (a)

Expected price per share a year hence will be: = 0.4 x Rs.10 + 0.4 x Rs.11 + 0.2 x Rs.12 = Rs.10.80

(b)

Probability distribution of the rate of return is Rate of return (Ri)

10%

20%

30%

Probability (pi)

0.4

0.4

0.2

Note that the rate of return is defined as: Dividend + Terminal price -------------------------------- - 1 Initial price (c )

The standard deviation of rate of return is : σ = pi (Ri – R)2 The σ of the rate of return on MVM’s stock is calculated below: --------------------------------------------------------------------------------------------------Ri pi pI ri (Ri-R) (R i- R)2 pi (Ri-R)2 --------------------------------------------------------------------------------------------------10 0.4 4 -8 64 25.6 20 0.4 8 2 4 1.6 30 0.2 6 12 144 28.8 --------------------------------------------------------------------------------------------------R = pi Ri pi (Ri-R)2 = 56 σ = 56 = 7.48%

2 (a) For Rs.1,000, 20 shares of Alpha’s stock can be acquired. The probability distribution of the return on 20 shares is Economic Condition High Growth Low Growth Stagnation Recession Expected return

Return (Rs) 20 x 55 = 1,100 20 x 50 = 1,000 20 x 60 = 1,200 20 x 70 = 1,400 =

Probability 0.3 0.3 0.2 0.2

(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 Low growth Stagnation Recession

20 x 75 = 1,500 20 x 65 = 1,300 20 x 50 = 1,000 20 x 40 = 800

0.3 0.3 0.2 0.2

Expected return =

(1,500 x 0.3) + (1,300 x 0.3) + (1,000 x 0.2) + (800 x 0.2) = Rs.1,200

Standard deviation of the return = [(1,500 – 1,200)2 x .3 + (1,300 – 1,200)2 x .3 + (1,000 – 1,200)2 x .2 + (800 – 1,200)2 x .2]1/2 = Rs.264.58 (c )

For Rs.500, 10 shares of Alpha’s stock can be acquired; likewise for Rs.500, 10 shares of Beta’s stock can be acquired. The probability distribution of this option is: Return (Rs) Probability (10 x 55) + (10 x 75) = 1,300 0.3 (10 x 50) + (10 x 65) = 1,150 0.3 (10 x 60) + (10 x 50) = 1,100 0.2 (10 x 70) + (10 x 40) = 1,100 0.2 Expected return = (1,300 x 0.3) + (1,150 x 0.3) + (1,100 x 0.2) + (1,100 x 0.2) = Rs.1,175 Standard deviation = [(1,300 –1,175)2 x 0.3 + (1,150 – 1,175)2 x 0.3 +

d.

(1,100 – 1,175)2 x 0.2 + (1,100 – 1,175)2 x 0.2 ]1/2 = Rs.84.41 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) (14 x 50) + (6 x 65) (14 x 60) + (6 x 50) (14 x 70) + (6 x 40)

= = = =

1,220 1,090 1,140 1,220

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

=

0.3 0.3 0.2 0.2

The expected return to standard deviation of various options are as follows : Expected return Standard deviation Expected / Standard Option (Rs) (Rs) return deviation a 1,150 143 8.04 b 1,200 265 4.53 c 1,175 84 13.99 d 1,165 58 20.09

3.

Option `d’ is the most preferred option because it has the highest return to risk

ratio.

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 6

= 7.83%

B:

0.08 + 0.04 + 0.15 +.12 + 0.10 + 0.06 6

= 0.0917

= 9.17%

C:

0.07 + 0.08 + 0.12 + 0.09 + 0.06 + 0.12 6

= 0.0900

= 9.00%

D:

0.09 + 0.09 + 0.11 + 0.04 + 0.08 + 0.16 6

= 0.095

= 9.50%

(a)

Return on portfolio consisting of stock A

(b)

Return on portfolio consisting of stock A and B in equal proportions = 0.5 (0.0783) + 0.5 (0.0917) = 0.085 = 8.5%

19

= 7.83%

4.

(c )

Return on portfolio consisting of stocks A, B and C in equal proportions = 1/3(0.0783 ) + 1/3(0.0917) + 1/3 (0.090) = 0.0867 = 8.67%

(d)

Return on portfolio consisting of stocks A, B, C and D in equal proportions = 0.25(0.0783) + 0.25(0.0917) + 0.25(0.0900) + 0.25(0.095) = 0.08875 = 8.88%

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 1 2 3 4 5 6 7 8 9 10 11

RA 15 -6 18 30 12 25 2 20 18 24 8.

RA = 15.09

RM 12 1 14 24 16 30 -3 24 15 22 12

RA-RA -0.09 -21.09 2.91 14.91 0-3.09 9.91 -13.09 4.91 2.91 8.91 -7.09

RM-RM -3.18 -14.18 -1.18 8.82 0.82 14.82 -18.18 8.82 -0.18 6.82 -3.18

(RA-RA) 0.01 444.79 8.47 222.31 9.55 98.21 171.35 24.11 8.47 79.39 50.27

(RM-RM) 10.11 201.07 1.39 77.79 0.67 219.63 330.51 77.79 0.03 46.51 10.11

RA-RA/RM-RM 0.29 299.06 -3.43 131.51 -2.53 146.87 237.98 43.31 -0.52 60.77 22.55

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 =

Alpha = =

935.86 975.61

=

0.96

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 = 6.

Rs.22.74

The SML equation is RA = RF + βA (RM – RF) Given RA = 15%.

RF = 8%, RM = 12%, we have

0.15 = .08 + βA (0.12 – 0.08) 0.07 i.e.βA =

= 1.75 0.04

Beta of stock A = 1.75 7.

The SML equation is: RX = RF + βX (RM – RF) We are given 0.15 = 0.09 + 1.5 (RM – 0.09) i.e., 1.5 RM = 0.195 or RM = 0.13% Therefore return on market portfolio = 13%

8.

RM = 12%

βX = 2.0

RX =18% g = 5%

Po = D1 / (r - g) Rs.30 = D1 / (0.18 - .05)

21

Po = Rs.30

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 Rf RM – Rf g βx

Revised

6% 6% 5% 2.0

8% 4% 4% 1.8

Revised Rx = 8% + 1.8 (4%) = 15.2% Price per share of stock X, given the above changes is 3.71 (1.04) = Rs.34.45 0.152 – 0.04

Chapter 10 OPTIONS AND THEIR VALUATION 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

= 0.7 x 100

= 70

=

0.6429

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 R = 1.10

u=? E = 45

d = 0.8 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

∆

Cu – 0 =

B

∆ C 8

S 1.10

x -0.8Cu

=

(-) 0.034375

= = =

- 0.34375 B ∆S+B ∆ x 40 + B

40

(1) (2)

Substituting (1) in (2) we get 8 8 or B

= = =

(-0.034365 x 40) B + B -0.375 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 u = 0.8

=

0

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

d2

=

ln (120 / 110) + 0.14 + 0.42/2 0.4

=

0.08701 + 0.14 + 0.08 0.4

=

0.7675

= = =

d1 -  t 0.7675 – 0.4 0.3675

N(d1) = N (d2) =

N (0.7675) ~ N (0.77) = 0.80785 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 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 ………

25

(A)

option and

The value of the call option gives an exercise price of Rs.85 can be obtained as t

=

follows:

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

d1

=

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) ---------------------------------------------0.18 x  1 ln (1.2) + 0.19

= 0.4243 =

N(d1) = d2 = = =

0.8775 = 0.88

N (0.88) d1 - t 0.8775 0.4532 =

=

0.81057

0.18 0.45

26

N (d2) = So = =

N (0.45) = 0.67364 6000 x 0.81057 – (5000 x 0.9048 x 0.67364) 1816

B0

V0 – S0 60000 – 1816 4184

= = =

Chapter 11 TECHNIQUES OF CAPITAL BUDGETING 1.(a)

NPV of the project at a discount rate of 14%. =

- 1,000,000 + 100,000 + 200,000 ---------- -----------(1.14) (1.14)2 + 300,000 + 600,000 + 300,000 ----------- ------------------3 4 (1.14) (1.14) (1.14)5 27

= (b)

- 44837

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)

= =

2.

- 1,000,000 + 89286 + 158028 + 207931 + 361620 + 155871 - 27264

Investment A a) b) c)

Payback period NPV

= 5 years = 40000 x PVIFA (12,10) – 200 000 = 26000 IRR (r ) can be obtained by solving the equation: 40000 x PVIFA (r, 10) = 200000 i.e., PVIFA (r, 10) = 5.000 From the PVIFA tables we find that PVIFA (15,10) = 5.019 PVIFA (16,10) = 4.883 28

Linear interporation in this range yields r = 15 + 1 x (0.019 / 0.136) = 15.14% d)

BCR

= = =

Benefit Cost Ratio PVB / I 226,000 / 200,000 = 1.13

Investment B a)

Payback period

b)

NP V =

= = c)

=

9 years

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

IRR (r ) can be obtained by solving the equation 40,000 x PVIFA (r, 5) + 30,000 x PVIFA (r, 2) x PVIF (r,5) + 20,000 x PVIFA (r, 3) x PVIF (r, 7) = 300,000 Through the process of trial and error we find that r = 1.37%

d)

BCR

= =

PVB / I 194,661 / 300,000

= 0.65

Investment C a)

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

b)

NPV

=

=

80.000 x PVIF (12,1) + 60,000 x PVIF (12,2) + 80,000 x PVIF (12,3) + 60,000 x PVIF (12,4) + 80,000 x PVIF (12,5) + 60,000 x PVIF (12,6) + 40,000 x PVIFA (12,4) x PVIF (12.6) - 210,000 111,371 29

c)

IRR (r) is obtained by solving the equation 80,000 x PVIF (r,1) + 60,000 x PVIF (r,2) + 80,000 x PVIF (r,3) + 60,000 x PVIF (r,4) + 80,000 x PVIF (r,5) + 60,000 x PVIF (r,6) + 40000 x PVIFA (r,4) x PVIF (r,6) = 210000 Through the process of trial and error we get r = 29.29%

d)

BCR

=

PVB / I =

321,371 / 210,000

=

1.53

Investment D a)

Payback period lies between 8 years and 9 years. A linear interpolation in this range provides an approximate payback period of 8.5 years. 8 + (1 x 100,000 / 200,000)

b)

NPV

=

= c)

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

IRR (r ) can be obtained by solving the equation 200,000 x PVIF (r,1) + 200,000 x PVIF (r,2) + 200,000 x PVIF (r,9) + 50,000 x PVIF (r,10) = 320000 Through the process of trial and error we get r = 8.45%

d)

BCR

=

PVB / I

=

282,840 / 320,000

=

0.88

Comparative Table Investment

A

B

C

D

a) Payback period (in years)

5

9

2.88

8.5

b) NPV @ 12% pa

26000

-105339

111371

-37160

c) IRR (%)

15.14

1.37

29.29

8.45

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 NPV Highest IRR Highest BCR 3. IRR (r) can be calculated by solving the following equations for the value of r. 60000 x PVIFA (r,7) = 300,000 i.e., PVIFA (r,7)

=

5.000

Through a process of trial and error it can be verified that r = 9.20% pa. 4.

The IRR (r) for the given cashflow stream can be obtained by solving the following equation for the value of r. -3000 + 9000 / (1+r) – 3000 / (1+r) = 0 Simplifying the above equation we get r = 1.61, -0.61; (or) 161%, (-)61% NOTE: Given two changes in the signs of cashflow, we get two values for the IRR of the cashflow stream. In such cases, the IRR rule breaks down.

5.

Define NCF as the minimum constant annual net cashflow that justifies the purchase of the given equipment. The value of NCF can be obtained from the equation NCF x PVIFA (10,8) NCF

6.

= = =

Define I as the initial investment that is justified in relation to a net annual cash inflow of 25000 for 10 years at a discount rate of 12% per annum. The value of I can be obtained from the following equation 25000 x PVIFA (12,10) i.e., I

7.

500000 500000 / 5.335 93271

PV of benefits (PVB) = + + + +

= =

I 141256

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

8.

=

122646

(A)

Investment

=

100,000

(B)

Benefit cost ratio

=

1.23 [= (A) / (B)]

The NPV’s of the three projects are as follows:

P

Project Q

0% 5%

400 223

500 251

600 312

10% 15%

69 - 66

40 - 142

70 - 135

25% 30%

- 291 - 386

- 435 - 555

- 461 - 591

R

Discount rate

9. (a)

NPV profiles for Projects P and Q for selected discount rates are as follows: Project P

b)

Q

Discount rate (%) 0 2950 500 5 1876 208 10 1075 - 28 15 471 - 222 20 11 - 382 (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) NPV (Q)

= =

1075 - 28

Given that NPV (P) . NPV (Q); and NPV (P) > 0, I would choose project P. From (a) we find that at a cost of capital of 20% NPV (P)

=

11

NPV (Q)

=

- 382

Again NPV (P) > NPV (Q); and NPV (P) > 0. I would choose project P. d)

Project P PV of investment-related costs =

1000 x PVIF (12,0) + 1200 x PVIF (12,1) + 600 x PVIF (12,2) + 250 x PVIF (12,3) = 2728 TV of cash inflows = 2000 x (1.12) + 4000 = 6240 The MIRR of the project P is given by the equation: 2728 = 6240 x PVIF (MIRR,5) (1 + MIRR)5 = 2.2874 MIRR = 18% (c)

Project Q PV of investment-related costs

=

1600

TV of cash inflows @ 15% p.a.

=

2772

The MIRR of project Q is given by the equation: 16000 (1 + MIRR)5 MIRR

=

2772

=

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) = 100 i.e., r = 12,98%

Project B NPV at a cost of capital of 12% = - 50 + 13 x PVIFA (12,6) = Rs.3.45 million IRR (r') can be obtained by solving the equation 13 x PVIFA (r',6) = 50 i.e., r' = 14.40% [determined through a process of trial and error] (b)

Difference in capital outlays between projects A and B is Rs.50 million Difference in net annual cash flow between projects A and B is Rs.12 million. NPV of the differential project at 12% = -50 + 12 x PVIFA (12,6) = Rs.3.15 million IRR (r'') of the differential project can be obtained from the equation 12 x PVIFA (r'', 6) = 50 i.e., r'' = 11.53%

11 (a)

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

(b)

Project M 34

Cost of capital PV of cash flows up to the end of year 2 PV of cash flows up to the end of year 3 PV of cash flows up to the end of year 4

= = = =

12% p.a 24.97 47.75 71.26

Discounted pay back period (DPB) lies between 3 and 4 years. Interpolating in this range we get an approximate DPB of 3.1 years. Project N Cost of capital PV of cash flows up to the end of year 1 PV of cash flows up to the end of year 2

= = =

12% per annum 33.93 51.47

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

Project M Cost of capital NPV

= =

=

(d)

Project N Cost of capital = 12% per annum NPV = Rs.20.63 million Since the two projects are independent and the NPV of each project is (+) ve, both the projects can be accepted. This assumes that there is no capital constraint. Project M Cost of capital = 10% per annum NPV = Rs.25.02 million Project N Cost of capital NPV

(e)

12% per annum - 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

= 10% per annum = 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. Project M Cost of capital = 15% per annum NPV = 16.13 million

35

Project N Cost of capital: 15% per annum NPV = Rs.17.23 million Again the two projects are mutually exclusive. So we choose the project with the higher NPV, i.e., choose project N. (f)

Project M Terminal value of the cash inflows: 114.47 MIRR of the project is given by the equation 50 (1 + MIRR)4 = 114.47 i.e., MIRR = 23.01% Project N Terminal value of the cash inflows: 115.41 MIRR of the project is given by the equation 50 ( 1+ MIRR)4 = 115.41 i.e., MIRR = 23.26%

36

Chapter 12 ESTIMATION OF PROJECT CASH FLOWS 1. (a)

Project Cash Flows

Year

0

1. Plant & machinery

(150)

(Rs. in million)

1

2

3

4

5

6

7

3. Revenues

250

250

250

250

250

250

250

4. Costs (excluding depreciation & 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

2. Working capital

(50)

9. Net salvage value of plant & machinery

48

10. Recovery of working capital 11. Initial outlay (=1+2) 12. Operating CF (= 8 + 5)

50

(200) 116.25 113.44 111.33 109.75 108.56 107.6 107.00

13. Terminal CF ( = 9 +10)

98

14.

NCF

(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

Year

0

1

1. Capital equipment (120) 2. Level of working capital 20 30 (ending) 3. Revenues 80 4. Raw material cost 24 5. Variable mfg cost. 8 6. Fixed operating & maint. 10 cost 7. Variable selling expenses 8 8. Incremental overheads 4 9. Loss of contribution 10 10.Bad debt loss 11. Depreciation 30 12. Profit before tax -14 13. Tax -4.2 14. Profit after tax -9.8 15. Net salvage value of capital equipments 16. Recovery of working capital 17. Initial investment (120) 18. Operating cash flow 20.2 (14 + 10+ 11) 19.  Working capital 20 10 20. Terminal cash flow 21. Net cash flow (17+18-19+20) (b)

2

3

4

5

6

40

50

40

30

20

120 36 12 10

160 48 16 10

200 60 20 10

160 48 16 10

120 36 12 10

12 6 10

16 8 10

20 10 10

16 8 10

12 6 10

22.5 11.5 3.45 8.05

16.88 35.12 10.54 24.58

7

80 24 8 10

8 4 10 4 12.66 9.49 7.12 5.34 57.34 42.51 26.88 6.66 17.20 12.75 8.06 2.00 40.14 29.76 18.82 4.66 25 16

30.55 41.46 52.80 39.25 25.94 14.00 10

10

(10)

(10)

(10) 41

(140) 10.20 20.55 31.46 62.80 49.25 35.94 55.00

NPV of the net cash flow stream @ 15% per discount rate =

3. (a)

(Rs. in million)

=

-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

A.

Initial outlay (Time 0) 38

i. ii. iii iv. B.

Cost of new machine Salvage value of old machine Incremental working capital requirement Total net investment (=i – ii + iii)

3,000,000 900,000 500,000 2,600,000

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

165,000

123,750

92,813

69,609

52,207

620,000

578,750

547,813

524,609

507,207

iii. Tax shield on incremental dep. iv. Operating cash flow ( i + iii) C.

Terminal cash flow (year 5) i. ii. iii. iv.

D. Year NCF (b)

Rs.

Salvage value of new machine Salvage value of old machine Recovery of incremental working capital Terminal cash flow ( i – ii + iii)

Rs.

1,500,000 200,000 500,000 1,800,000

Net cash flows associated with the replacement project (in Rs) 0 (2,600,000)

1

2

3

4

5

620000

578750

547813

524609

2307207

NPV of the replacement project = - 2600000 + 620000 x PVIF (14,1) + 578750 x PVIF (14,2) + 547813 x PVIF (14,3) + 524609 x PVIF (14,4) + 2307207 x PVIF (14,5) = Rs.267849

39

4.

Tax shield (savings) on depreciation (in Rs) Depreciation Tax shield Year charge (DC) =0.4 x DC

PV of tax shield @ 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.

B.

Initial outlay (at time 0) i. Cost of new machine ii. Salvage value of the old machine iii. Net investment

Rs.

400,000 90,000 310,000

Operating cash flow (years 1 through 5)

Year i. Depreciation of old machine

1

2

3

4

5

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

40

C.

Terminal cash flow (year 5) i. ii. iii.

D. Year NCF

Salvage value of new machine Salvage value of old machine Incremental salvage value of new machine = Terminal cash flow

Rs.

25000 10000 15000

Net cash flows associated with the replacement proposal. 0 (310000)

1 28700

2

3

21210

15656

4 11540

5 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. Fixed assets 2. Net working capital 3. Revenues 4. Costs (other than depreciation and interest) 5. Loss of rental 6. Depreciation 7. Profit before tax 8. Tax 9. Profit after tax 10. Salvage value of fixed assets 11. Net recovery of working capital

(15)

12. Initial outlay 13. Operating cash inflow

(23)

1

2

3

4

5

30

30

30

30

30

20 1 3.750 5.250 1.575 3.675

20 1 2.813 6.187 1.856 4.331

20 1 2.109 6.891 2.067 4.824

20 1 1.582 7.418 2.225 5.193

20 1 1.187 7.813 2.344 5.469

(8)

5.000 8.000

7.425

7.144 41

6.933

6.775

6.656

14. Terminal cash flow 15. Net cash flow

(23)

7.425

7.144

6.933

6.775

13.000 19.656

b. Cash flows form the point of equity investors Rs.in million Item

1. Equity funds 2. Revenues 3. Costs (other than depreciation and interest) 4. Loss of rental 5. Depreciation 6. Interest on working capital advance 7. Interest on term loans 8. Profit before tax 9. Tax 10. Profit after tax 11. Net salvage value of fixed assets 12. Net salvage value of current assets 13. Repayment of term term loans 14. Repayment of bank advance 15. Retirement of trade creditors 16. Initial investment 17. Operating cash inflow 18. Liquidation and retirement cash flows 19. Net cash flow

0

1

2

3

4

5

30

30

30

30

30

20 1 3.75

20 1 2.813

20 1 2.109

20 1 1.582

20 1 1.187

0.70

0.70

0.70

0.70

0.70

1.20 3.35 1.005 2.345

1.125 4.362 1.309 3.053

0.825 5.366 1.610 3.756

0.525 6.193 1.858 4.335

0.225 6.888 2.066 4.822

(10)

5.000 10.000 2.000

2.000

2.000

2.000 5.000 2.000

(10)

(10)

6.095

5.866

5.865

5.917

6.009

6.095

(2.0) 3.866

(2.0) 3.865

(2.0) 3.917

6.00 12.009

42

Chapter 13 RISK ANALYSIS IN CAPITAL BUDGETING 1. (a)

NPV of the project

(b)

NPVs under alternative scenarios:

= =

-250 + 50 x PVIFA (13,10) Rs.21.31 million

Pessimistic

(Rs. in million) Expected Optimistic

Investment Sales Variable costs Fixed costs Depreciation Pretax profit Tax @ 28.57% Profit after tax Net cash flow Cost of capital

300 150 97.5 30 30 - 7.5 - 2.14 - 5.36 24.64 14%

250 200 120 20 25 35 10 25 50 13%

200 275 154 15 20 86 24.57 61.43 81.43 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.

(c)

(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.

Accounting break even point (under ‘expected’ scenario) 43

Fixed costs + depreciation Contribution margin ratio Break even level of sales

= Rs. 45 million = 60 / 200 = 0.3 = 45 / 0.3 = Rs.150 million

Financial break even point (under ‘xpected’ scenario)

2. (a)

i.

Annual net cash flow

= 0.7143 [ 0.3 x sales – 45 ] + 25 = 0.2143 sales – 7.14

ii.

PV (net cash flows)

= [0.2143 sales – 7.14 ] x PVIFA (13,10) = 1.1628 sales – 38.74

iii.

Initial investment

= 200

iv.

Financial break even level of sales

= 238.74 / 1.1628

Sensitivity of NPV with respect to quantity manufactured and sold: (in Rs) Pessimistic Expected Optimistic Initial investment Sale revenue Variable costs Fixed costs Depreciation Profit before tax Tax Profit after tax Net cash flow NPV at a cost of capital of 10% p.a and useful life of 5 years

(b)

= Rs.205.31 million

30000 24000 16000 3000 2000 3000 1500 1500 3500

30000 42000 28000 3000 2000 9000 4500 4500 6500

30000 54000 36000 3000 2000 13000 6500 6500 8500

-16732

- 5360

2222

Sensitivity of NPV with respect to variations in unit price.

Initial investment Sale revenue Variable costs

Pessimistic

Expected

Optimistic

30000 28000 28000

30000 42000 28000

30000 70000 28000

44

Fixed costs Depreciation Profit before tax Tax Profit after tax Net cash flow NPV (c)

3000 2000 9000 4500 4500 6500 (-) 5360

3000 2000 37000 18500 18500 20500 47711

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

Initial investment Sale revenue Variable costs Fixed costs Depreciation Profit before tax Tax Profit after tax Net cash flow NPV (d)

3000 2000 -5000 -2500 -2500 - 500 - 31895

Pessimistic

Expected

Optimistic

30000 42000 56000 3000 2000 -11000 -5500 -5500 -3500 -43268

30000 42000 28000 3000 2000 9000 4500 4500 6500 - 5360

30000 42000 21000 3000 2000 16000 8000 8000 10000 7908

Accounting break-even point i. ii. iii.

Fixed costs + depreciation Contribution margin ratio Break-even level of sales

= Rs.5000 = 10 / 30 = 0.3333 = 5000 / 0.3333 = Rs.15000

Financial break-even point

3.

i. ii.

Annual cash flow PV of annual cash flow

iii. iv.

Initial investment Break-even level of sales

= 0.5 x (0.3333 Sales – 5000) = 2000 = (i) x PVIFA (10,5) = 0.6318 sales – 1896 = 30000 = 31896 / 0.6318 = Rs.50484

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

 NPV =

12

2

22 + (1.1)4 (1.1)6

32

+ (1.1)2 = 1.00  (NPV) = Rs.1.00 million 4.

Expected NPV 4 At =  - 25,000 t t=1 (1.08) =

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.

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

Expected NPV 4 At 46

 t=1 = =

(1.06) 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

= A1

…. (1)

- 10,000 t

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 2t

4

 (NPV) =  t=1 (1.06)2t 2

12

= =

22

= =

32

= =

42

…….. (2)

[(2,000 – 3,100)2 x 0.2 + (3,000 – 3,100)2 x 0.5 + (4,000 – 3,100)2 x 0.3] 490,000 [(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 [(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

[(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 get =

47

490,000 / (1.06)2 + 690,000 / (1.06)4 + 490,000 / (1.06)6 + 560,000 / (1.08)8 [ 490,000 x 0.890 + 690,000 x 0.792 + 490,000 x 0.705 + 560,000 x 0.627 ] = 1,679,150 NPV = 1,679,150 = Rs.1,296 NPV – NPV Prob (NPV < 0) = Prob.

0 - NPV <

NPV 0 – 3044 = Prob Z < 1296

NPV

= Prob (Z < -2.35) The required probability is given by the shaded area in the following normal P (Z < - 2.35) = = = =

curve.

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: 48

[Q(P – V) – 3,000 – 2,000] (0.5)+ 2,000 5 NPV  t =1

0 +

(1.1)t

- 30,000 (1.1)5

0.5 Q (P – V) – 500 5  t=1

=

------------------------------------ - 30,000 (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

Valu e 800 1,00 0 1,20 0 1,40 0 1,60 0 1,80 0

Pro b 0.1 0 0.1 0 0.2 0 0.3 0 0.2 0 0.1 0

PRICE

Cumulati ve Prob.

Two digit random numbers

0.10

Valu e

Pro b

00 to 09

20

0.20

10 to 19

30

0.40

20 to 39

40

0.70

40 to 69

50

0.4 0 0.4 0 0.1 0 0.1 0

0.90

70 to 89

1.00

90 to 99

49

Cumulati ve Prob.

Two digit random numbers

Value

0.40

00 to 39

15

0.80

40 to 79

20

0.90

80 to 89

40

1.00

90 to 99

VARIABLE COST Two digit Cumu random Pro numbers b lative Prob. 0.3 0.30 00 to 29 0 0.5 0.80 30 to 79 0 0.2 1.00 80 to 99 0

Exhibit 2 Simulation Results

Ru n

1 2 3 4 5 6 7 8 9 Ru n

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

QUANTITY (Q) Rando Corresm ponding Numbe Value r 03 800 32 1,200 61 1,400 48 1,400 32 1,200 31 1,200 22 1,200 46 1,400 57 1,400 QUANTITY (Q) Rando Corresm ponding Numbe Value r 92 1,800 25 1,200 64 1,400 14 1,000 05 800 07 800 34 1,200 79 1,600 55 1,400 57 1,400 53 1,400 36 1,200 32 1,200 49 1,400 21 1,200 08 .800 85 1,600 61 1,400 25 1,200 51 1,400 32 1,200

PRICE (P) Random CorresNumber ponding value

VARIABLE COST (V) NPV Rando Corres- 1.8955 Q(P-V)m pondin 31,895.5 Number g value

38 20 69 30 30 20 60 30 19 20 88 40 78 30 11 20 20 20 PRICE (P) Random CorresNumber ponding value

17 15 -24,314 24 15 2,224 03 15 -18,627 83 40 -58,433 11 15 -20,523 30 20 13,597 41 20 -9,150 52 20 -31,896 15 15 -18,627 VARIABLE COST (V) NPV Rando Corres1.8955 Q(P-V)m pondin 31,895.5 Number g value

77 65 04 51 39 90 63 91 54 12 78 79 22 93 84 70 63 68 81 76 47

30 30 20 30 20 50 30 50 30 20 30 30 20 50 40 30 30 30 40 30 30

38 36 83 72 81 40 67 99 64 19 22 96 75 88 35 27 69 16 39 38 46 50

20 20 40 20 40 20 20 40 20 15 15 40 20 40 20 15 20 15 20 20 20

2,224 -9,150 -84,970 -12,941 -62,224 13,597 -9,150 -1,568 -5,359 -18,627 7,910 -54,642 -31,896 -5,359 13,597 -9,150 -1,568 7,910 13,597 -5,359 -9,150

31 32 33 34 35 36

Ru n

37 38 39 40 41 42 43 44 45 46 47 48 49 50

52 76 43 70 67 26

1,400 1,600 1,400 1,600 1,400 1,200

61 18 04 11 35 63

30 20 20 20 20 30

58 41 49 59 26 22

QUANTITY (Q) Random Corres Number pondin g Value 89 1,600 94 1,800 09 .800 44 1,400 98 1,800 10 1,000 38 1,200 83 1,600 54 1,400 16 1,000 20 1,200 61 1,400 82 1,600 90 1,800

PRICE (P) Random CorresNumber ponding value

Expected NPV

=

86 00 15 84 23 53 44 30 71 70 65 61 48 50

= = =

Variance of NPV

40 20 20 40 20 30 30 20 30 30 30 30 30 30

-5,359 -31,896 -31,896 -31,896 -18,627 2,224

VARIABLE COST (V) NPV Rando Corres1.8955 Q(P-V)m pondin 31,895.5 Number g value

59 25 29 21 79 77 31 10 52 19 87 70 97 43

NPV 50 1/ 50 NPVi i=1 1/50 (-7,20,961) 14,419 50 NPVi – NPV)2 i=1

=

1/50

= =

1/50 [27,474.047 x 106] 549.481 x 106 51

20 20 20 20 15 15

20 15 15 15 20 20 20 15 20 15 40 20 40 20

28,761 -14,836 -24,314 34,447 -31,896 -12,941 -9,150 -16,732 -5,359 -3,463 -54,642 -5,359 -62,224 2,224

Standard deviation of NPV

7.

= =

549.481 x 106 23,441

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

Rs.30,000 – Rs.30,000 Rs.30,000 10% - 10% 10% Rs.3,000 – Rs.3,000 Rs.3,000 Rs.2,000 – Rs.2,000 Rs.2,000 0.5 – 0.5 0.5 5–5 5 0–0 0 Can assume any one of the values 1,400* 800, 1,000, 1,200, 1,400, 1,600 and 1,800 P Can assume any of the values 20, 30, 30** 40 and 50 V Can assume any one of the values 20* 15,20 and 40 ---------------------------------------------------------------------------------------* The most likely values in the case of Q, P and V are the values that have the probability associated with them I k F D T N S Q

highest

** 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

NPV

5 =  t=1 5 =  t=1

[Q (30-20) – 3,000 – 2,000] x 0.5 + 2,000

0 +

(1.1)t

- 30,000 (1.1)5

5Q - 500 - 30,000 (1.1)t

The net present values for various values of Q are given in the following table: 52

Q NPV

800 -16,732

1,000 -12,941

1,200 -9,150

1,400 -5,359

1,600 -1,568

1,800 2,224

Sensitivity analysis with reference to P The relationship between P and NPV, given the most likely values of other variables is defined as follows: 5 NPV =  t=1

=

[1,400 (P-20) – 3,000 – 2,000] x 0.5 + 2,000

0 +

(1.1)t

- 30,0 (1.1)5

700 P – 14,500

5  t=1

- 30,000 t

(1.1)

The net present values for various values of P are given below : P (Rs) 20 30 - 40 50 NPV(Rs) -31,896 -5,359 21,179 47,716 8.

NPV -5 (Rs.in lakhs) PI 0.9

0

5

10

15

20

1.00

1.10

1.20

1.30

1.40

Prob.

0.03

0.10

0.40

0.30

0.15

0.02

6 Expected PI = PI =  (PI)j P j j=1 = 1.24 6  (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. Standard deviation of P1 =

53

Since the risk associated with the investment is much less than the maximum risk acceptable to the company for the given level of expected PI, the company must should accept the investment. 9.

The NPVs of the two projects calculated at their risk adjusted discount rates are 6 3,000 Project A: NPV =  - 10,000 = Rs.2,333 t t=1 (1.12)

Project B:

NPV

=

5  t=1

as follows:

11,000 - 30,000 = Rs.7,763 t

(1.14)

PI and IRR for the two projects are as follows: Project

A

B

PI IRR

1.23 20%

1.26 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 2 3  

 

  

1 = 0.94 2 = 0.88 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 + + + + 2 3 4 (1.08) (1.08) (1.08) (1.08) (1.08)5

54

6,580

7,040

7,380

+

+ (1.08)2

(1.08) =

7,600 +

5,600 +

(1.08)3

(1.08)4

(1.08)5

27,386

Net present value of the Project

= (27,386 – 30,000 = Rs. –2,614

MINICASE Solution: 1. The expected NPV of the turboprop aircraft 0.65 (5500) + 0.35 (500) NPV = - 11000 + (1.12) 0.65 [0.8 (17500) + 0.2 (3000)] + 0.35 [0.4 (17500) + 0.6 (3000)] + (1.12)2 = 2369

2. If Southern Airways buys the piston engine aircraft and the demand in year 1 turns out to be high, a further decision has to be made with respect to capacity expansion. To evaluate the piston engine aircraft, proceed as follows: First, calculate the NPV of the two options viz., ‘expand’ and ‘do not expand’ at decision point D2: 0.8 (15000) + 0.2 (1600) Expand : NPV = - 4400 + 1.12 = 6600 0.8 (6500) + 0.2 (2400) Do not expand : NPV = 1.12 = 5071

55

Second, truncate the ‘do not expand’ option as it is inferior to the ‘expand’ option. This means that the NPV at decision point D2 will be 6600 Third, calculate the NPV of the piston engine aircraft option. 0.65 (2500+6600) + 0.35 (800) NPV = – 5500 + 1.12

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

= 7857 1.12

56

Abandonment : 8000 Thus it makes sense to sell off the aircraft after year 1, if the demand in year 1 turns out to be low. The NPV of the turboprop aircraft with abandonment possibility is 0.65 [5500 +{0.8 (17500) + 0.2 (3000)}/ (1.12)] + 0.35 (500 +8000) NPV = - 11,000 + (1.12) 12048 + 2975 = - 11,000 +

= 2413 1.12

Since the turboprop aircraft without the abandonment option has a value of 2369, the value of the abandonment option is : 2413 – 2369 = 44 5. The value of the option to abandon if the piston engine aircraft can be sold for 4400 at the end of year 1: If the demand in year 1 turns out to be low, the payoffs for the ‘continuation’ and ‘abandonment’ options as of year 1 are as follows: 0.2 (6500) + 0.8 (2400) Continuation :

= 2875 1.12

Abandonment : 4400 Thus, it makes sense to sell off the aircraft after year 1, if the demand in year 1 turns out to be low. The NPV of the piston engine aircraft with abandonment possibility is: 0.65 [2500 + 6600] + 0.35 [800 + 4400] NPV = - 5500 + 1.12 5915 + 1820 = - 5500 +

= 1406 1.12

For the piston engine aircraft the possibility of abandonment increases the NPV 57

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

58

Chapter 14 THE COST OF CAPITAL 1(a) Define rD as the pre-tax cost of debt. Using the approximate yield formula, rD calculated as follows:

rD

=

(b) After tax cost = 2.

5.

12.60 x (1 – 0.35) = 8.19%

WACC

=

9 + (100 – 92)/6 -------------------0.4 x100 + 0.6x92

=

0.1085 (or) 10.85%

=

0.4 x 13% x (1 – 0.35) + 0.6 x 18% 14.18%

= 4.

14 + (100 – 108)/10 ------------------------ x 100 = 12.60% 0.4 x 100 + 0.6x108

Define rp as the cost of preference capital. Using the approximate yield formula rp can be calculated as follows:

rp

3.

can be

Cost of equity = (using SML equation)

10% + 1.2 x 7% = 18.4%

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%

Given 0.5 x 14% x (1 – 0.35) + 0.5 x rE = 12% where rE is the cost of equity capital. Therefore rE – 14.9% 59

Using the SML equation we get 11% + 8% x β = 14.9% where β denotes the beta of Azeez’s equity. Solving this equation we get β = 0.4875. 6(a)

The cost of debt of 12% represents the historical interest rate at the time the debt was originally issued. But we need to calculate the marginal cost of debt (cost of raising new debt); and for this purpose we need to calculate the yield to maturity of the debt as on the balance sheet date. The yield to maturity will not be equal to12% unless the book value of debt is equal to the market value of debt on the balance sheet date.

(b)

The cost of equity has been taken as D1/P0 ( = 6/100) whereas the cost of equity is (D1/P0) + g where g represents the expected constant growth rate in dividend per share.

7.

The book value and market values of the different sources of finance are provided in the following table. The book value weights and the market value weights are provided within parenthesis in the table. (Rs. in million) Source Book value Market value Equity 800 (0.54) 2400 (0.78) Debentures – first series 300 (0.20) 270 (0.09) Debentures – second series 200 (0.13) 204 (0.06) Bank loan 200 (0.13) 200 (0.07) Total 1500 (1.00) 3074 (1.00)

8. Project

Beta

P Q R S

0.6 0.9 1.5 1.5

Required return based on SML equation (%) 14.8 17.2 22.0 22.0

Expected return (%) 13 14 16 20

Given a hurdle rate of 18% (the firm’s cost of capital), projects P, Q and R would have been rejected because the expected returns on these projects are below 18%. Project S would be accepted because the expected return on this project exceeds 18%.An appropriate basis for 60

accepting or rejecting the projects would be to compare the expected rate of return and the required rate of return for each project. Based on this comparison, we find that all the four projects need to be rejected. 9. (a)

Given rD x (1 – 0.3) x 4/9 + 20% x 5/9 = 15% rD = 12.5%,where rD represents the pre-tax cost of debt.

(b)

Given 13% x (1 – 0.3) x 4/9 + rE x 5/9 = 15% rE = 19.72%, where rE represents the cost of equity.

10.

Cost of equity = D1/P0 + g = 3.00 / 30.00 + 0.05 = 15% (a) The first chunk of financing will comprise of Rs.5 million of retained earnings costing 15 percent and Rs.25 million of debt costing 14 (1-.3) = 9.8 per cent The second chunk of financing will comprise of Rs.5 million of additional equity costing 15 per cent and Rs.2.5 million of debt costing 15 (1-.3) = 10.5 per cent (b) The marginal cost of capital in the first chunk will be : 5/7.5 x 15% + 2.5/7.5 x 9.8% = 13.27% The marginal cost of capital in the second chunk will be : 5/7.5 x 15% + 2.5/7.5 x 10.5% = 13.50% Note : We have assumed that (i) The net realisation per share will be Rs.25, after floatation costs, and (ii) The planned investment of Rs.15 million is inclusive of floatation costs

11.

The cost of equity and retained earnings rE = D1/PO + g = 1.50 / 20.00 + 0.07 = 14.5% The cost of preference capital, using the approximate formula, is : 11 + (100-75)/10 rE

=

= 15.9% 0.6 x 75 + 0.4 x 100

61

The pre-tax cost of debentures, using the approximate formula, is : 13.5 + (100-80)/6 rD

=

= 19.1% 0.6x80 + 0.4x100

The post-tax cost of debentures is 19.1 (1-tax rate) = 19.1 (1 – 0.5) = 9.6% The post-tax cost of term loans is 12 (1-tax rate) = 12 (1 – 0.5) = 6.0% The average cost of capital using book value proportions is calculated below : Source of capital

Equity capital Preference capital Retained earnings Debentures Term loans

Component Cost (1) 14.5% 15.9% 14.5% 9.6% 6.0%

Book value Rs. in million (2) 100 10 120 50 80 360

Book value Product of proportion (1) & (3) (3) 0.28 4.06 0.03 0.48 0.33 4.79 0.14 1.34 0.22 1.32 Average cost11.99% capital

The average cost of capital using market value proportions is calculated below : Source of capital

Equity capital and retained earnings Preference capital Debentures Term loans

Component cost (1)

Market value Market value Product of Rs. in million (2) (3) (1) & (3)

14.5% 15.9% 9.6% 6.0%

200 7.5 40 80

0.62 0.02 0.12 0.24

327.5

12 62

Average cost capital

8.99 0.32 1.15 1.44 11.90%

(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 rd =

8.5 =

0.6 x 112 + 0.4 x 100

= 7.93 107.2

rd (1 – 0.3) = 5.55 c. Post-tax cost of preference 9 + (100 – 106) / 5 7.8 = = 7.53% 0.6 x 106 + 0.4 x 100 103.6 d. Cost of equity using the DDM 2.80 (1.10) + 0.10 = 0.385 + 0.10 80 = 0.1385 = 13.85% e. Cost of equity using the CAPM 7 + 1.1(7) = 14.70% f.

WACC 0.50 x 14.70 + 0.10 x 7.53 + 0.40 x 5.55 63

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

64

Chapter 15 CAPITAL BUDGETING : EXTENSIONS 1.

EAC (Plastic Emulsion)

= = =

300000 / PVIFA (12,7) 300000 / 4.564 Rs.65732

EAC (Distemper Painting) = = =

180000 / PVIFA (12,3) 180000 / 2.402 Rs.74938

Since EAC of plastic emulsion is less than that of distemper painting, it is the preferred alternative. 2.

PV of the net costs associated with the internal transportation system =

=

1 500 000 + 300 000 x PVIF (13,1) + 360 000 x PVIF (13,2) + 400 000 x PVIF (13,3) + 450 000 x PVIF (13,4) + 500 000 x PVIF (13,5) - 300 000 x PVIF (13,5) 2709185

EAC of the internal transportation system = = = 3.

2709185 / PVIFA (13,5) 2709185 / 3.517 Rs.770 311

EAC [ Standard overhaul] = = =

500 000 / PVIFA (14,6) 500 000 / 3.889 Rs.128568

………

(A)

………

(B)

EAC [Less costly overhaul] = = =

200 000 / PVIFA (14,2) 200 000 / 1.647 Rs.121433

Since (B) < (A), the less costly overhaul is preferred alternative.

65

4. (a)

Base case NPV = = =

(b)

-12,000,000 + 3,000,000 x PVIFA (20,6) -12,000,000 + 997,8000 (-) Rs.2,022,000

Issue costs = 6,000,000 / 0.88 - 6,000,000 =

Rs.818 182

Adjusted NPV after adjusting for issue costs = = (c)

- 2,022,000 – 818,182 - Rs.2,840,182

The present value of interest tax shield is calculated below : Year 1 2 3 4 5 6 7 8 9

Debt outstanding at the beginning 6,000,000 6,000,000 5,250,000 4,500,000 3,750,000 3,000,000 2,225,000 1,500,000 750,000

Interest

Tax shield

1,080,000 1,080,000 945,000 810,000 675,000 540,000 400,500 270,000 135,000

324,000 324,000 283,000 243,000 202,000 162,000 120,000 81,000 40,500

Present value of tax shield 5. (a)

= Rs.1,022,076

Base case BPV = =

(b)

Present value of tax shield 274,590 232,697 172,538 125,339 88,513 60,005 37,715 21,546 9,133

- 8,000,000 + 2,000,000 x PVIFA (18,6) - Rs.1,004,000

Adjusted NPV after adjustment for issue cost of external equity = = =

Base case NPV – Issue cost - 1,004,000 – [ 3,000,000 / 0.9 – 3,000,000] - Rs.1,337,333 66

(c)

The present value of interest tax shield is calculated below : Year 1 2 3 4 5 6

Debt outstanding at the beginning 5,000,000 5,000,000 4,000,000 3,000,000 2,000,000 1,000,000

Interest

Tax shield

750,000 750,000 600,000 450,000 300,000 150,000

300,000 300,000 240,000 180,000 120,000 60,000

Present value of tax shield

67

=

Present value of tax shield 260,880 226,830 157,800 102,924 59,664 25,938 Rs.834,036

Chapter 18 RAISING LONG TERM FINANCE

1

Underwriting commitment

Shares procured

Excess/ shortfall

Credit

Net 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.

3.

Underwriting commitment

Shares procured

Excess/ Shortfall

Credit

Net 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

-

-

Po = Rs.220 S = Rs.150 N=4 a. The theoretical value per share of the cum-rights stock would simply be Rs.220 b.

The theoretical value per share of the ex-rights stock is : 68

NPo+S

4 x 220 +150 =

= Rs.206

N+1

4+1

c. The theoretical value of each right is : Po – S 220 – 150 = = Rs.14 N+1 4+1 The theoretical value of 4 rights which are required to buy 1 share is Rs.14x14=Rs.56. 4.

Po = Rs.180 N=5 a. The theoretical value of a right if the subscription price is Rs.150 Po – S 180 – 150 = = Rs.5 N+1 5+1 b. The ex-rights value per share if the subscription price is Rs.160 NPo + S 5 x 180 + 160 = = Rs.176.7 N+1 5+1 c. The theoretical value per share, ex-rights, if the subscription price is Rs.180? 100? 5 x 180 + 180 = Rs.180 5+1 5 x 180 + 100 = Rs.166.7 5+1

69

Chapter 19 CAPITAL STRUCTURE AND FIRM VALUE 1.

Net operating income (O) Interest on debt (I) Equity earnings (P) Cost of equity (rE)

: : : :

Rs.30 million Rs.10 million Rs.20 million 15%

Cost of debt (rD) Market value of equity (E) Market value of debt (D) Market value of the firm (V)

: : : :

10% Rs.20 million/0.15 =Rs.133 million Rs.10 million/0.10 =Rs.100 million Rs.233 million

2.

Box

Cox

Market value of equity 2,000,000/0.15 2,000,000/0.15 = Rs.13.33 million = Rs.13.33 million Market value of debt 0 1,000,000/0.10 =Rs.10 million Market value of the firm Rs.13.33million =23.33 million (a) Average cost of capital for Box Corporation 13.33. 0 x 15% + x 10% 13.33 13.33

= 15%

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 Interest on debt Equity earnings Cost of equity

Rs.6,000,000 Rs.3,000,000 Rs.3,000,000 15% 70

Cost of debt Market value of equity Market value of debt Market value of the firm

Average cost of capital 20 30 15% x + 10% 50 50

10% Rs.20 million Rs.30 million Rs.50 million

= 12%

(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.

4.

rE = 20 = So D/E = 2

rA + (rA-rD)D/E 12 + (12-8) D/E

E

D

D+E

D+E

1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

E rE (%)

rD (%)

11.0 11.0 11.5 12.5 13.0 14.0 15.0 16.0 18.0 20.0

6.0 6.5 7.0 7.5 8.5 9.5 11.0 12.0 13.0 14.0

rA =

rE + D+E

D rD D+E

11.00 10.55 10.60 11.00 11.20 11.75 12.60 13.20 14.00 14.20

The optimal debt ratio is 0.10 as it minimises the weighted average cost of capital. 5. (a) If you own Rs.10,000 worth of Bharat Company, the levered company which is valued more, you would sell shares of Bharat Company, resort to personal leverage, and buy the shares of Charat Company. (b) The arbitrage will cease when Charat Company and Bharat Company are valued alike

71

6.

7.

The value of Ashwini Limited according to Modigliani and Miller hypothesis is Expected operating income 15 = = Rs.125 million Discount rate applicable to the 0.12 risk class to which Aswini belongs The average cost of capital(without considering agency and bankruptcy cost) at various leverage ratios is given below. D

E

E

D+E

D+ E

rD %

rE %

0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10

4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0

12.0 12.0 12.5 13.5 13.5 14.0 14.5 15.0 15.5 16.0

rA =

rE + D+E (%)

D rD D+E

12.0 11.2 10.8 10.36 9.86 9.30 8.68 8.14 7.90 7.72 Optimal

b. The average cost of capital considering agency and bankruptcy costs is given below . D E E D rD rE rA = rE + rD D+E D+ E % % D+E D+E (%) 0 1.00 4.0 12.0 0.10 0.90 4.0 12.0 0.20 0.80 4.0 13.0 0.30 0.70 4.2 14.0 0.40 0.60 4.4 15.0 0.50 0.50 4.6 16.0 0.60 0.40 4.8 17.0 0.70 0.30 5.2 18.0 0.80 0.20 6.0 19.0 0.90 0.10 6.8 20.0 8. The tax advantage of one rupee of debt is :

12.0 11.2 11.2 11.06 10.76 10.30 9.68 9.04 8.60 8.12 Optimal

72

1-(1-tc) (1-tpe)

(1-0.55) (1-0.05) =

1 -

(1-tpd)

(1-0.25) = 0.43 rupee Chapter 20 CAPITAL STRUCTURE DECISION

1.(a) Currently No. of shares = 1,500,000 EBIT = Rs 7.2 million Interest = 0 Preference dividend = Rs.12 x 50,000 = Rs.0.6 million EPS = Rs.2 (EBIT – Interest) (1-t) – Preference dividend EPS = No. of shares (7,200,000 – 0 ) (1-t) – 600,000 Rs.2 = 1,500,000 Hence t = 0.5 or 50 per cent The EPS under the two financing plans is : Financing Plan A : Issue of 1,000,000 shares (EBIT - 0 ) ( 1 – 0.5) - 600,000 EPSA

= 2,500,000

Financing Plan B : Issue of Rs.10 million debentures carrying 15 per cent interest (EBIT – 1,500,000) (1-0.5) – 600,000 EPSB = 1,500,000 The EPS – EBIT indifference point can be obtained by equating EPSA and EPSB (EBIT – 0 ) (1 – 0.5) – 600,000

(EBIT – 1,500,000) (1 – 0.5) – 600,000 73

= 2,500,000

1,500,000

Solving the above we get EBIT = Rs.4,950,000 and at that EBIT, EPS is Rs.0.75 under both the plans (b)

As long as EBIT is less than Rs.4,950,000 equity financing maximixes EPS. When EBIT exceeds Rs.4,950,000 debt financing maximises EPS.

2. 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 (a)

(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 (Rs.)

EPSA (Rs.)

2,000,000 2,160,000 3,000,000 4,000,000 4,400,000 More than 4,400,000 3.

EPSB (Rs.)

0.50(I) 0.54(I) 0.75(I) 1.00(II) 1.10(II) (III)

0.35(II) 0.40(II) 0.66(II) 0.98(III) 1.10(II) (II)

EPSC (Rs.) 0.33(III) 0.40(II) 0.75(I) 1.17(I) 1.33(I) (I)

Plan A : Issue 0.8 million equity shares at Rs. 12.5 per share. Plan B : Issue Rs.10 million of debt carrying interest rate of 15 per cent. (EBIT – 0 ) (1 – 0.6) EPSA

= 74

1,800,000 (EBIT – 1,500,000) (1 – 0.6) EPSB

= 1,000,000

Equating EPSA and EPSB , we get (EBIT – 0 ) (1 – 0.6) (EBIT – 1,500,000) (1 – 0.6) = 1,800,000 1,000,000 Solving this we get EBIT = 3,375,000 or 3.375 million Thus the debt alternative is better than the equity alternative when EBIT > 3.375 million EBIT – EBIT Prob(EBIT>3,375,000) = Prob

3.375 – 7.000 >

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.

7. a.

18 = [ ROI + ( ROI – 8 ) 0.7 ] ( 1 – 0.5) ROI = 24.47 per cent EBIT Interest coverage ratio = Interest on debt 150 = 40 = 3.75 EBIT + Depreciation

b.

Cash flow coverage ratio = Loan repayment instalment

75

Int.on debt + (1 – Tax rate) = 150 + 30 40 + 50

8.

= 2 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

= = 9.

277.94 167.80 1.66

(a) If the entire outlay of Rs. 300 million is raised by way of debt carrying 15 per cent interest, the interest burden will be Rs. 45 million. Considering the interest burden the net cash flows of the firm during a recessionary year will have an expected value of Rs. 35 million (Rs.80 million - Rs. 45 million ) and a standard deviation of Rs. 40 million . Since the net cash flow (X) is distributed normally X – 35 40 has a standard normal deviation Cash flow inadequacy means that X is less than 0. 0.35 Prob(XC, or 0 otherwise F. Dividends per share

2.

Given the constraints imposed by the management, the dividend per share has to be between Rs.1.00 (the dividend for the previous year) and Rs.1.60 (80 per cent of earnings per share) Since share holders have a preference for dividend, the dividend should be raised over the previous dividend of Rs.1.00 . However, the firm has substantial investment requirements and it would be reluctant to issue additional equity because of high issue costs ( in the form of underpricing and floatation costs) Considering the conflicting requirements, it seems to make sense to pay Rs.1.20 per share by way of dividend. Put differently the pay out ratio may be set at 60 per cent.

3.

According to the Lintner model Dt = cr EPSt + (1-c)Dt –1 EPSt =3.00, c= 0.7, r=0.6 , and Dt-1 Hence Dt = 0.7 x 0.6 x 3.00 + (1-0.7)1.20 80

= Rs.1.62

4.

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

81

Chapter 23 Debt Analysis and Management 1. (i) Initial Outlay (a) Cost of calling the old bonds Face value of the old bonds Call premium

250,000,000 15,000,000 265,000,000

(b) Net proceeds of the new bonds Gross proceeds Issue costs

250,000,000 10,000,000 240,000,000

(c) Tax savings on tax-deductible expenses Tax rate[Call premium+Unamortised issue cost on the old bonds] 0.4 [ 15,000,000 + 8,000,000] Initial outlay i(a) – i(b) – i(c) (ii)

Annual Net Cash Savings (a) Annual net cash outflow on old bonds Interest expense - Tax savings on interest expense and amortisation of issue expenses 0.4 [42,500,000 + 8,000,000/10]

9,200,000 15,800,000

42,500,000 17,400,000 25,100,000

(b) Annual net cash outflow on new bonds Interest expense - Tax savings on interest expense and amortisation of issue cost 0.4 [ 37,500,000 – 10,000,000/8]

15,500,000 22,000,000 3,100,000

Annual net cash savings : ii(a) – ii(b) (iii)

37,500,000

Present Value of the Annual Cash Savings Present value of an 8-year annuity of 3,100,000 at a 82

discount rate of 9 per cent which is the post –tax cost of new bonds 3,100,000 x 5.535 Net Present Value of Refunding the Bonds (a) Present value of annual cash savings (b) Net initial outlay (c) Net present value of refunding the bonds : iv(a) – iv(b). 2. (i) Initial Outlay (a) Cost of calling the old bonds Face value of the old bonds Call premium

17,158,500

(iv)

17,158,500 15,800,000 1,358,500

120,000,000 4,800,000 124,800,000

(b) Net proceeds of the new issue Gross proceeds Issue costs

120,000,000 2,400,000

(c) Tax savings on tax-deductible expenses Tax rate[Call premium+Unamortised issue costs on the old bond issue] 0.4 [ 4,800,000 + 3,000,000] Initial outlay i(a) – i(b) – i(c) (ii)

Annual Net Cash Savings (a) Annual net cash out flow on old bonds Interest expense - Tax savings on interest expense and amortisation of issue costs 0.4[19,200,000 + 3,000,000/5]

117,600,000 3,120,000

4,080,000

19,200,000 7,920,000 11,280,000

(b) Annual net cash outflow on new bonds Interest expense - Tax savings on interest expense and amortistion of issue costs 0.4[18,000,000 + 2,400,000/5]

7,392,000 10,608,000 672,000

Annual net cash savings : ii(a) – ii(b) (iii)

18,000,000

Present Value of the Annual Net Cash Savings Present value of a 5 year annuity of 672,000 at

83

as discount rate of 9 per cent, which is the post-tax new bonds (iv)

Net Present Value of Refunding the Bonds (a) Present value of annual net cash savings (b) Initial outlay (c) Net present value of refunding the bonds : iv(a) – iv(b)

3. Yield to maturity of bond P 8 160 918.50 = + t t=1 (1+r)

2,614,080

2,614,080 4,080,000 - 1,466,000

1000 (1+r)8

r or yield to maturity is 18 percent Yield to maturity of bond Q 5 120 761 =  + t=1 (1+r)t

1000 (1+r)5

r or yield to maturity is 20 per cent Duration of bond P is calculated below Year

1 2 3 4 5 6 7 8

Cash flow

Present Value Proportion of at 18% bond’s value

160 160 160 160 160 160 160 160

135.5 114.9 97.4 82.6 69.9 59.2 50.2 308.6

Proportion of bond’s Value x Time

0.148 0.125 0.106 0.090 0.076 0.064 0.055 0.336

0.148 0.250 0.318 0.360 0.380 0.384 0.385 2.688 4.913

Duration of bond Q is calculated below Year

Cash flow

Present Value at 20%

Proportion of bond’s value

84

Proportion of bond’s Value x Time

cost of

1 2 3 4 5

120 120 120 120 1120

100.0 83.2 69.5 57.8 450.2

0.131 0.109 0.091 0.076 0.592

0.131 0.218 0.273 0.304 2.960 3.886

Volatility of bond P 4.913 = 4.16 1.18 4.

Volatility of bond Q 3.886 = 3.24 1.20

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 99000

=

112500 +

(1.1236)

(1.1236)(1+r2)

Solving this for r2 we get r2 = 13.94% 85

To get the forward rate for year 3, r3, the following equation may be set up : 13,000 99,500

=

13,000

113,000

+ (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 : 13,500 100,050

=

13,500

13,500

+ (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 : 13,750 100,100

=

13,750 +

(1.1236)

13,750

+ (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%

86

Chapter 25 HYBRID 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 =

PV (Exercise price)

=

1.856

25/(1.16)

The ratio of the value of call option to stock price corresponding to numbers 0.495 and 1.856 can be found out from Table A.6 by interpolation. Note the table gives values for the following combinations 1.75

2.00

0.45

44.6

50.8

0.50

45.3

51.3

Since we are interested in the combination 0.495 and 1.856 we first interpolate between 0.450 and 0.500 and then interpolate between 1.75 and 2.00 Interpolation between 0.450 and 0.500 gives 1.75

2.00

0.450

44.6

50.8

0.495

45.23

51.25

0.500

45.3

51.3

87

Then, interpolation between 1.75 and 2.00 gives 1.75 0.495

45.23

1.856 47.78

2.00 51.25

Chapter 24 LEASING, HIRE PURCHASE, AND PROJECT FINANCE 1. Year 1.Investment(I) 2.Revenues(Rt) 3.Costs(other than (Depreciation)(Ct) 4.Depreciation(Dt) 5.Profit before tax (Rt-Ct-Dt) 6.Profit after tax: 5(1-t) 7.Net salvage value 8.Net cash flow (1+6+4+7) 9.Discount factor at 11 percent 10.Present value (8x9)

NPV of the Purchase Option 0 (1,500)

1

2

1,700

1,700

3 1,700

(Rs.in ‘000) 4

5

1,700

1,700

900 500

900 333.3

900 222.2

900 148.1

900 98.8

300 210

466.7 326.7

577.8 404.5

651.9 456.3

701.2 490.8 300

(1,500)

710

610

626.7

604.4

889.6

1.000 (1,500)

0.901 639.7

0.812 495.3

0.731 458.1

0.659 398.3

0.593 527.5

NPV(Purchases)= - 1500+639.7+495.3+458.1+398.3+527.5 = 1018.9

NPV of the Leasing Option Year 1.Revenues(Rt) 2.Costs(other than lease rentals)(Ct) 3.Lease rentals(Lt) 4.Profit before tax (Rt-Ct-Lt) 5.Profit after tax (which also reflects the net

0 -

(Rs. in ‘000) 4 5 1,700 1,700

1 1,700

2 1,700

3 1,700

420

900 420

900 420

900 420

900 420

900 0

-420

380

380

380

380

800

88

cash flow)(1-t) 6.Discount factor at 13 per cent 7.Present value(5x6)

-294

266

266

266

266

560

1.000 -294

0.885 -235.4

0.783 208.3

0.693 184.3

0.613 163.1

0.543 304.1

NPV(Leasing) = -294+235.4+208.3+184.3+163.1+304.1 = 801.2

2.

Under the hire purchase proposal the total interest payment is 2,000,000 x 0.12 x 3 = Rs. 720,000 The interest payment of Rs. 720,000 is allocated over the 3 years period using the sum of the years digits method as follows: Year Interest allocation 366 1

x Rs.720,000

= Rs.395,676

666

222 2

x Rs.720,000 = Rs.240,000 666 78

3

x Rs.720,000 = Rs.84,324 666

The annual hire purchase instalments will be : Rs.2,000,000 + Rs.720,000 = Rs.906,667 3 The annual hire purchase instalments would be split as follows Year 1 2 3

Hire purchase instalment Interest Rs.906,667 Rs.395,676 Rs.906,667 Rs.240,000 Rs.906,667 Rs. 84,324

The lease rental will be as follows : 89

Principal repayment Rs. 510,991 Rs. 666,667 Rs. 822,343

Rs. 560,000 per year for the first 5 years Rs. 20,000 per year for the next 5 years

The cash flows of the leasing and hire purchse options are shown below Year

Leasing - LRt (1-tc)

High Purchase -It(1-tc) -PRt

Dt(tc)

1 -560,000(1-.4)=-336,000 -395,676(1-.4) -510,991 2 -560,000(1-.4)=-336,000 -240,000(1-.4) -666,667 3 -560,000(1-.4)=-336,000 - 84,324(1-.4) -822,343 4 -560,000(1-.4)=-336,000 5 -560,000(1-.4)=-336,000 6 - 20,000(1-.4)= - 12,000 7 - 20,000(1-.4)= - 12,000 8 - 20,000(1-.4)= - 12,000 9 - 20,000(1-.4)= - 12,000 10 - 20,000(1-.4)= - 12,000

500,000(0.4) 375,000(0.4) 281,250(0.4) 210,938(0.4) 158,203(0.4) 118,652(0.4) 88,989(0.4) 66,742(0.4) 50,056(0.4) 37,542(0.4) 200,000

Present value of the leasing option 5 336,000 10 = -   t=1 (1.10)t t=6

12,000 = - 1,302,207 (1.10)t

Present value of the hire purchase option 548,397

660,667

=-

760,437

-

(1.10)2

(1.10) 63,281

84,375

47,461 +

(1.10)3 35,596

+

(1.10)5

(1.10)6

20,023

215,017

(1.10)4 26,697 +

(1.10)7

(1.10)8

90

NSVt

-It(1-tc)-PRt+ Dt(tc)+NSVt -548,397 -660,667 -760,437 84,375 63,281 47,461 35,596 26,697 20,023 215,017

+ (1.10)9

(1.10)10

= - 1,369,383 Since the leasing option costs less than the hire purchase option , Apex should choose the leasing option.

Chapter 26 WORKING CAPITAL POLICY Average inventory 1

Inventory period = Annual cost of goods sold/365 (60+64)/2 =

= 62.9 days 360/365 Average accounts receivable

Accounts receivable = period

Annual sales/365 (80+88)/2

=

= 61.3 days 500/365 Average accounts payable

Accounts payable period

= Annual cost of goods sold/365 (40+46)/2 =

= 43.43 days 360/365

Operating cycle Cash cycle

= =

Inventory period

=

62.9 + 61.3 = 124.2 days 124.2 – 43.43 = 80.77 days (110+120)/2

2.

= 750/365 (140+150)/2 91

56.0 days

Accounts receivable = period

=

52.9 days

=

30.7 days

1000/365 (60+66)/2

Accounts payable period

= 750/365

Operating cycle = 56.0 + 52.9 = 108.9 days Cash cycle = 108.9 – 30.7 = 78.2 days 3.

1.

Rs. 3,600,000 900,000 2,700,000

Sales Less : Gross profit (25 per cent) Total manufacturing cost Less : Materials 900,000 Wages 720,000 Manufacturing expenses

1,620,000 1,080,000

2. Cash manufacturing expenses (80,000 x 12) 3. Depreciation : (1) – (2) 4. Total cash cost Total manufacturing cost Less: Depreciation Cash manufacturing cost Add: Administration and sales promotion expenses

960,000 120,000 2,700,000 120,000 2,580,000 360,000 2,940,000

A : Current Assets

Rs.

Total cash cost Debtors

Raw material stock

2,940,000 x 2

=

12

12

Material cost

900,000 x 1

=

12

2=

490,000

x

1=

75,000

12

Cash manufacturing cost Finished goods stock

x

2,580,000 x1=

x

12

12

92

1=

215,000

Cash balance

A predetermined amount Sales promotion expenses

Prepaid sales promotion expenses Cash balance

=

100,000

x 1.5 =

15,000

=

100,000

=

995,000

120,000 x 1.5 =

12

12

A predetermined amount A : Current Assets

B : Current Liabilites Material cost Sundry creditors

Rs.

900,000 x 2=

x

12

2

= 150,000

12

Manufacturing expenses outstanding

One month’s cash manufacturing expenses

=

80,000

Wages outstanding

One month’s wages

=

60,000

B : Current liabilities

290,000

Working capital (A – B) Add 20 % safety margin Working capital required

705,000 141,000 846,000

93

Chapter 27 CASH AND LIQUIDITY MANAGEMENT 1. The forecast of cash receipts, cash payments, and cash position is prepared in the statements given below (Rs. in 000’s)

Forecast of Cash Receipts

November December January February March April May June 1. Sales 120 2. Credit sales 84 3. Cash sales 36 4. Collection of receivables (a) Previous month (b) Two months earlier 5. Sale of machine 6. Interest on securities 7. Total receipts (3+4+5+6)

120 84 36 33.6

150 105 45

150 105 45

150 105 45

200 140 60

42.0 56.0 56.0 63.0 63.0 84.0 70.0 3.0 235.0 179.0 203.0

33.6 50.4

42.0 50.4

42.0 63.0

129.0

137.4

150.0

200 140 60

(Rs. in 000’s)

Forecast of Cash Payments December 1. Purchases 60 2. Payment of accounts payable 3. Cash purchases 4. Wage payments 5. Manufacturing expenses 6. General, administrative & selling expenses

January

February

March

200 140 60

April

May

June

60 60

60 60

60 60

80 60

80 80

80 80

3 25

3 25

3 25

3 25

3 25

3 25

32

32

32

32

32

32

15

15

15

15

15

15

94

7. Dividends 8. Taxes 9. Acquisition of machinery

30 35 80

Total payments(2to9)

135

135

215

135

220

(Rs.in 000’s)

Summary of Cash Forecast

1. Opening balance 2. Receipts 3. Payments 4. Net cash flow(2-3) 5. Cumulative net cash flow 6. Opening balance + Cumulative net cash flow 7. Minimum cash balance required 8. Surplus/(Deficit)

155

January

February

March

28 129.0 135.0 (6.0) (6.0)

137.4 135.0 2.4 (3.6)

150.0 215.0 (65.0) (68.6)

22.0

24.4

30.0 (8.0)

30.0 (5.6)

April

May

June

235.0 135.0 100.0 31.4

179.0 155.0 24.0 55.4

203.0 220.0 (17.0) (38.4)

(40.6)

59.4

83.4

66.4

30.0 (70.6)

30.0 29.4

30.0 53.0

30.0 36.4

2. The projected cash inflows and outflows for the quarter, January through March, is shown below . Month

December (Rs.)

Inflows : Sales collection Outflows : Purchases Payment to sundry creditors Rent Drawings Salaries & other expenses Purchase of furniture Total outflows(2to6)

22,000

January (Rs.)

February (Rs.)

March (Rs.)

50,000

55,000

60,000

20,000 22,000 5,000 5,000 15,000 -

22,000 20,000 5,000 5,000 18,000 25,000

25,000 22,000 5,000 5,000 20,000 -

47,000

73,000

52,000

95

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 (Rs.) 1. Opening balance 2. Inflows 3. Outflows 4. Net cash flow (2 - 3) 5. Cumulative net cash flow 6. Opening balance + Cumulative net cash flow 7. Minimum cash balance required 8. Surplus/(Deficit)

February (Rs.)

March (Rs.)

5,000 50,000 47,000 3,000 3,000

55,000 73,000 (18,000) (15,000)

60,000 52,000 8,000 (7,000)

8,000 8,000 -

(10,000) 8,000 (18,000)

(2,000) 8,000 (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

30,00 0 20,00 0

46,00 0 20,00 0

62,00 0 20,00 0

78,000

5

6

7

8

9

10

94,000

1,10,00 0

1,26,0 00

1,42,0 00

1,58,0 00

1,74,0 00

20,000

20,000

20,000

20,000

20,000

20,000

4,000 1,74,0 00

4,000 1,90,0 00

Books of Datta Co: Opening Balance Add: Cheque received Less: Cheque issued Closing Balance

20,000 4,000

4,000 46,00 0

4,000 62,00 0

4,000 78,00 0

4,000 94,000 1,10,0 00

4,000 1,26,00 0

4,000 1,42,0 00

4,000 1,58,0 00

30,00

30,00

30,00

30,000 30,000

30,000

50,000

70,000

Books of the Bank: Opening

96

1,06,0

Balance Add: Cheques realised Less: Cheques debited Closing Balance

0

0 -

-

30,00 0

0

30,00 0

-

-

-

-

-

30,00 0

-

30,000 30,000

20,000 50,000

20,000 70,000

90,000

00

20,000

20,000

4,000 1,06,0 00

4,000 1,22,0 00

20,000 90,000

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 is 2bT C = I b = Rs.1200, T= Rs.2,500,000, I = 5% (10% dividend by two)

So, 2 x 1200 x 2,500,000 C =

= Rs.346,410 0.05

5. 3

3 b2

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 6,000 RP =

+ 100,000 4 x .00033

= 49,695 + 100,000 = Rs.149,695 UL = 3RP – 2LL = 3 x 149,695 – 2 x 100,000 97

= Rs.249,085

Chapter 28 CREDIT MANAGEMENT 1.

Δ RI = [ΔS(1-V)- ΔSbn](1-t)- k ΔI ΔS ΔI = x ACP x V 360 Δ S = Rs.10 million, V=0.85, bn =0.08, ACP= 60 days, k=0.15, t = 0.40 Hence, ΔRI = [ 10,000,000(1-0.85)- 10,000,000 x 0.08 ] (1-0.4) -0.15 x 10,000,000 x 60 x 0.85 360 = Rs. 207,500

2.

Δ RI = [ΔS(1-V)- ΔSbn] (1-t) – k Δ I Δ I = (ACPN – ACPo)

ΔS

So +V(ACPN) 360

360

98

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

(60-45) 15,000,000 + 0.8 x 60 x 1,500,000

360 = 123750 – 123750 = Rs. 0 3.

360

Δ RI = [ΔS(1-V) –Δ DIS ] (1-t) + k Δ I Δ DIS = pn(So+ΔS)dn – poSodo ΔI =

ΔS

So (ACPo-ACPN) -

x ACPN x V

360

360

So =Rs.12 million, ACPo=24, V=0.80, t= 0.50, r=0.15, po=0.3, pn=0.7, ACPN=16, ΔS=Rs.1.2 million, do=.01, dn= .02 Hence ΔRI = [ 1,200,000(1-0.80)-{0.7(12,000,000+1,200,000).020.3(12,000,000).01}](1-0.5)

12,000,000 + 0.15

1,200,000 (24-16) -

x 16 x 0.80

360

360

= Rs.79,200 4.

Δ RI = [ΔS(1-V)- ΔBD](1-t) –kΔ I ΔBD=bn(So+ΔS) –boSo ΔI =

So

ΔS (ACPN –ACPo) +

360

x ACPN x V 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 - 0.15

Rs.6,000,000 (40-25) +

x 40 x 0.75 99

360

360

= - Rs.289.495 5. 30% of sales will be collected on the 10th day 70% of sales will be collected on the 50th day ACP = 0.3 x 10 + 0.7 x 50 = 38 days Rs.40,000,000 Value of receivables =

x 38 360

= Rs.4,222,222 Assuming that V is the proportion of variable costs to sales, the investment in receivables is : Rs.4,222,222 x V 6. 30% of sales are collected on the 5th day and 70% of sales are collected on the 25th day. So, ACP = 0.3 x 5 + 0.7 x 25 = 19 days Rs.10,000,000 Value of receivables =

x 19 360

= Rs.527,778 Investment in receivables = 0.7 x 527,778 = Rs.395,833 7. Since the change in credit terms increases the investment in receivables, ΔRI = [ΔS(1-V)- ΔDIS](1-t) – kΔI So=Rs.50 million, ΔS=Rs.10 million, do=0.02, po=0.70, dn=0.03,pn=0.60, ACPo=20 days, ACPN=24 days, V=0.85, k=0.12 , and t = 0.40 ΔDIS = 0.60 x 60 x 0.03 – 0.70 x 50 x 0.2 = Rs.0.38 million 50 ΔI=

10 (24-20) +

360

x 24 x 0.85 360

= Rs.1.2222 million Δ RI = [ 10,000,000 (1-.85) – 380,000 ] (1-.4) – 0.12 x 1,222,222 = Rs.525,333

100

8.

The decision tree for granting credit is as follows :

Grant credit

Customer pays(0.95) Profit 1500

Customer pays(0.85) Grant credit Profit 1500

Customer defaults(0.05) 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 Initial order

+

Probability of payment and repeat order

{ 0.85(1500)-0.15(8500)} + = 0 +

x

Expected profit on repeat order

0.85 {0.95(1500)-.05(8500)} 850 = Rs.850

9. Profit when the customer pays = Rs.10,000 - Rs.8,000 = Rs.2000 Loss when the customer does not pay = Rs.8000 Expected profit = p1 x 2000 –(1-p1)8000 Setting expected profit equal to zero and solving for p1 gives : p1 x 2000 – (1- p1)8000 = 0 p1 = 0.80 Hence the minimum probability that the customer must pay is 0.80

MINICASE Solution: Present Data        

Sales : Rs.800 million Credit period : 30 days to those deemed eligible Cash discount : 1/10, net 30 Proportion of credit sales and cash sales are 0.7 and 0.3. 50 percent of the credit customers avail of cash discount Contribution margin ratio : 0.20 Tax rate : 30 percent Post-tax cost of capital : 12 percent ACP on credit sales : 20 days 101

Effect of Relaxing the Credit Standards on Residual Income Incremental sales : Rs.50 million Bad debt losses on incremental sales: 12 percent ACP remains unchanged at 20 days ∆RI = [∆S(1 – V) - ∆Sbn] (1 – t) – R ∆ I ∆S where ∆ I =

x ACP x V 360

∆ RI = [50,000,000 (1-0.8) – 50,000,000 x 0.12] (1 – 0.3) 50,000,000 - 0.12 x

x 20 x 0.8 360

= 2,800,000 – 266,667 = 2,533,333 Effect of Extending the Credit Period on Residual Income ∆ RI = [∆S(1 – V) - ∆Sbn] (1 – t) – R ∆ I where ∆I = (ACPn – ACPo)

∆S

So + V (ACPn) 360

360

∆RI = [50,000,000 (1 – 0.8) – 50,000,000 x 0] (1 – 0.3)

800,000,000 - 0.12

(50 – 20) x

50,000,000 + 0.8 x 50 x

360

360

= 7,000,000 – 8,666,667 = - Rs.1,666,667 Effect of Relaxing the Cash Discount Policy on Residual Income ∆RI = [∆S (1 – V) - ∆ DIS] (1 – t) + R ∆ I where ∆ I = savings in receivables investment So ∆S 102

(ACPo – ACPn) – V

= 360

x ACPn 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 Orders Per Year (U/Q)

1 2 5 10

Order Quantity (Q)

Ordering Cost (U/Q x F)

Units

Rs.

250 125 50 25

Carrying Cost Total Cost Q/2xPxC of Ordering (where and Carrying PxC=Rs.30) Rs. Rs.

200 400 1,000 2,000

3,750 1,875 750 375

2 UF b. Economic Order Quantity (EOQ) =

3,950 2,275 1,750 2,375

2x250x200 =

PC

30 103

2UF

= 58 units (approx)

2. a EOQ = PC U=10,000 , F=Rs.300, PC= Rs.25 x 0.25 =Rs.6.25 2 x 10,000 x 300 EOQ =

= 980 6.25 10000

b. Number of orders that will be placed is

= 10.20

980 Note that though fractional orders cannot be placed, the number of orders relevant for the year will be 10.2 . In practice 11 orders will be placed during the year. However, the 11th order will serve partly(to the extent of 20 percent) the present year and partly(to the extent of 80 per cent) the following year. So only 20 per cent of the ordering cost of the 11th order relates to the present year. Hence the ordering cost for the present year will be 10.2 x Rs.300

3.

c. Total cost of carrying and ordering inventories 980 = [ 10.2 x 300 + x 6.25 ] = Rs.6122.5 2 U=6,000, F=Rs.400 , PC =Rs.100 x 0.2 =Rs.20 2 x 6,000 x 400 EOQ =

= 490 units 20 U

Q’(P-D)C

U

Δπ = UD +

-

FQ’

Q*

2

6,000

2

6,000

= 6000 x .5 +

490

x 400 1,000

1,000 (95)0.2 -

Q* PC -

490 x 100 x 0.2 -

2

2

= 30,000 + 2498 – 4600 = Rs.27898

104

4.

U=5000 , F= Rs.300 , PC= Rs.30 x 0.2 = Rs.6 2 x 5000 x 300 EOQ =

= 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 Δπ = 5000 x 1.5 +

5,000 -

707

1,000

1000 x 28.5 x 0.2 -

x 300

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 Δπ = 5000 x 3.0 + 707 = 15,000 +1372 – 3279 5.

5000 -

2000x27x0.2 x 300-

2000

707x30x0.2 -

2

2

= Rs.13,093

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 (Units)

5(0.6)

10(0.2)

15(0.2)

4(0.3) 6(0.5) 8(0.2)

20*(0.18) 30 (0.30) 40 (0.12)

40(0.06) 60(0.10) 80(0.04)

60(0.06) 90(0.10) 120(0.04)

Note that if the DUR is 4 units with a probability of 0.3 and the LT is 5 days with 105

a probability of 0.6, the requirement for the combination DUR = 4 units and LT = 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 outs(in tonnes)

Stock out Cost

Probability

1

2

3

4

Tonnes 73.6 43.6 33.6

13.6

0

Expected Stock out

5 [3x4]

Carrying Cost

Total Cost

6 [(1)x1,000]

7 [5+6]

Rs. 73,600 43,600

Rs. 73,600 48,400

0 30

0 120,000

0 0.04

Rs. 0 4,800

10 40

40,000 160,000

0.10 0.04

10,400

33,600

44,000

20 30 60

80,000 120,000 240,000

0.04 0.10 0.04

24,800

13,600

38,400

13.6 33.6

54,400 134,400

0.16 0.04

43,296

0

43,296

106

43.6 73.6

174,400 294,400

0.10

*

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 = 30 x 40 + 2.00

SR (L)

30 x 1,000 x 40

= 3,391 units

7. Item

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Annual Usage (in Units)

400 15 6,000 750 1,200 25 300 450 1,500 1,300 900 1,600 600 30 45

Price per Unit Rs.

Annual Usage Value Rs.

20.00 150.00 2.00 18.00 25.00 160.00 2.00 1.00 4.00 20.00 2.00 15.00 7.50 40.00 20.00

8,000 2,250 12,000 13,500 30,000 4,000 600 450 6,000 26,000 1,800 24,000 4,500 1,200 900 1,35,200 107

Ranking

6 10 5 4 1 9 14 15 7 2 11 3 8 12 13

Cumulative Value of Items & Usage

Item No.

Rank

5 10 12 4 3 1 9 13 6 2 11 14 15

1 2 3 4 5 6 7 8 9 10 11 12 13

Annual UsageValue (Rs.)

30,000 26,000 24,000 13,500 12,000 8,000 6,000 4,500 4,000 2,250 1,800 1,200 900

Cumulative Annual Usage Value (Rs.)

30,000 56,000 80,000 93,500 105,500 113,500 119,500 124,000 128,000 130,250 132,050 133,250 134,150

Cumulative Cumulative % of Usage % of Items Value

22.2 41.4 59.2 69.2 78.0 83.9 88.4 91.7 94.7 96.3 97.7 98.6 99.2 108

6.7 13.3 20.0 26.7 33.3 40.0 46.7 53.3 60.0 66.7 73.3 80.0 86.7

7 8

14 15

Class

600 450

No. of Items

A B C

134,750 135,200

% to the Total

4 3 18

99.7 100.0

Annual Usage Value Rs.

26.7 20.0 53.3

93.3 100.0

% to Total Value

93,500 26,000 15,700

15

69.2 19.2 11.6

135,200

Chapter 30 WORKING 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

b.

0.99

20

0.02

360 x

c.

0.98

20

0.03

360 x

0.97

= 0.182

= 18.2%

= 0.367

= 36.7%

= 0.318

= 31.8%

35

109

d.

0.01

360 x

0.99

= 0.364

= 36.4%

= 0.104

= 10.4%

=

=

10

2. a. 0.01

360 x

0.99 b.

35

0.02

360 x

0.98 c.

21%

35

0.03

360 x

0.97

d.

0.21

= 0.223

= 22.3%

50

0.01

360 x

= 0.145

= 14.5%

0.99 25 3. 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 million Method 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

110

Chapter 31 WORKING 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 account Yi = EBDIT/Sales ratio for the ith account The estimates of a and b are : y2. 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 given the accompanying table. 111

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

(Yi-Y)

(Xi-X)2

Account Number

Xi

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0.90 0.75 1.05 0.85 0.65 1.20 0.90 0.84 0.93 0.78 0.96 1.02 0.81 0.76 1.02

15 0.1076 20 -0.0424 10 -0.2576 14 0.0576 16 -0.1424 20 0.4076 24 0.1076 26 0.0476 11 0.1376 18 -0.0124 12 0.1676 25 0.2276 26 0.0176 30 -0.0324 28 0.2276

16 17 18 19 20 21 22 23 24 25

0.76 0.68 0.56 0.62 0.92 0.58 0.70 0.52 0.45 0.60

10 -0.0324 12 -0.1124 4 -0.2324 18 -0.1724 -4 0.1276 20 -0.2124 8 -0.0924 15 –0.2724 6 –0.3424 7 –0.1924

19.81

391

G R O U P I

G R O U P II

Yi

(Xi-X)

-0.64 0.0116 0.4096 4.36 0.0018 19.0096 -5.64 0.0664 31.8096 -1.64 0.0033 2.6896 0.36 0.0203 0.1296 4.36 0.1661 19.0096 8.36 0.0116 69.8896 10.36 0.0023 107.3296 -4.64 0.0189 21.5296 2.36 0.0002 5.5696 -3.64 0.0281 13.2496 9.36 0.0518 87.6096 10.36 0.0003 107.3296 14.36 0.0010 206.2096 12.36 0.0518 152.7696 -5.64 -3.64 -11.64 2.36 -19.64 4.36 - 7.64 -0.64 -9.64 -8.64

13.42 =

15

0.0010 0.0126 0.0540 0.0297 0.0163 0.0451 0.0085 0.0742 0.1172 0.0370 0.8311

Sum of Xi for group 1 X1 =

(Yi-Y)2

=

0.8947

15

112

(Xi-X)(Yi-Y) -0.0689 -0.1849 -1.4529 -0.0945 -0.513 1.7771 0.8995 0.4931 -0.6385 -0.0293 -0.6101 2.1303 0.1823 -0.4653 2.8131

31.8069 0.1827 13.2496 0.4091 135.4896 2.7051 5.5696 -0.4069 385.7296 -2.5061 19.0096 -0.9261 58.3696 0.7059 0.4096 0.1743 92.9296 3.3007 74.6496 1.6623 1661.76

9.539

Sum of Xi for group 2

6.39

X2 =

= 10 Sum of Yi for group 1 = 15 Sum of Yi for group 2 10

1

0.8311 = 0.0346

1661.76

n-1 1 n-1

9.60

25-1 Yi – Y)2 =

xy =

= 10

n-1 y2=

19.67

96 =

Xi –X)2 =

= 15

Y2 = 1

0.6390

295

Y1 =

x 2 =

= 10

= 69.24 25-1

Xi-X)(Yi-Y) =

10.0007 = 0.4167 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 10.07 a =

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

b=

=

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 point The Zi score for various accounts are shown below 113

Zi scores for various accounts Account No.

Zi Score

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

7.1046 6.7373 7.4720 6.6918 5.6938 9.4728 8.0847 7.9378 6.8514 6.7018 7.1426 8.9231 7.7554 7.8870 9.2498 5.7090 5.4405 3.8398 5.7292 5.1571 5.7038 5.1265 4.7946 3.3890 4.4097

The Zi scores arranged in an ascending order are shown below Account Number

Zi Score

24 18 25 23 22 20 17

3.3890 3.8398 4.4097 4.7946 5.1265 5.1571 5.4405

Good(G) or Bad (B) B B B B B B B 114

5 21 16 19 4 10 2 9 1 11 3 13 14 8 7 12 15 6

5.6938 5.7038 5.7090 5.7292 6.6918 6.7018 6.7373 6.8514 7.1046 7.1426 7.4720 7.7554 7.8870 7.9378 8.0847 8.9231 9.2498 9.4728

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

115

Chapter 4 ANALYSING FINANCIAL PERFORMANCE Net profit 1.

Return on equity = Equity =

Net profit

Net sales

Total assets

x Net sales

=

1 0.05 x 1.5 0.3

= 0.7

So

Debt Note :

x Total assets

= 1-0.7 = 0.3 Total assets

Hence Total assets/Equity = 1/0.3 PBT

= 0.25 or 25 per cent

Equity

Total assets

2.

x

Equity

= Rs.40 million PBIT

Times interest covered =

= 6 116

Interest So PBIT = 6 x Interest PBIT – Interest = PBT = Rs.40 million 6 x Interest = Rs.40 million Hence Interest = Rs.8 million 3.

Sales = Rs.7,000,000 Net profit margin = 6 per cent Net profit = Rs.7000000 x 0.06 = 420,000 Tax 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 borrowing CA+BB = 1.5 CL+BB 1500+BB =

1.5

600+BB BB = 120 1,000,000 5.

Average daily credit sales =

= 2740 365

160000 ACP =

= 58.4 2740

If the accounts receivable has to be reduced to 120,000 the ACP must be: 117

120,000 x 58.4 = 43.8days 160,000

Current assets 6.

Current ratio =

= 1.5 Current liabilities Current assets - Inventories

Acid-test ratio =

= 1.2 Current liabilities

Current liabilities

= 800,000 Sales Inventory turnover ratio = = 5 Inventories Current assets - Inventories Acid-test ratio = Current liabilities Current assets

= 1.2

Inventories

This means

Current liabilities

= 1.2 Current liabilities Inventories

1.5

-

= 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 = 0.60 Equity = 50,000 + 60,000 = 110,000 So Debt = 0.6 x 110,000 = 66,000 Hence Total assets = 110,000+66,000 = 176,000 118

Total assets turnover ratio = 1.5 So Sales = 1.5 x 176,000 = 264,000 Gross profit margin = 20 per cent So Cost of goods sold = 0.8 x 264,000 = 211,200 Day’s sales outstanding in accounts receivable = 40 days Sales So Accounts receivable = x 40 360 264,000 =

x 40

= 29,333

360 Cost of goods sold Inventory turnover ratio =

211,200 =

Inventory

= 5 Inventory

So Inventory = 42,240 Assuming that the debt of 66,000 represent current liabilities Cash + Accounts receivable Acid-test ratio = Current liabilities Cash + 29,333 =

= 1.2 66,000

So Cash = 49867 Plant and equipment = Total assets - Inventories – Accounts receivable – Cash = 176,000 42240 29333 – 49867 = 54560 Pricing together everything we get

Equity capital Retained earnings Debt(Current liabilities)

50,000 60,000 66,000

Balance Sheet Plant & equipment Inventories Accounts receivable Cash

176,000 Sales

54,560 42,240 29,333 49,867 176,000

264,000 119

Cost of goods sold

211,200

Cash & bank balances + Receivables + Inventories + Pre-paid expenses 8. (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 (ii) Acid-test ratio =

22,500,000 =

= 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

(v) Inventory turnover period

=

72,000,000 =

Inventory 365

= 3.6 20,000,000

(vi) Average collection period =

=

Net sales/Accounts receivable 365 = 57.6 days 120

95,000,000/15,000,000 Net sales (vii) Total assets turnover ratio

95,000,000

=

=

= 1.27

Total assets

75,000,000

Profit after tax (ix) Net profit margin

=

5,100,000 =

= 5.4%

Net sales PBIT

95,000,000

15,100,000

(x) Earning power =

= Total assets

Equity earning (xi) Return on equity =

= 20.1% 75,000,000

5,100,000 = Net worth

= 15.7% 32,500,000

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

Current ratio Acid-test ratio Debt-equity ratio Times interest covered ratio Inventory turnover ratio Average collection period Total assets turnover ratio Net profit margin ratio Earning power Return on equity

Omex 1.42 0.75 1.31 3.02 3.6 57.6 days 1.27 5.4% 20.1% 15.7%

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 13.4 121

Standard 1.5 0.80 1.5 3.5 4.0 60 days 1.0 6% 18% 15%

8.8 + 6.7 Debt-equity ratio =

= 0.98 6.5 + 9.3 57.4

Total assets turnover ratio =

= 1.96 [(34 – 6.6) + (38 – 6.7)] / 2

3.0 Net profit margin =

= 5.2 percent 57.4 5

Earning power =

= 17.0 percent [(34 – 6.6) + (38 – 6.7)] / 2 3.0

Return on equity =

= 20.2 percent (13.9 + 15.8) / 2

(b) Dupont Chart for 20 x 5 Net sales +/Non-op. surplus deficit 57.8

Net profit margin 5.2%

Net profit 3.0

–

÷

Total costs 54.8

Net sales 57.4 Return on total assets 10.2% Net sales 57.4

122

Total asset turnover 1.96

Average fixed assets 21.4

÷

+ Average total assets 29.35

Average net current assets 54.0

+ Average other assets 2.55

(c) Common size and common base financial statements Common Size Financial Statements Profit and Loss Account

     

Net sales Cost of goods sold Gross profit Operating expenses Operating profit Non-operating surplus / deficit  PBIT  Interest  PBT  Tax  Profit after tax

Regular (in million) 20 X 4 20 X 5 39.0 57.4 30.5 45.8 8.5 11.6 4.9 7.0 3.6 4.6 0.5 0.4 4.1 1.5 2.6 2.6

5.0 2.0 3.0 3.0

Balance Sheet 123

Common Size (%) 20 X 4 20 X 5 100 100 78 80 22 20 13 12 9 8 1 1 11 4 7 7

9 3 5 5

 Shareholders’ funds  Loan funds Total  Net fixed assets  Net current assets  Other assets Total

Regular (in million) 20 X 4 20 X 5 13.9 15.8 13.5 15.5 27.4 31.3 19.6 23.2 5.1 5.7 2.7 2.4 27.4 31.3

Common Size (%) 20 X 4 20 X 5 51 50 49 50 100 100 72 74 19 18 10 8 100 100

Common Base Year Financial Statements Profit and Loss Account

     

Net sales Cost of goods sold Gross profit Operating expenses Operating profit Non-operating surplus / deficit  PBIT  Interest  PBT  Tax  Profit after tax

Regular (in million) 20 X 4 20 X 5 39.0 57.4 30.5 45.8 8.5 11.6 4.9 7.0 3.6 4.6 0.5 0.4 4.1 1.5 2.6 2.6

5.0 2.0 3.0 3.0

Common Base Year(%) 20 X 4 20 X 5 100 147 100 150 100 136 100 43 100 128 100 80 100 100 100 100 100

122 133 115 100 115

Balance Sheet Regular (in million) 20 X 4 20 X 5 124

Common Base Year(%) 20 X 4 20 X 5

 Shareholders’ funds  Loan funds Total  Net fixed assets  Net current assets  Other assets Total

13.9 13.5 27.4 19.6 5.1 2.7 27.4

15.8 15.5 31.3 23.2 5.7 2.4 31.3

100 100 100 100 100 100 100

114 115 114 118 112 89 114

(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?

125

Chapter 5 BREAK-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)-F EBIT=Rs.30,000 , Q=5,000 , P=Rs.30 , V=Rs.20 So, 30,000 = 5,000(30-20)-F So, F = Rs.20,000.

3.

DOL =

Q(P-V) 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

126

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

= 1.71 600(1,000-600)-1,00,000

4.

DOL(Q=15000) = 2.5 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 = = P-V 12-7

=10,000 units

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 income Q = 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, the Pre-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 + 100,000 Q = = 30,000 units 12-7 127

6.

P-V = 0.30

P-V = Rs.6

F=20,000

P 20000 Q =

6 = 3,333 P =

6

= Rs.20 0.30

Break even point in rupees = Rs.66,666 When net income is Rs.60,000 20,000 +60,000 Q = = 13,333 6 Sales in rupees = 13,333 x Rs.20 = Rs.266,666

10,000 7. (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.32000 10 per cent increase in production means that the quantity is 3300 bags At that production Profit = 3,300(30-16)-10,000 = Rs.36200 So, the percentage change in profit is : 36200-32000 = 13.1% 32000 (c) A 10 per cent increase in selling price means that P= Rs.33 Break-even point when P= Rs.33 10,000 Q =

= 588.2 bags 33-16

(d) A 50 per cent increase in fixed costs means that F=Rs.15,000 Break-even point when F= Rs.15,000 15,000 128

Q =

= 882.4 bags

33-16 (e) If V= Rs.20, the break-even point is : 10,000 Q = = 1000 bags 30-20 8. Selling price per unit Variable cost per unit Contribution margin per unit Contribution margin ratio Total fixed costs Break-even point in units Break-even sales(Rs.) Net income(loss)before tax No.of units sold

A Rs.10 Rs.6 Rs.4 0.4 Rs.16000 4000 Rs.40000 Rs.30000 11500

B C D Rs.16.66 Rs.20 Rs.10 Rs.8.33 Rs.12 Rs.5 Rs.8.33 Rs.8 Rs.5 0.5 0.4 0.5 Rs.100000 Rs.160000 Rs.60000 12000 20000 12000 Rs.200000 Rs.400000 Rs.120000 Rs.80000 Rs.(40000) Rs.40000 21600 15000 20000

9. (a) Break-even point for product P 30,000 = 3,000 units 30-20

Break-even point for product Q 100,000 = 5,000 units 50-30 Break-even point for product R 200,000 = 5,000 units 80-40 (b) The weighted contribution margin is : 5000 8,000 6,000 x Rs.10 + x Rs.20 + 19000 19000 19000

10.

EBIT DFL = Dp 129

x Rs.40

= Rs.23.68

EBIT – I T at Q = 20000 EBIT= 20000(Rs.40-Rs.24)=Rs.320,000 Rs.320,000 DFL(Q=20,000) = Rs.10,000 Rs.320,000-Rs.30,000 (1-.5) = 11. (a)

(b)

EBIT

=

1.185 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 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 15,000 F+I

(c)

BEP

= P–V Rs.40,000 + Rs.10,000

Firm A :

= 10,000 units Rs.20 – Rs.15

Rs.70,000 + Rs.20,000 Firm B :

= 4,500 units

130

Rs.50 – Rs.30 Rs.100,000 + Rs.40,000 Firm C :

= 2,333 units Rs.100 – Rs.40 Q(P-V)

(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 = EBIT – I -

Dp (1-T)

Rs.60,000 Firm A :

= 1.44 Rs.5000 Rs.60,000-Rs.10,000 (1-.4) Rs.130,000

Firm B :

= 1.30 Rs.5,000 Rs.130,000-Rs.20,000 (1-.5) Rs.80,000

Firm C :

= 5.333 Rs.10,000 Rs.80,000-Rs.40,000131

(1-.6) (f)

DTL

= DOL x DFL

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

Chapter 6 FINANCIAL 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 of sales

Net sales Cost of goods sold Gross profit Selling expenses General & administration expenses Depreciation Operating profit Non-operating surplus/deficit Earnings before interest and taxes Interest Earnings before tax Tax Earnings after tax

Proforma income statement for year 3 assuming sales of 1020

100.0 76.33 23.67 7.40 6.63 6.75 2.90 1.07 3.96 1.24 2.72 1.00 1.72

1020.0 778.57 241.43 75.48 67.63 68.85 29.58 10.91 40.39 12.65 27.74 10.20 17.54 132

Dividends (given) Retained earnings

2.

8.00 9.54

The proforma income statement of Modern Electronics for year 3 using the the combination method is given below : Average per cent of sales

Net sales Cost of goods sold Gross profit Selling expenses General & administration expenses Depreciation Operating profit Non-operating surplus/deficit Earnings before interest and taxes Interest Earnings before tax Tax Earnings after tax Dividends (given) Retained earnings

100.0 76.33 23.67 7.40 Budgeted Budgeted 1.07 Budgeted 1.00 Budgeted

133

Proforma income statement for year 3

1020.0 778.57 241.43 75.48 55.00 60.00 50.95 10.91 61.86 12.0 49.86 10.20 39.66 8.00 31.66

3.

The proforma balance sheet of Modern Electronics Ltd for year 3 is given below Average of percent of sales or some other basis

Projections for year 3 based on a forecast sales of 1400

Net sales

100.0

1020.0

ASSETS Fixed assets (net) Investments

40.23 No change

410.35 20.00

Current assets, loans & advances : Cash and bank Receivables Inventories

1.54 22.49 21.60

15.71 229.40 220.32

Prepaid expenses Miscellaneous expenditure & losses

5.09 No change

51.92 14.00 961.70

LIABILITIES :

134

Share capital : Equity Reserves & surplus

No change Proforma income statement

150.00 160.66

Secured loans: Term loans Bank borrowings

No change No change

175.00 199.00

Current liabilities : Trade creditors Provisions

17.33 5.03

176.77 51.31

External funds requirement

Balancing figure

48.96 961.7

A 4.

EFR =

L -

S

800 =

190 300 – 0.06 x 1,300 (1-0.5)

1000

S – m S1 (1-d)

S

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 Profits before tax Taxes Profit after tax (6% on sales) Dividends Retained earnings

1,300 195 117 78 39 39

135

Projected Balance Sheet as at 31.12 2001 Liabilities

Assets

Share capital Retained earnings Term loans (80+72) Short-term bank borrowings (200 + 72) Accounts payable Provisions

150 219 152 272

Fixed assets Inventories Receivables Cash

520 260 195 65

182 65

1,040

A 5.

(a)

EFR =

L -

S

S

150

30

=

S – m S1 (1 –d)

x 80 – (0.625) x 240 x (0.5)

160

1,040

160

= (60 – 7.5) = 52.5 (b) Projected Balance Sheet as on 31.12.20X1 Liabilities Share capital Retained earnings (40 + 7.5) Term loans Short-term bank borrowings Trade creditors Provisions

Assets

56.25 47.50

Net fixed assets Inventories

90 75

46.25 30.00

Debtors Cash

45 15

37.50 7.50 225.00

225.00

136

(c) i) ii) iii)

20X0 1.50 0.53 14.3%

Current ratio Debt to total assets ratio Return on equity

20X1 1.80 0.54 14.5%

(d) A EFR 20X1=

L

S – mS1 (1 – d)

S

S

150 =

30 20 – 0.0625 x 180 x 0.5

160

160

= 9.38 150 x (1.125) EFR 20X2 =

30 x 1.125 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) EFR 20X3

=

33.75 x (1.11) 200

187.31 =

37.46 200

8.11 187.31 x (1.1)

EFR 20X4 =

37.46 x (1.1) x 20 – 0.0625 x 240 x 0.5

220

=

x 20 – 6.88

200

=

20 – 0.0625 x 220 x 0.5

200

220

7.49 137

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) 75.00 Term loans(20+16.87) 36.87 Debtors (30x240/160) 45.00 Short-term bank borrowings 30.00 Cash (10x240/160) 15.00 Trade creditors 37.50 Provisions 7.50 225.00

6.

EFR

A

L

=

-

225.00

m (1+g) (1-d) -

S S S g Given 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 7.

(a)

EFR =

L S – mS1 (1-d)

S

S

320

70

=

x 100 – (0.05) (500) (0.5)

400

400

= Rs.50 (b)

Let CA = denote Current assets 138

CL SCL STL FA and LTL i. 

= Current liabilities = Spontaneous current liabilities = Short-term bank borrowings = Fixed assets = Long-term loans

Current ratio  CA i.e greater than or equal to 1.25 or CL CA



STL +SCL



As at the end of 20X1, CA = 20x0 x 1.25 = 237.50 SCL = 70 x 1.25 = 87.50 Substituting these values, we get 1.25 (STL + 87.5) 237.50 or 1.25 STL x  

ii.

  or STL = 1.25 i.e STL  Rs.102.50 Ratio of fixed assets to long term loans 1.25 FA  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 = 42.50 LTL = LTL (20X1)- LTL (20X1) = 130.00 – 80.00 = 50.00 Hence, the suggested mix for raising external funds will be : Short-term borrowings 42.50 Long-term loans 7.50 Additional equity issue -139

50.00

A 8.

EFR =

L  S – m S1 (1-d)

S

S A

Therefore, mS1(1-d) –

S 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 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 (a)

g=

.05 (1-0.6) 2.5 =

A/S –m(1-d)A/E

=

3.70 per cent

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 = 0.466 The 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) 2.5 140

(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

Chapter 32 CORPORATE VALUATION 1. (a) The calculations for Hitech Limited are shown below : Year 2 EBIT PBT 86 + Interest expense 24 - Interest income (10) - Non-operating income (5) EBIT 95

Year3 102 28 (15) (10) 105

Tax on EBIT Tax provision on income statement + Tax shield on interest expense - Tax on interest income - Tax on non-operating income Tax on EBIT

26 9.6 (4) (2) 29.6

32 11.2 (6) (4) 33.2

NOPLAT Net investment Non-operating cash flow (post-tax)

65.4 (50) 3

71.8 (50) 6

141

FCFF

18.4

27.8

(b) The financing flow for years 2 and 3 is as follows : Year 2 After-tax interest expense 14.4 Cash dividend 30 - Net borrowings (30) +  Excess marketable securities 30 - After-tax income on excess (6) marketable securities - Share issue (20) 18.4 (c)

27.8

Year 2 310 360 65.4 400 50

Invested capital (Beginning) Invested capital (Ending) NOPLAT Turnover Net investment

Post-tax operating margin Capital turnover ROIC Growth rate FCF 2.

Year 3 16.8 40 (30) 10 (9)

Year 3 360 410 71.8 460 50

16.35% 1.29 21.1% 16.1% 15.4

15.61% 1.28 19.9% 13.9% 21.8

Televista Corporation 0 Base year 1. 2. 3. 4.

Revenues EBIT EBIT (1-t) Cap. exp. - Depreciation 5. Working capital 6. Working capital 7. FCFF (3-4-6) Discount factor

1600 240 156 200 120 400

1

2

3

4

5

1920 288 187 240 144 480 80 11

2304 346 225 288 173 576 96 13

2765 415 270 346 207 691 115 16

3318 498 323 415 249 829 138 19

3650 547 356 -

0.876 0.767 142

0.672

.589

912 83 273

Present 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 period 0.5 [12% + 1.00 x 6%] + 0.5 [14% (1 - .35)] 9% + 4.55% = 13.55% Present value of FCFF during the explicit forecast period = 9.64 + 9.97 + 10.76 + 11.19 = 41.56 273

273

Horizon value = = 0.1355 – 0.10 0.0355

= 7690

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 1 2 3 4 5

kd(1-t) = 15% (1-t) 15 (0.94) = 14.1% 15 (0.88) = 13.2% 15 (0.82) = 12.3% 15 (0.76) = 11.4% 15 (0.70) = 10.5%

ke = Rf +  x Market risk premium ka = wd kd (1-t)+ we ke 12 + 1.3 x 7 = 21.1% 0.5 x 14.1 + 0.5 x 21.1 = 17.6% 21.1% 0.5 x 13.2 + 0.5 x 21.1 = 17.2% 21.1% 0.5 x 12.3 + 0.5 x 21.1 = 16.7% 21.1% 0.5 x 11.4 + 0.5 x 21.1 = 16.3% 21.1% 0.5 x 10.5 + 0.5 x 21.1 = 15.8%

kd(1-t) ke ka

WACC in the transition period = 14 (1 – 0.3) = 9.8% = 11 + 1.1 x 6 = 17.6% = 0.44 x 9.8 + 0.56 x 17.6 = 14.2%

kd(1-t) ke

WACC for the stable growth period = 13 (1 – 0.3) = 9.1% = 11 + 1.0 x 5 = 16% 143

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 EBIT Tax rate (%) rate (%) 0 90 1 40 126 6 2 40 176 12 3 40 247 18 4 40 346 24 5 40 484 30 6 34 649 30 7 28 830 30 8 22 1013 30 9 16 1175 30 10 10 1292 30 11 10 1421 30

EBIT (1-t)

Cap. Dep. WC FCFF D/E Beta WACC PV exp. % Factor

Present value

118 155 203 263 339 454 581 709 822 905 995

100 140 196 274 384 538 721 922 1125 1305 1436 1580

30.6 27.6 27.4 20.8 12.0 13.4 15.4 16.7 16.9 16.6 476

60 84 118 165 230 323 432 553 675 783 862 948

26 39 50 70 98 132 169 206 239 263 289

36 38 44 39 26 33 43 53 61 68 74

1:1 1.3 1:1 1.3 1:1 1.3 1:1 1.3 1:1 1.3 0.8:1 1.1 0.8:1 1.1 0.8:1 1.1 0.8:1 1.1 0.8:1 1.1 0.5: 1.1 1.0

17.6 17.2 16.7 16.3 15.8 14.2 14.2 14.2 14.2 14.2 13.7

.850 .726 .622 .535 .462 .405 .354 .310 .272 .238

673.4 The present value of continuing value is : FCF11

74 x PV factor 10 years =

k–g

x 0.238

= 476

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 continuing The explicit forecast period of 10 years value This adds up to Rs.685.4 million as shown below

MINI CASE Solution: Solution: 144

1. Revenues 2. PBIT 3. NOPAT = PBIT (1 – .35) 4. Depreciation 5. Gross cash flow 6. Gross investment in fixed assets 7. Investment in net current assets 8. Total investment 9. FCFF (5) – (8)

1 950 140 91

2 1,000 115 74.8

3 1,200 130 84.5

4 1,450 222 144.3

5 1,660 245 159.3

6 1,770 287 186.6

55 146 100

85 159.8 250

80 164.5 85

83 227.3 100

85 244.3 105

87 273.7 120

10

15

70

70

70

54

155 9.5

170 57.3

175 69.3

174 99.6

110 36

265 (105.2)

0.4

1.0 x 12 x (1 – 0.35)

WACC =

+

1.4

{8 + 1.06 (8)} 1.4

= 14% 99.6 (1.10) Continuing Value =

= 2739.00 0.14 – 0.10 2739

Present 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 33 VALUE BASED MANAGEMENT 1. The value created by the new strategy is calculated below : 145

Sales Gross margin (20%) Selling and general administration (8%) Profit before tax Tax Profit after tax Fixed assets Current assets Total assets Equity

Current Values (Year 0)

Income Statement Projection 1

2

3

4

5

2000 400 160

2240 448 179

2509 502 201

2810 562 225

3147 629 252

3147 629 252

240 72 168

269 81 188

301 90 211

337 101 236

378 113 264

378 113 264

Balance Sheet Projections 672 753 843 944 672 753 843 944 1344 1505 1696 1888 1344 1505 1686 1888

944 944 1888 1888

600 600 1200 1200

Cash Flow Projections 188 211 236 60 67 75 132 148 166 72 81 90 44 49 55

Profit after tax Depreciation Capital expenditure Increase in current assets Operating cash flow Present value of the operating cash flow Residual value Present value of residual value Total shareholder value Pre-strategy value Value of the strategy

= = = = = =

147 264 / 0.15 = 1760 1760 / (1.15)4 = 1007 147 + 1007 = 1154 168/0.15 = 1120 1154 – 1120 = 34

2. According to the Marakon approach M r–g = B k–g r - .10 2

=

k - .10 r - .10 = 2k - .20 146

264 84 185 101 62

264 94 94 264

r = 2k - .10 r/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 20X1 PBIT (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) (c) Cost of equity 6% + 0.9 (6%) = 1.4% (d) Average cost of capital 0.5 x 8% (1 - .35) + 0.5 x 11.4% = 8.3% (e) EVA for 20X1 NOPAT - Average cost of capital x Capital employed 15.6 - .083 x 100 = 7.3 4. I r c* T

= = = =

Rs.200 million 0.40 0.20 5 years 200 (0.40 – 0.20) 5

Value 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. 2. 3. 4. 5. 6. 7. 8.

Revenues Costs PBDIT Depreciation PBIT NOPAT Cash flow (4+6) Capital at charge

2,000 2,000 2,000 2,000 2,000 1,400 1,400 1,400 1,400 1,400 600 600 600 600 600 200 200 200 200 200 400 400 400 400 400 240 240 240 240 240 440 440 440 440 440 1,000 800 600 400 200 147

9. Capital charge (8x0.14) 140 112 84 56 28 10. EVA (6-9) 100 128 156 184 212 5 440 NPV =  - 1000 = 440 x 3.433 – 1000 = 510.5 t=1 (1.14)t NPV = 

EVAt (1.14)t

6.

= 100 x 0.877 + 128 x 0.769 + 156 x 0.675 + 184 x 0.592 + 212 x 0.519 = 510.3

Equipment cost = 1,000,000 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 Annuity amount =

881,600 =

PVIFA14%, 4yrs

2.914

= Rs.302,540 Depreciation charge under sinking fund method 1 2 3 4 1,000,000 837,460 652,164 440,927 162,540 185,296 212,237 240,810 140,000 117,244 91,303 61,730 302,540 302,540 302,540 302,540

Capital Depreciation Capital charge Sum 7.

Investment Life Cost of capital Salvage value

: : : :

Rs.2,000,000 10 years 15 per cent 0 2,000,000

Economic depreciation

= FVIFA(10yrs, 15%)

148

2,000,000 =

= 98,503 20.304

8.

Investment Life Cost of capital Salvage value

: : : :

Rs.5,000,000 5 years 12 per cent Nil

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

Capital Depreciation Capital charge Sum

1 5,000,000 786,963 600,000 1,386,963

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

Economic depreciation

= FVIFA(5yrs, 12%) 5,000,000 =

= Rs.787,030 6.353

9.

Investment Net working capital Life Salvage value Annual cash flow Cost of capital Straight line depreciation

= = = = = = =

Rs.100 million Rs.20 million 8 yrs Rs.20 million (Net working capital) Rs.21.618 million 15% Rs.10 million per year

80 Economic depreciation

80

=

= FVIFA(8, 15%)

 Profit after tax  Depreciation  Cash flow

Year 1 11.618 10.000 21.618

Year 4 11.618 10.000 21.618 149

= Rs.5.828 million 13.727

 Book capital (Beginning)  ROCE  ROGI  CFROI

100

70

11.62% 21.62% 15.79%

16.59% 21.62% 15.79%

150

Chapter 34 MERGERS, ACQUISITIONS AND RESTRUCTURING 1. The pre-amalgamation balance sheets of Cox Company and Box Company and the postamalgamation 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 Pooling method Purchase method 35 45 27.5 30 2.5 62.5 77.5

Cox

Box

Fixed assets Current assets Goodwill Total assets

25 20

10 7.5

45

17.5

Share capital (face value @ Rs.10) Reserves & surplus Share premium Debt

20

5

25

20

10 15 45

10 2.5 17.5

20 17.5 42.5

10 17.5 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 gives ER = 0.6 3. PVA = Rs.25 million, PVB = Rs.10 million Benefit = Rs.4 million, Cash compensation = Rs.11 million Cost = Cash compensation – PVB = Rs.1 million NPV to Alpha = Benefit – Cost = Rs.3 million NPV to Beta = Cash Compensation – PVB = Rs.1 million 4. Let A stand for Ajeet and J for Jeet PVA = Rs.60 x 300,000 = Rs.18 million PVJ = Rs.25 x 200,000 = Rs.5 million Benefit = Rs.4 million PVAJ = 18 + 5 + 4 = Rs.23 million 151

Exchange ratio = 0.5 The share of Jeet in the combined entity will be : 100,000 = = 0.25 300,000 + 100,000 a) True cost to Ajeet Company for acquiring Jeet Company Cost = 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 million The 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 million shares to shareholders of Unibex.

So shareholders of Unibex will end up with 152

0.667 

= 0.1177 or 11.77 per cent 5+0.667

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 5000 Rs.45000 Rs.90000 2

Number of shares Aggregate earnings Market value P/E

B 2000 Rs.4000 Rs.24000 6

A&B 6333 Rs.49000 Rs.114000 2.33

7. (a) The maximum exchange ratio acceptable to shareholders of Vijay Limited is : S1 ER1

=

-

(E1+E2) PE12 +

S2

P1S2

12 =

-

(36+12) 8 +

8

= 0.1 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

153

(c)

12 ER1

(48) PE12

= -

+ 8

240 9 x 12

ER2

= PE12 (48) - 72

Equating ER1 and ER2 and solving for PE12 gives, PE12 = 9 When PE12 = 9 ER1 = ER2 = 0.3 Thus ER1 and ER2 intersect at 0.3 8.

The present value of FCF for first seven years is 16.00 14.30 PV(FCF) = 2 (1.15) (1.15)

0

9.7 (1.15)3

10.2

+

+

0 + (1.15)4

16.7 +

(1.15)5

(1.15)6

(1.15)7

= - Rs.20.4 million The horizon value at the end of seven years, applying the constant growth model is FCF8 V4

=

18 =

= 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

154

MINICASE Solution: (a)

Book value per share

Modern Pharma

Magnum Drugs

2300

650 = Rs.115

20 450

Earnings per share

= Rs.65 10 95

= Rs.22.5 20 Rs.320

Market price per share

Exchange Ratio 65 115 9.5

= Rs.9.5 10 Rs.102

22.5 102 320

Exchange ratio that gives equal weightage to book value per share, earnings per share, and market price per share 65

9.5 +

115

102 +

22.5

320

0.57 + 0.42 + 0.32 =

3

= 0.44 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 10 155

Equating this with Rs.22.5, we get (450 + 95) (1.05) = 22.5 20 + 10ER This 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 ER1 =

(E1 + E2) P/E12 +

S2

P1 S2

- 20 = 10 (f)

(450 + 95) 13 +

= 0.21 320 x 10

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 156

- S1

(E1 + E2) P/E12 +

S2

P/E12 (E1 + E2) – P2S2

P1S2

- 20

(450 +95) P/E12 +

10

P2S1 =

102 x 20 = P/E12 (450 +95) – 1020

320 x 10

- 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 = 6528000 2 297025 P/E 12 = 4043900 P/E 297025 P/E12 = 4043900 P/E12 = 13.61

157

Chapter 37 INTERNATIONAL FINANCIAL MANAGEMENT 1. The annualised premium is : Forward rate – Spot rate

12 x

Spot rate

Forward contract length in months

46.50 – 46.00 =

12 x

46.00 2.

= 4.3% 3

100 100 (1.06) =

x 1.07 x F 1.553

106 x 1.553 F =

= 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 107

1 + foreign interest rate 1 + domestic interest rate in Japan

= 158

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 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 0 1 2 3 4 5

Cash flow in dollars Expected exchange (million) rate -200 46 50 48.17 70 50.44 90 52.82 105 55.31 80 57.92

Cash flow in rupees (million) -9200 2408.5 3530.8 4753.8 5807.6 4633.6

Given a rupee discount rate of 20 per cent, the NPV in rupees is : 2408.5 NPV

=

-9200

+

3530.8 +

(1.18)2 5807.6

(1.18)3

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 F

4753.8 +

1 + foreign interest rate 1 + .015 159

(1.18)4

= 1.60 1 + .020 F = $ 1.592 / £

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 (1 + expected inflation in Japan)2

8. Expected spot rate = Current spot rate x 2 years from now

(1 + expected inflation in UK)2

(1.01)2 = 163.46 yen / £

= 170 x 2

(1.03)

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

160

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) (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.

161

Chapter 40 CORPORATE 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 (1+Risk-free rate)1

= Spot price + Present value of – Present value storage costs 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.

162

163

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164