Question

Capital Structure Analysis

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, Po	$15
Shares outstanding, no	200,000
Tax rate, T (federal-plus-state)	40%

The firm is considering selling bonds and simultaneously repurchasing some of its stock. If it moves to a capital structure with 25% debt based on market values, its cost of equity, r_s, will increase to 11% to reflect the increased risk. Bonds can be sold at a cost, r_d, 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.

1. What effect would this use of leverage have on the value of the firm?
   I. Increasing the financial leverage by adding debt results in an increase in the firm's value.
   II. Increasing the financial leverage by adding debt results in a decrease in the firm's value.
   III. Increasing the financial leverage by adding debt has no effect on the firm's value.
   -Select-IIIIIIItem 1
   
2. What would be the price of Rivoli's stock? Do not round intermediate calculations. Round your answer to the nearest cent.
   $   per share
   
3. What happens to the firm's earnings per share after the recapitalization? Do not round intermediate calculations. Round your answer to the nearest cent.
   The firm -Select-increaseddecreasedItem 3 its EPS by $   .
   
4. The $500,000 EBIT given previously is actually the expected value from the following probability distribution:

   Probability	EBIT
   0.10	($ 75,000)
   0.20	150,000
   0.40	450,000
   0.20	800,000
   0.10	1,375,000

   
   Determine the times-interest-earned ratio for each probability. Use a minus sign to enter negative values, if any. Do not round intermediate calculations. Round your answers to two decimal places.

   Probability	TIE
   0.10
   0.20
   0.40
   0.20
   0.10

   
   What is the probability of not covering the interest payment at the 25% debt level? Do not round intermediate calculations. Round your answer to two decimal places.
   
     %

Answer 1

Original value of the firm (D = $0):

V = D + S = 0 + ($15)(200,000) = $3,000,000.

Original cost of capital:

WACC = wdrd(1-T) + wers= 0 + (1.0)(10%) = 10%.

With financial leverage (wd=30%):

WACC = wdrd(1-T) + wers= (0.3)(7%)(1-0.40) + (0.7)(11%) = 8.96%.

Because growth is zero, the value of the company is:

V =FCF/WACC=(EBIT)(1-T)/WACC=($500,000)(1-0.40)/0.0896=$3,348,214.286..

Increasing the financial leverage by adding $900,000 of debt results in an increase in the firm’s value from $3,000,000 to $3,348,214.286.

b-What would be the price of Rivoli’s stock?

Using its target capital structure of 30% debt, the company must have debtof:

D = wd V = 0.30($3,348,214.286) = $1,004,464.286.

Therefore, its debt value of equity is:

S = V–D = $2,343,750.

Alternatively, S = (1-wd)V = 0.7($3,348,214.286) = $2,343,750.

The new price per share, P, is:

P = [S + (D–D0)]/n0= [$2,343,750 + ($1,004,464.286–0)]/200,000= $16.741.

c-What happens to the firm’s earnings per share after the recapitalization?

The number of shares repurchased, X, is:

X = (D–D0)/P = $1,004,464.286 / $16.741 = 60,000.256~60,000.

The number of remaining shares, n, is:

n = 200,000–60,000 = 140,000.

Initial position:

EPS = [($500,000–0)(1-0.40)] / 200,000 = $1.50.

With financial leverage:

EPS = [($500,000–0.07($1,004,464.286))(1-0.40)] / 140,000= [($500,000–$70,312.5)(1-0.40)] / 140,000= $257,812.5 /140,000 = $1.842.

Thus, by adding debt, the firm increased its EPS by $0.342.

d-The $500,000 EBIT given previously is actually the expected value from the

following probability distribution:

Probability EBIT

0.10 ($100,000)

0.20 200,000

0.40 500,000

0.20 800,000

0.10 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?

30% debt:TIE =EBIT/I=EBIT/$70,312.5

Probability TIE

0.10 ( 1.42)

0.20 2.84

0.40 7.11

0.20 11.38

0.10 15.64

The interest payment is not covered when TIE < 1.0. The probability of this occurring is 0.10, or 10 percent.