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1. Protos, Inc., has no debt outstanding and a total market value of $300,000. Earnings before interest and taxes, EBIT, are projected to be $25,000 if economic conditions are normal. If there is strong expansion in the economy, then EBIT will be 25 percent higher. If there is a recession, then EBIT will be 50 percent lower. Money is considering a $100,000 debt issue with an interest rate of 6 percent. The proceeds will be used to repurchase shares of stock. There are currently 5,000 shares outstanding. Ignore taxes for this problem.

a) Calculate earnings per share, EPS, under each of the three economic scenarios before any debt is issued. Also calculate the

percentage changes in EPS when the economy expands or enters a recession.

b) Repeat part (a) assuming that Protos goes through with recapitalization. What do you observe?

2.  Repeat parts (a) and (b) in Problem 1 assuming Protos has a tax rate of 25 percent.

3.- The company with the common equity accounts shown here has declared a stock dividend of 15 percent when the market value of its stock is $45 per share. What effects on the equity accounts will the distribution of the stock dividend have?

4.- Sangria Corporation has a target capital structure of 65 percent common stock and 35 percent debt. Its cost of equity is 16 percent, and the cost of debt is 6 percent. The relevant tax rate is 25 percent. What is Sangria’s WACC?

5.- Given the following information for Telefonica Co., find the WACC.

Assume the company’s tax rate is 15 percent.

Debt: 5,000 bonds outstanding, 5 percent coupon, $1,000 par value, 10 years to maturity, selling for 105 percent of par; the bonds make semiannual payments.

Common stock:

185,000 shares outstanding, selling for $60 per share; the beta is 1.20.

Market: 8 percent market risk premium and 4 percent risk-free rate.

 

Sample Solution

1. Protos, Inc. Capital Structure and EPS:

a) Without Debt:

  • Normal Economy: EBIT = $25,000, Shares Outstanding = 5,000, EPS = $25,000 / 5,000 = $5.
  • Expansion: EBIT = $25,000 * 1.25 = $31,250, EPS = $31,250 / 5,000 = $6.25, Change in EPS = ($6.25 – $5) / $5 * 100% = 25% increase.
  • Recession: EBIT = $25,000 * 0.5 = $12,500, EPS = $12,500 / 5,000 = $2.5, Change in EPS = ($5 – $2.5) / $5 * 100% = 50% decrease.

b) With Debt:

  • Normal Economy:
    • Interest Expense = $100,000 * 6% = $6,000.
    • EBIT after interest = $25,000 – $6,000 = $19,000.
    • EPS = $19,000 / (5,000 + 100,000/($45 per repurchased share)) = $3.68.
  • Expansion and Recession: Similar calculations with adjusted EBITs.

Observations:

  • Debt increases leverage, amplifying EPS changes in both directions.
  • Repurchasing shares further reduces shares outstanding, increasing EPS.

2. Protos, Inc. with Tax (25%):

  • Repeat calculations above, adjusting EBIT for taxes before calculating EPS.
  • Tax reduces EPS in all scenarios.

3. Stock Dividend Effect:

  • Total common stock will increase by 15% of outstanding shares.
  • Retained earnings will decrease by the amount of dividends declared.
  • Book value per share will decrease due to the share dilution (stock split).

4. Sangria Corporation’s WACC:

  • Weight of equity = 65%.
  • Weight of debt = 35%.
  • Cost of equity = 16%.
  • Cost of debt = 6% * (1 – 0.25) = 4.5% (adjusted for tax).
  • WACC = 0.65 * 16% + 0.35 * 4.5% = 11.05%.

5. Telefonica Co.’s WACC:

Cost of Debt:

  • Yield to maturity = 5% / (105% * 10) = 4.76%.
  • Semi-annual cost of debt = 4.76% / 2 = 2.38%.

Cost of Equity:

  • Capital Asset Pricing Model (CAPM):
    • Risk-free rate = 4%.
    • Market risk premium = 8%.
    • Beta = 1.20.
    • Cost of equity = 4% + 1.20 * 8% = 13.6%.

Weighted Average Cost of Capital (WACC):

  • Equity weight = 185,000 * $60 / (185,000 * $60 + 5,000 * $1,000 * 1.05) = 89.14%.
  • Debt weight = 10.86%.
  • WACC = 0.8914 * 13.6% + 0.1086 * 2.38% = 12.34%

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