Question

The Rivoli Company has no debt outstanding and its financial position is given by the following data: Market value of Assets $10,000 EBIT $ 1,500 Stock price $10 Shares outstanding 1,000 Tax rate 35% The firm is considering selling bonds and simultaneously repurchasing some of its stock. If it moves to a capital structure with 40% debt based on market values, the bonds can be sold at a cost, rd, of 8%. Rivoli is a no-growth firm and all of its earnings are paid out as dividends.

a. What is Rivoli’s current cost of equity?

b. If the risk free rate is 3 percent and the market risk premium is 5 percent, what is Rivoli’s unlevered beta?

c. What is the levered beta at the new capital structure of 40 percent debt?

d. What is the new cost of equity under the capital structure financed with 40 percent debt?

e. What is its new weighted average cost of capital?

f. What is the new total corporate value of Rivoli?

g. What is the new stock price?

h. How many shares remain outstanding after the recapitalization?

Answer 1

(a)

EBIT = 1500

less: tax @ 35% -525

Net income = 975

All income is distributed, so dividends = 975

No. of shares 1000

Dividend per share= 0.975

Stock price 10

Cost of Equity with no growth = Dividend/Market price

0.975/10= 0.0975 or 9.75%

So, cost of Equity is 9.75%

(b)

Required rate of return = Risk free rate + (equity Beta*market Risk premiym)

9.75%=3%+(E.B.*5)

6.75%=E.B.*5 6.75/5

Equity beta or unlevered beta= 1.35

company is all equity, so unlevered beta or beta of asset is 1.35

(c) new capital structure is 40% debt

so Equity = 60% or 0.60

Debt = 40% or 0.40

Levered beta or Equity beta formula = Unlevered or Asset beta * (1 +( (1-tax rate)*Debt/Equity))

1.35 * (1 + ((1-0.35)*0.40/0.60))

1.935

So, unlevered beta is 1.935

(d) new cost of Equity

Required rate of return or Cost of equity= Risk free rate + (equity Beta*market Risk premiym)

3%+(1.935*5%)

12.675

So, new cost of Equity at 40% debt is 12.68%