The Rivoli Company has no debt outstanding and its financial position is given by the
following data:
Assets (book = market)
EBIT
Cost of equity rs
Stock price P0
Shares outstanding, n0
Tax rate, T(federal-plus-state)
$3,000,000
500,000
10%
$15
200,000
40%
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 ate paid out as dividends, and
earnings are expectationally constant over time.
a- What effect would this use of leverage have on the value of the firm?
Original value of the firm (D = $0):
V = D + S = 0 + ($15)(200,000) = $3,000,000.
Original cost of capital:
WACC = wd rd(1-T) + wers
= 0 + (1.0)(10%) = 10%.
With financial leverage (wd=30%):
WACC = wd rd(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
( EBIT )(1  T ) ($500,000)(1  0.40)


 $3,348,214.286. .
WACC
WACC
0.0896
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 debt
of:
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
0.10
0.20
0.40
0.20
0.10
EBIT
($100,000)
200,000
500,000
800,000
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
EBIT
=
.
I
$70,312.5
Probability
0.10
0.20
0.40
0.20
0.10
TIE
( 1.42)
2.84
7.11
11.38
15.64
The interest payment is not covered when TIE < 1.0. The probability of
this occurring is 0.10, or 10 percent.