Cost Of Capital Problems.docx

1. A limited company issues 8% preference shares which are irredeemable. The face value of share is $100 but they are issued at $105. The floatation cost is $3 per share. 2. A company issues 10000, 8% preference shares of $100 each redeemable after 20 years at face value. The floatation costs are $3 per share. Redeemable value = $100; Sale value = $100-$3 = $97 Annual dividend = $8 per share. 3. Baibhav Ltd., issued 10,000, 12% preference shares of Rs 100 each at a premium of 6%; the floatation cost being 2.5% on issue price. The shares are to be redeemed after 5 years at a premium of 5%. Compute the cost of preference share capital. 4. Suppose that you are offered a 10 year, 8 per cent coupon, Rs. 1000 par value bond for a price of Rs. 875. Interest from this bond is payable semi-annually. What yield do you expect to earn from the same, if you plan to keep it till maturity? 5. Suppose the same bond in Q4 has a call provision that kicks in 4 years from issue. If the firm calls the bonds on the first date possible, it will have to pay Rs. 1080 as call price. Calculate Yield. 6. If D0 = $1.72, P0 = $43, and g = 5%, what’s the cost of common equity based upon the DCF approach? 7. The future earnings, dividends and common stock price of Carpetto Technologies are expected to grow at 7% per year. Carpetto’s common stock currently sells at $23.00 per share; its last dividend was $2.00. a. Using DCF approach, what is the cost of common equity? b. If the firm.s beta is 1.6, the risk-free rate is 9% and average expected market return is 13%. Recalculate the cost of firm’s equity using CAPM approach. c. If the firm’s bonds earn a return of 12%, based on the bond-yield-plus-risk-premium approach, what will be the cost of equity? d. If you have confidence in the inputs used in the three approaches, what is your estimate for Carpetto’s cost of equity? 8. Voyages Jules Verne’s ordinary shares had a dividend payout equal to €1.25 and it is commonly known that the firm expects dividends paid to increase by 8 per cent for the next two years and by 2 per cent thereafter. If the current price of Voyages Jules Verne’s ordinary shares is €17.80, then what is the cost of ordinary shares for the firm? 9. La Lampe Magique SA currently has €300 million of market value debt outstanding. The 9 per cent coupon bonds (semi-annual pay) have a maturity of 15 years and are currently priced at €1 440.03 per bond. The firm also has an issue of 2 million preference shares outstanding with a market price of €12.00. The preference shares offer an annual dividend of €1.20. La Lampe Magique also has 14 million ordinary shares outstanding with a price of €20.00. The firm is expected to pay a €2.20 ordinary share dividend one year from today, and that dividend is expected to increase by 5 per cent per year forever. If La Lampe Magique is subject to a 40 per cent marginal tax rate, then what is the firm’s weighted average cost of capital?

10. The Jackson Company has just paid a dividend of $3.00 per share on its common stock, and it expects this dividend to grow by 10 percent per year, indefinitely. The firm has a beta of 1.50; the risk-free rate is 10 percent; and the expected return on the market is 14 percent. The firm's investment bankers believe that new issues of common stock would have a flotation cost equal to 5 percent of the current market price. 11. End of Chapter Case: Coleman Technologies Inc. Coleman Technologies is considering a major expansion program that has been proposed by the company’s information technology group. Before proceeding with the expansion, the company must estimate its cost of capital. Assume that you are an assistant to Jerry Lehman, the financial vice president. Your first task is to estimate Coleman’s cost of capital. Lehman has provided you with the following data, which he believes may be relevant to your task: 1. The firm’s tax rate is 40%. 2. The current price of Coleman’s 12% coupon, semiannual payment, noncallable bonds with 15 years remaining to maturity is $1,153.72. Coleman does not use short-term interestbearing debt on a permanent basis. New bonds would be privately placed with no flotation cost. 3. The current price of the firm’s 10%, $100 par value, quarterly dividend, perpetual preferred stock is $111.10. 4. Coleman’s common stock is currently selling for $50 per share. Its last dividend (D0) was $4.19, and dividends are expected to grow at a constant rate of 5% in the foreseeable future. Coleman’s beta is 1.2, the yield on T bonds is 7%, and the market risk premium is estimated to be 6%. For the bond-yield-plus-risk-premium approach, the firm uses a risk premium of 4%. 5. Coleman’s target capital structure is 30% debt, 10% preferred stock, and 60% common equity. To structure the task somewhat, Lehman has asked you to answer the following questions. A. (1) What sources of capital should be included when you estimate Coleman’s WACC? (2) Should the component costs be figured on a before-tax or an after-tax basis? (3) Should the costs be historical (embedded) costs or new (marginal) costs? B. What is the market interest rate on Coleman’s debt and its component cost of debt? C. (1) What is the firm’s cost of preferred stock? (2) Coleman’s preferred stock is riskier to investors than its debt, yet the preferred’s yield to investors is lower than the yield to maturity on the debt. Does this suggest that you have made a mistake? D. (1) Why is there a cost associated with retained earnings? (2) What is Coleman’s estimated cost of common equity using the CAPM approach? E. What is the estimated cost of common equity using the DCF approach? F. What is the bond-yield-plus-risk-premium estimate for Coleman’s cost of common equity? G. What is your final estimate for rs? H. Explain in words why new common stock has a higher cost than retained earnings.

I. (1) What are two approaches that can be used to adjust for flotation costs? (2) Coleman estimates that if it issues new common stock, the flotation cost will be 15%. Coleman incorporates the flotation costs into the DCF approach. What is the estimated cost of newly issued common stock, considering the flotation cost? J. What is Coleman’s overall, or weighted average, cost of capital (WACC)? Ignore flotation costs. K. What factors influence Coleman’s composite WACC? L. Should the company use the composite WACC as the hurdle rate for each of its projects? Explain. Solution

1. Kp = $8/($105-$3) = 7.84% 2. Kp = 8 + (100 - 97) / 20 = 8.27% (100 + 97) / 2 3.

4. Calculate YTM, INT=40 N=2*10=20 YTM=5%*2=10% 5. The bond is callable six years before maturity, we will calculate YTC for 4 years (time when the call option can be exercised) INT= 40 N=2*4=8 Maturity Value=Rs. 1080 YTC=6.87*2=13.7% 6. D1 = D0 (1+g) D1 = $1.72 (1 + .05)

D1 = $1.81 kcs

= (D1 / P0)+ g = ($1.81 / $43) + 0.05 = 9.2%

7. a. rs =

D1 $2.14 +g= + 7% = 9.3% + 7% = 16.3%. P0 $23

b. rs = rRF + (rM – rRF)b = 9% + (13% – 9%)1.6 = 9% + (4%)1.6 = 9% + 6.4% = 15.4%.

c. rs = Bond rate + Risk premium = 12% + 4% = 16%.

d. Since you have equal confidence in the inputs used for the three approaches, an average of the three methodologies probably would be warranted.

rs =

16.3%  15.4%  16% = 15.9%. 3

8.

Cost of capital is 10 per cent. 9. Step 1: Total amount of debt, ordinary shares and preference shares: Debt = €300 000 000 (given) Preference shares = €12 × 2 000 000 = €24 000 000 Ordinary shares = €20 × 14 000 000 = €280 000 000 Total capital at market value = €604 000 000 xDebt = 300/604 = 0.4967 xp = 24/604 = 0.0397

xe = 280/604 = 0.4636 Step 2: Cost of capital components: Cost of debt: €1 440.03 = €45 × PVIFA(30, YTM/2) + €1 000 × PVIF(30, YTM/2) Solving, we find that YTM = 0.0484 (this is a pre-tax number). Cost of preference shares:

k ps 

D €1.20   0.10 Pps €12.00

Cost of ordinary shares:

Step 3: Combine using the WACC formula.

10. rs = 10% + 1.5(4%) = 16%. P0 =

3.00(1.10) 0.16−0.10

1. 11. Sol in Excel

= $55.00