FM Questions

Chapter 1 No problems, only review questions

Chapter 2 PROBLEMS

1.

Determine the future values utilizing a time preference rate of 9 per cent: (i) The future value of Rs 15,000 invested now for a period of four years. (ii) The future value at the end of five years of an investment of Rs 6,000 now and of an investment of Rs 6,000 one year from now. (iii) The future value at the end of eight years of an annual deposit of Rs 18,000 each year. (iv) The future value at the end of eight years of annual deposit of Rs 18,000 at the beginning of each year. (v) The future values at the end of eight years of a deposit of Rs 18,000 at the end of the first four years and withdrawal of Rs 12,000 per year at the end of year five through seven. 2. Compute the present value of each of the following cash flows using a discount rate of 13 per cent: (i) Rs 2,000 cash outflow immediately. (ii) Rs 6,000 cash inflow one year from now. (iii) Rs 6,000 cash inflow two years from now. (iv) Rs 4,000 cash outflow three years from now. (v) Rs 7,000 cash inflow three years from now. (vi) Rs 3,000 cash inflow four years from now. (vii) Rs 4,000 cash inflow at the end of each of the next five years. (viii) Rs 4,000 cash inflow at the beginning of each of the next five years. 3. Determine the present value of the cash inflows of Rs 3,000 at the end of each year for next 4 years and Rs 7,000 and Rs 1,000 respectively at the end of years 5 and 6. The appropriate discount rate is 14 per cent. 4. Assume an annual rate of interest of 15 per cent. The sum of Rs 100 received immediately is equivalent to what quantity received in ten equal annual payments, the first payment to be received one year from now. What could be the annual amount if the first payment were received immediately? 5. Assume a rate of interest of 10 per cent. We have a debt to pay and are given a choice of paying Rs 1,000 now or some amount X five years from now. What is the maximum amount that X can be for us to be willing to defer payment for five years? 6. We can make an immediate payment now of Rs 13,000 or pay equal amount of A for the next 5 years, first payment being payable after 1 year. (a) With a time value of money of 12 per cent, what is the maximum value of A that we would be willing to accept? (b) What maximum value of A we would be willing to accept if the payments are made in the beginning of the year? 7. Assume that you are given a choice between incurring an immediate outlay of Rs 10,000 and having to pay Rs 2,310 a year for 5 years (first payment due one year from now); the discount rate is 11 per cent. What would be your choice? Will your answer change if Rs 2,310 is paid in the beginning of each year for 5 years? 8. Compute the present value for a bond that promises to pay interest of Rs 150 a year for thirty years and Rs 1,000 at maturity. This first interest payment is paid one year from now. Use a rate of discount of 8 per cent. 9. Exactly twenty years from now Mr Ahmed will start receiving a pension of Rs 10,000 a year. The payment will continue for twenty years. How much is pension worth now, assuming money is worth 15 per cent per year? 10. Using an interest rate of 10 per cent, determine the present value of the following cash flow series: End of period 0 1–6 7 8 9–12

(each period)

(each period)

Cash-flow (Rs) – 10,000 + 2,000 – 1,500 + 1,600 + 2,500

11. Find the rate of return in the following cases: (i) You deposit Rs 100 and would receive Rs 114 after one year.

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(ii) You borrow Rs 100 and promise to pay Rs 112 after one year. (iii) You borrow Rs 1,000 and promise to pay Rs 3,395 at the end of 10 years. (iv) You borrow Rs 10,000 and promise to pay Rs 2,571 each year for 5 years. A bank has offered a deposit scheme, which will triple your money in 9 years; that is, if you deposit Rs 100 today, you can receive Rs 300 at the end of 9 years. What rate of return would you earn from the scheme? You have Rs 6,000 to invest. How much would it take you to double your money if the interest rate is (a) 6%, (b) 10%, (c) 20%, and (d) 30%? Assume annual compounding. Would your answer change if compounding is done half-yearly? Show computations. You had annual earnings of Rs 45,000 in 19X1. By 19X8, your annual earnings have grown to Rs 67,550. What has been the compound annual rate of growth in your earnings? You are planning to buy a 200 square meters of land for Rs 40,000. You will be required to pay twenty equal annual instalments of Rs 8,213. What compound rate of interest will you be paying? Jai Chand is planning for his retirement. He is 45 years old today, and would like to have Rs 3,00,000 when he attains the age of 60. He intends to deposit a constant amount of money at 12 per cent at each year in the public provident fund in the State Bank of India to achieve his objective. How much money should Jai Chand invest at the end of each year for the next 15 years to obtain Rs 3,00,000 at the end of that period? (a) At age 20, how much should one invest at the end of each year in order to have Rs 10 lakh at age 50, assuming 10 per cent annual growth rate? (b) At age 20, how much lump sum should one invest now in order to have 10 lakh at the age of 50, assuming 10 per cent annual growth rate? Your grandfather is 75 years old. He has total savings of Rs 80,000. He expects that he will live for another 10 years, and will like to spend his savings by then. He places his savings into a bank account earning 10 per cent annually. He will draw equal amount each year—the first withdrawal occurring one year from now—in such a way that his account balance becomes zero at the end of 10 years. How much will be his annual withdrawal? You buy a house for Rs 5 lakh and immediately make cash payment of Rs 1 lakh. You finance the balance amount at 12 per cent for 20 years with equal annual instalments. How much are the annual instalments? How much of the each payment goes towards reducing the principal? You plan to buy a flat for Rs 200,000 by making Rs 40,000 down payment. A house financing company offers you a 12-year mortgage requiring end-of-year payments of Rs 28,593. The company also wants you to pay Rs 5,000 as the loan-processing fee, which they will deduct from the amount of loan given to you. What is the rate of interest on loan? An investment promises to pay Rs 2,000 at the end of each year for the next 3 years and Rs 1,000 at the end of each year for years 4 through 7. (a) What maximum amount will you pay for such investment if your required rate is 13 per cent? (b) If the payments are received at the beginning of each year, what maximum amount will you pay for investment? Mr Sundaram is planning to retire this year. His company can pay him a lump sum retirement payment of Rs 2,00,000 or Rs 25,000 lifetime annuity—whichever he chooses. Mr Sundaram is in good health and estimates to live for at least 20 more years. If his interest rate is 12 per cent, which alternative should he choose? Which alternative would you choose: (a) an annuity of Rs 5,000 at the end of each year for 30 years; (b) an annuity of Rs 6,600 at the end of each year for 20 years; (c) Rs 50,000, in cash right now? In each case, the time value of money is 10 per cent. Ms. Punam is interested in a fixed annual income. She is offered three possible annuities. If she could earn 8 per cent on her money elsewhere, which of the following alternatives, if any, would she choose? Why? (i) Pay Rs 80,000 now in order to receive Rs 14,000 at the end of each year for the next 10 years. (ii) Pay Rs 1,50,000 now in order to receive Rs 14,000 at the end of each year for the next 20 years. (iii) Pay Rs 1,20,000 now in order to receive Rs 14,000 at the end of each year for the next 15 years. You have come across the following investment opportunity: Rs 2,000 at the end of each year for the first 5 years plus Rs 3,000 at the end of each year from years 6 through 9 plus Rs 5,000 at the end of each year from years 10 through 15. (a) How much will you be willing to pay for this investment if your required rate of return is 14 per cent? (b) What will be your answer if payments are received at the beginning of each year? You have borrowed a car loan of Rs 50,000 from your employer. The loan requires 10 per cent interest and five equal end-of-year payments. Prepare a loan amortisation schedule.

27. If the nominal rate of interest is 12 per cent per annum, calculate the effective rate of interest when a sum is compounded (a) annually, (b) semi-annually, (c) quarterly, and (d) monthly. 28. What amount would an investor be willing to pay for Rs 1,000, ten-year debenture that pays Rs 75 interest half-yearly and is sold to yield 18 per cent? 29. The Madura Bank pays 12 per cent interest and compounds interest quarterly. If one puts Rs 1,000 initially into a savings account, how much will it have grown in 7½ years? 30. An already issued government bond pays Rs 50 interest half-yearly. The bond matures in 7 years. Its face value is Rs 1,000. A newly issued bond, which pays 12 per cent annually, can also be bought. How much would you like to pay for the old bond? How much would you pay for the bond if it is redeemed at a premium of 10 per cent? 31. If you deposit Rs 10,000 in an account paying 8 per cent interest per year compounded quarterly and you withdraw Rs 100 per month, (a) How long will the money last? (b) How much money will you receive? 32. XY Company is thinking of creating a sinking fund to retire its Rs 800,000 preference share capital that matures on 31 December 19X8. The company plans to put a fixed amount into the fund at the end of each year for eight years. The first payment will be made on 31 December 19X1, and the last on 31 December 19X8. The company expects that the fund will earn 12 per cent a year. What annual contribution must be made to accumulate to Rs 8,00,000 as of 31 December 19X8? What would be your answer if the annual contribution is made in the beginning of the year, the first payment being made on 31 December 19X0? 33. In January 19X1, X Ltd issued Rs 10 crore of five-year bonds to be matured on 1 January 19X6. The interest was payable semi-annually on January 1 and July 1; the interest rate was 14 per cent per annum. Assume that on 1 January 19X2, new four-year bond of equivalent risk could be purchased at face value with an interest rate of 12 per cent and that you had purchased a Rs 1,000 X Ltd bond when the bonds were originally issued. What would be its market value on January 1, 19X2? 34. You want to buy a 285-litre refrigerator of Rs 10,000 on an instalment basis. A distributor of various makes of refrigerators is prepared to do so. He states that the payments will be made in four years, interest rate being 13%. The annual payments would be as follows: Rs Principal

10,000

Four years of interest at 13%, i.e., Rs 10,000 × 0.13 × 4

5,200 15,200

Annual payments, Rs 15,200/4

3,800

What rate of return the distributor is earning? 35. You have approached a loan and chit fund company for an eight-year loan of Rs 10,000; payments to the company to be made at the end of year. The loan officer informs you that the current rate of interest on the loan is 12% and that the annual payment will be Rs 2,013. Show that this annual cash flow provides a rate of return of 12% on the bank’s investment of Rs 10,000. Is 12% the true interest rate to you? In other words, if you pay interest of 12% on your outstanding balance each year, will the remainder of the Rs 2,013 payments be just sufficient to repay the loan? 36. If a person deposits Rs 1,000 on an account that pays him 10 per cent for the first five years and 13 per cent for the following eight years, what is the annual compound rate of interest for the 13-year period?

Chapter 3 PROBLEMS

1. Suppose you buy a one-year government bond that has a maturity value of Rs 1,000. The market interest rate is 8 per cent. (a) How much will you pay for the bond? (b) If you purchased the bond for Rs 904.98, what interest rate will be you earn on your investment? 2. The Brightways Company has a perpetual bond that pay Rs 140 interest annually. The current yield on\ this type of bond is 13 per cent. (a) At what price will it sell? (b) If the required yield rises to 15 per cent, what will be the new price? 3. The Nutmate Limited has a ten-year debenture that pays Rs 140 annual interest. Rs 1,000 will be paid on maturity. What will be the value of the debenture if the required rate of interest is (a) 12 per cent, (b) 14 per cent and (c) 16 per cent?

4. What will be the yield of a 16 per cent perpetual bond with Rs 1,000 par value, when the current price is (a) Rs 800, (b) Rs 1,300 or (c) Rs 1,000? 5. You are considering bonds of two companies. Taxco’s bond pays interest at 12 per cent and Maxco’s at 6 per cent per year. Both have face value of Rs 1,000 and maturity of three years. (a) What will be the values of bonds if the market interest rate is 9 per cent? (b) What will be the values of the bonds if the market interest rate increases to 12 per cent? (c) Which bond declines more in the value when the interest rate rises? What is the reason? (d) If the interest rate falls to 6 per cent, what are the values of bonds? (e) If the maturity of two bonds is 8 years (rather than 3 years), what will be the values of two bonds if the market interest rate is (a) 9 per cent, (b) 6 per cent and (c) 12 per cent? 6. Three bonds have face value of Rs 1,000, coupon rate of 12 per cent and maturity of 5 years. One pays interest annually, one pays interest half-yearly, and one pays interest quarterly. Calculate the prices of bonds if the required rate of return is (a) 10 per cent, (b) 12 per cent and (c) 16 per cent. 7. On 31 March 2003, Hind Tobacco Company issued Rs 1,000 face value bonds due 31 March 2013. The company will not pay any interest on the bond until 31 March 2008. The half-yearly interest is payable from 31 December 2008; the annual rate of interest will be 12 per cent. The bonds will be redeemed at 5 per cent premium on maturity. What is the value of the bond if the required rate of return is 14 per cent? 8. Determine the market values of the following bonds, which pay interest semi-annually: Bond A B C D

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Interest Rate Required Rate Maturity Period (Years) 16% 14% 12% 12%

15% 13% 8% 8%

25 15 20 10

If the par values of bonds are Rs 100 and if they are currently selling for Rs 95, Rs 100, Rs 110 and Rs 115, respectively, determine the effective annual yields of the bonds? Also calculate the semi-annual yields? A 20-year 10% Rs 1,000 bond that pays interest half-yearly is redeemable (callable) in twelve years at a buy-back (call) price of Rs 1,150. The bond’s current yield to maturity is 9.50% annually. You are required to determine (i) the yield to call, (ii) the yield to call if the buy-back price is only Rs 1,100, and (iii) the yield to call if instead of twelve years the bond can be called in eight years, buyback price being Rs 1,150. A fertilizer company holds 15-year 15% bond of ICICI Bank Ltd. The interest is payable quarterly. The current market price of the bond is Rs 875. The company is going through a bad patch and has accumulated a substantial amount of losses. It is negotiating with the bank the restructuring of debt. Recently the interest rates have fallen and there is a possibility that the bank will agree for reducing the interest rate to 12 per cent. It is expected that the company will be able service debt t the reduce interest rates. Calculate stated and the expected yields to maturity? You are thinking of buying BISCO’s a preference share Rs 100 par value that will pay a dividend of 12 per cent perpetually. (a) What price should you pay for the preference share if you are expecting a return of 10 per cent? (b) Suppose that BISCO can buy back the share at a price of Rs 110 in seven years. What maximum price should you pay for the preference share? The share of Premier Limited will pay a dividend of Rs 3 per share after a year. It is currently selling at Rs 50, and it is estimated that after a year the price will be Rs 53. What is the present value of the share if the required rate of return is 10 percent? Should the share be bought? Also calculate the return on share if it is bought, and sold after a year. An investor is looking for a four-year investment. The share of Skylark Company is selling for Rs 75. They have plans to pay a dividend of Rs 7.50 per share each at the end of first and second years and Rs 9 and Rs 15 respectively at the end of third and fourth years. If the investor’s capitalisation rate is 12 percent and the share’s price at the end of fourth year is Rs 70, what is the value of the share? Would it be a desirable investment? A company’s share is currently selling at Rs 60. The company in the past paid a constant dividend of Rs 1.50 per share, but it is now expected to grow at 10 per cent compound rate over a very long period. Should the share be purchased if required rate of return is 12 per cent? The earnings of a company have been growing at 15 per cent over the past several years and are expected to increase at this rate for the next seven years and thereafter, at 9 per cent in perpetuity. It is

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currently earning Rs 4 per share and paying Rs 2 per share as dividend. What shall be the present value of the share with a discount rate of 12 per cent for the first seven years and 10 per cent thereafter? A company retains 60 per cent of its earnings, which are currently Rs 5 per share. Its investment opportunities promise a return of 15 per cent. What price should be paid for the share if the required rate of return is 13 per cent? What is the value of growth opportunities? What is the expected rate of return from the share if its current market price is Rs 60? The total assets of Rs 80,000 of a company are financed by equity funds only. The internal rate of return on assets is 10 per cent. The company has a policy of retaining 70 per cent of its profits. The capitalisation rate is 12 per cent. The company has 10,000 shares outstanding. Calculate the present value per share. A prospective investor is evaluating the share of Ashoka Automobiles Company. He is considering three scenarios. Under first scenario the company will maintain to pay its current dividend per share without any increase or decrease. Another possibility is that the dividend will grow at an annual (compound) rate of 6 per cent in perpetuity. Yet another scenario is that the dividend will grow at a high rate of 12 per cent per year for the first three years; a medium rate of 7 per cent for the next three years and thereafter, at a constant rate of 4 per cent perpetually. The last year’s dividend per share is Rs 3 and the current market price of the share is Rs 80. If the investor’s required rate of return is 10 per cent, calculate the value of the share under each of the assumptions. Should the share be purchased? Vikas Engineering Ltd has current dividend per share of Rs 5, which has been growing at an annual rate of 5 per cent. The company is expecting significant technical improvement and cost reduction in its operations, which would increase growth rate to 10 per cent. Vikas’ capitalisation rate is 15 per cent. You are required to calculate (a) the value of the share assuming the current growth rate; and (b) the value of the share if the company achieves technical improvement and cost reduction. Does the price calculated in (b) make a logical sense? Why? Consider the following data of four auto (two / three-wheelers) companies. Companies

EPS (Rs)

DIV (%)

Share Price (Rs)

1. Bajaj 2. Hero Honda 3. Kinetic 4. Maharashtra Scooters

11.9 10.2 12.0 20.1

50 22 25 25

275.00 135.00 177.50 205.00

The face value of each company’s share is Rs 10. Explain the relative performance of the four companies. The dividend per share of Skyjet Company has grown from Rs 3.5 to Rs 10.5 over past 10 years. The share is currently selling for Rs 75. Calculate Skyjet’s capitalisation rate. Rama Tours and Travels Limited has current earnings per share of Rs 8.60, which has been growing at 12 per cent. The growth rate is expected to continue in future. Rama has a policy of paying 40 per cent of its earnings as dividend. If its capitalisation rate is 18 per cent, what is the value of the share? Also calculate value of growth opportunities. A company has the following capital in its balance sheet: (a) 12-year 12% secured debentures of Rs 1,000 each; principal amount Rs 50 crore (10 million = crore); the required rate of return (on debentures of similar risk) 10 per cent; (b) 10-year 14% unsecured debentures of Rs 1,000 each; principal amount Rs 30 crore; interest payable half-yearly; the required rate of return 12 per cent; (c) preference share of Rs 100 each; preference dividend rate 15%; principal amount Rs 100 crore; required rate of return 13.5 per cent; and (d) ordinary share capital of Rs 200 crore at Rs 100 each share; expected dividend next year, Rs 12; perpetual dividend growth rate 8 per cent; the required rate of return 15 per cent. Calculate the market values of all securities. Satya Systems Company has made net profit of Rs 50 crore. It has announced to distribute 60 per cent of net profit as dividend to shareholders. It has 2 crore ordinary shares outstanding. The company’s share is currently selling at Rs 240. In the past, it had earned return on equity of 25 per cent and expects to main this profitability in the future as well. What is the required rate of return on Satya’s share? A company has net earnings of Rs 25 million (1 crore = 10 million). Its paid-up share capital is Rs 200 million and the par value of share is Rs 10. If the company makes no new investments, its earnings are expected to grow at 2 per cent per year indefinitely. It does have an investment opportunity of investing Rs 10 million that would generate annual net earnings of Rs 2 million (1 million = 10 lakh)

for next 15 years. The company’s opportunity cost of capital is 10 per cent. You are required: (a) to find the share value if the company does not make the investment; (b) to calculate the proposed investment’s NPV; and (c) to determine the share value if the investment is undertaken? 27. Gujarat Bijali Ltd has earnings of Rs 80 crore and it has 5 crore shares outstanding. It has a project that will produce net earnings of Rs 20 crore after one year. Thereafter, earnings are expected to grow at 8 per cent per annum indefinitely. The company’s required rate of return is 12.5 per cent. Find the P/E ratio. 28. Symphony Limited is an all-equity financed company. It has 10 million shares outstanding, and is expected to earn net cash profits of Rs 80 million. Shareholders of the company have an opportunity cost of capital of 20 per cent. (a) Determine the company share price if it retained 40 per cent of profits and invested these funds to earn 20 per cent return. Will the share price be different if the firm retained 60 per cent profits to earn 20 per cent? (b) What will be the share price if investments made by the company earn 24 per cent and it retains 40 per cent of profits? Will share price change if retention is 60 per cent? 29. Sonata Company has no investment opportunities. It expects to earn cash earnings per share of Rs 10 perpetually and distribute entire earnings as dividends to shareholders.(a) What is the value of the share if shareholders’ opportunity cost of capital is 15 per cent? (b) Suppose the company discovers an opportunity to expand its existing business. It estimates that it will need to invest 50 per cent of its earnings annually for ten years to produce 18 per cent return. Management does not foresee any growth after this ten-year period. What will be Sonata’s share price if shareholders’ opportunity cost of capital is 15 per cent?

Chapter 4 PROBLEMS

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On 1 January 2009, Mr Y.P. Sinha purchased 100 shares of L&T at Rs 212 each. During the year, he received total dividends of Rs 700. Mr Sinha sold all his shares at Rs 215 each on 31 December 2009. Calculate Mr Sinha’s (i) capital gain amount, and (ii) total return in (a) rupee amount and (b) percentage. The closing price of share last year was Rs 50. The dividend per share was Rs 5 during the year. The current year closing price is Rs 57. Calculate the percentage return on the share, showing the dividend yield and the capital gain rate. You acquired Telco’s 200 shares at Rs 87 each last year. The par value of a share is Rs 10. Telco paid a dividend of 15 per cent during the year. You sold 200 shares at a total value of Rs 18,500 after one year. What is your (i) dividend yield, (ii) rate of capital gain, and (iii) total rupee and percentage returns. You bought Infosys share for Rs 4,250 two years ago. You held the stock for two years, and received dividend per share of Rs 90 and Rs 125 respectively at the end of the first and the second years. You sold the share for Rs 4,535 after two years. What was your two-year holding period return on Infosys share? You expect to earn a return of 17 per cent on a share. If the inflation rate is 5.5 per cent, what is your real rate of return? Suppose shares of Hind Ltd and Nirmala Ltd were selling at Rs 100 two years ago. Hind’s price fell in the first year by 12 per cent and rose by 12 per cent in the second year. The reverse was the case for Nirmala’s share price — it increased by 12 per cent and then decreased by 12 per cent. Would they have the same price after two years? Why or why not? Show computations. An asset is expected to earn the following rates of return for the period 2004-10: Year 2004 Return (%) 15.3

2005 −5.6

2006 17.3

2007 25.0

2008 16.8

2009 9.5

2010 28.8

What is the seven-year holding period return from the asset? How much is the annual compound rate of return? 8.

The following are the returns on the share of Reliable Company for past five years: Year Return (%)

1 5.3

2 15.6

3 −7.3

4 15.0

5 19.8

Calculate the average return for the five years. Also calculate the standard deviation and variance of the returns for the period. 9. The economy of a country may experience rapid growth or moderate growth or recession. There is 0.15 probability of rapid growth and the stock market return is expected to be 19.5 per cent. The probability of moderate growth is 55 per cent with a 14 per cent expectation of the stock market return. There is 0.30 probability of recession and the stock market return is expected to be 7 per cent. Calculate the expected stock market return and the standard deviation of the return. 10. An asset has the following possible returns with associated probabilities: Possible returns Probability

20% 0.10

18% 0.45

8% 0.30

0 0.05

– 6% 0.10

Calculate the expected rate of return and the standard deviation of that rate of return. 11. Securities X and Y have the following characteristics: Security X

Security Y

Return

Probability

Return

Probability

30% 20% 10% 5% – 10%

0.10 0.20 0.40 0.20 0.10

– 20% 10% 20% 30% 40%

0.05 0.25 0.30 0.30 0.10

You are required to calculate the expected return and standard deviation of return for each security. Which security would you select for investment and why? 12. The distribution of returns for share P and the market portfolio is given below: Returns (%) Probability

Share P

Market

0.30 0.40 0.30

30 20 0

–10 20 30

You are required to calculate the expected returns, standard deviation and variance of the returns of share P and the market. 13. The following are the returns during seven years on a market portfolio of shares and 91-day Treasury Bills: You are required to calculate (i) the realised risk premium of shares over treasury bills in each year and (ii) the average risk premium of shares over treasury bills during the period. Can the realised premium be negative? Why? Portfolio of

Treasury YearShares (%)

Bills (%)

1

.5

11.4

2

6.8

9.8

3

26.8

10.5

4

24.6

9.9

5

3.2

9.2

6

15.7

9.2

7

12.3

11.2

14. The stock market and treasury bills returns are expected to be as follows: Economic Conditions

Probability

Market Return (%)

Treasury Bills (%)

Growth

0.20

28.5

9.7

Decline

0.30

–5.0

9.5

Stagnation

0.50

17.9

9.2

You are required to calculate (i) the expected market and treasury bills returns and (ii) the expected risk premium. 15. Suppose that returns of Sunshine Company Limited’s share are normally distributed. The mean return is 20 per cent and the standard deviation of returns is 10 per cent. Determine the range of returns in which about 2/3rd of the company’s returns fall. 16. Suppose the rates of return on Maneklal Engineering Ltd’s share have a normal distribution with a mean of 22 per cent and a standard deviation of 25 per cent. What is the probability of the return being 30 per cent?

Chapter 5 PROBLEMS

1.

An asset has the following possible returns with associated probabilities: Possible returns 20%

18%

8%

0

–6%

Probability

0.45

0.30

0.05

0.10

0.10

Calculate the expected rate of return and the standard deviation of the rate of return. 2.

Securities X and Y have the following characteristics: Security X Return

Security Y

Probability

Return

Probability

0.10 0.20 0.40 0.20 0.10

–20% 10% 20% 30% 40%

0.05 0.25 0.30 0.30 0.10

30% 20% 10% 5% –10%

You are required to calculate (a) the expected return and standard deviation of return for each security and (b) the expected return and standard deviation of the return for the portfolio of X and Y, combined with equal weights. 3.

The distribution of returns for share P and the market portfolio M is given below: Returns (%) Probability

P

M

0.30 0.40 0.30

30 20 0

–10 20 30

You are required to calculate the expected returns of security P and the market portfolio, the covariance between the market portfolio and security P and beta for the security. 4.

The standard deviation of return of security Y is 20 per cent and of market portfolio is 15 per cent. Calculate beta of Y if (a) Cory, m = 0.70, (b) Cory,m = + 0.40, and (c) Cory, m = – 0.25.

5.

An investor holds a portfolio, which is expected to yield a rate of return of 18 per cent with a standard deviation of return of 25 per cent. The investor is considering of buying a new share (investment being 5 per cent of the total investment in the new portfolio). The new share has the following distribution of return: Return

Probability

40% 30% –10%

6.

0.3 0.4 0.3

If the correlation coefficient between the returns of the new portfolio and the new security is +0.25, calculate the portfolio return and the standard deviation of return of the new portfolio. The Sunrise and Sunset companies have the following probability distribution of returns: Returns (%) Economic conditions

Probability

Sunrise

Sunset

High growth Normal growth Slow growth Stagnation Decline

0.1 0.2 0.4 0.2 0.1

32 20 14 –5 –10

30 17 6 –12 –16

You are required (a) to determine the expected covariance of returns and (b) the correlation of returns between the Sunrise and Sunset companies. 7.

Two shares, P and Q, have the following expected returns, standard deviation and correlation: E(rp) = 18%

E(rQ) = 15%

E(σ

(r σ

P

= 23% Cor σ

Q

Q

= 19%

=0

(a) Determine the minimum risk combination for a portfolio of P and Q. (b) If the correlation of returns of P and Q is –1.0, then what is the minimum risk portfolio of P and Q?

Chapter 6 PROBLEMS 1. The returns on the share of Delite Industries and the Sensex for the past five years are given below: Sensex (%)

Delite (%)

– 12.5 1.7 7.2 11.5 6.3

2.

3.

– 5.1 6.7 7.1 18.9 11.9

Calculate the average return on Delite’s share and Sensex. What is Delite’s beta? Royal Paints Limited is an all-equity firm without any debt. It has a beta of 1.21. The current risk-free rate is 8.5 per cent and the historical market premium is 9.5 per cent. Royal is considering a project that is expected to generate a return of 20 per cent. Assuming that the project has the same risk as the firm, should the firm accept the project? Calculate Excel Company Limited’s equity beta given the following information: Correlation between the returns on Excel’s share and Sensex = 0.725 Variance of the returns on Excel’s share = 0.006455 Variance of the returns on Sensex = 0.001589

4.

The returns for 48 months (Apr-04 — Mar-08) on the BHEL shares and Sensex (market) are given below: Months

Sensex Returns

BHEL Returns

Months

Sensex BHEL Returns Returns

Apr-04 May-04 Jun-04 Jul-04 Aug-04 Sep-04 Oct-04 Nov-04 Dec-04 Jan-05 Feb-05 Mar-05

1.154 – 15.835 0.753 7.817 0.421 7.541 1.588 9.908 5.909 – 0.708 2.409 – 3.292

– 3.001 – 25.796 15.344 8.524 1.333 3.997 8.886 – 0.778 24.157 – 2.494 14.347 – 10.601

Apr-06 May-06 Jun-06 Jul-06 Aug-06 Sep-06 Oct-06 Nov-06 Dec-06 Jan-07 Feb-07 Mar-07

6.761 4.929 – 13.651 – 19.309 2.026 2.596 1.269 4.778 8.890 10.554 6.457 5.835 4.075 0.917 5.666 3.810 0.661 – 8.323 2.205 9.534 – 8.181 – 13.525 1.036 3.857

Apr-05 May-05 Jun-05 Jul-05 Aug-05 Sep-05 Oct-05 Nov-05 Dec-05 Jan-06 Feb-06 Mar-06

– 5.212 9.110 7.129 6.138 2.227 10.621 – 8.595 11.359 6.931 5.554 4.540 8.772

3.331 11.103 – 1.816 16.370 6.169 14.541 – 7.292 25.718 – 2.835 29.665 12.723 10.894

Apr-07 May-07 Jun-07 Jul-07 Aug-07 Sep-07 Oct-07 Nov-07 Dec-07 Jan-08 Feb-08 Mar-08

6.122 10.019 4.845 12.485 0.729 9.961 6.146 12.576 – 1.494 9.092 12.877 7.601 14.729 28.562 – 2.393 2.560 4.771 – 3.582 – 13.005 – 20.128 – 0.397 10.557 – 11.004 – 9.879

(a) Calculate BHEL’s beta using (i) data for 48 months from Apr-04 — Mar-08, (ii) data for 24 months from Apr-04 — Mar-06, and (iii) data for 24 months from Apr-06 — Mar-08. Based on your calculations, comment on beta stability. (b) Assume that risk free rate is 7.9 per cent and risk premium is 12 per cent. Calculate BHEL expected rate of return. 5.

6.

7.

The following are the regression (characteristics) lines of three assets: Asset A: rA = 1.53% + 0.89rM

Cor = 0.78

Asset B: rB = –0.65% + 1.18rM

Cor = 0.83

Asset C: rC = 0.85% + 1.29rM

Cor = 0.65

(a) Which asset is the most risky (systematic risk)? (b) How much is the systematic and unsystematic risk for each asset? Sunlite Soap Limited is an all-equity firm. It has a beta of 1.21. The current risk-free rate is 6.5 per cent and the market premium is 9.0 per cent. Sunlite is considering a project with similar risk, but the project will be financed 30 per cent by debt and 70 per cent by equity. Debt is risk free. What is the expected rate of return on equity that the project should earn to be acceptable by the firm? You have a portfolio of the following four shares: Share

Beta

A B C D

0.80 1.25 1.00 0.60

Investment (Rs) 100,000 100,000 075,000 125,000

What is the expected rate of return on your portfolio if the risk-free rate of return is 9 per cent and the expected market rate of return is 16 per cent?

Chapter 7 PROBLEMS

1.

2.

3.

4.

5.

Ram Jethabhai has purchased a 3-month call option on a company’s share with an exercise price Rs 51. The current price of the share is Rs 50. Determine the value of call option at expiration if the share price turns out to be either Rs 47 or Rs 54. Draw a diagram to illustrate your answer. Sunder Lal has sold a 6-month call option on a company’s share with a exercise price of Rs 100. The current share price is Rs 100. Calculate the value of call option to Sunder Lal at maturity if the share price increases to Rs 110 or decreases to Rs 90. Draw a diagram to illustrate your answer. You have bought one 6-month call option on a share with an exercise price of Rs 98 at a premium of Rs 3. The share has a current price of Rs 100. You expect share to either rise to Rs 108 or fall to Rs 95 after six months. What will be your pay-off when option matures? Draw a diagram to explain. Radhika Krishnan has purchased a call option on a share at a premium of Rs 5. The current share price is Rs 44 and the exercise price is Rs 42. At maturity the share price may either increase to Rs 45 or fall to Rs 43. Will Radhika exercise her option? Why? Meena Vasudevan has purchased a 3-month put option on a company’s share with an exercise price Rs 101. The current price of the share is Rs 100. Determine the value of put option at expiration if the share price turns out to be either Rs 97 or Rs 104. Draw a diagram to illustrate your answer.

6.

7.

8.

9.

10.

11.

12.

13. 14.

15.

16.

17.

18.

19.

20.

21.

22.

S. Rammurthy has sold a 6-month put option on a company’s share with an exercise price of Rs 100. The current share price is Rs 100. Calculate the value of put option to Rammurthy at maturity if the share price increases to Rs 110 or decreases to Rs 90. Draw a diagram to illustrate your answer. You have bought one 6-month put option on a share with an exercise price of Rs 96 at a premium of Rs 4. The share has a current price of Rs 100. You expect share to either rise to Rs 108 or fall to Rs 95 after six months. What will be your pay-off when option matures? Draw a diagram to explain. You buy a 3-month European put on a share for Rs 4 with an exercise price of Rs 50. The current share price is Rs 52. When will you exercise your option and when will you make a profit? Draw a diagram to illustrate your answer. Shyam sells a 6-month put with an exercise price of Rs 70 at a premium of Rs 5. Under what situation option will be exercised? When will Shyam make profit? Draw a diagram to illustrate Shyam’s profit or loss position with the share prices at maturity. V. Sridharan has purchased a put option on a share at a premium of Rs 5. The current share price is Rs 44 and the exercise price is Rs 42. At maturity the share price may either increase to Rs 45 or fall to Rs 43. Will he exercise his option? Why? Madan Modi holds 50 share of Zeta Zerox Company. He is intending to write calls on Zetas’s shares. If he writes a call contract for 50 shares with an exercise price of Rs 50 each share, determine the value of his portfolio when the option expires if (a) the current share price of Rs 45 rises to Rs 65, or (b) the share price falls to Rs 40. You buy a call option on a share with an exercise price of Rs 100. You also buy a put option on the same share with an exercise price of Rs 97. What profit or loss will you have on maturity from your portfolio of call and put? Explain with the help of a diagram. In Exercise (12) above, assume that you paid a call premium of Rs 3 and a put premium of Rs 5. How would your profit pattern change? Show with the help of a diagram. R.K. Ramachandran has purchased 3-month call on a share with an exercise price of Rs 50 at a premium of Rs 4. He has also bought a 3-month put on the same share with an exercise price of Rs 50 at a premium of Rs 2. Determine Ramchandran’s position at maturity if the share price is either Rs 52 or Rs 45. The share of Ashok Enterprises is currently selling for Rs 100. It is known that the share price will either turn to be Rs 108 or Rs 90. The risk-free rate of return is 12 per cent per annum. If you intend to buy a 3-month call option with an exercise price of Rs 97, how much should you pay for buying the option today? Assume no arbitrage opportunity. A share has a current share price of Rs 100. The share price after six months will be either Rs 115 or Rs 90. The risk-free rate is 10 per cent per annum. Determine the value of a 6-month call option on the share with an exercise price of Rs 100 using the risk-neutral arguement. Zenith Company’s share is currently selling for Rs 60. It is expected that after two months the share price may either increase by 15 per cent or fall by 10 per cent. The risk-free rate is 9 per cent per annum. What should be the value of a two-month European call option with an exercise price of Rs 65? What is the value of a two-month European put option with an exercise price of Rs 65? Determine the price of a European call option on a share that does not pay dividend. The current share price is Rs 60, the exercise price Rs 55, the risk-free rate is 10 per cent per annum, the share return volatility is 40 per cent per annum and the time to expiration is six months. Calculate the value of a European put option on a share that does not pay dividend. The current share price is Rs 86, the exercise price Rs 93, the risk-free rate is 12 per cent per annum, the share return volatility is 60 per cent per annum and the time to expiration is four months. A company has a total market value of Rs 230 crore. The face of its debt (assume pure discount debt) is Rs 95 crore. The standard deviation of the firm’s share return is 25 per cent and debt has a maturity of 8 years. The risk-free rate is 12 per cent. What is the value of the company’s equity? On 26 August 2002, Infosys call option with an exercise of Rs 3,400 is selling at a premium of Rs 186.15 and call option with an exercise of Rs 3,500 is selling at a premium of Rs 38.10. The current share price is Rs 3,469. The lot size is 100. What will be your net profit at share price at expiration ranging from Rs 3200 to Rs 3700 if you buy call with the exercise of Rs 3,500 and sell call with the exercise price of Rs 3,400? Draw a profit graph. VSNL’s share price is expected to decline due to non-payment of its dues by the WorldCom, lowering margins and other negative sentiments in the market. The current share price is Rs 123.70 and the daily volatility of the VSNL share is 2.74 percent. Based on the Value at Risk (VaR), the probability of the

share price going above Rs 142.5 is quite low. The put on the VSNL share with an exercise price of Rs 150 is selling for Rs 7.50. Should you buy the put? Draw a profit graph. 23. The put on the Infosys share is selling with an exercise price Rs 3,400 at a premium of Rs 37.50 on 22 August 2002. On the same day, the call is selling at a premium of Rs 32.50 with an exercise price of Rs 3,300. The spot price of the share is Rs 3,370. The lot size is 100. What will be your net profit at share price at expiration ranging from Rs 3,200 to Rs 3,700 if you buy call with the exercise price of Rs 3,500 and buy put with the exercise price of Rs 3,300? Draw a profit graph.

Chapter 8 PROBLEMS

1.

The following are the net cash flows of an investment project: Cash Flows (Rs) C0

C1

C2

– 5,400 + 3,600

2.

3. 4.

+ 14,400

Calculate the net present value of the project at discount rates of 0, 10, 40, 50 and 100 per cent. A machine will cost Rs 100,000 and will provide annual net cash inflow of Rs 30,000 for six years. The cost of capital is 15 per cent. Calculate the machine’s net present value and the internal rate of return. Should the machine be purchased? A project costs Rs 81,000 and is expected to generate net cash inflow of Rs 40,000, Rs 35,000 and Rs 30,000 over its life of 3 years. Calculate the internal rate of return of the project. The G.K. Company is evaluating a project with following cash inflows: Cash Flows (Rs)

5.

C1

C2

C3

C4

C5

1,000

800

600

400

200

The cost of capital is 12 per cent. What is the maximum amount the company should pay for the machine? Consider the following three investments: Cash Flows (Rs) Projects

C0

C1

C2

X

– 2,500

0

+ 3,305

Y

– 2,500

+ 1,540

+ 1,540

Z

– 2,500

+ 2,875

0

The discount rate is 12 per cent. Compute the net present value and the rate of return for each project. 6. You want to buy a 285 litre refrigerator for Rs 10,000 on an instalment basis. A distributor is prepared to sell the refrigerator on instalments. He states that the payments will be made in four years, interest rate being 12 per cent. The annual payments will be as follows:

Rs Principal 10,000 Four year of interest at 12%, i.e., Rs 10,000 × 0.12 × 4 4,800 14,800 Annual payments (Rs 14,800 ÷ 4)

7.

3,700

What rate of return is the distributor earning? If your opportunity cost of capital is 14 per cent will you accept the offer? Why? Compute the rate of return of the following projects: Cash Flows (Rs) Projects

C0

C1

C2

C3

X Q

8.

– 20,000 – 20,000

+ 8,326 0

+ 8,326 0

+ 8,326 + 24,978

Which project would you recommend? Why? A firm is considering the following two mutually exclusive investments: Cash Flows (Rs) Projects A B

9.

C0

C1

C2

C3

– 25,000 – 28,000

+ 15,000 + 12,672

+ 15,000 + 12,672

+ 25,640 + 12,672

The cost of capital is 12 per cent. Compute the NPV and IRR for each project. Which project should be undertaken? Why? You have an opportunity cost of capital of 15 per cent. Will you accept the following investment? Cash Flows (Rs) C0

C1

+ 50,000

– 56,000

10. Is the following investment desirable if the opportunity cost of capital is 10 per cent: Cash Flows (Rs) C0

C1

C2

C3

C4

+ 100,000

– 33,625

– 33,625

– 33,625

– 33,625

11. Consider the following two mutually exclusive investments: Cash Flows (Rs) Projects A B

C0

C1

C2

C3

– 10,000 – 10,000

+ 12,000 + 10,000

+ 4,000 + 3,000

+ 11,784 + 12,830

(a) Calculate the NPV for each project assuming discount rates of 0, 5, 10, 20, 30 and 40 per cent; (b) draw the NPV graph for the projects to determine their IRR, (c) show calculations of IRR for each project confirming results in (b). Also, state which project would you recommend and why? 12. For Projects X and Y, the following cash flows are given: Cash Flows (Rs) Projects X Y

C0

C1

C2

C3

– 750 – 750

+ 350 + 250

+ 350 + 250

+ 159 + 460

(a) Calculate the NPV of each project for discount rates 0, 5, 8, 10, 12 and 20 per cent. Plot these on an PV graph. (b) Read the IRR for each project from the graph in (a). (c) When and why should Project X be accepted? (d) Compute the NPV of the incremental investment (Y – X) for discount rates, 0, 5, 8, 10, 12 and 20 per cent. Plot them on graph. Show under what circumstances would you accept X? 13. The following are two mutually exclusive projects. Cash Flows (Rs) Projects

C0

C1

I

– 25,000

+ 30,000

II

– 25,000

0

C2

C3

C4

0

0

43,750

Assume a 10 per cent opportunity cost of capital. Compute the NPV and IRR for each project. Comment on the results. 14. Consider the following projects:

Cash Flows (Rs) Projects A B C D

C0

C1

C2

– 1,000 – 1,000 – 1,300 – 1,300

+ 600 + 200 + 100 0

+ 200 + 200 + 100 0

C3

C4

+ 200 + 600 + 100 + 300

+ 1,000 + 1,000 + 1,600 + 1,600

(a) Calculate the payback period for each project. (b) If the standard payback period is 2 years, which project will you select? Will your answer be different if the standard payback is 3 years? (c) If the cost of capital is 10 per cent, compute the discounted payback for each project? Which projects will you recommend if the standard payback is (i) 2 years; (ii) 3 years? (d) Compute the NPV of each project? Which projects will you recommend? 15. A machine will cost Rs 10,000. It is expected to provide profits before depreciation of Rs 3,000 each in years 1 and 2 and Rs 4,000 each in years 3 and 4. Assuming a straight-line depreciation and no taxes, what is the average accounting rate of return? What will be your answer if the tax rate is 35 per cent? 16. A firm has the following information about a project: Income Statement (Rs ’ 000)

Cash revenue Cash expenses Gross profit Depreciation Net profit

C1

C2

C3

16 8 8 4 4

14 7 7 4 3

12 6 6 4 2

The initial investment of the project is estimated as Rs 12,000. (a) Calculate the project’s accounting rate of return. (b) If it is found that the initial investment will be Rs 9,000 and cash expenses will be more by Rs 1,000 each year, what will be the project’s accounting rate of return. Also, calculate the project’s NPV if the cost of capital is 9 per cent. 17. An investment project has the following cash flows: Cash Flows (Rs) C0

C1

C2

– 150

+ 450

– 300

What are the rates of return of the investment? Assume a discount rate of 10 per cent. Is the investment acceptable? 18. A firm is considering the following project: Cash Flows (Rs) C0

C1

– 50,000 + 11,300

C2

C3

C4

C5

+ 12,769 + 14,429 + 16,305 + 18,421

(a) Calculate the NPV for the project if the cost of capital is 10 per cent. What is the project’s IRR? (b) Recompute the project’s NPV assuming a cost of capital of 10 per cent for C1 and C2, of 12 per cent for C3 and C4, and 13 per cent for C5. Should the project be accepted? Can the internal rate of return method be used for accepting or rejecting the project under these conditions of changing cost of capital over time? Why or why not? 19. A finance executive has calculated the profitability index for a new proposal to be 1.12. The proposal’s initial cash outlay is Rs 500,000. Find out the proposal’s annual cash inflow if it has a life of 5 years and the required rate of return is 8 per cent. 20. Project P has the following cash flows: Cash Flows (Rs)

C0

C1

C2

– 800

+ 1,200

– 400

Calculate the project’s IRRs. If the required rate of return is 25 per cent, would you accept the project. Why?

Chapter 9 PROBLEMS 1. The Ess Kay Refrigerator Company is deciding to issue 2,000,000 of Rs 1,000, 14 per cent 7-year debentures. The debentures will have to be sold at a discount rate of 3 per cent. Further, the firm will pay an underwriting fee of 3 per cent of the face value. Assume a 35% tax rate. Calculate the after-tax cost of the issue. What would be the after-tax cost if the debenture were sold at a premium of Rs 30? 2. A company issues new debentures of Rs 2 million, at par; the net proceeds being Rs 1.8 million. It has a 13.5 per cent rate of interest and 7 year maturity. The company’s tax rate is 52 per cent. What is the cost of debenture issue? What will be the cost in 4 years if the market value of debentures at that time is Rs 2.2 million? 3. A company has 100,000 shares of Rs 100 at par of preference shares outstanding at 9.75 per cent dividend rate. The current market price of the preference share is Rs 80. What is its cost? 4. A firm has 8,000,000 ordinary shares outstanding. The current market price is Rs 25 and the book value is Rs 18 per share. The firm’s earnings per share is Rs 3.60 and dividend per share is Rs 1.44. How much is the growth rate assuming that the past performance will continue? Calculate the cost of equity capital. 5. A company has 5,000,000 ordinary shares outstanding. The market price of the share is Rs 96 while the book value is Rs 65. The firm’s earnings and dividends per share are Rs 10 and Rs 7 respectively. The company wants to issue 1,000,000 shares with a net proceeds of Rs 80 per share. What is the cost of capital of the new issue? 6. A company has paid a dividend of Rs 3 per share for last 20 years and it is expected to continue so in the future. The company’s share had sold for Rs 33 twenty years ago, and its market price is also Rs 33. What is the cost of the share? 7. A firm is thinking of raising funds by the issuance of equity capital. The current market price of the firm’s share is Rs 150. The firm is expected to pay a dividend of Rs 3.55 next year. The firm has paid dividend in past years as follows:

8.

Year

Dividend per Share (Rs)

2003 2004 2005 2006 2007 2008

2.00 2.20 2.42 2.66 2.93 3.22

The firm can sell shares for Rs 140 each only. In addition, the flotation cost per share is Rs 10. Calculate the cost of new issue. A company is considering the possibility of raising Rs 100 million by issuing debt, preference capital, and equity and retaining earnings. The book values and the market values of the issues are as follows: (Rs in millions) Ordinary shares Reserves Preference shares Debt

Book Value

Market Value

30 10 20 40

60 — 24 36

100

120

The following costs are expected to be associated with the above-mentioned issues of capital. (Assume a 35 per cent tax rate.)

(i) The firm can sell a 20-year Rs 1,000 face value debenture with a 16 per cent rate of interest. An underwriting fee of 2 per cent of the market price would be incurred to issue the debentures. (ii) The 11 per cent Rs 100 face value preference issue fetch Rs 120 per share. However, the firm will have to pay Rs 7.25 per preference share as underwriting commission. (iii) The firm’s ordinary share is currently selling for Rs 150. It is expected that the firm will pay a dividend of Rs 12 per share at the end of the next year, which is expected to grow at a rate of 7 per cent. The new ordinary shares can be sold at a price of Rs 145. The firm should also incur Rs 5 per share flotation cost. Compute the weighted average cost of capital using (i) book value weights (ii) market value weights. 9. A company has the following long-term capital outstanding as on 31 March 2008: (a) 10 per cent debentures with a face value of Rs 500,000. The debentures were issued in 2003 and are due on 31 March 2010. The current market price of a debenture is Rs 950. (b) Preference shares with a face value of Rs 400,000. The annual dividend is Rs 6 per share. The preference shares are currently selling at Rs 60 per share. (c) Sixty thousand ordinary shares of Rs 10 par value. The share is currently selling at Rs 50 per share. The dividends per share for the past several years are as follow: Year

Rs

Year

Rs

2003 2004 2005 2006

2.00 2.16 2.37 2.60

2000 2001 2002 2003

2.80 3.08 3.38 3.70

Assuming a tax rate of 35 per cent, compute the firm’s weighted average cost of capital. 10. A company is considering distributing additional Rs 80,000 as dividends to its ordinary shareholders. The shareholders are expected to earn 18 per cent on their investment. They are in 30 per cent tax and incur an average brokerage fee of 3 per cent on the reinvestment of dividends received. The firm can earn a return of 12 per cent on the retained earnings. Should the company distribute or retain Rs 80,000? 11. The Keshari Engineering Ltd has the following capital structure, considered to be optimum, on 31 June 2008. Rs in million 14% Debt 10% Preference Ordinary equity

93.75 31.25 375.00

Total

500.00

The company has 15 million shares outstanding. The share is selling for Rs 25 per share and the expected dividend per share is Rs 1.50, which is expected to grow at 10 per cent. The company is contemplating to raise additional funds of Rs 100 million to finance expansion. It can sell new preference shares at a price of Rs 23, less flotation cost of Rs 3 per share. It is expected that a dividend of Rs 2 per share will be paid on preference. The new debt can be issued at 10 per cent rate of interest. The firm pays taxes at rate of 35 per cent and intends to maintain its capital structure. You are required (i) to calculate the after-tax cost (a) of new debt, (b) of new preference capital, and (c) of ordinary equity, assuming new equity comes only from retained earnings which is just sufficient for the purpose, (ii) to calculate the marginal cost of capital, assuming no new shares are sold, (iii) to compute the maximum amount which can be spent for capital investments before new ordinary shares can be sold, if the retained earnings are Rs 700,000, and (iv) to compute the marginal cost of capital if the firm spends in excess of the amount computed in (iii). The firm can sell ordinary shares at a net price of Rs 22 per share. 12. The following is the capital structure of X Ltd as on 31 December 2008. Rs in million Equity capital (paid up) Reserves and surplus 10% Irredeemable Preference shares 10% Redeemable Preference shares 15% Term loans

563.50 485.66 56.00 28.18 377.71

Total

1,511.05

The share of the company is currently selling for Rs 36. The expected dividend next year is Rs 3.60 per share anticipated to be growing at 8 per cent indefinitely. The redeemable preference shares were issued on 1 January 2003 with twelve-year maturity period. A similar issue today will be at Rs 93. The market price of 10% irredeemable preference share is Rs 81.81. The company had raised the term loan from IDBI in 2003. A similar loan will cost 10% today. Assume an average tax rate of 35 per cent. Calculate the weights average cost of capital for the company using book-value weights. 13. The following capital structure is extracted from Delta Ltd’s balance sheet as on 31 March 2008: (Rs ’000) Equity (Rs 25 par) Reserves Preference (Rs 100 par) Debentures Long-term loans

66,412 65,258 3,000 30,000 5,360 170,030

The earnings per share of the company over the period 2004–2008 are: Year

Rs

Year

Rs

2004 2005 2006 2007 2008

2.24 3.00 4.21 3.96 4.80

1994 1995 1996 1997 1998

4.40 5.15 5.05 6.00 6.80

The equity share of the company is selling for Rs 50 and preference for Rs 77.50. The preference dividend rate and interest rate on debenture respectively are 10 per cent and 13 per cent. The long-term loans are raised at an interest rate of 14 per cent from the financial institution. The equity dividend is Rs 4 per share. Calculate the weighted average cost of capital for Delta Ltd, making necessary assumptions. 14. A company has the following capital structure at the end of 31 March 2008: (Rs in million)

Share Capital Reserve Long-term loans

6,808 34,857 538,220

The company’s EPS, DPS, average market price and ROE for last seven years are given below: Year

EPS

DPS

AMP

ROE

2002 2003 2004 2005 2006 2007 2008

21.55 22.14 26.40 20.16 20.40 23.09 22.00

5.28 5.76 5.76 6.53 7.68 11.53 7.68

143.04 187.52 312.32 587.52 366.72 416.64 355.20

20.9 18.6 11.7 11.0 9.5 10.3 8.4

Note: EPS, DPS and AMP adjusted for bonus issues. You are required to calculate: (a) growth rate g, using alternative methods; (b) cost of equity, using dividend – growth model, and (c) weighted average cost of capital, using (i) book-value weights and (ii) market-value weights. Assume that the interest rate on debt is 11 per cent and the corporate income tax rate is 35 per cent. 15. Eskayef Limited manufactures human and veterinary pharmaceuticals, bulk drugs, skin care products, and vaterinary feed supplements and markets bio-analytical and diagnostic instruments. On 31 March 2003, the company has a paid-up share capital of Rs 75 million and reserves of Rs 325.90 million. It does not employ long-term debt. The following are other financial highlights on the company during 2003–2008:

Year

EPS (Rs)

DPS (Rs)

Book Value (Rs)

Market Value

2003 2004 2005 2006 2007 2008

6.21 10.91 11.57 11.47 10.44 11.23

2.00 2.50 2.50 2.70 3.00 3.20

26.03 34.44 43.52 37.98 45.42 53.45

100.00 205.00 209.38 164.00 138.88 155.00

Note: (1) Years 2003, 2004 and 2005 closed on 30 November while years 2006, 2007 and 2008 on 31 March. (2) Market value is the averages of high and low share prices. You are required to calculate (a) ROE, (b) dividend payout, (c) retention ratio, (d) growth rate, (e) dividend yield, (f) earnings yield and (g) cost of equity.

Chapter 10 PROBLEMS

1.

Following data relate to five independent investment projects: Projects A B C D E

2.

Annual Cash Inflow (Rs)

500,000 120,000 92,000 5,750 40,000

125,000 12,000 15,000 2,000 6,000

Life in Years 8 15 20 5 10

Assume a 10 per cent required rate of return and a 35 per cent tax rate. Rank these five investment projects according to each of the following criteria: (a) payback period, (b) accounting rate of return, (c) net present value index, and (d) internal rate of return. A company has to choose one of the following two mutually exclusive projects. Both the projects will be depreciated on a straight-line basis. The firm’s cost of capital is 10 per cent and the tax rate is 35 per cent. The before-tax cashflows are: Project X Y

3.

Initial (Rs) Outlay

C0

C1

– 20,000 4,200 – 15,000 4,200

C2

C3

C4

C5

4,800 4,500

7,000 4,000

8,000 5,000

2,000 1,000

Which project should the firm accept if the following criteria are used: (a) payback period, (b) internal rate of return, (c) net present value, and (d) profitability index. From the following data calculate (i) net present value, (ii) internal rate of return, and (iii) payback period for the following projects. Assume a required rate of return of 10 per cent and a 35 per cent tax rate. Assume straight-line depreciation for tax purpose, and that tax is calculated on book loss or profit on the sale of asset. Project

Initial cash outlay Salvage value Earnings before depreciation and taxes Year 1 Year 2 Year 3 Year 4 Year 5 Expected life

M

N

(Rs)

(Rs)

100,000 Nil

140,000 20,000

25,000 25,000 25,000 25,000 25,000 5 years

40,000 40,000 40,000 40,000 40,000 5 years

4.

(a) A company has to choose one of the following three mutually exclusive projects. Which project is the most desirable? Assume a required rate of return of 12 per cent. Projects O P Q

5.

C0

C1

Rate of Return (%) 24 15 17

(b) Compute the corresponding incremental cash flow for projects P and Q in problem 4(a). Which project is more desirable? Kemp & Co. is faced with a problem of choosing among two alternative investments. It can invest either in Project A right now or wait for a year and invest in Project B. The following are the cash flows of the two projects:

A B

(Rs) (Rs)

C0

C1

C2

C3

– 6,000 —

8,000 – 8,000

2,000 12,000

2,000 4,000

Assume a required rate of return of 10 per cent. Which project should the firm select? Use the present value and internal rate of return methods. Also calculate the rate of return for incremental cash flows. Is the following investment desirable if the firm’s cost of capital is 10 per cent?

(Rs)

7.

C3

(Rs) – 50,000 25,270 25,270 25,270 (Rs) – 25,000 5,000 5,000 25,570 (Rs) – 28,000 12,670 12,670 12,670

Projects

6.

C2

C0

C1

C2

C3

C4

7,000

7,000

7,000

7,000

–25,000

The following data relate to a proposed new machine. Should it be acquired? Assume after-tax required rate of return of 10 per cent and a 40 per cent income tax rate. For simplicity assume that machines are depreciated on straight-line basis for tax purposes. Assume no tax on the profit or loss from the rate of asset. Rs Purchase price of the new machine Installation cost Increase in working capital at the time of purchase of new machine Cash salvage value of the new machine in four years Annual cash savings (before depreciation and taxes) Cash salvage value of the old machine today Cash salvage value of the old machine in four years Current book value of the old machine Service life of both machines is four years

8.

9.

40,000 8,000 10,000 14,000 16,000 20,000 4,000 16,000

Ram Singh, 45 years of age, has received an inheritance of Rs 300,000 from his father. He is currently working in materials management in a company, and his salary is Rs 36,000 per year, which he does not expect to change if he remains in his present employment till his retirement age of 58. He is considering two alternative investments of his inheritance. The first alternative is to continue in his present employment and to deposit Rs 300,000 in 13-year fixed deposit yielding 15 per cent compound interest. The second would be to purchase and operate a general store. He knows that to own a store, he will have to spend Rs 240,000 including Rs 100,000 for merchandise and the balance for building and fixtures. If he purchases the store, an additional Rs 60,000 will have to be invested for working capital needs. The expected annual receipts of this store are Rs 390,000. Annual out-of-pocket costs are estimated at Rs 300,000. As Ram Singh would manage his own store, he would have to leave his present employment. At the end of 13 years, when he wishes to retire in any event, he estimates the store would be sold for Rs 50,000. The applicable personal income tax rate is 30 per cent. Which course of action would be more profitable for Ram Singh? Why? The Manekshaw Company is considering the purchase of a new machine. The old machine is in good working condition, and will last for six years. However, the new machine will operate efficiently. It is expected that materials, labour and other direct expenses of the operations will be saved to the extent of Rs 16,000 per year. The new machine will cost Rs 80,000 and will be useful for six years. The old

machine has a book value of Rs 64,000. The after-tax minimum required rate of return expected by the company is 10 per cent. Assume a 25 per cent written down depreciation and a 35 per cent tax rate of income. Assume that profit or loss from the sale of the assets are taxed at35 per cent. What action should be taken by the company if (a) the salvage value of the old machine is zero; (b) the salvage value of the old machine today is Rs 16,000 and if retained for six years it has zero salvage value; and (c) the salvage value of the old machine today is Rs 16,000, and if retained for six years, its salvage value will be Rs 2,000. 10. X Company is using a fully depreciated machine having a current market value of Rs 20,000. The salvage value of the machine eight years from now would be zero. The company is considering replacing this machine by a new one costing Rs 102,500, and having an estimated salvage value of Rs 12,500. With the use of the new machine, annual sales are expected to increase from Rs 80,000 to Rs 92,500. Operating efficiencies with the new machine will save Rs 12,500 per year as operating expenses. Depreciation will be charged on written down basis at 25 per cent. The cost of capital is 11 per cent. The new machine has a 8-year life and the company’s taxation rate is 35 per cent. Assume that book profit or loss from the sale of the asset is taxable at corporate tax rate. Should the company replace the old machine? Show calculations on incremental cash flow basis. How would your decision be affected if another new machine is available at a cost of Rs 175,000 with a salvage value of Rs 25,000. The machine is expected to increase sales by Rs 12,500 a year and save Rs 30,000 of operating expenses annually over its 8-year life. 11. Alpha Limited is considering replacing its old machine by a new machine. The new machine will cost Rs 360,000. The supplier of the new machine has agreed to accept the old machine at a value of Rs 40,000 in exchange for the new machine. Old machine has been fully depreciated for tax purposes, but it has a book value of Rs 20,000 in the accounting statements meant for external reporting. If the old machine is sold in the market, it cannot fetch more than Rs 30,000. After 10 years, it can be sold for Rs 6,000. The new machine has an expected life of 10 years and a salvage value of Rs 40,000 after 10 years. Alpha uses the old machine for producing a special component used in its main product The production from old or new machine would be 15,000 units each year. The following are the projected revenues and costs from the old and new machines: Old Machine (Rs) Sales

New Machine (Rs)

1,080,000

1,080,000

240,000 180,000 90,000 75,000 120,000 2,000

195,000 120,000 100,000 50,000 130,000 36,000

707,000

631,000

Profit before tax Tax

373,000 186,500

449,000 224,500

Profit after tax

186,500

224,500

Material cost Direct labour Indirect labour Variable overheads Allocated fixed overheads Depreciation

Depreciation is calculated on a straight-line basis. For tax purposes, written down depreciation at 25 per cent per annum is allowed. If Alpha’s required rate of return is 12 per cent, should the old machine be replaced? What would be your decision if the component could be bought from outside at a cost of Rs 40 per unit? Assume that as per the current laws in India, depreciation is based on the block of assets. 12. ABC Co. is using a five-year old machine, which was bought for a cost of Rs 129,000. The machine is depreciated over its 12-year original life. The current market price of the machine is Rs 40,000. The salvage value of the machine at the end of its life is estimated to be zero. The company is thinking of replacing this machine by a new machine which will cost Rs 175,000, and would need an installation cost of Rs 25,000. The life of the machine is estimated to be 7 years with a disposal value of Rs 18,000 at the end of its life. Because of the greater capacity of the new machine, it is expected that annual sales will increase from Rs 1,800,000 to Rs 1,870,000. The operating efficiency is not likely to change. The current operating expenses (excluding depreciation) are Rs 1,080,000. The company expects an additional working capital investment of Rs 25,000 if it buys the new machine. The company’s cost of capital is 12 per cent.

Assume that the company will be allowed to depreciate the cost of machine on diminishing balance basis at 25 per cent for tax purposes. Assume a corporate tax rate of 35 per cent. You may also assume that no tax is paid on salvage value and it is adjusted for calculating depreciation as per the income tax rules. Would you recommend replacement of the machine? What would be your consideration in arriving at the decision? 13. A company has decided to buy a new machine either by an outright cash purchase at Rs 175,000 or by hiring it at Rs 42,000 per year for the life of the machine. The other relevant data are as follows: Purchase price of the machine (Rs) Estimated life (years) Estimated salvage value if the machine is bought (Rs) Annual cost of maintenance (whether hired or purchased) (Rs)

175,000 5 21,000 3,500

For simplicity assume that the company depreciates its assets on straight-line basis and pays tax at 50 per cent. Assuming a cost of capital of 10 per cent, which alternative is preferable? 14. A company is considering two mutually exclusive projects. Project P will require gross investment of Rs 250,000, and working capital of Rs 50,000. It is expected to have a useful life of ten years and a salvage value of Rs 30,000 at the end of ten years. At the end of five years, an additional investment of Rs 45,000 will have to be made to restore the efficiency of the equipment. The additional investment will be written off to depreciation over the last five years. The project is expected to yield before-tax cash flow (annual) of Rs 90,000. Project Q will require an investment of Rs 300,000 and working capital of Rs 60,000. It is expected to have a useful life of ten years with a residual salvage value of Rs 25,000 at the end of ten years. The annual cash flow returns from this project before income tax have been estimated at Rs 80,000 for each of the first five years, and at Rs 160,000 for each of the last five years. Depreciation is to be charged at 25 per cent on declining balance on the block of assets as per the current tax laws. The corporate income tax rate is 50 per cent, and the opportunity cost of capital is 18 per cent. Calculate the NPV for each project. Which project is better? 15. The Bright Company is evaluating a project, which will cost Rs 100,000 and will have no salvage value at the end of its 5-year life. The project will save costs of Rs 40,000 a year. The company will finance the project by a 14 per cent loan and will repay loan in equal instalments of Rs 20,000 a year. If the firm’s tax rate is 50 per cent and the after-tax cost of capital is 18 per cent, what is the NPV of the project? Assume straight-line depreciation for tax purposes. 16. The Vikrant Corporation is considering a new project, which costs Rs 50,000. The project will provide cost savings of Rs 30,000 a year for 5 years. It would be financed by a 5-year loan with the following payment schedule: Total Payment Interest at 15% 14,916 7,500 14,916 6,388 14,916 5,108 14,916 3,637 14,916 1,947

Principal 7,416 8,528 9,808 11,279 12,969

Balance 42,584 34,056 24,248 12,969 0

The corporate tax rate is 50 per cent. The project has the same risk as the firm’s risk. The firm’s cost of capital is 12 per cent. Calculate the project’s NPV. 17. A company is considering replacing its existing machine by a more efficient new machine. The cost of production per unit is estimated as follows: Cost production per unit (Rs) Old Machine Materials Labour Variable overheads Fixed overheads

040 060 030 020 150

New Machine 38 40 15 30 123

For the old machine, fixed overheads include allocations from other departments and the depreciation. In case of the new machine, fixed overheads also include its maintenance cost of Rs 2 per unit. The old machine was bought 5 years ago for a cost of Rs 300,000, and has a book value of Rs 200,000 now after being depreciated on a straight-line basis for both book as well as tax purposes. It has a remaining life of 10 years. It has a capacity to produce 3,000 units each year, and its capacity is fully utilised. The new machine would cost Rs 500,000 and would have a salvage value of Rs 50,000 at the end of its life of 10 years. The supplier of the new machine has agreed to buy back the old machine at 50 per cent of its book value in exchange for the new machine. He has also agreed that the remaining amount could be paid in two instalments: half of the amount now and half, a year later. The new machine is capable of producing 4,000 units each year. The company is confident of selling the additional units by reducing its current price per unit of Rs 200 by 10 per cent. It is also expected that for operating the new machine, a working capital investment of Rs 25,000 would be required. Should the new machine be acquired? Assume tax rate of 50 per cent and required rate of return of 15 per cent. Further, assume that depreciation can be charged on straight-line basis for computing tax, and ordinary tax is applicable on the gain or loss from the sale of asset. 18. A firm is considering an investment project involving an initial cost of Rs 200,000. The life of the project is estimated as 5 years. The project will provide annual net cash inflow of Rs 70,000. The cost of capital is 10 per cent. Should the project be accepted? A subsequent evaluation revealed that firm had not considered price level changes in its estimates of cash flows and the cost of capital. The expected annual rate of inflation is 5 per cent. If inflation is accounted for, what would be the firm’s decision? 19. The Indopax Company is considering investment in a machine that produces Product X. The machine will cost Rs 500,000. In the first year 10,000 units of X will be produced and the price will be Rs 20 per unit. The volume is expected to increase by 20 per cent and the price of the product by 10 per cent. The material used to manufacture the product is becoming more expensive. The cost of production is therefore expected to increase by 15 per cent. The production cost in the first year will be Rs 10 per unit. Assume for simplicity that the company will charge straight-line depreciation on the machine for tax purposes. There will be no salvage values of the 5-year life of the machine. The tax rate is 35 per cent, and the discount rate is 20 per cent, based on the expected general inflation rate of 10 per cent. Should the machine be bought? 20. Lodha Chemical Company is considering a project involving a cash outlay of Rs 6 million. Sales are expected to be Rs 1.20 million in year 1 and Rs 2 million in year 2 and thereafter, to grow at 10 per cent due to general rise is price. Operating expenses are estimated to be Rs 600,000 in year 1 and to rise at 10 per cent thereafter. An initial working capital of Rs 500,000 would be needed and afterwards working capital is expected to be 25 per cent of sales. The life of the project is 7 years, and it could be sold for 20 per cent of its original cost adjusted for inflation. Depreciation is charged at 25 per cent on the written down value basis. The company pays tax at 35 per cent. Assume that no tax is payable on the sale of the project at the end of its life. Calculate the project’s NPV when the opportunity cost of capital is 21 per cent. Would your answer change if you analyze the project in real terms?

Chapter 11 PROBLEMS

1.

The Damodar Company is considering two mutually exclusive projects with different lives. The costs (cash flows) of the projects are given below: Cash Flows (Rs ’000)

2.

Project

C0

C1

C2

C3

C4

X Y

150 75

30 40

30 40

30

30

The discount rate is 10 per cent. Which project should be selected and why? The K&K Company has two alternative investment projects, A and B. A, short-lived project, will cost Rs 150,000 initially and involve annual operating cash expenses of Rs 40,000 for 4 years. B, on the other hand, will cost Rs 200,000 and involve annual operating expenses of Rs 25,000 for 7 years. Projects have no salvage value. The discount rate is 12 per cent. Which project do you recommend?

3.

4.

5.

6.

7.

8.

9.

A firm is evaluating two mutually exclusive machines. Machine P will require an initial investment of Rs 120,000 and provide annual net cash inflows after taxes of Rs 42,000 for 6 years. Machine Q will involve an investment of Rs 300,000 and provide annual net cash inflows after taxes of Rs 80,000 for 8 years. Machine Q is riskier than machine P. The required rate of return of Machine Q is 14 per cent and of Machine P is 12 per cent. Which machine should be selected? A company is thinking of replacing an old machine. The machine was bought 4 years ago for Rs 100,000. It is expected to last for 3 years more and to produce an annual net cash inflow of Rs 60,000. The new alternative machine will cost Rs 150,000 and provide net cash flows of Rs 90,000, Rs 90,000, Rs 80,000, Rs 80,000 and Rs 70,000 from year 1 through year 5. There is no salvage value for machines. The cost of capital is 12 per cent. Should the old machine be replaced? R.K. Company had acquired 5 years ago a machine for Rs 300,000. The current net salvage value of the machine is Rs 60,000. It is expected to last another 3 years and provide net cash inflows of Rs 70,000, Rs 60,000, and Rs 50,000. The salvage value of the machine after 3 years is estimated as Rs 40,000. A technologically superior design is available now. The new machine will cost Rs 300,000 and have a life of 5 years. It will provide annual net cash inflows of Rs 150,000, Rs 130,000, Rs 120,000, Rs 100,000 and Rs 80,000. It is also expected that the new machine will have a net salvage value of Rs 20,000 after 5 years. The required rate of return is 10 per cent. Should the firm replace old machine now or after 3 years. Radiant Engineers Ltd has two machines doing the same job. Due to improved processing and manufacturing, the company is in a position to sell one of the machines. Machine X needs repairing costing Rs 10,000 to be operative for next three years. Its annual operating costs are expected to be Rs 12,500 and it could be sold for Rs 8,000 after 3 years. Its market value today is Rs 20,000. Machine Y has a market value of Rs 45,000 today and Rs 10,000 after 8 years. Its annual operating costs are Rs 9,000 and would require repairs costing Rs 12,000 after 3 years. The book values of Machines X and Y are Rs 12,000 and Rs 24,000 respectively. Assume that depreciation is charged on straight-line basis for computing tax. The tax rate is 45 per cent and the required rate of return is 10 per cent. Which machine should be sold? A company manufactures product X by operating two machines, each of which has a capacity of 5,000 units a year. Assume for simplicity that machines have infinite life and no salvage value. The cost of manufacturing one unit of the product is Rs 6. The demand is high between September to February, and machines work full capacity during this period. During March to July, the demand is low and machines work at 50% of capacity. The company is considering whether to replace these machines with available new designed machines. The new machines have the same capacity and therefore, two such machines would be needed to meet peak demand. Each new machine costs Rs 30,000 and lasts indefinitely. The cost of production would be Rs 3 per unit. Should the company buy new machines? The Wangers Ltd has kegged one of its special wines costing Rs 150,000. Its value is expected to increase over time in the following manner: At = Rs 200,000 ln t. The firm’s cost of capital is 13 per cent. Determine the optimum time of bottling for the wine. Assume continuous compounding. You have a tract of land on which trees can be grown. The initial cost of planting the trees is Rs 80,000. The net revenue realisable from the harvesting of trees would be as follows:

At = Rs 80,000(1 + t )0.5 The opportunity cost of capital is 10 per cent. What is optimum time for harvesting the trees? Assume continuous compounding. 10. A firm is considering the following two Projects, M and N:

Investment (Rs) Annual net cash inflow (Rs) Life (years) Cost of capital (per cent)

Project M

Project N

250,000 80,000 6 10

250,000 60,000 10 10

Because of capital rationing imposed by management, the firm can choose only one project. Which project should be selected? Why? 11. Consider the following investment projects: Cash Flows (Rs) Project

C0

C1

C3

L M

– 3,000 – 3,950

2,250 + 2,700

+ 2,700 + 3,240

(a) Calculate the NPV and PI for each project assuming a 20 per cent cost of capital. (b) Which project should be accepted if only one project can be accepted because of capital rationing. 12. A firm has a budget ceiling of Rs 100,000 for capital expenditures. The following proposal with associated profitability index and IRR have been identified: Proposals A B C D E F

Cash Outlay (Rs)

Profitability Index

Internal Rate of Return (%)

100,000 50,000 40,000 30,000 20,000 10,000

1.22 1.17 1.46 1.72 1.13 1.04

15 14 20 25 13 11

Which project(s) should be undertaken? Which method would you prefer in making your recommendation and why? 13. Zee Company is evaluating the following seven investment proposals. The company has a capital expenditure ceiling of Rs 150 million, and therefore, can accept just enough proposals. You are required to rank proposals according to profitability index and indicate the group of proposals to be accepted. Project

Cash Outlay NPV (Rs million) (Rs million)

O P Q S T U V

10 50 20 60 100 80 40

1.8 8.0 4.0 3.6 25.0 18.0 4.0

Chapter 12 PROBLEMS

1.

If following is the only available information, which project should be accepted? (i) Project A has ENCF Rs 10,000, σ

A

= Rs 500; Project B has

ENCF = Rs 10,000, σ

A

= Rs 1,000

(ii) Project A has ENCF = Rs 10,000

σ

A

= Rs 1,000; Project B has

ENCF = Rs 12,000, σ

B

= Rs 500

(iii) Project A has ENCF = Rs 500

σ

A

= Rs 500; Project B has

ENCF = Rs 12,000, σ

B

= Rs 1,000

(iv) Project A has ENCF = Rs 10,000,

σ

A

= Rs 500; Project B has

ENCF = Rs 12,000, σ 2.

B

= Rs 600

A firm is considering two investment projects, Project A requires a net cash outlay of Rs 6,000; B requires Rs 5,000. Both projects have an estimated life of 3 years. The net cash inflows have been estimated as: For Project A, year 1, a 0.40 chance of Rs 2,000 and a 0.60 chance of Rs 3,000; year 2, a 0.30 chance of Rs 4,000 and a 0.70 chance of Rs 2,000; year 3 a 0.50 chance of Rs 3,000 and a 0.50

3.

4.

5.

chance of Rs 2,200; For Project B, year 1, a 0.30 chance of Rs 1,000 and a 0.70 chance of Rs 2,000; year 2, a 0.20 chance of Rs 2,000 and a 0.80 chance of Rs 1,000; year 3, a 0.40 chance of Rs 2,000, and a 0.60 chance of Rs 4,000. Assume a 10 per cent discount rate. Which project should be accepted and why? The Walchand Company is considering two mutually exclusive projects. The expected cash flows and the associated certainty-equivalent coefficients for each project are as follows: Year

Project A Rs

Certainty Equivalent

Project B Rs

Certainty Equivalent

0 1 2 3 4 5

– 5,000 – 1,000 – 2,000 – 3,300 – 4,000 – 1,000

1.00 0.90 0.80 0.70 0.60 0.30

– 8,000 – 6,000 – 5,000 – 4,000 – 3,000 – 1,000

1.00 0.90 0.70 0.60 0.50 0.25

To account for the riskiness of the projects, the company uses the certainty-equivalent approach. Which of the two projects should be selected if the risk-free discount rate is 6 per cent? If the firm were to use risk-adjusted discount rates instead of certainty-equivalent approach, what rates would be used in order to obtain an equivalent solution? The Lalchand Co. is analysing two mutually exclusive proposals, each costing Rs 30,000 and having a five-year expected life. Each project will have expected cash flows which will increase by Rs 3,000 each year after the first year, and will not have any value after the fifth year. The first year possible net cash inflows for project 1 are Rs 10,000, Rs 14,000 and Rs 16,000 with associated probabilities of 0.25, 0.50 and 0.25, respectively. The first year possible net cash inflows for Project 2 are Rs 4,000, Rs 12,000 and Rs 25,000 with associated probabilities of 0.20, 0.50 and 0.30, respectively. Project 1 is considered less risky and can be evaluated at 8 per cent, while Project 2 is more risky and can be evaluated at 10 per cent rate of discount. Which project should be chosen? The Weston Co. is thinking of building a plant to manufacture a new product recently developed by its R&D department. Several alternatives are available to the firm regarding the size of the plant. The company can construct a large plant, which will cost Rs 500,000. Under different demand conditions the cash flows with associated probabilities are expected to be as follows: Large Plant Demand condition High Medium Low

Probability 0.50 0.40 0.10

Cash inflow (Rs) year 1–10 125,000 100,000 50,000

The alternative to building a large plant is to build a smaller plant for Rs 200,000 now, with an option to build an additional plant after two years, if the product achieves sufficient success. The small plant has a capacity to maintain Rs 80,000 in cash flows. Under high or medium demand the plant will be fully utilised.

The expected cash flows with associated probabilities are as follows: Small Plant Demand condition High Medium Low

Probability 0.50 0.40 0.10

Cash inflow (Rs) year 1–2 80,000 80,000 40,000

After two years, the company can review the situation to expand the smaller plant. If the company experiences a high initial demand for the first two years, a Rs 300,000 addition could be built, increasing yearly revenue potential by Rs 60,000.

The company estimates the net cash flows with associated probabilities under different demand conditions as follows: High Initial Demand: Additional Plant of Rs 300,000 Demand condition

Probability

High Medium Low

0.60 0.30 0.10

Cash inflow (Rs) year 3–10 140,000 110,000 80,000

If only medium demand was achieved in the first two years then a Rs 150,000 addition would be considered. The expected cash flows and probabilities are as follows: Medium Initial Demand: Additional Plant of Rs 150,000

6.

Demand condition

Probability

High Medium Low

0.60 0.30 0.10

Cash inflow (Rs) year 3–10 110,000 80,000 25,000

The company also considers the possibility of not building any addition regardless of the level of demand. Design a decision tree and solve for the most profitable alternative. Assume a 10 per cent discount rate and that the plants do not have any salvage value. A management group of a company has determined its relative utility values for cash flows as follows: Cash Flow Rs

Utilities

– 20,000 – 10,000 – 1,000 0 + 10,000 + 9,000 + 8,000 + 7,000

– 100 – 40 –3 0 +30 +25 +18 +10

Given this utility function, which of the following projects should be accepted? Why? Project A

Project B

Cash flow Rs

Prob.

– 20,000 –10,000 ––9,000 ––8,000 ––7,000

0.10 0.20 0.25 0.30 0.15

7.

Cash flow (Rs)

Prob.

–10,000 –7,000 –8,000 –9,000 —

0.15 0.25 0.40 0.20 —

A company is considering buying an equipment for a new process. The equipment will cost Rs 245,700. The company has made the following estimates of the after-tax cash flows over the equipments possible life of two years: Year 1

Year 2

NCF

Prob.

NCF

Prob.

153,500

0.5

125,000

0.5

122,800 184,300 240,500 307,000

0.7 0.3 0.4 0.6

The outcome of year 2 is dependent on the outcome of year 1. Use a decision tree approach to answer the following questions (assume 12 per cent discount rate): (a) What is the equipment’s expected net present value?

8.

(b) If the worst outcome occurs, then what would be the project’s net present value? (c) What net present value will be realised if the best outcome occurs? What is its probability? (d) What is the probability of the company realising a net present value less than zero? The R&D department of a company has developed a new product with an expected life of six years. The manufacturing of the product will require investment of Rs 3 lakh. The following annual profit from the investment is expected: Selling price Less: Unit variable cost Materials Labour Overheads

25 8 4 3

Contribution

15 10

Sales revenue (30,000 units) Less: Variable costs

750,000 450,000

Contribution Less: Fixed costs (including depreciation Rs 50,000) 120,000

300,000

Profit before tax Less: Tax at 50%

180,000 90,000

Profit after tax

90,000

Assume that the company can charge depreciation on straight-line basis for tax purpose. If the company has a discount rate of 10 per cent, calculate the investment’s NPV. Identify the factors which are most critical to the decision. To answer this question, calculate the volume, selling price, unit variable cost, and cash outlay, at which the investment’s NPV would be zero, other things remaining the same.

Chapter 13 PROBLEMS

1.

2.

3.

4.

ACC is considering building a cement manufacturing plant in Sri Lanka. The project will cost Rs 800 crore and the present value of the cash flows will be Rs 700 crore. The finance director is not in favour of the proposal since it has a negative NPV. The marketing director, on the other hand, thinks that the potential market for cement in Sri Lanka is enormous. He argues that the company should build the plant now to establish it competitive position and expand after 3 years. The cost of expansion will be Rs 2,000 crore and the present value of cash flows will be Rs 2,100. The demand for cement is expected to fluctuate. The standard deviation of the values of cash flows is estimated to be 32 per cent. The risk-free rate is 7.5 per cent. What is the value of the option to expand? L&T is thinking of entering into a joint venture to build a multi-purpose commercial complex in Dehradun, the capital of Uttaranchal with a local real estate developer. The development is expected to cost Rs 1,200 crore, and have a present value of cash flows of Rs 1,000 crore. The economic life of the project is 30 years. The joint venture will be on 50-50 per cent basis where two partners will share costs and benefits equally. L&T will have a right to sell the complex to the local developer any time over the next seven years for Rs 450 crore. L&T’s finance manager finds that the standard deviation in the value of real estate companies is 35 per cent. Assume that the risk-free rate is 7.8 per cent. What is the value of L&T’s right to abandon? What should L&T do? A company is analysing an investment project. It will cost Rs 185 crore, and will generate annual cash flows of Rs 24 crore for ever. The company’s cost of capital is 10 per cent. A simulation on the project’s cash flows shows that the value of the project will have a standard deviation of 25 per cent. Suppose that the company has rights to this project for 25 years. The current yield on 25-year government bond is 5 per cent. What is the project’s DCF value? What is the value of the project as an option? Why is there a difference between these two values? A firm is considering a project that is expected to cost Rs 50 crore. The project, on an average, will generate after-tax cash flows of Rs 7.50 crore per annum over its estimated economic life of 15 years. The firm’s cost of capital is 15 per cent, and the risk-free rate is 8 per cent. The firm thinks that the cash flows will fluctuate and variance of the value of the cash flows will be 0.0676. As an alternative to taking up the project now, it is thinking of delaying the project. What should the firm do?

Chapter 14 PROBLEMS

1.

2.

3.

A company has assets of Rs 1,000,000 financed wholly by equity share capital. There are 100,000 shares outstanding with a book value of Rs 10 per share. Last year’s profit before taxes was Rs 250,000. The tax rate is 35 per cent. The company is thinking of an expansion programme that will cost Rs 500,000. The financial manager considers the three financing plans: (i) selling 50,000 shares at Rs 10 per share, (ii) borrowing Rs 500,000 at an interest rate of 14 per cent, or (iii) selling Rs 500,000 of preference shares with a dividend rate of 14 per cent. The profit before interest and tax are estimated to be Rs 375,000 after expansion. You are required to calculate: (a) the after-tax rate of return on assets, (b) the earnings per share, and (c) the rate of return on shareholders’ equity for each of the three financing alternatives. Also, suggest which alternative should be accepted by the firm. A company is considering to raise Rs 200,000 to finance modernisation of its plant. The following three financing alternatives are feasible: (i) The company may issue 20,000 shares at Rs 10 per share, (ii) The company may issue 10,000 shares at Rs 10 per share and 1,000 debentures of Rs 100 denomination bearing a 14 per cent rate of interest. (iii) The company may issue 5,000 shares at Rs 10 per share and 1,500 debentures of Rs 100 denominations bearing a 14 per cent rate of interest. If the company’s profits before interest are (a) Rs 5,000, (b) Rs 12,000, (c) Rs 25,000, what are the respective earnings per share, rate of return on total capital and rates of return on total equity capital, for each of the three alternatives? Which alternative would you recommend and why? If the corporate tax rate is 35 per cent, what are your answers to the above questions? How do you explain the difference in your answers? The Apex Limited is a newly incorporated company and wants to plan an appropriate capital structure. It can issue 15 per cent debt and 11 per cent preference capital and has a 35 per cent tax rate. The firm’s initial requirement for funds is Rs 400 lakh and equity shares can be sold for a net price of Rs 25 per share. The possible capital structures are: Alternatives 1 2 3 4 5 6

4.

5.

6.

Equity 100% 75% 75% 50% 50% 30%

Preference — — 25% 20% — 20%

Debentures — 25% — 30% 50% 50%

(i) Construct an EBIT–EPS chart for the six alternatives over an EBIT range of Rs 10 lakh to Rs 80 lakh. (ii) Determine the indifference points for first and fourth alternatives and for fourth and sixth alternatives. (iii) Is the maximisation of EPS at a specific level of EBIT the only function of a firm’s capital structure? If not, are the points determined in (ii) truly ‘indifference’ points? Empire Ltd needs Rs 1,000,000 to build a new factory which will yield EBIT of Rs 150,000 per year. The company has to choose between two alternative financing plans: 75 per cent equity and 25 per cent debt or 50 per cent equity and 50 per cent debt. Under the first plan shares can be sold at Rs 50 per share, and the interest rate on debt will be 14 per cent. Under the second plan shares can be sold for Rs 40 per share and the interest rate on debt will be 16 per cent. Determine the EPS for each plan assuming a 35 per cent tax rate. Howard Company is considering three financing plans: all equity; 60 per cent equity and 40 per cent debt; and 40 per cent equity and 60 per cent debt. Total funds needed are Rs 300,000. EBIT is expected to be Rs 45,000. Shares can be sold at the rate of Rs 20 per cent share. Funds can be borrowed as follows: up to and including Rs 60,000 at 14 per cent; Rs 60,000 to Rs 150,000 at 16 per cent and over Rs 150,000 at 18 per cent. Compute the EPS of each plan. Assume a tax rate of 35 per cent. XYZ Ltd wishes to raise Rs 1,000,000 to finance the acquisition of new assets. It is considering three alternative ways of financing assets: (i) to issue only equity shares at Rs 20 per share, (ii) to borrow Rs 500,000 at 14 per cent rate of interest and issue equity shares at Rs 20 per share for the balance or (iii) to borrow Rs 750,000 at 14 per cent rate of interest and issue equity shares at Rs 20 per share for the

balance. The following are the estimates of the earnings from the assets with their probability distribution: EBIT (Rs) 80,000 120,000 160,000 200,000 320,000

7.

Probabilities 0.10 0.20 0.40 0.20 0.10

You are required to (i) calculate the earnings per share (ii) compute the indifference points, and (iii) determine the financial risk, for each of the three alternatives. Assume a tax rate of 35 per cent. For X Ltd the following data is available: EBIT Rs 200 Contribution Interest

8.

9.

400 100

If the company’s sales are expected to decline by 5 per cent, determine the percentage change in EPS. The expected earnings of firms A and B are Rs 120,000 with a standard deviation of Rs 30,000. Firm A is non-levered. Firm B is levered and has to pay annual interest charges of Rs 30,000. Which firm is more risky? Why? Rastogi Ltd is considering two plans (a) 15% debt or (b) issue of 100,000 shares of Rs 10 each to finance a proposed expansion at a cost of Rs 1,000,000. The company expects EBIT with associated probabilities as follows:

EBIT (Rs)

Probabilities

100,000 150,000 200,000 250,000 300,000 400,000

0.05 0.10 0.30 0.40 0.10 0.05

Determine the expected EBIT and coefficient of variation of EBIT. Also calculate expected EPS and its variability under two plans. Comment on your results. The company has 100,000 shares outstanding, and the corporate tax rate is 35 per cent. 10. A large chemical company is considering acquiring two small companies. The following is the financial data about two companies: (Rs in lakh) Company 1

Company 2

108.65 43.46 65.19 52.69

108.65 35.85 72.80 61.40

12.50 9.27

11.40 6.95

PBT Less: Tax (35%)

3.23 1.13

4.45 1.56

PAT

2.10

2.89

92.70 30.90 61.80

92.70 46.35 46.35

Sales Less: Variable cost Contribution Less: Fixed cost EBIT Less: Interest

Total assets Equity Debt

What would be the effect on companies’ profitability and risk if sales fluctuate by 10 per cent? If the chemical company intends to acquire a less risky firm, which one should it buy? Give reasons.

11. Indus Engineering Company has gross sales of Rs 137.5 crore and profit after tax of Rs 7.15 crore in the year 2008. The company is considering expanding its capacity by adding 30 per cent more to its existing fixed assets. Sales are likely to increase by Rs 55 crore. For the proposed expansion, PBIT to sales ratio is 18 per cent. The company has never borrowed in the past. The finance director has recommended that the company should raise 15 per cent interest bearing debt for financing the expansion. In his opinion, given 35 per cent corporate income tax rate, the effective cost of debt will be 9.75 per cent, and considering the current net worth (see balance sheet given below), debt-equity ratio will be only 0.22, which is quite low for an engineering firm. Indus is a highly capital intensive company; its fixed costs are 70 per cent of the total costs. It is notable that the performance of engineering industry is quite susceptible to economic changes. Should the company borrow? Give your analysis by making appropriate assumptions. Balance Sheet as on 31 December 2008 (Rs in crore) Share capital (4 crore shares at Rs 10) 40.0 Fixed assets Reserve 95.0 Current assets: Net worth 135.0 Debtors Current liabilities 35.5 Inventory Cash 20.5 170.5 170.5

100.0 20.0 30.0

12. Volga is a large manufacturing and marketing company in the private sector. In 2008, the company had a gross sales of Rs 980.2 crore. The other financial data for the company are given below:

Some Financial Data for Volga, 2008 Items Net worth Borrowing EBIT Interest Fixed costs (excluding interest)

Rs in crore 152.31 165.47 43.17 34.39 118.23

You are required to calculate (a) debt-equity ratio; (b) debt ratio; (c) interest coverage, (d) operating leverage, (e) financial leverage and (f) combined leverage. Interpret your results and comment on the Volga’s debt policy.

Chapter 15 PROBLEMS 1. X Co. has a net operating income of Rs 200,000 on an investment of Rs 1,000,000 in assets. It can raise debt at a 16 per cent rate of interest. Assume that taxes do not exist. (a) Using the NI approach and an equity-capitalisation rate of 18 per cent, compute the total value of the firm and the weighted average cost of capital if the firm has (i) no debt, (ii) Rs 300,000 debt, (iii) Rs 600,000 debt. (b) Using the NOI approach and an overall capitalisation rate of 12 per cent, compute the total value of the firm, value of shares and the cost of equity if the firm has (i) no debt, (ii) Rs 300,000 debt, (iii) Rs 600,000 debt. 2. Firm L and Firm U are in the same risk class and are identical in every respect except that Firm L is levered and Firm U is unlevered. Firm L has 12 per cent Rs 400,000 debentures outstanding. Both firms earn 18 per cent before interest and taxes on their total assets of Rs 800,000. Assume a corporate tax rate of 50 per cent and a pure equity capitalisation rate of 15 per cent. (a) Compute the total value of the firms using (i) the NI approach, (ii) the NOI approach. (b) Using the NOI approach, calculate the after-tax weighted average cost of capital for both the firms. Which of the two firms has an optimum capital structure and why? (c) According to the NOI approach, the values for Firms A and B computed in part (a) using the NI approach are not in equilibrium. Under such a situation, an investor can secure same return at

3.

lower cash outlay through the arbitrage process. Assume that an investor owns 5 per cent of L’s shares, show the arbitrage process. When would this arbitrage process stop? The values for two firms X — an unlevered firm and Y—a levered firm with Rs 600,000 debt at 6 per cent rate of interest are given as below. An investor holds Rs 20,000 worth of Y’s shares. Show the process by which he can earn same return at a lesser cost. X Rs Net operating income, Cost of debt, INT = kd D

200,000 —

200,000 36,000

Net income, NI

200,000

164,000

X Rs Equity-capitalisation rate, ke Market value of equity, E Market value of debt, D Total value of firm, V = E + D Overall capitalisation rate, ko

4.

Y Rs

0.111

Y Rs 0.125

1,800,000 1,312,000 — 600,000 1,800,000 1,912,000 0.1111 0.1046

Two firms A and B are identical in all respect except that B has Rs 500,000 debt outstanding at a 6 per cent rate of interest. The values of the two

Net operating income

A Rs

B Rs

150,000

150,000

Cost of debt, kd

—

30,000

Net income NI

150,000

120,000

0.10

0.15

1,500,000

800,000

—

500,000

1,500,000

1,300,000

0.10

0.1154

Equity-capitalisation rate, ke Market value of equity, E Market value of debt, D Total value of firm, V = E + D Overall capitalisation rate, ke

Assume that an investor owns 10 per cent of A’s shares. How can the investor obtain same return at a lower cost? 5. Sppose X = Rs 50,000, kd = 0.06, Eu = Vu = Rs 500,000, El = Rs 280,000. Dl = Rs 250,000 and Vl = Dl + El = Rs 530,000. Calculate the cost of equity and the weighted average cost of capital for two firms. If an investor owns 5 per cent of the levered firm’s shares, how can he be benefited by resorting to the arbitrage process? 6. A new company proposes to invest Rs 10 lakh in assets and will maintain its capital structure at book value. It is expected to earn a net operating income of Rs 160,000. The company wants to have an optimum mix of debt and equity. The cost of debt and the equity-capitalisation rate at different debtequity ratio are as follows: (a) What is the optimum capital structure for this company? (b) If the M-M hypothesis is valid, what should be the equity-capitalisation rate at different debt-equity ratios? Debt-Equity Ratio

Cost of Debt

Equity-capitalisation Rate

— 10: 90 20: 80 30: 70 40: 60 50: 50 60: 40

— 0.05 0.05 0.06 0.07 0.08 0.10

0.125 0.130 0.136 0.143 0.160 0.180 0.200

7.

The values for the two firms X and Y in accordance with the traditional theory are given below: X Rs

Y Rs

Expected net operating income, Total cost of debt, kd D = INT

50,000 0

50,000 10,000

Net income, – INT

50,000

40,000

0.10

0.11

500,000 0 500,000 0.10

360,000 200,000 560,000 0.09

0

0.556

Cost of equity, ke Market value of shares, E Market value of debt, D Total value of firm, V = E + D Average cost of capital, ko = X/V Debt–equity ratio

8.

Compute the values for firms X and Y as per the M-M thesis. Assume that (i) corporate income taxes do not exist and (ii) the equilibrium value of ko is 12.5 per cent. The following are the equilibrium value for two firms M and N as per the Modigliani-Miller approach: M Rs

N Rs

Net operating income , Total cost of debt, INT = kd D

12,000 0

12,000 2,000

Net income, – INT Overall capitalisation rate, ko

12,000 0.08

10,000 0.08

M Rs

N Rs

Total value of firm, V = X/ko

1,50,000

1,50,000

Market value of debt, D Market value of shares, E = V – D Cost of debt, kd = INT/D

0 1,50,000 0

40,000 1,10,000 0.05

0.08

0.091

Cost of equity, ke = ( – INT)/E

Recompute the values for firms M and N in accordance with the traditional theory. Assume that the cost of equity of firm M is 10 per cent and for firm N it is 10.5 per cent. 9.

Firm L and U have same expected earnings before interest and taxes of Rs 25,000. Firm U has employed 100 per cent equity of Rs 100,000 while firm L has employed Rs 50,000 equity and Rs 50,000 debt at an expected rate of return (cost of debt) of 15 per cent. You are required to calculate for each firm: (a) earnings of all investors and (b) value of interest tax shield under the following alternatives: (i) no corporate and personal taxes; (ii) 50 per cent corporate taxes and zero personal taxes; (iii) 50 per cent corporate taxes and 30 per cent personal taxes; and (iv) 50 per cent corporate taxes, 20 per cent personal taxes on dividend income and 40 per cent personal taxes on interest income. 10. A company has set its target debt-equity ratio at 1:1 and target payout ratio at 40 per cent. The company wants to achieve a growth rate of 20 per cent per annum. The company is expecting before tax return on assets of 21 per cent. Its sales-to-assets ratio is 1.8 times. The current interest rate is 12 per cent. The corporate tax rate for the company is 35 per cent. Can the company sustain its intended growth? What should it do to achieve the growth rate? 11. Hindustan Lever Limited (HLL): From the following financial data for years from 1992 to 2002 (year ending 31 December) for HLL in Table 15.14, critically review the company’s financing practice. 12. Philips India Limited: Table 15.15 gives data for Philips India Limited for the years from 1990 to 2002. The Company changed its accounting period from March to December in 1993, thus, data for the year 1993 are for 9 months. Comment on the company’s investment and financing policy. Table 15.14: Hindustan Lever Limited (Rs in crore) Year

GFA

NCA

INVST

NW

Debt

NS

PBIT

INT

PAT

1992 330.5 1993 365.6

323.1 285.8

12.3 51.0

333.3 385.7

200.3 115.2

1221.1 1505.0

197.0 244.9

32.2 27.2

60.0 79.8

1994 1995 1996 1997 1998 1999 2000 2001

491.8 563.8 953.6 1035.2 1273.4 1349.7 1539.4 1778.3

299.7 193.0 168.9 567.2 895.3 1151.8 1087.1 1349.7

191.5 122.8 328.8 544.6 729.5 1068.1 1832.2 1668.9

538.3 638.3 937.5 1260.8 1712.4 2102.6 2487.6 3043.0

146.5 160.2 260.1 186.6 264.3 177.3 111.6 83.7

1721.3 2039.4 2798.8 3337.8 6560.7 7736.8 9426.1 10116.5

327.4 385.2 654.2 874.2 1130.5 1420.1 1668.4 1865.6

29.5 97.3 20.2 122.1 57.0 185.2 33.9 232.0 29.3 404.7 22.4 570.3 13.2 808.2 7.7 1079.8

2002 1836.9

1639.0

2397.7

3658.2

58.3

10588.2

2154.4

9.2 1300.3

Table 15.14: Philips India Limited (Rs in crore) Year GFA

NCA

1990 154.7

82.1

1991 162.1

INVST

NW

TD

STBB

LTB

DEBN

NS

PAT

2.1

41.3

116.5

12.1

104.4

56.7

391.2

–8.2

97.1

7.6

63.6

101.8

16.0

85.8

48.3

523.1

26.7

1992 181.8

122.9

12.2

76.5

114.6

31.1

83.6

41.2

689.5

21.5

1993 232.1

112.8

13.8

129.3

69.3

6.4

52.9

22.8

672.0

9.0

1994 253.1

141.3

13.2

175.9

62.5

12.8

39.6

3.2

1092.7

33.7

1995 319.2

223.4

14.7

187.4

169.7

91.3

63.4

3.0

1454.4

22.1

1996 376.1

194.3

19.6

190.9

186.9

71.5

100.3

32.7

1438.8

11.8

1997 386.0

175.8

16.7

171.7

168.3

47.6

80.7

32.7

1509.4

44.6

1998 414.8

217.8

15.5

176.2

195.7

44.8

110.9

72.2

1620.1

39.2

1999 330.4

213.1

14.0

191.6

159.9

35.4

104.5

50.0

1662.9

41.4

2000 363.3

134.1

14.0

167.8

127.3

25.8

86.5

53.8

1444.4

–3.1

2001 334.7

40.0

17.3

147.3

66.1

45.9

20.2

0.0

1459.5

40.4

2002 605.4

67.6

1.9

306.4

48.0

5.5

42.5

8.3

1492.8

85.5

GFA = gross fixed assets; NCA = net current assets; INVST = investment; NW = net worth; TD = total debt borrowings; STBB = short-term bank borrowings; LTB = long-term borrowings including debentures; DEBN = debentures; NS = net sales; PAT = profit after tax.

Chapter 16 Problems

1.

2.

A company’s equity beta is 1.84 and it has a debt ratio of 50 percent. The risk free rate is 9 per cent and the average market premium is 8.5 per cent. The company is considering a project that has zero debt capacity and the expected rate of return of the project is 18 per cent. The business risk of the project is similar to the firm. Should the company accept the project? A power equipment company has 85 per cent debt-to-assets ratio and an equity beta of 1.25. The riskfree rate is 6.5 per cent and the expected market rate of return is 12.5 per cent. The corporate taxes are 35 per cent. What is the opportunity cost of capital of the company? How much is the required return on the equity?

3. 4.

5.

A software company has no debt. Its unlevered beta is 1.0. Assume that the corporate tax rate is 30 per cent. If the company wants its beta to increase to 2.50, how much leverage should it take? A firm’s debt ratio is 60 percent. The risk-free rate is 8 per cent and the expected market return is 14 per cent. The asset beta of the company is 1.10. Calculate the firm’s cost of equity. How much is the business risk premium and the financial risk premium for the firm’s equity? Suppose the risk-free rate is 8 per cent, the market risk premium is 9 per cent and the tax rate is 30 per cent. A firm has the following market values and beta based on the market data and the company’s own analysis for various sources of financing: Source of Capital

Market value (Rs in crore)

Ordinary share capital Debentures Public deposits

6.

7.

8.

9.

10.

11.

12.

1.

500 400 100

Beta 1.45 0.30 0.15

You are required to calculate (i) the required rate of return for each source of finance; (ii) the weighted average cost of capital; (iii) the asset beta; and (iv) the opportunity cost of capital on the firm’s assets. An engineering company has a debt-to-market value ratio of 40 per cent. The company can raise new debt at 12 per cent. The corporate tax rate for the company is 35 per cent. The company has estimated the required return on equity as 22 per cent. What is the company’s weighted average cost of capital? The company is thinking of raising its debt-to-market value ratio to 60 per cent. What will be the company’s new weighted cost of capital? A project will require an investment of Rs 100,000 and generate post-tax free cash flows of Rs 15,000 in perpetuity. The project’s all-equity cost of capital is 15 percent. The project will support a perpetual 10 percent debt of Rs 50,000. (i) Calculate project’s NPV. (ii) Suppose the tax rate is 35 percent. Calculate the project’s APV. (iii) Calculate the project’s minimum required rate of return? A firm’s all-equity cost of capital is 15 percent. The cost of debt is 10 percent and debt ratio is 35 percent. The corporate tax rate is 35 percent. Calculate MM’s tax-adjusted levered cost of capital. What will be the adjusted levered cost of capital under the Miles-Ezzell formula? Why the adjusted cost of capital under the MM and the Miles-Ezzell formulae differ? A firm’s cost of equity is 20 percent. The cost of debt is 10 percent and debt ratio is 40 percent. The corporate tax rate is 35 percent. Calculate MM’s tax-adjusted levered cost of capital. What will be the adjusted levered cost of capital under the Miles-Ezzell formula? Torrent Automotive Company’s debt capacity is 50 per cent of the market value of its assets. The company’s equity beta is 1.40. The risk-free rate is 9 per cent and the average market premium is 12 per cent. The corporate tax rate is 30 per cent. The company is considering an investment project in the existing line of business requiring an investment of Rs 100 crore. The project is expected to generate the after-tax free cash flows of Rs 15 crore in perpetuity. What is the project’s NPV if it has the zero debt capacity? Suppose that the company can borrow 30 per cent of the cost of the project for an indefinite period, how will you evaluate the project? Show calculations. Delhi Transport Company is intending to expand its fleet of trucks. It is considering buying 30 Tata trucks for Rs 600 lakh. The company expects the fleet to have a useful life of six years and generate earnings before interest, taxes and depreciation of Rs 120 lakh per year. Delhi Transport Company is a zero-debt company. Assume that the corporate tax rate is 34 percent and straight-line depreciation is allowed for tax purposes. The company’s all-equity opportunity cost of capital is 20 percent. (a) What is the NPV of the new fleet of trucks? (b) Suppose that Delhi Transport Company will raise 5-year debt of Rs 300 lakh at 10 percent rate of interest per year. The principal will be paid entirely at the end of the sixth year. What is the project’ APV? ABC Ltd is an all-equity financed company. The firm is thinking of investing in a project that will involve an initial outlay of Rs 20 crore. It is expected that the project will generate free cash flows (net of taxes) of Rs 3 crore each year over a period of five years. The project has business risk similar to the firm. The firm’s unlevered cost of capital is 16 percent. ABC Ltd is contemplating to borrow a fiveyear 10 percent loan of Rs 20 crore from a financial institution to finance the project. The principal is repayable in four equal instalments starting from the end of year two. The firm will have to incur flotation cost of Rs 20 lakh to raise debt from the financial institution. The corporate tax rate is 34 percent. Calculate the project’s APV. Indo Software Company has cost of equity of 20 per cent, cost of debt of 10 per cent and debt-to-total assets ratio of 20 per cent. The company is considering an expansion project. The project will need a

cash outlay of Rs 80 crore. It is expected to generate annual EBDIT of Rs 20 crore for 8 years. The project will require Rs 1 crore each year for net working capital and capital expenditure. IndoSoftware will be able to borrow 40 per cent of the project’s cost from a financial institution. The interest rate is 10 per cent p.a., and the loan amount will be repaid in equal annual instalments over eight years. The corporate tax rate is 34 per cent. Assume straight-line depreciation for computing taxes and zero terminal value of the project. Should the company accept the project?

2. Delite Manufacturing Company is expanding its business in the rural area of Andhra Pradesh. The expansion will cost the company Rs 24 crore. It is expected that expansion benefits will last for 12 years and it will increase revenue by Rs 10 crore growing at 10 percent each year for three years, then at 5 percent each year for next four years followed by no growth period of the last four years. The cost of goods sold is expected to be 60 percent and other expenses 15 percent of revenue. Depreciation will be charged on straight-line basis. Working capital is estimated to be 25 percent of the revenue to be incurred at the end of the previous period. The corporate tax rate is 34 percent. The firm has debt-equity ratio of 1:1 and its levered beta and the cost of equity are 1.20 and 22 percent, respectively. The risk-free rate of return is 10 percent. The project has 1.5 times of the firm’s business risk. The market cost of debt is 10 percent per annum. The firm will be able to raise subsidised loan of Rs 12 crore from the government of India’s rural development funds at 8 percent annual interest. The loan will be paid at the end of year 12. Find out project’s APV. What is the value of the subsidised loan? 12. Dhatu Industries Limited is a manufacturer of iron and steel. It has an equity beta of 1.10. The target debt-equity ratio of the company is 2:1. The company is intending to diversify into different lines of businesses. It is considering a cement project requiring an investment of Rs 105 crore. The company will be able to raise Rs 70 crore loan from a financial institution at 10 per cent p.a. The loan is repayable at the end of 5 years. The project is expected to generate annual profit before interest and taxes of Rs 22 crore for 7 years. Assume that the project’s cost can be depreciated over its life of 7 years on the straight-line basis. The company has identified one public limited cement company as a proxy for the project. This company has an equity beta of 1.3 and debt-equity ratio of 1.5:1. The riskfree rate is 7 per cent and the market risk premium is 8 per cent. The corporate tax rate is 30 per cent. Should Dhatu undertake the cement project? 13. Suppose that Dhatu Industries Limited in (9) above decides to locate the cement project in an economically backward area. As a consequence, it is able to negotiate the loan amount from the financial institution at 8 per cent instead of the market rate of interest of 10 per cent. Evaluate the viability of the project showing the sources of value for the project. 14. Suppose that Dhatu Industries Limited in (9) above does not have to pay any taxes on the income of the cement project since it is located in the backward area. How does this affect the profitability of the project? 15. A firm has debt capacity equal to debt-equity ratio of 1:1. The firm’s interest payments are Rs 5 lakh per year. The risk-free rate is 8 percent and the market risk premium is 9 percent. The unlevered beta of the firm is 1.20 and beta of debt is zero. The firm’s annual revenues are estimated as Rs 100 lakh each year; the cost of goods sold will be Rs 45 lakh and general and administrative expenses will be Rs 20 lakh. All revenues and expenses are on cash basis and are expected to remain same forever. The corporate tax rate is 34 percent. What is the value of the firm’s equity? What is the total value of the firm? 16. PQR Ltd is an all-equity firm. It has unlevered cost of equity of 20 percent, corporate tax rate of 30 percent, and annual cash flows of Rs 40 crore in perpetuity. The firm is thinking of restructuring its capital. It wants to replace its equity by issuing perpetual debt of Rs 25 crore at 12 percent annual interest rate. Calculate (i) PQR’s total value and equity value before restructuring; (ii) PQR’s total value and equity value after restructuring. 17. Brite Ltd is considering a project unrelated to its existing business. The firm collected the following information of similar firms in the industry to determine the risk of the project: Average debt-equity: 0.8:1; average equity beta: 1.6 and average cost of debt: 12 percent. The project’s target debt-equity is 0.5:1. The risk-free rate is 6 percent and the market risk premium is 9 percent. Brite’s corporate tax rate is 35 percent. The initial outlay on project is estimated as Rs 50 crore. (i) The expected post-tax

free cash flows at the end of the first year are Rs 5 crore which will remain constant thereafter for indefinite period. Should the investment be made? (ii) Suppose that the expected post-tax free cash flows of Rs 5 crore at the end of the first year will grow at 8 percent per year until the end of sixth year and will remain constant thereafter for indefinite period. What is the value of investment? (iii) Suppose that the expected post-tax free cash flows of Rs 5 crore at the end of the first year will grow at 6 percent per year until the end of sixth year and at 2 percent thereafter for indefinite period. What is the value of investment? 18. The following information relate to NM Company: target debt-equity ratio 0.75:1; the unlevered cost of capital 18 percent; the annual interest rate 10 percent; corporate tax rate 35 percent; expected pre-tax cash flows for indefinite period Rs 10.80 crore. (i) What is the value of NM Company if it is entirely financed by equity? (ii) If the firm is levered, what is its cost of equity? (iii) Calculate the levered firm’s weighted average cost of capital. What is the value of the firm under the FCF approach? (iv) Calculate the value of the firm’s equity using flow-to-equity approach and APV approach. 19. The market value of equity of XYZ Ltd is Rs 140 crore. It has 10 crore outstanding shares. The market value of the firm’s debt is Rs 70 crore. The firm intends to maintain the current market value debt ratio forever. The expected interest rate is 12 percent. The firm’s equity beta is 1.20 and the corporate tax rate is 30 percent. The risk free rate is 6 percent and the risk premium is 8.5 percent. The firm’s expected post-tax free cash flows next year are Rs 25 crore. The free cash flows are expected to grow at 10 percent for eight years and thereafter, at 5 percent for ever. How much is the value of the firm? What is the value of equity? How much is the value per share? 20. The market value of equity of a firm is Rs 200 crore. It has one crore outstanding shares. The firm intends to maintain the market value debt ratio of 40 percent forever. The expected interest rate is 10 percent. The firm’s equity beta is 1.50 and the corporate tax rate is 30 percent. The risk free rate is 6 percent and the risk premium is 8.5 percent. The firm’s expected post-tax free cash flows next year are Rs 40 crore. The free cash flows are expected to grow at 12 percent for five years, at 8 percent for next five years and thereafter, at 5 percent forever. How much is the value of the firm? What is the value of equity? How much is the value per share?

Chapter 17 Problems 1. A company earns Rs 10 per share at an internal rate of 15 per cent. The firm has a policy of paying 40 per cent of earnings as dividends. If the required rate of return is 10 per cent, determine the price of the share under (i) Walter’s model, (ii) Gordon’s model. 2. Saraswati Glass Works has an investment of Rs 30 crore divided into 30 lakh ordinary shares. The profitability rate of the firm is 20 per cent and the capitalisation rate is 12.5 per cent. What is the optimum dividend payout for the firm if Walter’s model is used? What shall be the price of the share at optimum payout? Shall your answer change if the profitability rate is assumed to be 15 per cent? What would happen if profitability rate is 10 per cent? Show computations. 3. The following data relate to a firm: earnings per share Rs 10, capitalisation rate 10 per cent, retention ratio 40 per cent. Determine the price per share under Walter’s and Gordon’s models if the internal rate of return is 15 per cent, 10 per cent and 5 per cent. 4. Manex Company has outstanding 50 lakh shares selling at Rs 120 per share. The company is thinking of paying a dividend of Rs 10 per share at the end of current year. The capitalisation rate for the risk class of this firm is 10 per cent. Using Modigliani and Miller’s model you are required: (i) to calculate the price of the share at the end of the current year if dividends are paid and if they are not paid; ( ii) to determine the number of shares to be issued if the company earns Rs 9 crore, pays dividends and makes new investments of Rs 6.60 crore? 5. A company has outstanding 10 lakh shares. The company needs Rs 5 crore to finance its investments, for which Rs 1 crore is available out of profits. The market price of per share at the end of current year is expected to be Rs 120. If the discount rate is 10 per cent, determine the present value of a share using the MM model. 6. The current market price of a company’s shares is Rs 125 per share. The expected earnings per share and dividend per share are Rs 10 and Rs 5 respectively. The shareholders’ expected rate of return is 15 per cent. Suppose the company declares that it will switch to 100 per cent payout policy, issuing shares as necessary to finance growth. Use the perpetual-growth model to show that current price of share is unchanged. 7. The following data relate to a firm in the cotton textile industry:

Rs in crore Share capital (at Rs 10 per share) Reserve Profit after tax Dividends paid P/E ratio

12.50 7.50 1.85 1.50 13.33

You are required (a) to comment on the firm’s dividend policy using Walter’s model; (b) to determine the optimum payout ratio using Walter’s model; (c) to determine the price – earnings ratio at which dividend payout will have no effect on share price. 8. Turant Pharma is thinking of diversifying its business in the field of energy. The firm has decided to make a capital expenditure of Rs 35 crore in an energy project. The project is expected to yield a positive net present value of Rs 25 crore. The firm is also considering a payment of dividends of Rs 20 crore. The internal funds available with the firm are Rs 10 crore. It has a paid-up share capital of Rs 50 crore divided into 5 crore shares of Rs 10 each. The current price of the firm’s share is Rs 25. The firm has not borrowed funds in the past, and would continue with this policy in the future. Given the firm’s capital expenditure and the policy of zero borrowing, show the implications of the payment of dividends for the shareholder value. Will your answer be different if Turant decides not to pay any dividends? Assume no taxes and no issue costs. 9. The share of X Company is selling for Rs 100. It is a no-tax paying company. The price of X’s share is expected to be Rs 115 after one year. Company Y is identical to company X in terms of risk and the future earnings potential. It is a dividend paying company, and is expected to pay a dividend of Rs 10 per share after one year. Assume dividend income is taxed at 35 per cent and there is no tax on capital gains. What should be the current price of B’s share and how much should be its before-tax expected return? 10. The shares of Firm A and Firm B have identical risk. Both have an after-tax required rate of return of 15 per cent. Firm A pays no dividend, while Firm B is a high dividend paying firm. The price of Firm A’s share is expected to be Rs 60 after one year and the price of Firm B Rs 50 with Rs 10 dividend per share. Assume that the income tax rate is 40 per cent and capital gain tax rate is 20 per cent. Determine the current prices of Firm A’s and Firm B’s shares. 11. The expected before-tax incomes (consisting of dividend and capital gains) on shares of firms X, Y and Z are given below: Share

Dividend income (Rs)

Capital gain (Rs)

X Y Z

0 5 10

10 5 0

Suppose that the current price of each share is Rs 60. Further, an investor is in 50 per cent tax bracket and capital gain tax rate is 20 per cent. Which share will give highest after-tax return to the investor? Now suppose that the each share was expected to have expected after-tax yield of 12 per cent for the investor. Determine the price of each share.

Chapter 18 PROBLEMS 1. B. Das Co. has been a fast-growing firm and has been earning very high return on its investment in the past. Because of the availability of highly profitable investment internally, the company has been following a policy of retaining 70 per cent of earnings and paying 30 per cent of earnings as dividends. The company has now grown matured and does not have enough profitable internal opportunities to reinvest its earnings. But it does not want to deviate from its past dividend policy on the ground that investors have been accustomed to it and any change may not be welcome by them. The company, thus, invests retained earnings in the short-term government securities. Is the company justified in following the current dividend policy? Give reasons to support your answer. 2. D. Damodar Co. is a fast-growing firm in the engineering industry. In the past, the firm has earned a return of 25 per cent on its investments and this trend is likely to continue. The firm has been retaining 25 per cent of its earnings and paying 75 per cent of earnings as dividends. This policy has been justified on the grounds that dividends are generally preferred over retained earnings by shareholders.

3.

Is the current dividend policy justified if most of the shareholders are wealthy persons in high tax brackets? Will your answer change if most of the shareholders of the company were (a) retired persons with no other source of income and (b) the financial institutions? The following data relate to the Brown Limited and the Crown Limited which belong to the same industry and sell the same product: Brown Ltd Market Price Year Rs

EPS Rs

DPS Rs

High

2005 2006 2007 2008 2009

3.60 3.90 3.70 3.20 3.80

2.00 2.00 2.00 2.00 2.00

48 53 51 59 60

Low Book value Rs Rs* 52 34 30 31 35

37.20 38.80 40.60 42.30 43.20

*The face value per share is Rs 10. Crown Ltd Market Price

4.

Year Rs

EPS Rs

DPS Rs

High

2005 2006 2007 2008 2009

3.50 3.00 2.50 6.00 5.00

1.75 1.50 1.25 3.00 2.50

38 42 42 50 48

Low Book value Rs Rs* 34 32 28 30 27

30.50 32.50 33.75 36.50 38.50

*The face value per share is Rs 10. Calculate payout ratio, dividend yield, earnings yield and price–earning ratio. Which company is more profitable? Explain the reason for the difference in the market prices of the two companies’ shares. A multinational pharmaceutical company in India has following information about its EPS and dividends payment from 1987 to 2004. You are required to answer the following questions: (a) What minimum annual percentage dividend increase the company intends to give to its shareholders? (b) Is there any relationship between the earnings increase and the rise in dividends? (c) Do you think that the company has a long-term target payout ratio? (d) The company’s payout in 2003 was 150 per cent. How will you explain this? (e) What clientele does the company have? EPS Change in DPS Change in Payout Year Rs EPS (%) Rs DPS (%) (%) 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

13.9 15.9 16.4 18.4 19.8 23.6 24.7 25.9 27.8 30.7 30.1 31.2 33.9 34.9 81.8 44.9

–7.2 14.2 3.1 12.8 7.4 19.3 4.7 4.5 7.6 10.2 –2.0 3.7 8.7 2.9 134.5 –45.1

5.3 5.9 6.5 7.4 8.3 9.4 10.5 11.5 13.0 14.2 15.1 15.9 17.2 19.1 21.6 23.5

11.7 11.7 10.5 14.3 11.7 13.4 11.8 9.4 12.9 9.5 6.1 5.7 7.7 11.5 12.9 8.6

37.9 37.0 39.7 40.2 41.8 39.7 42.4 44.4 46.6 46.3 50.1 51.1 50.7 54.9 26.4 52.3

2008 2009 5.

53.6 36.5

19.5 –32.0

80.5 28.2

243.1 –65.0

150.1 77.2

Ashoka Ltd has a capital structure shown below: Rs (crore) Equity share capital (Rs 10 par, 5 crore shares) 50 Preference share capital (Rs 100 par, 50 lakh shares) Share premium 50 Reserves and surpluses 80 Net worth 230

6.

Show the changed capital structure if the company declares a bonus issue of shares in the ratio of 1:5 to ordinary shareholders when the issue price per share is Rs 100. How would the capital structure be affected if the company had split its stock five-for-one instead of declaring bonus issue? Polychem Co.’s current capital structure as on 31 March, 2009 is as follows: Rs (crore) Share capital (Rs 100 par, 2 crore shares) Share premium Reserves and surpluses

7.

50

200 100 190 490

The current market price of the company’s shares is Rs 140 per share. The earnings per share for the year 2008 was Rs 17. The company has been paying a constant dividend of Rs 6.50 per share for the last ten years. What shall be the effect on earnings per share, dividend, share price and the capital structure if the company (i) splits its shares two-for-one or (ii) declares a bonus issue of one-for-twenty? Surendra Auto Limited is considering a bonus shares issue. The following data are available: Rs (crore) Paid up share capital Reserves Previous three years’ pre-tax profit

Year 1 Year 2 Year 3

12 16 8.0 8.6 8.3

Recommend the maximum bonus ratio. Give reasons.

Chapter 19 Only review Questions

Chapter 20 PROBLEMS 1. A firm is thinking of a rights issue to raise Rs 5 crore. It has a 5 lakh shares outstanding and the current market price of the share is Rs 170. The subscription price on the new share will be Rs 125 per share. (i) How many shares should be sold to raise the required funds? (ii) How many rights are needed to purchase one new share? (iii) What is the value of one right? 2. A company is considering a rights offering to raise funds to finance new projects, which require Rs 4.5 crore. The flotation cost will be 10 per cent of funds raised. The company currently has 20 lakh shares outstanding and the current market price of its share is Rs 100. The subscription price has been fixed at Rs 50 per share. (i) How many shares should be sold to raise the funds required for financing the new projects? (ii) How many rights are required to buy one new share? (iii) What is the value of one right? (iv) Show the impact on a shareholder’s wealth who holds required rights to buy one new share if (a) he exercises rights, or (b) sells his rights, or (c) does not exercise rights. 3. G Company, started in 1922, is a diversified company. Having commenced operation as trading and servicing of engineering equipments, it diversified into manufacturing and marketing. The company’s

proposed capital expenditures include (a) expansion of the capacity of diesel engine from 22,500 units to 32,500 units in 2009-10, 40,000 units in 2010-11 and 55,000 units in 2011-2012at a cost of Rs 37.9 crore, (b) manufacture of 3-wheeler diesel unit, a forward integration project, at a cost of Rs 18.8 crore, with installed capacity of 8,000 units in 2009-10, 10,000 units in 2010-11 and 20,000 units in 2011-12, (c) manufacture of vibratory compactors at a cost of Rs 2.06 crore, (d) R&D capital expenditure of Rs 3.62 crore for developing a portable diesel low noise, smaller HP engines, (e) investment of Rs 49.4 crore in the equity of three companies, (f) investment of Rs 73.0 crore in a subsidiary for the manufacture of engineering plastics and (g) normal capital expenditure of Rs 35 crore for the enhancement of long-term resources. Of the first project only cost equal to Rs 30.1 crore will be met of the present issue. The company has proposed to issue 144 lakh equity shares of Rs 10 each at a premium of Rs 70 each totalling to Rs 115.21 crore in the ratio of 1 : 1 on rights basis. The Rs 10 paid-up share of the company has a market price of Rs 102.50 and a net asset value (NAV) of Rs 44.80. The company has made the following projections: 1009-10

2010-11

2011-12

Revenues (Rs crore)

360.00

420.00

563.00

Net profit (Rs crore)

17.10

18.10

25.30

EPS (Rs)

11.78

7.38

9.00

NAV (Rs)

62.96

71.87

78.86

The following are a few indicators of the company’s performance during last two years: 2007-08

2008-09

Revenues (Rs crore)

250.0

285.0

Pre-tax profits (Rs)

10.7

12.0

Equity dividend (%)

20.0

23.0

Borrowing (Rs crore)

57.0

74.0

Interest (Rs crore)

7.0

12.0

EPS (Rs)

–

7.2

Source: The Economic Times. Critically evaluate G Company’s rights issue.

1.

Source: The Economic Times, 4 January 1993.

Chapter 21 PROBLEMS 1. In January 2004, a company announced two types of convertible debentures. First, it issued 50 lakh 10 per cent fully convertible debentures of Rs 1000 each at par. Each convertible debenture was fully convertible into 5 shares of Rs 200 (i.e., Rs 100 par plus a premium of Rs 100) after two years from the date of allotment of debentures. The company also announced a public issue of 50 lakh 10 per cent partly convertible debentures of Rs 2000 each. Like the first issue, Rs 1000 of the debenture’s face value was convertible into 5 shares. The non-convertible portion of the debenture was to be redeemed at the end of 10 years from the date of allotment. At the time of these issues, the company’s share was selling for Rs 120. Analyze both types of debentures by making appropriate assumptions. 2. Kamani Limited has total assets Rs 1000 crore. Its equity, divided in 25 crore outstanding shares, has market value of Rs 800 crore. Currently the company has debt of Rs 400 crore. The company has just made an issue of debentures (Rs 100 each) of the total amount of Rs 400 crore plus one warrant of Re 10 for each debenture. A warrant will entitle the debenture holders to apply for one equity share at an exercise price of Rs 15 at the end of two years. The annual standard deviation of the share price variability before the debenture issue is: σ = 4.5. Assume that the interest rate is 10 per cent. What is the value of a warrant?

Chapter 22 PROBLEMS 1. A company wants to lease a Rs 10 lakh equipment. The lessor requires eight annual end-of-the-year lease payments of Rs 175,000. The company’s marginal tax rate is 35 per cent. If it buys the equipment, it can write-off the written-down cost of asset at 25 per cent. The company’s borrowing rate is 15 per cent. Should the company lease the equipment? Use equivalent loan method to answer the question. 2. A cement manufacturer is considering to lease a drying equipment which is worth Rs 75 lakh. It will have to pay five annual beginning-of-the-year lease rentals of Rs 20 lakh. The tax rate is 35 per cent and the manufacturer can write-off the cost of equipment at 25 per cent written down basis for 5 years. The manufacturer’s effective borrowing rate is 16 per cent. Should the equipment be leased? Show that equivalent loan method and net advantage of lease method will lead to the same answer. 3. Readymade Garments Limited wants to lease a computer system for the purpose of colour matching. The system will cost Rs 30 lakh, and if bought can be depreciated over its life of 5 years. The annual rentals, payable at the end of year for 5 years, will be Rs 8.4 lakh. The applicable written-down depreciation rate is 25 per cent. The lessor will maintain the computer system at its cost which works out to be Rs 50,000 per year. At the end of its useful life, the system can be sold for 50 per cent of its depreciated value. The company’s borrowing rate is 14 per cent and tax rate is 35 per cent. Should the system be leased? Show your calculations. 4. A firm proposes to lease an asset of Rs 20 lakh. The annual, end of the year, lease rentals will be Rs 5 lakh for 5 years. The firm is not in a position to pay tax for next 5 years. The depreciation rate (WDV) is 25 per cent per annum. The lessor’s marginal tax rate is 35 per cent. Calculate the net present value of lease to the lessee and the lessor. What are the break-even rentals to the lessee and the lessor? How can both benefit from the deal? Show your computations. Assume that the lessee’s post-tax borrowing rate is 14 per cent. 5. You are planning to buy or lease an IBM notebook. It will cost you Rs 1,50,000. You can lease it for 8 years for Rs 2,500 per month payable in the beginning of the month. As per the tax rules, you can neither claim depreciation nor deduct interest on your personal borrowings from your income. Your friend is willing to lend you Rs 1,50,000 at 10 per cent per annum. Should you lease the notebook or borrow from your friend and buy it? 6. A company is considering whether it should buy or lease equipment that costs Rs 80 lakh. A finance company has offered to lease the equipment for 5 years at annual lease payments Rs 20 lakh at the beginning of each year. The owner of the equipment can claim depreciation on written-down basis at 25 per cent each year. The company’s (lessee’s) tax rate is 35 per cent, and its cost of borrowing is 14 per cent, and the cost of capital is 16 per cent. (a) Should the company buy the asset or lease it? (b) What would your answer be if (a) we assume that the equipment has a salvage value of Rs 10 lakh at the end of its life, and that the lessor will maintain the equipment which would otherwise cost the lessee Rs 1 lakh each year? (b) Instead of lease the company goes for a hire purchase, how much maximum hire-purchase instalment should it be prepared to pay each year?

Chapter 23 Only review questions

Chapter 24 PROBLEMS 1. The comparative balance sheets of Doba Company showed the following changes in balance sheet items from 19X1 to 19X2: Rs Working capital 127,500 Long-term investments 45,000 Land 48,000 Machinery (less accumulated depreciation) 90,000 15% Debentures 240,000 Share capital 60,000

increase increase increase increase increase increase

Reserves and surplus

2.

10,500 decrease

The following additional data are provided: (i) Net profit for the year was Rs 157,500 (ii) Accumulated depreciation for 19X1 was Rs 67,500 and for 19X2 Rs 90,000. (iii) A machine of Rs 112,500 was purchased during the year; depreciation expenses for the year was Rs 22,500. (iv) A bonus issue of shares of Rs 60,000 was made during the year. (v) A cash dividend of Rs 87,000 was declared and paid during the year. Prepare a statement of changes in financial position for Doba Company. The comparative balance sheets for Soma Pvt. Ltd are given below: Table 24.30: Soma Pvt. Ltd Comparative Balance Sheets for the year ended on 31 December

Assets Cash Debtors Stock Prepaid expenses Plant and machinery Goodwill Total Equities Creditors Provision for depreciation Debentures Premium on debentures issue Share capital Share premium Reserves and surplus Total

3.

(Rs) 19X2

19X1

82,000 104,000 112,000 22,000 380,000 36,000

22,000 24,000 60,000 14,000 360,000 40,000

736,000

520,000

30,000 100,000 102,000 12,000 190,000 30,000 272,000

14,000 60,000 102,000 18,000 90,000 – 236,000

736,000

520,000

The company made a net profit of Rs 66,000 during the year. Prepare a statement of changes in financial position on (a) working capital basis, (b) cash basis. Also prepare a schedule of working capital changes. From the following data of Kamdhenu Company, prepare a statement of changes in financial position. Table 24.31: Kamdhenu Company Balance Sheets for the year ended on 31 March

Assets Cash Debtors Stock Long-term investments Machinery Buildings Land Total Liabilities and Equity Provision for depreciation: Machinery Buildings Provision for doubtful debts Creditors Outstanding expenses Loan (adjust security of machinery)

(Rs) 19X2

19X1

30,000 45,000 20,000 15,000 20,000 45,000 10,000

22,500 40,000 16,000 25,000 12,500 37,500 10,000

185,000

163,500

3,750 9,000 1,500 20,000 2,250 22,500

1,500 6,000 1,000 16,500 1,750 25,000

Share capital Reserves and surplus Total

100,000 26,000

100,000 11,750

185,000

163,500

Additional data: (i) Net profit for the year 19X2 is Rs 27,500. (ii) Machinery costing Rs 2,500, on which depreciation of Rs 500 has accumulated, was sold for Rs 3,000. The gain is included in net profit. (iii) Investments costing Rs 10,000 were sold during the year for Rs 12,500. The gain is included in net profit. (iv) Cash dividends paid during the year, Rs 13,250. 4. Prepare (a) a statement of changes in financial position on (i) working capital basis, (ii) cash basis, and (b) a schedule of changes in working capital from the following data: Table 24.32: M Company Balance Sheet for the year ended on 30 June Assets

19X1

19X2 Equities

(Rs) 19X1

19X2

Cash 15,000 9,000 Creditors 60,000 Marketable Bills payable 15,000 securities 21,000 15,000 Accrued expenses 6,000 Debtors 30,000 45,000 Tax payable 9,000 Stock 36,000 45,000 Long-term debt 0 Fixed assets, net 150,000 1,65,000 Share capital Other nonincluding current assets 24,000 15,000 reserve 180,000

0 24,000 6,000 15,000 45,000

270,000 3,00,000

210,000

270,000 300,000 Table 24.33: M Company

Profit and Loss Account for the year ended 30 June Sale Expenses: Cost of goods sold Selling, general and administrative expenses Depreciation Interest Profit before tax Less: Tax Profit after tax Reserve, 30 June 19X1

(Rs) 150,000 75,000 15,000 15,000 3,000

Less: Cash dividends Reserve, 30 June 19X2

5.

108,000 42,000 21,000 21,000 120,000 141,000 9,000 132,000

Balance sheet and profit and loss account of JB Sons Company Limited as on December 31, 19X1 and 19X2 are as follows: Table 24.34: JB Sons Balance Sheet as on 31 December

Liabilities

19X1

19X2 Assets

Accounts payable 15,000 25,000 Cash balance Cash credit 13,000 10,000 Accounts Outstanding receivable

(Rs) 19X1

19X2

5,000

2,000

10,000

8,000

expenses Long-term loan Capital Surplus

2,000 3,000 30,000 20,000 30,000 30,000 10,000 12,000 100,000 1,00,000

Loan and advances 5,000 – Inventories 20,000 25,000 Fixed assets (net) 60,000 65,000 100,000100,000 Table 24.35: JB Sons Company

Profit and Loss Account for the year 19X2

(Rs)

Sales Less: Cost of goods sold (including depreciation of Rs 10,000)

200,000 170,000

Gross profit Less: Other expenses Income before tax Less: Income-tax provision Income after tax

6.

30,000 20,000 10,000 5,000 5,000

Prepare a statement of sources and uses of funds. (C.A., adapted) A company finds on 1 January, 19X3, that it is short of funds with which to implement its programme of expansion. On 1 January, 19X1, it had a cash credit balance of Rs 180,000. From the following information, prepare a statement for the board of directors to show how the overdraft of Rs 68,750 as at the 31 December, 19X2 has arisen: 19X1 Rs

19X2 Rs

19X1 Rs

19X2 Rs

Fixed assets 750,000 11,20,000 Trade creditors 270,000 350,000 Stock and stores 190,000 3,30,000 Share capital Debtors 380,000 3,35,000 (in shares of 250,000 300,000 Bank balance 180,000 – Rs 10 each) Bank overdraft – 68,750 Bills receivables 87,500 95,000

7.

The profit for the year ended December 31, 19X2 before charging depreciation and taxation amounted to Rs 240,000. The 5,000 shares were issued on 1 January 19X2 at a premium of Rs 5 per share, and Rs 137,500 was paid in March 19X2 by way of income tax. Dividend was paid as follows: on the capital on 31 December, 19X1 at 10% less tax at 25%; 19X2 (interim) 5 per cent free of tax. (C.A., adapted) From the following data of Pandit Sons Limited, prepare a statement of sources and uses of funds: Table 24.36: Pandit Sons Limited

Liabilities Accumulated depreciation Creditors Bills payable Debentures Equity capital Premium on shares Retained earning

Balance Sheet as on 31 December

(Rs ’000)

19X2 19X1 Assets

19X2 19X1

275 150 100 75 50 25 500 250 550 400 60 – 336 325 1,871 1,225

Cash 315 285 Marketable securities 106 50 Debtors 150 125 Inventories 95 70 Investments 70 110 Machinery 500 350 Buildings 600 200 Land 35 35 1,871 1,225 Table 24.37: Pandit Sons Limited

Income Statement for the year ended December 31, 19X2 Sales

(Rs ’000) 600

Cost of goods sold Gross margin on sales Operating expenses: Depreciation — machinery — buildings Other expenses Net margin from operations Gain on sales on long-term investments Total Loss on sales of machinery (proceeds from sales Rs 15,000) Net income

8.

337 263 50 80 100

230 33 12 45 5 40

From the following balance sheet of Alpha Ltd, make (1) statement of changes in the working capital, and (2) funds flow statement: Table 24.38: Alpha Co. Balance Sheet (Rs)

Liabilities

19X1

Equity share capital 300,000 8% Redeemable Preference capital 150,000 Capital reserve – General reserve 40,000 Profit and loss account 30,000 Proposed dividend 42,000 Sundry creditors 25,000 Bills payable 20,000 Liabilities for expenses 30,000 Provision for taxation 40,000

19X2 Assets 400,000

100,000 20,000 50,000 48,000 50,000 47,000 16,000

19X1

19X2

Goodwill 100,000 Land and building 200,000 Plant 80,000 Investments 20,000 Sundry debtors 140,000 Stock 77,000 Bills receivable 20,000 Cash in hand 15,000 Cash at bank 10,000 Preliminary expenses 15,000

80,000

170,000 109,000 30,000 10,000 8,000 10,000

36,000 50,000

677,000 817,000

9.

170,000 200,000 30,000

677,000 817,000

Additional data: (i) A piece of land has been sold out in 19X2 and the profit on sale has been carried to capital reserve. (ii) A machine has been sold for Rs 10,000. The written down value of the machine was Rs 12,000. Depreciation of Rs 10,000 is charged on plant account in 19X2. (iii) The investments are trade investments; Rs 3,000 by way of dividend is received including Rs 1,000 from pre-acquisition profit which has been credited to investment account. (iv) An interim dividend of Rs 20,000 has been paid in 19X2. (C.A., adapted) The following are the summaries of the balance sheets of C Victory Limited as on 31 December, 19X1 and 31 December 19X2: Table 24.39: C Victory Ltd Balance Sheet

Liabilities Sundry creditors Bills payable Bank overdraft Provision for taxation Reserves Profit and loss account

19X1

19X2 Assets

(Rs) 19X1

19X2

39,500 41,135 Cash at bank 2,500 33,780 11,525 Sundry debtors 87,490 59,510 – Stock 111,040 Land and 40,000 50,000 building 148,500 50,000 50,000 Plant and machinery 112,950 39,690 41,220 Goodwill –

2,700 73,360 97,370 144,250 116,200 20,000

Share capital

200,000 260,000 462,480 453,880

462,480 453,880

The following additional information is obtained from the general ledger: (a) During the year ended December 19X2 an interim dividend of Rs 26,000 was paid. (b) The assets of another company were purchased for Rs 60,000 payable in fully paid shares of the company. These assets consisted of stock Rs 22,000, machinery Rs 18,000, and goodwill Rs 20,000. In addition sundry purchases of plant were made totalling Rs 5,600. (c) Income-tax paid during the year amounted to Rs 25,000. (d) The net profit for the year before tax was Rs 65,530. You are required to prepare a statement showing the sources and application of funds for the year 19X2 and a schedule setting out changes in working capital. (C.A., adapted) 10. The comparative balance sheets of Bombay Industries Ltd as on 31 December, 19X1 and 19X2 are as under: Table 24.40: Bombay Industries Ltd Balance Sheet (Rs) Liabilities Current Liabilities Sundry creditors Provision for taxation Liabilities for expenses Total current liabilities

19X1

19X2 Assets

40.40

43.20

10.80 2.60 53.80

Long-term Loans 22.00 Total liabilities 75.80

19X1

19X2

Current Assets Cash at bank 44.60 47.80 Debtors 10.80 17.00 12.20 Stock-in-trade 44.00 67.20 Miscellaneous 30.20 8.00 1.00 Total current assets 129.60 140.00 56.40 21.00 Fixed Assets 77.40 Plant, mach. & bldng. Less: Total

Owner’s Equity Paid-up capital

280.00 320.00

Reserves and surplus Total equity

Land 140.60 163.60 Total fixed 420.60 483.60 assets Investments

283.40 368.00

depreciation

25.80

34.20

257.60 333.80 50.00

50.00

307.60 383.80 42.40 25.20

Intangible Assets16.80

12.00

Total non-current Total Capital

assets 496.40 561.00 Total Assets

366.80 421.00 496.40 561.00

The income for the year amounted to Rs 57.80 lakh after charging depreciation of Rs 8.40 lakh but before making the following adjustments: (i) profit on land purchased and sold in 19X2, Rs 15.60 lakh; (ii) loss on sale of marketable securities Rs 2.80 lakh, included under miscellaneous current assets; (iii) write off intangible assets Rs 4.80 lakh; (iv) write off long-term investments Rs 17.20 lakh. The dividend declared and paid during the year amounted to Rs 25.60 lakh. From the above particulars prepare: (i) statement of sources and application of funds, and (ii) statement of changes in working capital. (C.A., adapted) 11. Following are the summarised balances of PQ Limited on 30 June, 19X1 and 19X2: Table 24.41: PQ Limited Balances as on 30 June

(Rs)

19X1 Dr.

19X2 Cr.

Dr.

Cr.

Equity share capital: 30,000 shares of Rs 10 each issued and fully paid Capital reserve 14% Debentures Debenture discount Freehold property at cost Freehold property at valuation Plant and machinery at cost Depreciation on plant and machinery Debtors Stock and work-in-progress Creditors Profit and loss account Net profit for the year Dividend in respect of 19X1 Provision for doubtful debts Trade investment at cost Bank

– 300,000 – 300,000 – – – 49,200 – – – 50,000 – – 1,000 – 122,000 – – – – – 165,000 – 223,000 – 283,000 – – 107,600 – 122,000 104,600 – 154,600 – 124,000 – 162,500 – – 37,400 – 49,200 – 112,000 – 112,000 – – – 76,500 – – 30,000 – – 3,100 – 6,400 – – 47,000 – – 13,500 – 77,800 573,600 573,600 843,100 843,100

You are informed that: (i) The capital reserve on 30 June, 19X2 represented the realised profit on the sale of one freehold property together with the surplus arising on revaluation. (ii) During the year ended 30 June, 19X2, plant costing Rs 18,000 against which a depreciation provision of Rs 13,500 had been made was sold for Rs 7,000. (iii) On 1 July, 19X1, Rs 50,000 debentures were issued for cash at a discount of Rs 1,000. (iv) The net profit for the year is arrived at after crediting the profit on the sale of machinery and charging debenture interest. You are required to prepare a statement which will explain why bank borrowing has increased by Rs 64,300 during the year ended 30 June 19X2. Taxation is to be ignored. (C.A., adapted) 12. From the information provided, you are required to prepare a “Source and Disposition of Funds” statement explaining how CD Limited has improved cash position in the year ended 31 December 19X2. The summarised balance sheets of CD Limited as on 31 December 19X1 and 31 December 19X2 were as follows: Table 24.42: CD Ltd Balance Sheet Liabilities

19X1

19X2 Assets

(Rs) 19X1

19X2

Issued share capital 100,000 1,50,000 Share premium 15,000 35,000 Profit and loss 28,000 70,000 Debentures 70,000 30,000 Bank overdraft 14,000 – Creditors 34,000 48,000 Proposed dividends 15,000 20,000 Depreciation: Plant 45,000 54,000 Fixtures 13,000 15,000

Freehold property 110,000 130,000 Plant and machinery 120,000 151,000 Fixtures and fittings, at cost 24,000 29,000 Stocks 37,000 51,000 Debtors 43,000 44,000 Bank balance – 16,000 Premium on redeemed debentures – 1,000

334,000 422,000

334,000 422,000

The following additional information is relevant: (i) There had been no disposal of freehold property in the year. (ii) A machine tool which has cost Rs 8,000 and in respect of which Rs 6,000 depreciation has been provided was sold for Rs 3,000 and fixtures, which had cost Rs 5,000 in respect of which depreciation of Rs 2,000 had been provided, were sold for Rs 1,000. The profits and losses on these transactions had been dealt with through the profit and loss account. (iii) The actual premium on the

redemption of debentures was Rs 2,000 of which Rs 1,000 has been written off to the profit and loss account. (iv) No interim dividend has been paid.(C.A., adapted) 13. GNFC In Chapter 2, the comparative balance sheets and profit and loss accounts for the years 2000 and 2001 for Gujarat Naramada Valley Fertilisers Company are given in Tables 2.3 and 2.8. Prepare funds flow statements for the year 2001. Explain its implications.

Chapter 25 PROBLEMS 1. The balance sheets and trading and profit and loss accounts for the year ended 30 June, 19X2 of S Ltd and T Ltd are given in Tables 4.30 and 4.31. You may assume that stocks have increased evenly throughout the year. You are required to: (a) Calculate three of the following ratios separately for each company: (i) net profit for the year as a percentage of net assets employed at 30 June, 19X2; (ii) net profit for the year as a percentage of sales; (iii) gross profit for the year as a percentage of sales; (iv) current assets to current liabilities at 30 June, 19X2; (v) liquid ratio at 30 June, 19X2; and (vi) stock turnover during the year. (b) Describe briefly the main conclusions which you draw from a comparison of the ratios which you have calculated for each company. (C.A., adapted) Table 25.30: S Ltd and T Ltd Balance Sheet as on 30 June, 19X2

(Rs) S Ltd

Fixed assets at cost Less: Provision for depreciation

T Ltd

60,000 20,000

30,000 10,000 40,000

Current assets Stock Debtors Cash Less: Current liabilities Net current assets Net assets Paid-up share capital Revenue reserve

20,000

57,000 22,000 11,000 90,000 30,000

30,000 20,000 10,000 60,000 30,000 60,000 100,000 95,000 5,000

30,000 50,000 45,000 5,000

100,000

50,000

Table 25.31: S Ltd and T Ltd Trading and Profit and Loss Account for the year ended 30 June, 19X2 S Ltd Sales Stock at July 1, 19X1 Add: Purchases Less: Stock at June 30, 19X2 Cost of goods sold Gross profit Less: General expenses Net profit for the year Add: Balance brought forward Less: Dividend paid 5,000

(Rs) T Ltd

160,000 39,000 114,000 153,000

120,000 20,000 85,000 105,000

57,000

30,000 96,000 64,000 56,000 8,000 3,000 11,000 6,000 5,000

75,000 45,000 39,000 6,000 1,000 7,000 2,000

Balance carried forward

2.

Extracts from financial accounts of XYZ Ltd are given below: Table 25.32: XYZ Ltd Year I Assets

Stock Debtors Payment in advance Cash in hand Sundry creditors Acceptances Bank overdraft

3.

10,000 30,000 2,000 20,000 – – – 62,000

Year II

Liabilities Assets Liabilities – – – – 25,000 15,000 – 40,000

20,000 30,000 – 15,000 – – – 65,000

– – – – 30,000 12,000 5,000 47,000

Sales amounted to Rs 350,000 in the first year and Rs 300,000 in the second year. You are required to comment on the solvency position of the concern with the help of accounting ratios. From the following information you are required to (a) analyze the relative position of ABC Ltd in the industry and (b) point out the deficiencies and suggest improvements. Table 25.33: ABC Ltd Balance Sheet as on 31 December, 19X1

(Rs)

Share capital 1,278,000 Fixed assets: Current liabilities: Equipment 600,000 Creditors 150,000 Less: Depreciation 80,000 520,000 Bank loan 300,000 Current assets: Cash 180,000 Debtors 240,000 Stock 660,000 Prepaid expenses 128,000 Total capital 1,728,000 Total assets 1,728,000 Table 25.34: ABC Ltd Profit and Loss for the year ended 31 December, 19X1 Sales Cost of goods sold Gross profit Operating expenses Profit before interest and taxes Interest Profit before taxes Tax Profit after taxes

(Rs) 345,000 150,000 195,000 90,000 105,000 24,000 81,000 27,000 54,000

Table 25.35: ABC Ltd Industry Averages Current ratio Quick ratio Debt-equity ratio Times interest earned Inventory turnover Fixed-assets turnover Total assets turnover Net profit margin Return on assets Return on equity

2.95 1.05 50% 2.60% 0.35 0.80 0.50 16% 15% 21%

4.

The two firms, M and N, have the following data:

Sales Total assets Net profit

N Rs

M Rs

800,000 4,000,000 750,000

200,000 600,000 420,000

Compute return on investment for both firms. Explain how the figures are similar and how they are different. 5. The summary of the balance sheets and the profit and loss accounts from 19X1 to 19X5 for Jagan Limited is given in Tables 25.36 and 25.37. During this period, the company undertook a major expansion programme. You are required to calculate important ratios for the five years and assess the financial health of the company. Also, explain the implications of the development of the financial health of the company for the shareholders. (C.A. Engg., adapted) Table 25.36: Jagan Ltd Balance Sheets

(Rs ’000)

19X1 19X2 19X3 19X4 19X5 Liabilities and Equity Creditors Debentures Share capital Reserves Total Asset Cash Debtors Stock Fixed assets, net Total

25 25 25 25 25 250 1,000 1,750 2,500 3,250 1,000 1,000 1,000 1,000 1,000 225 225 225 2,25 2,25 1,500 2,250 3,000 37,50 45,00 50 50 50 50 50 50 50 50 50 50 400 650 900 11,50 1,400 1,000 1,500 2,000 2,500 3,000 1,500 2,250 3,000 3,750 4,500 Table 25.37: Jagan Ltd

Profit and Loss Accounts (Summary) 19X1 Sales Cost of goods sold Gross profit Operating expenses EBIT Interest Profit before tax Tax Net profit No. of shares P/E ratio

6.

19X2 19X3

300 450 100 150 200 300 25 50 175 250 15 67.5 160 182.5 67.55 75.35 92.45 107.15 100 100 5 5

(Rs ’000) 19X4 19X5

600 750 900 200 250 300 400 500 600 100 150 200 300 350 400 127.5 195 270 172.5 155 130 73.55 65.15 53.1 98.95 89.85 76.9 100 100 100 4 3.5 3.5

Using the following data, complete the balance sheet given below: Gross profit (Rs) Shareholders’ equity (Rs) Gross profit margin Credit-sales to total-sales Total assets turnover Inventory turnover Average collection period (a 360-day year) Current ratio Long-term debt to equity

54,000 600,000 20% 80% 0.3 times 4 times 20 days 1.8 40%

Balance Sheet Creditors Long-term debt Shareholders’ equity

7.

......... ......... ......... ......... .........

Cash Debtors Inventory Fixed assets

......... ......... ......... ......... .........

Surendra Mohan and Sons are wholesale distributors of electric goods. Tables 25.38 and 25.39 contain their balance sheets and profit and loss statements during the period 19X1 to 19X3. You are required to critically evaluate the firm’s financial performance. Table 25.38: Surendra Mohan and Sons Comparative Balance Sheets

Liabilities and Capital Creditors Accrued expenses Total current liabilities Owner’s capital Total

Assets Cash Debtors Stock Prepaid expenses Total current assets Fixed assets Investments Total non-current assets Total

(Rs)

19X3

19X2

19X1

65,994 2,645 68,639 208,812 277,451

62,229 1,920 64,149 181,341 245,490

55,065 1,168 56,233 163,394 219,627

19X3

19X2

19X1

19,550 86,784 61,661 2,667 170,662 99,285 7,504 106,789 277,451

14,376 61,601 63,167 1,433 140,577 97,878 7,035 104,913 245,490

9,542 40,217 68,086 863 118,708 96,229 4,690 100,919 219,627

Table 25.39: Surendra Mohan and Sons Summarised Profit and Loss Statements Sales Cost of goods sold Gross profit Operating expenses Net profit

8.

(Rs)

19X3

19X2

19X1

481,053 310,720 170,333 141,377 28,956

457,172 275,514 181,658 137,984 43,674

399,291 229,878 169,413 120,593 48,820

The following are the comparative financial statements for three years for Plastic Works Limited. You are required to comment on the firm’s financial condition and indicate the areas which require management’s attention. Table 25.40: Plastic Works Limited Comparative Balance Sheets

Liabilities and Capital Bank borrowing Creditors Accrued expenses Provision for dividend Provision for taxes Total current liabilities Long-term loan Total liabilities

(Rs)

19X3

19X2

19X1

30,525 331,127 21,510 20,350 56,367 459,879 71,225 531,104

10,175 147,725 14,361 20,350 88,435 281,046 Nil 281,046

– 113,980 20,350 20,350 86,111 240,791 Nil 240,791

Share capital Reserves and surplus Net worth Total Funds Assets Cash Debtors Stock: Raw material Work in process Finished goods Prepaid expenses Total current assets Buildings, plant and equipment Misc. fixed assets Total non-current assets Total Assets

407,000 80,983 487,983 1019,087

407,000 88,826 495,826 776,872

407,000 67,067 474,067 714,858

99,164 215,356

35,922 207,780

13,930 211,196

133,577 47,882 266,534 17,350 779,863

107,409 50,179 177,788 13,726 592,804

98,411 42,230 174,892 12,697 553,356

19X3

19X2

19X1

229,314 9,910 239,224 1,019,087

177,047 7,021 184,068 776,872

161,502 – 161,502 714,858

Table 25.41: Plastic Works Limited Summarised Profit & Loss Statements for the year ended 31 December 19X3 Sales Cost of goods sold Gross profit Operating expenses Profit before taxes Taxes Net profit Dividends

9.

1,872,937 896,953 975,984

19X2

(Rs) 19X1

1,599,315 1,429,818 767,673 683,597 831,642 746,221

19X3

19X2

19X1

846,059 129,925 56,367 73,558 81,400

640,048 191,594 88,435 103,159 81,400

545,750 200,471 93,050 107,421 81,400

Tata Iron & Steel Company Limited (TISCO). TISCO was established in 1907 at Jamshedpur. It is the largest private sector company. Tables 25.42 and 25.43 give the profit and loss statements and balance sheets for the last seven years for the company. You are required to provide an analysis of the company’s financial performance. Table 25.42: Tata Iron and Steel Company Limited Summarised Balance Sheet as on 31 March 2000 ASEETS Gross fixed assets 10,668.33 Less: Cumulative depreciation 3,241.95

1995 2001

(Rs in crore) 1996

1997

1998

1999

6,962.89 7,408.46 7,850.82 8,948.52 10,032.17 11,258.17 1,749.41 2,014.90 2,324.42 2,648.48 2,973.59 3,720.08

Net fixed assets 7,426.38 Investments 818.89 Current Assets

5,213.48 5,393.56 5,526.40 6,300.04 7,058.58 7,538.09 220.65 410.94 664.90 626.08 588.84 850.83

Inventories 944.85 Receivables 1,868.77 Marketable investment 342.35

865.34 1,076.57 1,021.11 1,039.70 1,016.51 921.77 1,341.87 1,723.63 2,178.76 1,948.40 1,874.18 2,060.70 175.51 365.75 479.77 453.03 399.51 381.38

Cash and bank balance 232.87

162.44 239.78

3,388.84 Misc. expenses not written off 828.12 Total Assets 12,119.88 CAPITAL & LIABILITIES Net worth 4,558.40 Share capital 517.77 Equity capital 367.77 Preference capital 150.00 Reserves & surplus 4,040.63 Total borrowings 4,946.52 Current liabilities & provisions 2,614.96 Current liabilities 1,492.55 Sundry creditors 1,345.65 Others 146.90 Provisions 1,122.41 Tax provision 167.04 Dividend provision 147.11 Other provisions 808.26 Total Liabilities 12,531.46

437.09

251.38

462.96

336.19

2,545.16 3,603.04 3,931.02 3,904.09 3,626.39 3,603.63 31.33 167.99 278.32 896.98 1,118.53 920.29 7,835.11 9,209.78 9,920.87 11,274.16 11,992.83 12,531.46

2,688.04 4,888.43 336.87 507.77 336.87 367.77 0.00 140.00 2,351.17 4,380.66 3,582.73 4,672.56 1,564.34 2,970.47 1,421.51 1,696.38 1,256.72 1,574.35 164.79 122.03 142.83 1,274.09 21.24 180.20 118.24 183.89 3.35 910.00

7,835.11 9,209.78 9,920.87 11,274.16

3,742.40 3,974.02 4,064.88 4,164.42 367.23

367.38

367.55

367.77

367.23

367.38

367.55

367.77

0.00

0.00

0.00

0.00

3,375.17 3,606.64 3,697.33 3,796.65 3,842.07 4,082.49 5,212.44 5,503.26 1,625.31 1,864.36 1,996.84 2,325.15 1,326.82 1,385.47 1,414.66 1,463.35 1,203.97 1,251.00 1,296.61 1,340.17 122.85

134.47

118.05

123.18

298.49

478.89

582.18

861.80

18.96

111.40

150.58

185.53

156.97

165.66

147.25

147.11

122.56

201.83

284.35

529.16

11,992.83

12,119.88

Table 25.43: Tata Iron and Steel Company Limited Summarized Profit & Loss Account for the Year Ending on 31 March (Rs in crore) 1995 2001

1996

1997

1998

1999

Income Sales 7015.16 Less: Excise 796.86

4993.39 7822.58 440.77 920.83

6349.35

6919.4

7012.35

6885.12

592.61

696.49

724.34

710.09

Net sales 6218.3 Other income 68.51 Change in stocks –33.19 Non-recurring income 152.44 Total Income 6406.06

4552.62 6901.75 44.58 86.53 –17.35 –56.74 16.03 13.15 4595.88 6944.69

5756.74

6222.91

6288.01

6175.03

76.18

150.52

117.16

96.73

66.24

42.12

4.8

46.18

0.35

11.2

27.59

139.84

5899.51

6426.75

6437.56

6457.78

2000

PBDIT (EBITDA) 1291.98 Less: Depreciation 426.54

808.1 1507.68 262.26 492.25

1212.74

1260.45

1030.38

1058.26

297.61

326.83

343.23

382.18

PBIT 865.44 Less: Interest 388.35

545.84 1015.43 281.4 412.39

915.13

933.62

687.15

676.08

348.91

390.66

323.42

360.35

PBT 477.09 Less: Tax provision 54.5

264.44 603.04 0.25 49.6

566.22

542.96

363.73

315.73

0.43

73.75

41.65

33.5

PAT 422.59

264.19 553.44

565.79

469.21

322.08

282.23

118.24 196.09 0 21.52 145.95 335.83

156.97

165.66

147.25

147.11

0

16.57

14.73

16.18

408.82

286.98

160.1

118.94

530.35 1045.69 681.14 1718.7 4504.29 6812.71 1501.19 2732.1 1847.01

867.3

801.69

665.31

664.41

638.86

881.3

880.44

1007.98

5795.26

6238.2

6257.51

6189.62

2174.54

2205.36

2055.3

1998.68

Appropriation of Profit Equity Dividends 154.86 Dividend Tax 17.04 Retained earnings 250.69 Other Financial Items Cash profit 849.13 Cash flow from business activities 1323.94 Value of output 6154.84 Gross value added 2273.55 Net value added 1238.93 1876.93 1878.53 1712.07 1616.5

2239.85

10. Agro-Chemical & Pesticides Industry. The financial data in Table 25.44 related to ten agro-chemicals and pesticides companies for the year ending on March 31, 19X2. Provide a detailed analysis of the profitability and the market performance of the companies. How have these companies performed in relation to the industry performance? Show computations. 11. Glass Manufacturing Companies. The financial data in Table 25.45 are for the glass manufacturing companies for the year 19X1 and 19X2. Comment on the profitability and the market performance of the companies. How do they compare with the industry average? Table 25.44: Agro-Chemicals and Pesticides Companies Financial Data for the year ending on 31 March, 19X2 Searle Sales 1600 PBDIT 1.77 Dep. 0.50 PBIT 1.27 Int. 0.96 PBT 0.96 Tax 0.00 PAT 0.96 EPS 3.54

Buyer Cynamide UP straw United 218.43 101.17 33.69 22.75 5.33 1.34 28.36 21.41 17.07 18.21 17.07 18.21 8.25 4.00 8.82 14.21 54.38 20.01

(Rs crore)

Excel Khaitau Monsanto Montari Paushak

100.46

175.31

26.85

14.32

59.69

12.30

74.36

15.15

39.83

5.12

1.72

7.61

1.50

9.71

1.91

4.12

1.30

0.04

1.22

0.20

1.14

13.24

35.71

3.82

1.68

6.39

1.30

8.57

11.17

28.12

1.18

1.32

1.95

0.61

5.99

11.17

28.12

1.18

1.32

1.95

0.61

5.99

5.09

9.50

0.00

0.70

0.00

0.08

1.80

6.08

18.62

1.18

0.62

1.95

0.53

4.19

11.56

26.87

2.34

6.20

3.18

6.24

8.03

DPS 0.00 Book value 15.72 Market value 2100.00 280.00

24.00 3.50 10.10 2.50 2.30 2.20 1.70 2.50 5.00 268.5 52.23 62.37 19.21 25.40 14.67 27.18 57.85 33.72 630.00 47.50 250.00 120.00 130.00 280.00 58.00 590.00

Source: The Economics Times.

Table 25.45: Glass Manufacturing Companies Financial Data (Rs crore) Alembic Victory Industry Sales

PBIT

Interest

Tax

PAT

Per Share Data EPS DPS

BV

MV

19X2

Ashi

Borosil

Excel

Fgp.

Hind.

Indo.

Maha

Triveni

19X1 271.5 19X2 338.5 19X1 39.6 19X2 56.5 19X1 13.0 19X2 15.3 19X1 5.7 19X2 15.1 19X1 20.9 19X2 26.1

19.8

19.3

24.7

9.7

29.4

66.2

54.3

9.7

31.5 7.8

28.2

26.4

31.1

13.5

30.8

76.7

83.0

12.4

48.2 8.2

1.6

1.9

3.8

0.7

4.7

6.3

12.3

1.0

6.2 1.0

2.7

4.2

5.9

1.2

4.0

8.2

12.6

1.5

14.9 1.4

1.3

1.5

1.9

8.4

1.4

3.0

1.6

0.5

0.8 0.6

1.7

2.1

2.1

0.6

1.6

3.0

1.3

0.6

0.7 0.0

0.0

0.1

0.7

0.1

1.2

0.0

1.7

0.0

2.0 0.0

0.0

0.0

1.8

0.1

0.4

0.0

6.0

0.4

6.3 0.0

0.3

0.3

1.2

0.2

2.1

3.3

9.0

0.5

3.4 0.4

1.0

2.1

2.0

0.5

2.0

4.4

5.3

0.5

7.9 0.6

19X1 19X2 19X1 19X2

11.3 38.5 0.0 0.0

1.7 11.2 1.0 1.5

3.1 5.6 2.5 0.25

1.5 3.7 1.4 1.8

3.5 3.1 2.2 2.2

22.8 30.5 1.0 1.0

27.8 8.2 4.0 23.0

3.7 3.7 1.4 1.4

19X1

93.8

12.3

45.4

20.4

31.4

96.5

63.0

17.7

115.0 17.1

19X2

129.6

22.5

48.6

22.2

32.3

126.9

45.6

20.0

180.3 20.0

575.0

227.5

35.0

145.0

6.0

675.0

85.0

75.0

85.0

29.2 67.7 3.0 3.6

3.5 4.9 1.5 2.0

45.0

Chapter 26 PROBLEMS 1. Table 26.17 gives a summary of Bajaj’s financial items during the years from 20X5 to 20X9. Table 26.17: Bajaj Auto Limited: Summary of Financial Items (Rs crore) 20X9 Net Sales PBDIT Depreciation Interest Other Income PBT

20X8

20X7

20X6

20X5

3023.12 3089.33 2961.98 2643.22 2638.47 473.88 973.4 895.57 840.94 802.23 177.29 145.31 132.7 143.62 117.87 7.39 3.17 4.67 8.47 7.41 365.99 510.4 380.29 355.57 296.89 289.2 824.92 758.2 688.85 676.95

Tax Provision Net Profit Equity Dividend Retained Profit Current Assets Net Fixed Assets Current Liabilities Secured Loans

26.64 211.19 217.68 224.7 236.38 262.56 613.73 540.52 464.15 440.57 80.95 119.39 95.51 95.51 79.59 181.61 494.34 445.01 368.64 360.98 2061.62 2373.37 2197.01 1809.38 1363.55 1362.35 1114.25 921.81 682.91 603.95 1474.34 1740.67 1527.18 1259.83 988.27 55.97 101.58 41.08 27.54 22.04 20X9 20X8 20X7 20X6 20X5

Unsecured Loans 457.74 394.09 308.61 230.67 191.83 Total Liabilities 4624.58 5440.42 4578.61 3636.26 2962.84 Net Worth 2636.53 3204.08 2701.74 2118.22 1760.7 Bonus Ratio – – – – 1.02 EPS 25.13 50.31 44.39 38.08 54.35 DPS 8.00 10.00 8.00 8.00 10.00 Book Value Per Share 260.58 268.37 226.3 177.42 221.22 Market Value Per Share*257.70 384.00 615.80 594.30 601.70 * Closing price in March.

2.

Based on the company’s past performance and appropriate assumptions that you may like to make, develop a financial forecast for five years. Show the impact if your assumptions go wrong. Tables 26.18 and 26.19 contain Reliance Industries Limited’s profit and loss account and balance sheet for seven years. You are required to identify the trends in Reliance’s financial performance and policies. Using this information, prepare a financial plan for Reliance. Discuss the implications of your plan. Table 26.18: Reliance Industrie Ltd Summarized Profit & Loss Account during the Year Ending at 31 March (Rs crore) 2001

2000

1999

1998

1997

1996

1995 EARNINGS Sales 5,388.15

23,024.17

15,847.16

10,624.15

9,719.18

6,441.65

5,726.66

2,578.91

2,451.53

1,929.46

1,893.13

1,283.85

1,507.83

20,445.26

13,395.63

8,694.69

7,826.05

5,157.80

4,218.83

Other Income 312.59

976.79

976.56

629.19

363.09

318.78

271.85

Total Income 4,183.61

21,422.05

14,372.19

9,323.88

8,189.14

5,476.58

4,490.68

PBDIT 1,622.60

5,561.72

4,746.61

3,317.54

2,886.54

1,947.81

1,751.91

Depreciation 278.24

1,565.11

1,278.36

855.04

667.32

410.14

336.51

PBIT 1,344.36

3,996.61

3,468.25

2,462.50

2,219.22

1,537.67

1,415.40

Interest 279.51

1,215.99

1,008.00

728.81

503.55

169.97

110.13

PBT 1,064.85

2,780.62

2,460.25

1,733.69

1,715.67

1,367.70

1,305.27

135.00

57.00

30.00

63.00

45.00

0.00

Less: Excise 1,517.13 Net Sales 3,871.02

Tax 0.00

PAT 1,064.85

2,645.62

2,403.25

1,703.69

1,652.67

1,322.70

1,305.27

447.85

384.65

350.16

326.81

299.24

276.22

4.77

35.57

23.39

10.33

0.00

28.00

Corporate Dividend Tax 46.20 0.00

46.22

40.86

63.64

0.00

0.00

EPS (Rs) 23.34

22.04

17.56

16.94

28.85

27.87

Additional Information Equity Dividend 199.34 Preference Dividend 0.83

Book Value (Rs) 113.86

24.63 103.65

100.12

96.83 184.77 179.07

157.66

Table 26.19: Reliance Industries Ltd: Balance Sheet as at 31 March (Rs in crore) 2001

2000

1999

1998

1997

1996

1,053.49

1,053.45

933.39

931.90

458.45 458.23

0.00

292.95

252.95

187.95

0.00 200.00

13,711.88

12,636.35

11,183.00

10,862.75

8,012.49 7,747.07

14,765.37

13,982.75

12,369.34

11,982.60

8,470.94 8,405.30

Term Loans – Institutions 68.66 284.79 Term Loans – Banks 0.00 160.27 Non-Convertible Debentures 3,761.98 1,273.04 Working Capital Advances 237.76 405.63 Other Loans 6,067.39 816.19 Total Borrowings 10,135.79 2,939.92 Current Liabilities & Provisions Creditors 3,859.22 1,118.23 Provisions 863.50 201.57 Other 251.58 76.67 Total Current Liabilities 4,974.30 1,396.47 Total Liabilities 29,875.46 15,038.38 11,529.04

158.51

46.24

57.41

859.70 411.95

1,400.94

1,527.00

200.53

950.48 607.19

3,779.85

3,578.04

2,413.54

2,012.98 1,780.95

648.81

327.03

65.98

425.92 591.88

5,532.13

5,206.98

5,509.87

3,376.40 1,329.48

11,520.24

10,685.29

8,247.33

7,625.48 4,721.45

2,953.96

3,338.73

3,095.04

2,386.23 1,305.32

265.80

544.37

475.99

352.23 282.02

646.07

1,218.27

586.97

701.26 324.29

3,865.83

5,101.37

4,158.00

3,439.72 1,911.63

29,368.82

28,156.00

24,387.93

1995 CAPITAL & LIABILITIES Total Shareholders Funds Equity Share Capital 455.86 Preference Capital Paid Up 5.50 Reserves & Surplus 6,731.29 7,192.65 Borrowings

19,536.14

ASSETS Fixed assets Gross Block 5,315.40 Less: Accum. Depreciation 1,805.78

3.

25,355.99

24,330.95

18,650.33

17,848.33

10,955.92 6,885.50

11,841.53

9,214.06

6,691.93

4,944.47

3,491.20 2,141.34

Net Block 13,514.46 15,116.89 11,958.40 12,903.86 3,509.62 Capital Work in Progress 512.38 331.42 3,437.83 2,069.43 3,075.09 Total Fixed assets 14,026.84 15,448.31 15,396.23 14,973.29 6,584.71 Investments 6,726.11 6,066.56 4,294.59 4,282.33 1,993.41 Current Assets 9,122.51 7,853.95 8,465.18 5,132.31 2,950.92 Total Assets 29,875.4629,368.8228,156.0024,387.9319,536.14 15,038.38

7,464.72 4,744.16 3,708.63 4,488.71 11,173.35 9,232.87 4,455.68 1,952.91 3,907.11 3,852.60 11,529.04

Tables 26.20 and 26.21 give balance sheet and profit and loss account of Mason Industries Limited. What is the sustainable growth rate for the company? Table 26.20: Mason Industries Limited Balance Sheet, 31 December 2009 Rs ’ 000 Creditors 6,725 Borrowings 40,350 Share capital 40,000 Reserve & surplus 27,250

Rs ’ 000 Cash Debtors Inventory Gross block Less: Accumulated depreciation

114,325

4,035 9,415 20,175 107,700 27,000 114,325

Table 26.21: Mason Industries Limited: Profit & Loss Account, 31 December 2009 Sales Less: Cost of sales Gross profit Less: Selling & admin. Expenses Profit before interest and tax Less: Interest (at 12%) Profit before tax

4.

40,935 10,916 30,019 15,010 15,010 4,776 10,234

Fine Toys Limited has a capital structure comprising 45 per cent debt and 55 per cent equity at book values. The company’s payout ratio is 60 per cent. Management wants a growth rate of 20 per cent per annum in the future. Is this rate sustainable? After-tax interest rate is 5 per cent.

Chapter 27 PROBLEMS 1. The following cost of sales statements are available for D.D. manufacturers: Statement of Cost of Sales Items 1. 2. 3. 4.

Opening raw material inventory Purchases Closing raw material inventory Raw material consumed (1 + 2 – 3)

(Rs in crore)

19X1

19X2

19X3

5.2 25.6 6.8 24.0

6.8 33.5 7.6 32.7

7.6 45.6 9.2 44.0

5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

Wages and salaries Other mfg. expenses Depreciation Total cost (4 + 5 + 6 + 7) Opening work-in-process inventory Closing work-in-process inventory Cost of production Opening finished goods inventory Closing finished goods inventory Cost of goods sold Selling, administrative and other expenses Cost of sales (14 + 15)

8.1 3.2 1.8 37.1 1.8 2.0 36.9 3.2 2.8 37.3 1.3 38.6

11.2 4.4 2.0 50.3 2.0 3.1 49.2 2.8 3.6 48.4 1.9 50.3

15.3 5.8 2.6 67.7 3.1 4.6 66.2 3.6 2.9 66.9 2.1 69.0

The following are the additional data available: 19X1

19X2

19X3

45.9 7.3 8.3 10.8 3.7 4.6

60.1 9.8 10.8 14.9 4.6 8.0

82.7 13.7 14.9 20.5 8.0 12.0

Sales PBIT Debtors:

Opening Closing Creditors: Opening Closing

2.

You are required to calculate (i) operating cycle, (ii) net operating cycle, and (iii) cash conversion cycle for each of the three years. X & Co. is desirous to purchase a business and has consulted you, and one point on which you are asked to advise them is the average amount of working capital which will be required in the first year’s working. You are given the following estimates and are instructed to add 10 per cent to your computed figure to allow for contingencies: Figures for the Year Rs

Average amount backed up for stocks: Stocks of finished product Stocks of stores, materials, etc. Average credit given:

5,000 8,000 Figures for the Year Rs

Inland sales 6 weeks’ credit Export sales 1½ weeks’ credit Lag in payment of wages and other outgoings: Wages 1½ weeks Stocks, materials, etc. 1½ weeks Rent, royalties, etc. 6 months Clerical staff ½ month Manager ½ month Miscellaneous expenses 1½ months Payment in advance: Sundry expenses (paid quarterly in advance) Undrawn profits on the average throughout the year.

3.

3,12,000 78,000

260,000 48,000 10,000 62,000 4,800 48,000 8,000 11,000

Set up your calculations for the average amount of working capital required.(C.A., adapted) A pro forma cost sheet of a company provides the following particulars: Amount per unit Rs

Raw material Direct labour Overheads Total cost Profit Selling price

4.

80 30 60 170 30 200

The following further particulars are available: (a) Raw material in stock, on an average one month; materials in process, on average half a month; finished goods in stock, on an average one month. (b) Credit allowed by suppliers is one month; credit allowed to debtors is two months; lag in payment of wages is one and a half weeks; lag in payment of overhead expenses is one month; one-fourth of the output is sold against cash; cash in hand and at bank is expected to be Rs 25,000. You are required to prepare a statement showing working capital needed to finance a level of activity of 104,000 units of production. You may assume that production is carried on evenly throughout the year, and wages and overheads accrue similarly.(C.A., adapted) While preparing a project report on behalf of a client you have collected the following facts. Estimate the net working capital required for that project. Add 10 per cent to your computed figure to allow for contingencies. Amount per unit Rs

Estimated cost per unit of production is: Raw material Direct labour Overheads (exclusive of depreciation) Total cost Additional information: Selling price Level of activity Raw material in stock Work-in-progress (assume 50%completion stage) Finished goods in stock Credit allowed by suppliers Credit allowed to debtors Lag in payment of wages Cash at bank is expected to be Rs 125,000.

5.

Rs 106 per unit, 100,000 units of production per annum average 4 weeks average 2 weeks average 4 weeks average 4 weeks average 8 weeks average 1½ weeks

You may assume that production is carried on evenly throughout the year (52 weeks) and wages and overheads accrue similarly. All sales are on credit basis only. (M.Com., D.U., adapted) The following are the given cost of liquidity and illiquidity for different ratios of current assets to fixed assets of a firm. Determine the optimum ratio of current assets to fixed assets. Also show your answer on a graph. CA/FA 0.10 0.25 0.40 0.70 1.00 1.50 2.50

6.

42.4 15.9 31.8 90.1

Cost of Liquidity 138,000 275,000 550,000 1,100,000 2,200,000 4,140,000 6,890,000

Cost of Liquidity 2,200,000 1,650,000 1,100,000 830,000 690,000 550,000 276,000

GG Industries have estimated its monthly needs of net working capital for 19X1 as follows: The firm is rated to have average risk; therefore, working capital finance from a bank will cost the firm 16 per cent per annum. Long-term borrowing will be available at 14 per cent. The firm can invest excess funds in the form of inter- corporate lending at 12 per cent per annum.

(i) Assume the firm finances the maximum amount of its working capital requirements for the next year with long-term borrowing and investing any excess funds in the form of inter- corporate lending. Calculate GG Industries net interest cost during 19X1. Amount Rs lakh

Month January February March April May June

7.

Amount Rs lakh

Month

72.65 58.13 29.06 24.22 33.90 43.60

July August September October November December

58.12 72.66 82.30 87.19 92.02 87.17

(ii) Assume the firm finance all its working capital requirements for the next year with short-term borrowing. Determine GG Industries interest cost during 19X1. (iii) Discuss the return-risk trade-offs associated with the above two policies. A company wants to analyze the effect of its working capital investment and financing policies on shareholders’ return and risk. Assume that the firm has Rs 180 crore in fixed assets and Rs 150 crore in current liabilities. The company has a policy of maintaining a debt to total assets ratio of 60 per cent, where debt consists of both short-term debt from banks and long-term debt. The following data relate to three alternative policies:

Working Capital Policies

Investment in Bank Current Assets Borrowings (Rs crore) (Rs crore)

Aggressive Moderate Conservative

252 270 288

216 162 108

Projected Sales EBIT (Rs crore) (Rs crore) 531 540 549

53 54 55

Assume that bank borrowing will cost 16 per cent while the effective interest cost of long-term borrowing will be 18 per cent per annum. You are required to determine: (a) return on shareholders equity, (b) net working capital position, (c) current ratio, and (d) current assets to total assets ratio. Also evaluate the return-risk trade offs associated with these three policies.

Chapter 28 PROBLEMS 1. Delta Company has current sales of Rs 30 crore. To push up sales, the company is considering a more liberal credit policy. The current average collection period of the company is 25 days. If the collection period is extended, sales increase in the following manner.

2.

Credit Policy

Increase in Collection Period

Increase in Sales (Rs in lakh)

X

15 days

12

Y

25 days

27

Z

35 days

47

The company is selling its product at Rs 10 each. Average cost per unit at the current level is Rs 8 and variable cost per unit Rs 6. If the company required a return of 12 per cent on its investment, which credit policy is desirable? State your assumptions. (Assume a 360-day year). The credit terms of a firm currently is “net 30.” It is considering changing it to “net 60.” This will have the effect of increasing the firm’s sales. As the firm will not relax credit standards, the bad-debt losses are expected to remain at the same percentage, i.e., 3 per cent of sales. Incremental production, selling and collection costs are 80 per cent of sales and expected to remain constant over the range of anticipated sales increases. The relevant opportunity cost for receivables is 15 per cent. Current credit sales are Rs 300 crore and current level of receivables is Rs 30 crore. If the credit terms are changed, the current sale is expected to change to Rs 360 crore and the firm’s receivables level will also increase. The firm’s financial manager estimates that the new credit terms will cause the firm’s collection period to increase by 30 days.

3.

(a) Determine the present collection period and the collection period after the proposed change in credit terms. (b) What level of receivables is implied by the new collection period? (c) Determine the increased investment in receivables if the new credit terms are adopted. (d) Are the new credit terms desirable? The Syntex Company is planning to relax its credit policy to motivate customers to buy on credit terms of net 30. It is expected that the variable costs will remain 75 per cent of sales. The incremental sales are expected to be on credit basis. For the perceived increase in risk in liberalising the credit terms, the company requires higher required return. If the following is the projected information, which credit policy should the company pursue? Credit Policy A B C D

4.

5.

6.

7.

8.

Required Return Collection Period 20% 25% 32% 40%

40 45 55 70

New Sales (Rs) 600,000 500,000 400,000 300,000

X Ltd has current annual sales of Rs 60 crore and an average collection period of 30 days. The company is considering of liberalising its credit policy. If the collection period is extended, sales and bad debt are expected to increase in the following way:

Credit Policy

Increase in Collection Period

I II III IV

15 days 30 days 45 days 60 days

Increase in Sales Per cent Bad Rs (crore) Debt Losses 4.0 4.5 5.3 6.5

1.5 1.7 2.0 2.5

The firm sells its product for Rs 10 per unit. Average cost at current level of sales is 90 per cent for sales and variable cost is 80 per cent of sales. If the current bad debt loss is 1.5 per cent of sales and the required return is 18 per cent, which credit policy should be pursued? (Assume a 360-day year). State your assumptions. A company has a 15 per cent required rate of return. It is currently selling on terms of net 10. The credit sales of the company are Rs 120 crore a year. The company’s collection period currently is 60 days. If company offered terms of 2/10, net 30, 60 per cent of its customers will take the discount and the collection period will be reduced to 40 days. Should the terms be changed? A firm has current sales of Rs 7,200,000. The firm has unutilised capacity; therefore, with a view to boost its sales, it is considering lengthening its credit period from 30 days to 45 days. The average collection period will also increase from 30 to 45 days. Bad-debt losses are estimated to remain constant at 3 per cent of sales. The firm’s sales are expected to increase by Rs 360,000. The variable production, administrative and selling costs are 70 per cent of sales. The firm’s corporate tax rate is 35 per cent, and it requires an after-tax return of 15 per cent on its investment. Should the firm change its credit period? A firm has current sales of Rs 720,000. It is considering offering the credit terms ‘2, 10, net 30’ instead of ‘net 30.’ It is expected that sales will increase by Rs 20,000 and the average collection period will reduce from 30 days to 20 days. It is also expected that 50 per cent of the customers will take discounts and pay on 10th day and remaining 50 per cent will pay on 30th day. Bad-debt losses will remain at 2 per cent of sales. The firm’s variable cost ratio is 70 per cent, corporate tax rate is 50 per cent and opportunity cost of investment in receivables is 10 per cent. Should the company change its credit terms? The Electro Limited is a distributor of electric equipments. Its sales in 2004 amounted to Rs 22 crore and after tax profit Rs 1.10 crore. The company has been experiencing a declining profit margin for the last three years. It is felt that this is due to the loose credit policy. On investigation, a group of slow paying customers was identified. It is recommended that the credit policy should be tightened to eliminate them. Sales to this group amounted to about 20 per cent of the company’s total sales.

Table 28.8 gives information about the company’s cost structure. It is expected that if the slow-paying accounts are eliminated only variable costs would decline. It is also believed that bad-debt and collection expenses are entirely attributable to these accounts. Using this information, you are required to allocate Electro’s income and expenses between “slow-paying” accounts and “good” accounts. Table 28.8: The Electro Limited: Fixed and Variable Costs (Per cent of Sales)

Cost of goods sold Selling Administration Warehousing Bad-debts Collection

9.

Total

Fixed

Variable

85.0 4.6 2.4 2.4 0.4 0.2

– 2.0 0.8 1.0 – –

85.0 2.6 1.6 1.4 0.4 0.2

A study of credit files indicated that the collection period on ‘slow-paying’ accounts average to 50 days versus 35 days for all accounts. The balance of debtors for these accounts averaged Rs 885,000 during 2004. Should the Electro Limited tighten its credit policy? Make suitable assumptions. The PQR Company’s annual credit sales are Rs 60 crore. The company’s existing credit terms are 1/15, net 40. Generally 60 per cent of the customers avail the cash discount facility. The average collection period is 45 days. The percentage default rate is 0.5 per cent. The company is thinking of two alternative changes in credit terms: Credit Terms

Percentage Taking Collection Discount Period

Default Percentage

2/10, net 35

80

20

1.0

3/10, net 25

95

14

1.5

What strategy should be followed by PQR if sales are expected to remain stable and the required rate of return is 18 per cent? 10. Bansali Textiles Limited has annual sales of Rs 200 crore. It sells 80 per cent of its products on a 60-day credit. Its average collection period is 80 days. The company’s bad debts, based on the past experience, could be estimated as 0.9 per cent of credit sales. The company’s annual cost of administering credit sales is Rs 0.75 crore. It is possible to avoid Rs 0.20 crore of these costs if the company transfers credit administration to a factor. The factor will charge 1.75 per cent commission for his services. He can also extend advance against receivables to the company at an interest rate of 16.5 per cent after withholding 10 per cent as reserve. Should the company hire services of the factor?

Chapter 29 PROBLEMS 1. A company has Rs 4 per year carrying cost on each unit of inventory, an annual usage of 50,000 units and an ordering cost of Rs 100 per order. Calculate the economic order quantity. What shall be the total annual cost of EOQ? If a quantity discount of Re 0.25 per unit is offered to the company when it purchases in lots of 1,000 units, should the discount be accepted? 2. A firm’s estimated demand for a material during the next year is 2,500 units. Acquisition costs are Rs 400 per order and carrying cost is Rs 50 per unit. The safety stock is set at 25 per cent of the EOQ. The daily usage is 10 units and lead time is 10 days. Determine (a) the EOQ, (b) the safety stock, and (c) the reorder point. 3. A firm’s requirement of materials is 3,000 units (price Rs 20 per unit) for 6 days. The ordering cost per order is Rs 30 and the carrying cost is Re 0.50. If the schedule of discount given below is applicable to the firm, determine the most economical order quantity. Lot Size

Discount Rate

1 – 499

none

500 – 699

1%

4.

5.

700 – 999

2%

1000 – 2,499

4%

2500 and above

7%

AB Co. is considering a selective control for its inventories using the following data: You are required to prepare the ABC plan and also show the ABC plan on a chart. Units

Units Cost

7,000 8,000 10,000 6,000 8,000 2,000 5,000 4,000

10.00 9.00 2.00 8.00 1.00 60.00 0.40 40.00

Paul’s Sales India, a large retailer situated in the Western India, has been losing sales because of non availability of stock many times. The company’s average inventory is Rs 200 lakh. Its contribution ratio is 30 per cent. The inventory carrying cost is 3.5 per cent per annum. In a study carried out by the financial manager of the company, it was found that the company will lose sales if it carried an inventory less than Rs 450 lakh per annum. The range of inventories carried and expected lost sales are given below: Expected inventory level (Rs in lakh) 200 250 300 350 400 Expected lost sales (Rs in lakh) 250 180 120 50 20

450 0

The company’s working capital (excluding inventory) to sales ratio is 18 per cent. Assuming a tax rate of 35 per cent and an after-tax opportunity cost of 12 per cent, show which inventory policy the company should adopt.

Chapter 30 PROBLEMS 1. Kashiram & Co. is a manufacturer of children’s garments. The sales vary seasonally, and are highest in the month of May. The management of the company wishes to prepare a cash budget from the period January through June. The financial manager starts with the balance sheet of 1 January as shown in Table 30.5 and prepares a cash budget. Table 30.6 gives the sales for seven months. To prepare the cash budget, the following additional information is given: Table 30.5: Kashiram & Co's Balance Sheet, 1 January Liabilities & Capital

Amount (Rs ’000)

Assets

Amount (Rs ’000)

Current liabilities Other liabilities Share capital

3,000 10,800 317,280

Cash Debtors Inventory Fixed assets

84,480 42,000 123,000 81,600

Total funds

331,080

Total assets

331,080

Table 30.6: Sales Estimates (Rs ’000) December January February March

60,000 84,000 156,000 132,000

(Rs ’000) April May June July

228,000 288,000 108,000 108,000

(a) Sales for the month of December were Rs 60,000,000.

(b) (c) (d) (i) (f)

Credit sales are 70 per cent and cash sales 30 per cent of the total sales. Sales are collected after one month. Gross profit margin on sales is expected to be 25 per cent. Payments for the purchases are made one month in advance. A minimum inventory of Rs 60,000,000 at cost is always maintained. The company purchases sufficient inventory each month to take care of sales of the subsequent month. (g) Other monthly expenses are: (Rs ’000) Salary 9,600 Rent 2,400 Depreciation 720 Other 1% of sales

2.

3.

(h) A 16 per cent interest on borrowed funds is payable in the next month of every quarter on the outstanding balance. Borrowing is possible each month in the multiples of Rs 1,000,000. Kay Co. always prepares a cash budget for the months of January, February and March. Estimated sales for these months are Rs 500,000, Rs 600,000 and Rs 750,000 respectively. Actual sales for the month of December were Rs 520,000. About 80 per cent of Kay Co.’s total sales are on cash basis and 20 per cent credit sales collectible after one month. Kay Co. pays its creditors, which are usually about 40 per cent of sales, one month after the sale month. The forecasts of salary expenses for the coming three months are expected to be Rs 280,000 per month. Kay Co. is expected to spend about Rs 80,000 in February and Rs 190,000 in March on capital expenditures. A previously declared dividend of Rs 75,000 is to be paid in January and miscellaneous expenses are estimated to be Rs 15,000 per month. The company also has Rs 36,000 bills payable in February. (a) Prepare a statement showing the sale receipts. (b) Assuming that the 1 January cash balance is Rs 500,000 and that the minimum cash balance requirement of the company is Rs 500,000, prepare a cash budget for the next three months. (c) Explain the reason for estimated cash shortage that appears imminent. (d) Suppose that Kay Co. lends any surplus at 15 per cent per year for one month and borrows for three months at 18 per cent year when there is a cash shortage. Make the necessary changes in your cash budget prepared in (b) to make it balance. Assume that interest is paid at the end of any borrowing or lending period. Prepare a cash budget for the Kamp Manufacturing Company for three months of May, June and July. The company has a policy of maintaining a minimum cash balance of Rs 30,000. The company’s cash balance as on 30 April is Rs 30,000. Actual Sales (Rs) January February March April

4.

75,500 75,000 90,000 90,000

Estimated Sales (Rs) May June July August

105,000 120,000 150,000 150,000

Consider the following additional information: (a) Cash sales are 60 per cent of the total sales. The remaining sales are collected equally during the following two months. (b) Cost of goods manufactured is 75 per cent of sales. 80 per cent of this cost is paid after one month and the balance is paid after two months of the cost incurrence. (c) Fixed operating expenses are Rs 15,000 per month. Variable operating expenses are 10 per cent of sales each month. (d) Half yearly interest on 12% Rs 450,000 debentures is paid during July. (e) Rs 60,000 are expected to be invested in fixed assets during June. (f) An advance tax of Rs 15,000 will be paid in July. You are also required to determine whether or not borrowing will be necessary during the period and if yes, when and for how much. X Co. has average credit sales of Rs 1,500,000 per year. The working days per year are 300. If the company could reduce its bill processing time by two days, what would be the annual savings, assuming an interest rate of 18 per cent?

5.

6.

7.

8.

The Sirsa Company is a large wholesale distributor of consumer goods that sells mostly on credit. Collections from a particular location average Rs 200,000 per day. The total float averages 6 days for customers in this location. The opportunity cost of funds is 15 per cent. (a) The company has an offer from a bank to set up a lock-box system that will reduce float by 4 days, but the company will have to maintain a minimum balance of Rs 400,000 with the bank. Should the offer be accepted? (b) The bank also offers an option of a fixed fee of Rs 20,000 per year. What should the company do? A company has a central billing system. Its daily collections on an average are Rs 500,000. The total time for administering the collection is 6 days. (a) If a firm’s required rate of return is 10 per cent, what is the cost of the system to the firm? (b) If the management designs a lock-box system that reduces lag by 3 days, what is the reduction in cash balances? Garima Detergents has discovered that it takes about 10 days to collect the funds for use in the company once the cheques are received from the customers. The company’s annual turnover is Rs 9.70 crore. How much funds is to be freed if the company could reduce the collection time from 10 days to 8 days? If the freed funds could be used to reduce bank borrowings which costs 18 per cent per annum, what would be the net savings to the company? Assume a 360-day year and 35 per cent corporate tax rate. A company located in Ahmedabad wants to transfer Rs 15 lakh to its branch in Chennai. It will cost the company Rs 10 to mail the draft by a registered post. It will take 10 days for money to be finally transferred in Chennai. During these 10 days, the company is losing an opportunity of earning 12 per cent p.a. Alternatively, the company can instantaneously transfer the money telegraphically that will cost the company Rs 1,000. What should the company do?

Chapter 31 PROBLEMS 1. The following is the balance sheet and production plan of Neo-Pharma Ltd: Table 31.2: Neo-Pharma Limited Balance Sheet as on June 30, 20X2 (Rs in lakh) Liabilities Share capital Reserves Long-term loans Current liabilities: Sundry creditors 41 Other current liabilities 10 Bank borrowings 135 Provisions for tax and dividends 14

Assets 54 Fixed assets 8 Investments 4 Current assets: Raw materials Work-in-progress Finished goods Sundry debtors 200

266

31 5 64 7 49 91

Outstanding exports sales 15 Cash and bank balances 6 Misc. current assets 11 Advance tax payment 2 230 266

Notes: (i) Bills discounted with banks and outstanding as on June 30, 20X2 is Rs 500,000. (ii) An instalment of Rs 100,000 falls due on December 31, 20X2 as a part repayment of long-term loan. Table 31.3: Production Plan for The Year 20X2–03 (Rs in lakh) 20X1 (Actuals) Sales of which export sales 50 Cost of production of which: (a) Raw materials 151

266 211

20X2 (Projects) 75 173

291 238

(b) Wages and salaries

50

55

20X2 (Actuals) (c) Direct manufacturing expenses Gross profit Operating expenses Cost of sales Non-operating income Provision for taxation Net profit

10

20X2 (Projects) 10

55 44 255 4 8 7

53 42 280 3 8 6

Table 31.4: Projected Balance Sheet as on June 30, 20X3 (Rs in lakh) Liabilities

Assets

Share capital 54 Reserves 13 Long-term loans 3 Current liabilities of which: Work-in-progress 17 Other current liabilities 6 Bank borrowings 139 Provisions for tax and dividends 15 204

Fixed assets Investments Current assets of which: Raw materials

60

Finished goods Sundry debtors

52 98

Outstanding exports sales 27 Cash and bank balances 7 Misc. current assets 8 Advance tax payment 6

274

25 1

Sundry creditors

44

248 274

Notes: (i) Bills discounted with banks and outstanding as on June 30, 20X3, Rs 1,000,000. (ii) An instalment of Rs 250,000 falls due on December 31, 20X3 as a part repayment of long-term loan. Table 31.5: Working Capital Norms for Pharmaceutical Industry Raw materials and others Work-in-progress Finished goods Receivables and bills purchased and discounted.

2 ¾ months consumption ½ month’s cost of production 2 months cost of sales 1 ¼ months of sale

You are required to calculate the maximum permissible bank finance (MPBF) as per the Tandon Committee recommendations regarding Method 1 and Method 2. 2.

3.

Ananta Chemicals Limited is considering raising of Rs 15 crore by issuing CPs for 120 days. CPs will be sold at a discount of 11.25 per cent. Stamp duty charges will be 0.5 per cent of the size of the issue. The issuing and other charges will amount to Rs 3.75 lakh and rating charges to 0.40 per cent of the issue size. Calculate the effective cost of CP. XY Ltd is planning to sell a 90-day CP of Rs 100 for Rs 94.75. The company will have to incur expenses as follows: (a) rating of issue: 0.35 per cent, (b) stamp duty 0.5 per cent, (c) issuing charges 0.2 per cent and (d) dealer’s fee 0.15 per cent. What is the cost of CP?

Chapter 32 PROBLEMS 1. X Company Ltd intends to take over Y Company Ltd by offering two of its shares for every five shares in Y Company Ltd. Relevant financial data are as follows: X Co. Ltd

Y Co. Ltd

Earnings per share (Rs) Market price per share (Rs) Price-earnings ratio Number of shares (’000) Profit after tax (Rs ’000) Total market value (Rs ’000)

2.

2 100 50 100 200 10,000

What is the combined earnings per share? Calculate the P/E ratio of the combined firm. Has any wealth been created for shareholders? Alpha Ltd is considering the acquisition of Beta Ltd by making an offer of shares at 5 times of Beta’s present earnings. Alternatively, a reverse takeover is possible whereby Beta could offer to buy Alpha’s shares at 20 times its present earnings. What are the implications of these proposals? The relevant data are as follows: Alpha 2 40 20 400 800 16,000

Earnings per share (Rs) Market price per share (Rs) Price-earnings ratio Number of shares (’000) Profit after tax (Rs ’000) Total market value (Rs ’000)

3.

Rama Co.

Krishna Co.

800 200 4 15 60

600 300 2 10 20

Krishna Company expects an offer of 125 per cent of its current market price from Rama Company. (a) What is the exchange ratio of shares? How many new shares will be issued? (b) What is the acquiring company’s EPS after the merger? Assume 15 per cent synergy benefits accrue due to the merger. (c) If the price/earnings ratio after merger is at 20 times, what is the market price per share of the surviving company? The following data relate to Companies A and B:

Profit after-tax (Rs ’000) Equity shares (’000) Price-earnings ratio

5.

Beta 2 20 10 400 800 8,000

Calculate the effect on EPS. Would your answer be different if there are merger benefits of Rs 200,000 and Rs 100,000 in the first proposal and second proposals, respectively? Rama Company is considering the acquisition of Krishna Company with exchange of its shares. The financial data for the companies are as follows:

Profit after-tax (Rs ’000) No. of equity shares (’000) Earnings per share (Rs) Price-earnings ratio Market price per share (Rs)

4.

2 40 20 250 500 10,000

Company A

Company B

100 50 20

20 05 10

(a) If A and B merge by exchanging one share of Company A for each share of Company B, how would earnings per share of the two companies be affected? What is the market value exchange ratio? (b) If the exchange ratio were 3 shares of A for two shares of B, what would be the impact of earnings per share after merger. Assume that there would be synergy benefits equal to 20 per cent increase in the present earnings due to merger. (c) What exchange ratio would you suggest for the above merger? X Company wants to acquire Y Company. If the merger were effected through an exchange of shares, X Company would be willing to pay 40 per cent premium for Y Company’s shares. The following data are pertinent to Companies X and Y: Net Profit (Rs ’000) Number of shares (’000) Market price per share (Rs)

X Company

Y Company

1000 500 120

200 250 030

6.

(a) Compute the combined earnings per share. (b) What exchange ratio would you suggest? (c) If the exchange ratio were 1 share of Company X for each share of Company Y, what would happen? Sholapur Shoes Limited is evaluating the possibility of acquiring Kohalapur Shoes Limited. The following are data for the two companies: Sholapur Profit after-tax (Rs in lakh) Earnings per shares (Rs) Dividend per share (Rs) Number of shares (lakh) Total market capitalization (Rs in lakh)

7.

Kohalapur

54.75 7.30 4.20 7.50

9.90 2.20 1.20 4.50

1,000.00

135.00

(a) Calculate the price-earnings ratio of both the companies before merger. (b) Kohalapur’s earnings and dividends are expected to grow at 7.5 per cent without merger and at 10 per cent with merger. You are required to determine: (i) gain from the merger, (ii) the cost of merger if Kohalapur is paid cash of Rs 40 per share, and (iii) the cost of merger if the share exchange ratio is 0.25. Varun Chemicals Limited is proposing a takeover of Siddharth Pharm Limited. Varun’s main objective of the takeover is to increase its size as well as diversify its operations. Varun’s after-tax profits in the recent past have grown at 18 per cent per year and of Siddharth at 15 per cent per year. Both companies pay dividends regularly. Varun retains about 70 per cent of its profits and Siddharth 50 per cent. The summarised financial information for the two companies are given in the following. Summarised Profit and Loss Account (Rs in crore)

Net sales PBIT Interest PBT Provision for tax PAT Dividends Undistributed profit

Varun

Siddharth

4545 1590 750 1440 650 790 235 555

3500 480 25 455 205 250 125 125

Varun’s share is currently selling for Rs 52 and Siddharth’s Rs 75. The par value of both companies’ share is Rs 10. Varun’s land and building are stated at recent price. Siddharth’s land and buildings were revalued three years ago. There has been 30 per cent per year increase in the value of land and building. Summarised Balance Sheet (Rs crore) Varun

Siddharth

720 900 30

1650

190 350 10

550

775

280 250 50

580

Fixed Assets: Land and building, net Plant and machinery, net Furniture and fixtures, net Current Assets: Inventory Debtors Cash and bank balance Less: Current Liabilities Creditors Overdrafts Provision for tax Provision for dividends Net assets

400 350 25 230 35 145 60

470 1955

130 10 50 50

240 890

Paid up share capital Reserves and surplus Borrowing Capital employed

8.

250 1050

1300 655 1955

125 660

785 105 890

Varun’s management wants to determine the premium over the current market price of the shares which should be paid for the acquisition of Siddharth. Varun’s financial analyst is considering two options. The price should be determined using: (a) the dividend-growth formula, or (b) the balance sheet net worth adjusted for the current value of land and buildings plus the estimated average after tax profits for the next five years. After merger, Siddharth’s growth is expected to be 18 per cent each year. Grewal Industries Ltd is a diversified company with multiple businesses, and it also owns several subsidiary companies. Richa Foods Ltd is one of its subsidiaries that sell packaged food items. Grewal is in the process of consolidating its businesses and therefore, it is changing its strategic focus. In light of its new strategic focus, it has decided to sell Richa Foods Ltd. A number of companies, some from the reputed business houses, have shown considerable interest in buying Richa Foods. Table 32.22 and Table 32.23 contain the most recent Balance Sheet and Profit and Loss statement of Richa Foods Ltd: 32.22: Balance Sheet as at 31 December, 2004 Rs in crore Buildings Less: Accumulated depreciation

930 155

Plant & Machinery Less: Accumulated depreciation Furniture & Fixtures Less: Accumulated depreciation

124 81 39 8

Current assets Stock at cost Debtors Cash at bank Less: Creditors Trade creditors Acquired expenses Net assets 13% Long-term Loan

775 43 31 849

132 85 78 295 202 54

256

Shareholders’ Funds Ordinary share capital (Rs 10 share) General reserve Profit and Loss

39 888 388 500 233 54 213 500

Table 32.23: Profit and Loss Account for the Year Ended 31 May, 1995 (Rs in crore) Sales turnover Profit before interest and taxation Interest charges Profit before taxation Corporation tax Profit after taxation Dividend proposed and paid Transfer to general reserve Profit and Loss

1365 135 47 88 25 63 16 12 35

Richa Foods’ sales and profits have shown steady growth. The following are the possible realizable value of assets: (Rs in crore) Buildings Plant & machinery Furniture & Fixtures Stock

911 31 19 140

The book values of other assets are close approximation of their realisable value. A close competitor of Richa Foods has a price-earnings ratio of 12.5 and dividend yield of 5.4 per cent. The corporate income tax rate is 35 per cent. Calculate the value of Richa Foods using alternative methods. Which method do you suggest as most appropriate? Why should Grewal Industries Ltd sell its subsidiary?

Chapter 33 PROBLEMS 1. Gold is currently selling $340 an ounce. The price is likely to fluctuate. It could increase to $360 or could decrease to $320 an ounce after three months. A gold mine company will supply 3,000 ounces in the market after three months. The company is considering hedging its risk. It has two alternatives available. It can enter a futures contract to deliver gold after three months at a futures price of $342. Alternatively, the company can buy 3-month put option at an exercise price of $340 an ounce at a premium of $3 per ounce. What should company do? What will be the consequences if the company does not hedge? 2. A flour mill plans to purchase 100 quintals of wheat in three months. The wheat prices can be Rs 7,000 or Rs 7,500 or Rs 8,000 per quintal. The owner of the flour mill is worried about the possible change in price. How can he protect himself against the price risk? Show the consequences of your suggestion to him. 3. Suppose wheat futures price is $3.40 per bushel for 3-month contract. The spot price today is $3.00. The risk-free interest rate is 12 per cent per year. The present value of storage cost is $0.23. What is the present value of wheat? 4. In March 2004, three-month future on Sensex stock index traded at 5,686.4. The dividend yield was 1.4 per cent and interest rate 8 per cent per annum. What should be the spot index? 5. Company X and company Y need funds to finance expansion of their operations. X is a AAA-rated company while Y is a BBB-rated company. X can borrow funds at 11 per cent or LIBOR + 0.03 per cent floating rate. Y can borrow funds at 14 per cent or LIBOR + 1.5 per cent. Can X and Y benefit from swap? How can you structure a swap arrangement between Company X and Company Y? 6. Firm P can get a 5-year fixed-rate dollar loan at 9 per cent and Euro loan at 7 per cent. Firm Q, on the other hand, can get 5-year fixed-rate dollar loan at 11 per cent and Euro loan at 8 per cent. Suppose P wants to take Euro loan and Q dollar loan. Can you structure a swap so that the borrowing cost to each company is less? Assume that spot exchange rate is 1.2 dollar to one Euro.

Chapter 34 PROBLEMS 1. The current spot rate of British pound against the US dollar is UK£ 1.5763/US$. The 90-day forward rate is UK£ 1.5436. Calculate the annual forward discount or premium for the US dollar. 2. The 60-day forward rate of Indian rupee relative to the US dollar is: INR 40.85/US$. The spot rate is INR 38.95/US$. Is Indian rupee at a premium or discount? What is the annual percentage? 3. Suppose you have INR 10 million that you can invest for one year anywhere in the world without any restriction. You are considering to either invest in the US or in India. The interest rate on one-year bonds in India is 15 per cent and on one-year bonds in the US is 10 per cent. The current exchange rate is INR 39.80/US$. What should be the one-year forward rate so that you earn the same return whether you invest in India or in the US? 4. The expected inflation rate in France is 5 per cent and in Italy 7 per cent. The one-year loan in France returns 8 per cent. What should be the return on one-year loan in Italy?

5. 6.

7. 8.

9.

One-year Thai baht and US dollar forward rate is Baht 46.75/US$. The expected inflation rate in Thailand is 9 per cent and in the US 4 per cent. What is the current spot rate of exchange? The expected inflation rate in India is 5 per cent. The current spot rate between Indian rupee and South Korean Won is: Won 1.2345/INR and one-year forward rate is Won 1.2567. How much is the expected inflation rate in South Korea? The French franc-Japanese yen exchange rate is: ¥105.20/FF. The French franc-Indian rupee exchange rate is: INR 6.50/FF. What is the Japanese yen-Indian rupee exchange rate? A Thai company is expecting to receive US$ 5 million from an importer in the US after three months. The current spot exchange rate is Baht 43.75/US$ and 90-day forward rate is Baht 45.35/US$. What will be the consequences if the Thai firm (a) does not cover its exposure, (b) covers 60 per cent and keeps 40 per cent exposure uncovered, and (c) covers 100 per cent of its exposure by entering into a forward contract? Suppose the spot exchange rate at the time the Thai company receives payment is Baht 44.10 US$. What is the cost of the forward contract (partial and full)? An Indian firm is considering the possibility of building a plant to manufacture an industrial chemical in Thailand. The cost of investment is estimated to be Baht 25 million. The life of the investment is expected to be 12 years. It is expected the annual net cash flow in real terms will be Baht 4 million. The current spot exchange rate is Baht 1.105/INR. The risk-free interest rate in Thailand and India are 12 per cent and 10 per cent, respectively. The expected inflation rate in Thailand is 8 per cent. The Indian firm considers the opportunity cost of capital to be 7.25 per cent above the risk-free rate. Should the Indian firm make investment in Thailand? Show NPV calculations in Indian rupees using cash flows in (a) baht and (b) rupees.

Chapter 35 PROBLEMS 1. The following are the financial statements of Macro Company Limited for the year 20X1: Capital & Liabilities Rs (lakh)

Assets

Creditors Borrowings Paid-up share capital Reserve & surplus

Cash Inventory Debtors Net fixed assets

7,500 35,000 25,000 26,500 94,000

Rs (lakh)

Profit & Loss Sales Gross profit PBIT PBT PAT

2.

3.

4.

15,000 18,000 6,000 55,000 94,000 43,000 31,000 3,500 27,500 24,875

Calculate sustainable growth rate for Macro Company Limited. A firm has grown at 15 per cent in the past few years. Its after-tax ROI and after-tax interest rate have been, respectively, 16 per cent and 7 per cent. It now has a target growth rate of 18 per cent. The company expects its profitability and interest cost to remain constant and maintain its payout ratio at 60 per cent. How can the firm achieve its target growth? Show calculations. A manufacturing company earned PAT of Rs 123 crore in 2004 paying interest of Rs 24 crore. The company’s invested capital is Rs 1,340 crore and WACC 15 per cent. The tax rate is 35 per cent. Calculate the company’s EVA. Infosys Table 35.5 provides certain financial data for Infosys from year 2005 to year 2009. The company uses CAPM to calculate cost of equity. You are required to calculate the following: (i) MVA, (ii) EVA, (iii) M/B and (iv)sEconomic Return. Comment on the company’s market performance. Table 35.5: Infosys: Economic Value Added Analysis

2009 16,0 Avg. capital employed (Rs cr) Avg. debt-equity ratio Beta variant

25

2008 12,5 27

0 0.74

2007 9,1 47

0 0.76

2006 6,1 77

0 0.99

2005 4,3 31

0 0.78

0 0.98

Risk-free rate of rturn (%) Market premium (%) Operating profit (Rs cr)

7.0 7.0 6,4 34

8.0 7.0 6 40

9 Tax (Rs cr)

19

Market value of equity (Rs cr) Add: Market value of debt (Rs cr)

37

Less: Cash & cash equivalent (Rs cr)

52

85 82,3

69

3 26

82,1 54

0 1,3

61,0 73

0 8 01

1,15,3 07

48

13

69

6.8 7.0 2,0

3

1,15,3

82,3 62

54

07 0 1,6

75,8

7.5 7.0 2,6

3 86

62 0 1,9

37

77 6

75,8

Enteprise value (Rs cr)

8.0 7.0 3,8

0 5 90

82,1 54

61,0 73