Question

The Rivoli Company has no debt outstanding, and its financial position is given by the following data: Assets (Market value = Book value) $3,000,000 EBIT $500,000 Cost of equity, rS 10% Stock price, P0 $15 Shares outstanding, n0 200,000 Tax rate, T 40% Unlevered beta 1.0 The firm is considering selling bonds and simultaneously repurchasing some of its stock. If it moves to a capital structure with 30% debt based on market values, its cost of equity, rS, will increase to 11% to reflect the increased risk. Bonds can be sold at a cost, rd, of 7%. Rivoli is a no-growth firm. Hence, all its earnings are paid out as dividends. Earnings are expected to be constant over time. a) What effect would this use of leverage have on the value of the firm? Calculate the value of the company with a new level of debt. Also, calculate the value of equity and debt in U.S. dollars. b) The problem provides the new cost of equity. Use the cost of equity formula of M&M Proposition II with taxes to show that the new cost of equity is approximately 11%. c) What would be the price of Rivoli’s stock after announcing the recapitalization? d) Calculate the number of shares purchased during the recapitalization, the number of remaining shares outstanding. Also, prove that market capitalization of equity is equal to the number of shares outstanding times the price per share you calculated from part (c). Your answer to this question (market capitalization of equity) should be equal to the value of equity you calculated in part (a). e) What happens to the firm’s earnings per share after the recapitalization? Calculate EPS before and after the recapitalization. f) Calculate the beta of the company after the recapitalization (with debt), using the Hamada formula. g) The $500,000 EBIT given previously is actually the expected value from the following probability distribution: Probability EBIT 0.1 ($100,000) 0.2 200,000 0.4 500,000 0.2 800,000 0.1 1,100,000 Determine the times-interest-earned ratio for each probability. What is the probability of not covering the interest payment at the 30% debt level?

Answer 1

a) Value of Debt= 30% of Assets = 30% *$3,000,000 = $900,000

As per MM proposition with taxes, the value of firm will increase as now the firm will get tax advantage.

So, Value of levered firm = Value of Unlevered firm +tax rate * Debt

=3,000,000 +0.4*900000

=$3,360,000

And value of Debt = $900,000 ,

Value of Equity = 3360000-900000 = $2,460,000

b) As per MM proposition with taxes,

levered Cost of equity = unlevered cost of equity + (unlevered cost of equity - cost of debt) * D/E*(1-tax rate)

=0.10+ (0.10-0.07)*900000/2460000*(1-0.4) = 0.106585 or 10.66%

So the cost of equity will increase and reach close to 11%

c) After announcement,value of firm will become $3,360,000

So, share price = Value of equity/no. of shares = 3360000/200000 =$16.8 per share

d) No, of shares purchased = 900000/16.8 =53571 apx

No. of shares outstanding = 200000-53571 = 146429

New value of equity = 146429 * 16.8 = $2,460,000 which is the same as above.in part a)