1. CHAPTER 9 The Cost of Capital
Problem solving
Lidija Dedi

2. Problem 1:
Your company’ stock sells for $50 per share,

3. its last dividend was $2, its growth rate is a constant 5%, and the company will incur a flotation cost of 15% if it sells new common stock.
What is the firm’s cost of new equity?

4. P0 = $50
D0 = $2
g = 5%
F = 15%
ke = ?

5. cost of new equity?

6. Problem 2:
Alpha’s stock currently has a price of $50 per share and is expected to pay a year-end dividend of 2,50 per share.
The dividend is expected to grow at a constant rate of 4% per year
The company has insufficient retained earnings to fund capital projects and must therefore, issue new common stock.
The new stock has an estimated flotation cost of $3 per share

7. What is the company’s cost of equity capital?
The firm must issue new equity to fund its capital projects, so we need to find the cost of new equity capital, ke

8. Problem 3: Current market price of the firm’s stock is $28
Its last dividend was $2,20
Its expected dividend growth rate is 6%
Calculate cost of retained earnings?

9. We will use the dividend growth model

10. Problem 4: The company capital structure is 70% equity and 30% debt
The yield to maturity on the company’s bonds is 9%

11. The company’s year-end dividend is forecasted to be $0,80 a share
The company expects that its dividend will grow at a constant rate of 9% a year
The company’s stock price is $25
The company’s tax rate is 40%
The company anticipates that it will need to raise new common stock this year
Its investment bankers anticipate that the total flotation cost will equal 10% of the amount issued
Assume the company accounts for flotation costs by adjusting the cost of capital

12. Calculate the company’s WACC
After-tax cost of debt
cost of equity

14. Problem 5: Company’s capital structure
40% debt
60% common equity
The company has 20-year bonds outstanding with a 9% annual coupon that are trading at par
Tax rate is 40%

15. The risk-free rate is 5,5%
The market risk premium is 5%
The stock beta is 1,4
Calculate the company’s WACC

18. For the same company calculate WACC if
Market value of the company’s bonds is $80 and
Nominal value of the bonds is 100

20. Yield to maturity – Internal rate of return

21. Interpolation

22. WACC

23. Problem 6:
A company has determined that its optimal capital structure consists of 40 percent debt and 60 percent equity.
Assume the firm will not have enough retained earnings to fund the equity portion of its capital budget.
Also, assume the firm accounts for flotation costs by adjusting the cost of capital.

24. Given the following information, calculate the firm’s weighted average cost of capital
kd = 8%
Net income = $
Payout ratio = 50%
Tax rate = 40%
P0 = $25
Growth = 0%
Shares outstanding =
Flotation cost on additional equity = 15%

25. Dividend?
Since the firm will not have enough retained earnings to fund the equity portion of its capital budget, the firm will have to issue new common stock

26. Find the cost of new common stock!

27. WACC

28. Problem 7:
Alfa Corp. Wants to calculate its weighted average cost of capital (WACC)
CFO has the following information:
The company’s long-term bonds currently offer a yield to maturity of 8%
The company’s stock price is $32 a share
The company recently paid a dividend of $2 a share
The dividend is expected to grow at a constant rate of 6% a year

29. The company pays a 10% flotation cost whenever it issues new common stock
The company’s target capital structure is 75% equity and 25% debt
The company’s tax rate is 40%
The firm will be able to use retained earnings to fund the equity portion of its capital budget
What is the company’s WACC?

31. Problem 8:
Johnson Industries finances its projects with 40% debt, 10% preferred stock, and 50% common stock.
The company can issue bonds at a yield to maturity of 8,4%
The cost of preferred stock is 9%
The risk-free rate is 6,57%
The market risk premium is 5%
Johnson Industrie’s beta is equal to 1,3

32. Assume that the firm will be able to use retained earnings to fund the equity portion of its capital budget
The company tax rate is 30%
What is the company’s weighted average cost of capital (WACC)?

33. After-tax cost of debt
Cost of preferred stock

34. Cost of retained earnings

35. Problem 9: Company has a weighted average cost of capital of 11,5%
Its target capital structure is 55 percent equity and 45 percent debt
The company has sufficient retained earnings to fund the equity portion of its capital budget
The before-tax cost of debt is 9%

36. The company’s tax rate is 30%
If the expected dividend next period is $5 and the current stock price is $45, what is the company’s growth rate?

39. Problem 10:
ABC Steel has a capital structure with 30 percent debt (all long-term bonds) and 70 percent common equity
The yield to maturity on the company’s long-term bonds is 8%
The firm estimates that its overall composite WACC is 10%

40. The risk-free rate of interest is 5,5%
The market risk premium is 5%
The company’s tax rate is 40%
ABC uses CAPM to determine its cost of equity
What is the beta on ABC’s stock?

41. Data given

42. Step 1: determine the firm’s cost of equity using the WACC equation

43. Step 2: calculate the firm’s beta using the CAPM equation

44. Problem 11:
Arizona Inc., an all-equity firm, currently has a beta of 1,25
Risk-free rate 7%
Return for the “market” (KM) 14%

45. Suppose the firm sells 10% of its assets with beta = 1,25 and purchase the same proportion of new assets with a beta of 1,1
What will be the firm’s new overall required rate of return, and what rate of return must the new assets produce in order to leave the stock price unchanged?

47. Suppose the firm sells 10% of its assets with beta of 1,25 and purchase the same portion of new assets with a beta of 1,1
New beta?
Firm’s new required rate of return?

48. New required rate of return for new assets?

49. Problem 12: ABC Motors just reported earnings per share of $2,00
The stock has a price earnings ratio of 40, so the stock’s current price is $80 per share
Analysts expect that one year from now the company will have an EPS of $2,40 and it will pay its first dividend of $1,00 per share

50. The stock has a required return of 10%
What price earnings ratio must the stock have one year from now so that investors realize their expected return?

51. Data given:

52. Step 1: calculate the price of the stock one year from today

53. Step 2: calculate the P/E ratio one year from today

54. Have a nice day!