Mini Case: 15 – 19
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:
d = wd V = 0.2 ($2,659,574) = $53.19.
wd
Debt, D
0%
$ 0
20%
$ 53.1915
30%
$ 81.7439
40%
$108.6957
50%
$131.5789
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
VTotal
$250
− Debt
0
S
$250
n
10
P
$25.00
S
$250
Cash distr.
0
Wealth
$250
The stock price is $25 and the total wealth of shareholders is $2,500,000.
+ ST Inv.
10
10
website, in whole or in part.
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.
n = 10 – 2
= 8.
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
− Debt
0
53.1915
53.1915
S
$250
$265.9574
$212.7660
n
10
10
8
P
$25.00
$26.60
$26.60
S
$250
$265.9574
$212.7660
Cash distr.
0
0
53.1915
Wealth
$250
$265.9574
$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
Mini Case: 15 – 23
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website, in whole or in part.
required payment on the debt, and the firm will be bankrupt. The debtholders will
take over the firm and the equity holders will receive nothing. If L’s value is greater
than $2 million in one year, then management will repay the debt and the
stockholders will keep the company.
This option can be valued with the Black-Scholes Option Pricing Model:
V = PN(D1) – Xe–RTN(D2)
And n() is the cumulative normal distribution function, from either appendix a in the
R = 0.06
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
Mini Case: 15 – 24
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
0.40
2.13
1.87
0.45
2.14
1.86
0.50
2.16
1.84
0.55
2.17
1.83
0.60
2.20
1.80
0.65
2.22
1.78
0.70
2.25
1.75
0.75
2.28
1.72
0.80
2.31
1.69
0.85
2.34
1.66
0.90
2.38
1.62
0.95
2.41
1.59
decreases as well. A manager who knows this may choose to invest the proceeds
from borrowing in assets that are riskier than usual. This is called “bait and switch.”
This action decreases the value of the debt, because now its claim is riskier. It
increases the value of equity because the worse the stockholders can do is default on
the bonds, but the best they can do is potentially unlimited.
Mini Case: 15 – 25
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:
Finance long-term assets with long-term debt
Finance short-term assets with short-term debt.
Information asymmetries: