Question

Spam Corp. is financed entirely by common stock and has a beta of .70. The firm is expected to generate a level, perpetual stream of earnings and dividends. The stock has a price-earnings ratio of 7.90 and a cost of equity of 12.66%. The company’s stock is selling for $52. Now the firm decides to repurchase half of its shares and substitute an equal value of debt. The debt is risk-free, with an interest rate of 3%. The company is exempt from corporate income taxes. Assume MM are correct.

Calculate the cost of equity after the refinancing. (Enter your answer as a percent rounded to 2 decimal places.)
Calculate the overall cost of capital (WACC) after the refinancing. (Enter your answer as a percent rounded to 2 decimal places.)
Calculate the price-earnings ratio after the refinancing. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Calculate the stock price after the refinancing.
Calculate the stock’s beta after the refinancing. (Round your answer to 1 decimal place.)

Answer 1

a. Cost of equity after the refinancing = 22.31%

b. Cost of capital (WACC) after the refinancing = 12.66%

c. Price-earnings ratio after the refinancing = 4.48

d. Stock price after the refinancing = $51.99

e. Stock’s beta after the refinancing = 2.52

Step-by-step explanation:

Given:

Beta = 0.70

PE ratio = Price-earnings ratio = 7.90

Ke = Cost of equity = 12.66%

MPS = Market price per share = $52

Debt rate = 3%

Let assume that the company’s total number of shares outstanding is 1,000. Therefore, we have:

Equity market value = MPS * Number of shares = $52 * 1,000 = $52,000

By repurchasing half shares and substituting an equal value of debt, we have:

Debt = Equity market value / 2 = $52,000 / 2 = $26,000

Interest on debt = Debt * Debt rate = $26,000 * 3% = $780

Old EPS = MPS / PE ratio = $52 / 7.90 = $6.58 per share

Net income = Old EPS * Number of shares = $6.58 * 1,000 = $6,580

Earnings available to shareholders = Net income – Interest on debt = $6,580 – 780 = $5,800

New number of shares = 500

New EPS = Earnings available to shareholders / New number of shares = $5,800 / 500 = $11.60 per share

Therefore, we have:

a. Calculate the cost of equity after the refinancing. (Enter your answer as a percent rounded to 2 decimal places.)

Cost of equity after the refinancing = New EPS / MPS = $11.60 / $52 = 0.2231, or 22.31%

b. Calculate the overall cost of capital (WACC) after the refinancing. (Enter your answer as a percent rounded to 2 decimal places.)

Cost of capital (WACC) after the refinancing = (Weight of debt * Cost of debt) + (Weight of equity * New cost of equity) = (50% * 3%) + (50% * 22.31%) = 12.66%

c. Calculate the price-earnings ratio after the refinancing. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Price-earnings ratio after the refinancing = 1 / Cost of equity after the refinancing = 1 / 22.31% = 4.48

d. Calculate the stock price after the refinancing.

Stock price after the refinancing = Price-earnings ratio after the refinancing * New EPS = $11.60 * 4.48 = $51.99

e. Calculate the stock’s beta after the refinancing. (Round your answer to 1 decimal place.)

Stock’s beta after the refinancing = (Cost of equity after the refinancing – Cost of debt) / (WACC – Cost of debt) = (0.2231 - 0.03) / (0.1266 - 0.05) = 2.52