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i. Describe the recapitalization process and apply it to PizzaPalace. Calculate the
resulting the value of the debt that will be issued, the resulting market value of
equity, the price per share, the number of shares repurchased, and the remaining
shares. Considering only the capital structures under analysis, what is
PizzaPalace’s optimal capital structure?
Answer:
First, find the dollar value of debt. For example, for wd = 20%, the dollar value of
debt is:
We can then find the dollar value of equity:
S = V – D
We repeat this process for all the capital structures.
wdDebt, D
0% $ 0
Note: these are rounded; see Ch15 Mini Case.xls for full calculations.
The situation before the recap is:
Before
Debt
Vop $250
+ ST Inv. 0
The stock price is $25 and the total wealth of shareholders is $2,500,000.
Now consider the situation if the firm moves to a capital structure with wd = 20% by
issuing $53.1915 in debt but has not yet repurchased equity. The firm’s value of
operations increases because its WACC decreases. The firm also temporarily has
$531,915 in short-term investments.
Before Debt
After Debt,
Before Rep.
Vop $250 $265.9574
+ ST Inv. 0 53.1915
VTotal $250 $319.1489
− Debt 0 53.1915
Notice that the stock price increases and the wealth of shareholders increases.
The repurchase itself will not change the stock price. If investors thought that the
repurchase would increase the stock price, they would all purchase stock the day
before, which would drive up its price. If investors thought that the repurchase would
decrease the stock price, they would all sell short the stock the day before, which
would drive down the stock price.
The number of shares repurchased is:
# repurchased = (D - D0) / P
The number of remaining shares after the repurchase is:
# remaining = n0 - # rep.
Before
Debt
After
Debt,
Before
Rep. After Rep.
Vop $250 $265.9574 $265.9574
+ ST Inv. 0 53.1915 0
VTotal $250 $319.1489 $265.9574
Notice that the value of the equity declines as more debt is issued, because debt is
used to repurchase stock. But the total wealth of shareholders is the value of stock
after the recap plus the cash received in repurchase, and this total is not changed by
the repurchase.
There are some shortcuts we can take to find the values of S, P, and n after the
repurchase:
S = (1 – wd) Vop
nPost = nPrior
OldopNew
NewopNew
DV
DV
PPost =
iorPr
OldopNew
n
DV
We apply these relationships for each possible capital structure:
wd0% 20% 30% 40% 50%
rd0.0% 8.0% 8.5% 10.0% 12.0%
ws100% 80% 70% 60% 50%
This option can be valued with the Black-Scholes Option Pricing Model:
V = PN(D1) – Xe-RTN(D2)
where
And n() is the cumulative normal distribution function, from either appendix a in the
back of the text, or the NORMSDIST() function in excel.
in this case, P = $4
and calculating,
D1 = 1.552
D2 = 0.9552
The yield on this debt is calculated as
Price = (Face Value)/(1+Yield)N
so that
Yield = [Face Value/Price]1/N – 1.0
k. What is the value of L’s stock for volatilities between 0.20 and 0.95? What
incentives might the manager of L have if she understands this relationship? What might
debtholders do in response?
Answer: The mini case model shows the calculations for the table below.
Value of Stock and Debt
for Different Volatilities
Volatility Equity Debt
0.20 2.12 1.88
0.25 2.12 1.88
0.30 2.12 1.88
0.35 2.12 1.88
The value of the equity increases as the volatility increases—and the value of the debt
decreases as well. A manager who knows this may choose to invest the proceeds
Bondholders who face this possibility will write covenants into their bond contracts
l. How do companies manage the maturity structure of their debt?
Answer: Factors that influence the decision to issue long-term bonds rather than short-term
debt:
Maturity matching:
Information asymmetries:
Firms with better future prospects than expected by investors will know that issuing
