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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. Earnings per Share (EPS) under different scenarios:

a) No debt:

  • Normal: EBIT = $25,000, EPS = $25,000 / 5,000 shares = $5.00 per share
  • Expansion: EBIT = $25,000 * 1.25 = $31,250, EPS = $31,250 / 5,000 shares = $6.25 per share (25% increase)
  • Recession: EBIT = $25,000 * 0.5 = $12,500, EPS = $12,500 / 5,000 shares = $2.50 per share (50% decrease)

b) With $100,000 debt issue:

  • Normal: After repurchasing 2,000 shares with the debt proceeds (100,000 / 50 = 2,000), EBIT remains $25,000, but EPS increases due to fewer shares outstanding: EPS = $25,000 / 3,000 shares = $8.33 per share (66.6% increase from $5.00)
  • Expansion: Similar increase in EBIT, but EPS further rises: EPS = $31,250 / 3,000 shares = $10.42 per share (128.4% increase from $5.00)
  • Recession: Similar decrease in EBIT, but EPS remains higher due to fewer shares: EPS = $12,500 / 3,000 shares = $4.17 per share (66.6% decrease from $8.33)

Observations:

  • Recapitalization through debt and share repurchase increases EPS in all scenarios, but also amplifies volatility in economic downturns.
  • The company’s financial leverage increases, making it more sensitive to changes in interest rates and economic conditions.

2. Protos, Inc. EPS with 25% tax rate:

Repeat the calculations in part 1a and 1b (above) using the 25% tax rate. The results will be different due to the impact of taxes on EBIT and earnings available for common stockholders. The percentage changes in EPS might also be affected.

3. Stock Dividend and Equity Accounts:

A 15% stock dividend means existing shareholders receive 15% of their current holdings in additional shares. This will:

  • Increase the number of outstanding shares by 15%
  • Decrease the book value per share by 15% (total equity remains the same, but spread over a larger number of shares)
  • Have no impact on total equity or retained earnings

4. Sangria Corporation’s WACC:

  • Cost of equity: Ke = 16%
  • Cost of debt: Kd = 6% * (1 – 0.25) = 4.5% (adjusted for the tax shield)
  • Weight of equity: We = 65%
  • Weight of debt: Wd = 35%
  • WACC = Ke * We + Kd * Wd = 16% * 0.65 + 4.5% * 0.35 = 11.35%

5. Telefonica Co.’s WACC:

a) Cost of debt:

  • Coupon rate: 5%
  • Yield to maturity: 5% / 105% = 4.76% (adjusted for the bond price)
  • After-tax cost of debt: 4.76% * (1 – 0.15) = 4.04%

b) Cost of equity:

  • Beta: 1.20
  • Market risk premium: 8%
  • Risk-free rate: 4%
  • Cost of equity: Ke = Rf + Beta * (Rm – Rf) = 4% + 1.20 * (8% – 4%) = 12.8%

c) Weighted average cost of capital:

  • Weight of equity: We = 185,000 shares * $60/share / (5,000 bonds * $1,000 + 185,000 shares

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