Prepared by A.K.Mohideen, MBA, M.Phil, (Ph.D)
1
Unit-1
TIME VALUE 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 Cash-flow (Rs)
0 – 10,000
1–6 (each period) + 2,000
7 – 1,500
8 + 1,600
9–12 (each period) + 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. (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.
Prepared by A.K.Mohideen, MBA, M.Phil, (Ph.D)
2 12. 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?
13. 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.
14. 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?
15. 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?
16. 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?
17. (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?
18. 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?
19. 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?
20. 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?
21. 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?
22. 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?
23. 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.
24. 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.
25. 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?
26. 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.
Prepared by A.K.Mohideen, MBA, M.Phil, (Ph.D)
3 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?
Valuation of bonds and shares
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?
Prepared by A.K.Mohideen, MBA, M.Phil, (Ph.D)
4 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 Interest Rate Required Rate Maturity Period (Years)
A 16% 15% 25
B 14% 13% 15
C 12% 8% 20
D 12% 8% 10
9. 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?
10. 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, buy-back price being Rs 1,150.
11. 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?
12. 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?
13. 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.
14. 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?
15. 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?
16. 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 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?
Prepared by A.K.Mohideen, MBA, M.Phil, (Ph.D)
5 17. 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?
18. 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.
19. 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? 20. 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?
21. Consider the following data of four auto (two / three-wheelers) companies. EPS DIV Share Price
Companies (Rs) (%) (Rs)
1. Bajaj 11.9 50 275.00
2. Hero Honda 10.2 22 135.00
3. Kinetic 12.0 25 177.50
4. Maharashtra Scooters 20.1 25 205.00
The face value of each company‘s share is Rs 10. Explain the relative performance of the four companies.
22. 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.
23. 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.
24. 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.
25. 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?
26. 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?
Prepared by A.K.Mohideen, MBA, M.Phil, (Ph.D)
6 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?
Risk and return
PROBLEMS1. 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.
2. 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.
3. 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.
4. 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?
5. 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?
6. 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.
7. An asset is expected to earn the following rates of return for the period 2004-10: Year 2004 2005 2006 2007 2008 2009 2010
Return (%) 15.3 5.6 17.3 25.0 16.8 9.5 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 1 2 3 4 5
Return (%) 5.3 15.6 7.3 15.0 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
Prepared by A.K.Mohideen, MBA, M.Phil, (Ph.D)
7 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 20% 18% 8% 0 – 6%
Probability 0.10 0.45 0.30 0.05 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% 0.10 – 20% 0.05
20% 0.20 10% 0.25
10% 0.40 20% 0.30
5% 0.20 30% 0.30
– 10% 0.10 40% 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 30 –10
0.40 20 20
0.30 0 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 Probability Market Treasury
Conditions Return (%) 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.
Prepared by A.K.Mohideen, MBA, M.Phil, (Ph.D)
8 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?
PROBLEMS
1. An asset has the following possible returns with associated probabilities: Possible returns 20% 18% 8% 0 –6%
Probability 0.10 0.45 0.30 0.05 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 Security Y
Return Probability Return Probability
30% 0.10 –20% 0.05
20% 0.20 10% 0.25
10% 0.40 20% 0.30
5% 0.20 30% 0.30
–10% 0.10 40% 0.10
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 30 –10
0.40 20 20
0.30 0 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% 0.3
30% 0.4
–10% 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.
6. The Sunrise and Sunset companies have the following probability distribution of returns:
Returns (%) Economic conditions Probability Sunrise Sunset
High growth 0.1 32 30
Normal growth 0.2 20 17
Prepared by A.K.Mohideen, MBA, M.Phil, (Ph.D)
9
Stagnation 0.2 –5 –12
Decline 0.1 –10 –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(
P = 23% (r Q = 19%
Cor
Q = 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?
Option valuation
PROBLEMS1. 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.
2. 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.
3. 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.
4. 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?
5. 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. 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. 7. 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.
8. 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.
9. 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.
10. 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?
11. 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.
Prepared by A.K.Mohideen, MBA, M.Phil, (Ph.D)
10 12. 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.
13. 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.
14. 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.
15. 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.
16. 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.
17. 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?
18. 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.
19. 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.
20. 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?
21. 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.
22. 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.
Unit-II
Capital budgeting
PROBLEMS1. The following are the net cash flows of an investment project: Cash Flows (Rs)
Prepared by A.K.Mohideen, MBA, M.Phil, (Ph.D)
11 – 5,400 + 3,600 + 14,400
Calculate the net present value of the project at discount rates of 0, 10, 40, 50 and 100 per cent. 2. 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?
3. 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.
4. The G.K. Company is evaluating a project with following cash inflows: Cash Flows (Rs)
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?
5. 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) 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?
7. Compute the rate of return of the following projects: Cash Flows (Rs)
Projects C0 C1 C2 C3
X – 20,000 + 8,326 + 8,326 + 8,326
Q – 20,000 0 0 + 24,978
Which project would you recommend? Why?
8. A firm is considering the following two mutually exclusive investments: Cash Flows (Rs)
Projects C0 C1 C2 C3
A – 25,000 + 15,000 + 15,000 + 25,640
B – 28,000 + 12,672 + 12,672 + 12,672
The cost of capital is 12 per cent. Compute the NPV and IRR for each project. Which project should be undertaken? Why?
9. You have an opportunity cost of capital of 15 per cent. Will you accept the following investment? Cash Flows (Rs)
Prepared by A.K.Mohideen, MBA, M.Phil, (Ph.D)
12
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 C0 C1 C2 C3
A – 10,000 + 12,000 + 4,000 + 11,784
B – 10,000 + 10,000 + 3,000 + 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 C0 C1 C2 C3
X – 750 + 350 + 350 + 159
Y – 750 + 250 + 250 + 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 C2 C3 C4
I – 25,000 + 30,000
II – 25,000 0 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 C0 C1 C2 C3 C4 A – 1,000 + 600 + 200 + 200 + 1,000 B – 1,000 + 200 + 200 + 600 + 1,000 C – 1,300 + 100 + 100 + 100 + 1,600 D – 1,300 0 0 + 300 + 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?
Prepared by A.K.Mohideen, MBA, M.Phil, (Ph.D)
13 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) C1 C2 C3 Cash revenue 16 14 12 Cash expenses 8 7 6 Gross profit 8 7 6 Depreciation 4 4 4 Net profit 4 3 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 C2 C3 C4 C5
– 50,000 + 11,300 + 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?
PROBLEMS
1. The Damodar Company is considering two mutually exclusive projects with different lives. The costs (cash flows) of the projects are given below:
Prepared by A.K.Mohideen, MBA, M.Phil, (Ph.D)
14
Project C0 C1 C2 C3 C4
X 150 30 30 30 30
Y 75 40 40
The discount rate is 10 per cent. Which project should be selected and why?
2. 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. 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?
4. 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?
5. 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.
6. 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?
7. 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? 8. 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.
9. 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:
0.5
Rs 80,000(1 + )
tA
=
t
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: Project M Project N Investment (Rs) 250,000 250,000 Annual net cash inflow (Rs) 80,000 60,000
Prepared by A.K.Mohideen, MBA, M.Phil, (Ph.D)
15
Life (years) 6 10
Cost of capital (per cent) 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 – 3,000 2,250 + 2,700
M – 3,950 + 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: Cash Outlay Profitability Internal Rate Proposals (Rs) Index of Return (%)
A 100,000 1.22 15 B 50,000 1.17 14 C 40,000 1.46 20 D 30,000 1.72 25 E 20,000 1.13 13 F 10,000 1.04 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 10 1.8 P 50 8.0 Q 20 4.0 S 60 3.6 T 100 25.0 U 80 18.0 V 40 4.0
Cost of capital
PROBLEMS1. 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?
Prepared by A.K.Mohideen, MBA, M.Phil, (Ph.D)
16 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:
Year Dividend per Share (Rs)
2003 2.00 2004 2.20 2005 2.42 2006 2.66 2007 2.93 2008 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.
8. 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)
Book Value Market Value
Ordinary shares 30 60
Reserves 10 —
Preference shares 20 24
Debt 40 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 2.00 2000 2.80 2004 2.16 2001 3.08 2005 2.37 2002 3.38 2006 2.60 2003 3.70
Prepared by A.K.Mohideen, MBA, M.Phil, (Ph.D)
17 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 93.75 10% Preference 31.25 Ordinary equity 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) 563.50
Reserves and surplus 485.66
10% Irredeemable Preference shares 56.00 10% Redeemable Preference shares 28.18
15% Term loans 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) 66,412 Reserves 65,258 Preference (Rs 100 par) 3,000 Debentures 30,000 Long-term loans 5,360 170,030 The earnings per share of the company over the period 2004–2008 are:
Year Rs Year Rs
Prepared by A.K.Mohideen, MBA, M.Phil, (Ph.D) 18 2005 3.00 1995 5.15 2006 4.21 1996 5.05 2007 3.96 1997 6.00 2008 4.80 1998 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 6,808
Reserve 34,857
Long-term loans 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 21.55 5.28 143.04 20.9 2003 22.14 5.76 187.52 18.6 2004 26.40 5.76 312.32 11.7 2005 20.16 6.53 587.52 11.0 2006 20.40 7.68 366.72 9.5 2007 23.09 11.53 416.64 10.3 2008 22.00 7.68 355.20 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 Market Value (Rs) Value 2003 6.21 2.00 26.03 100.00 2004 10.91 2.50 34.44 205.00 2005 11.57 2.50 43.52 209.38 2006 11.47 2.70 37.98 164.00 2007 10.44 3.00 45.42 138.88 2008 11.23 3.20 53.45 155.00
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.
