Chapter 16 Appendix: The Miller Model and the Graduated Income Tax
16.17
a.
According to the Miller Model, in equilibrium:
r
B
(1 – T
C
) = r
S
where
r
B
= the pretax cost of debt (the interest rate)
T
C
= the corporate tax rate
r
S
= the required return on a firm’s equity
In this problem:
T
C
= 0.35
r
S
= 0.11
Therefore, in order for there to be equilibrium:
r
B
(1 – T
C
) = r
S
r
B
(1 – 0.35) = 0.11
r
B
= 0.11 / (1 – 0.35)
=
0.1692
The equilibrium interest rate is 16.92%.
b.
In order to determine whether each group would prefer to hold debt or equity, it is necessary
to compare the afterpersonal tax interest rate to the required return on unlevered equity for
each of the three groups of investors. A group of investors will prefer to hold the security that
offers them the highest rate of return.
The required rate of return to equity holders is 11%. Since the effective personal tax rate on
equity distributions is zero, personal taxes do not change the required return to equity holders.
The market interest rate is 16.92%.
The afterpersonal tax interest rate for investors who face a 10% tax on interest income is
15.23% {= 0.1692 * (1  0.10)}. Since the afterpersonal tax interest rate (15.23%) is greater
than the required return on equity (11%), this group is better off holding debt.
Investors whose interest income is taxed at 10% will buy debt.
The afterpersonal tax interest rate for investors who face a 20% tax on interest income is
13.54% {= 0.1692 * (1  0.20)}. Since the aftertax interest rate (13.54%) is greater than the
required return on equity (11%), this group is also better off holding debt.
Investors whose interest income is taxed at 20% will buy debt.
The afterpersonal tax rate interest rate for investors who face a 40% tax on interest income is
10.15% {= 0.1692 * (1  0.40)}. Since the aftertax interest rate (10.15%) is less than the
required return on equity (11%), this group is also better off holding equity.
Investors whose interest income is taxed at 40% will buy equity.
c.
According to the Miller Model, firm value does not vary with capital structure in equilibrium.
Therefore, Firm A’s value would be equal to an allequity financed firm with EBIT of $1
million in perpetuity.
V
A
= [(EBIT)(1 – T
C
)] / r
S
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= [($1,000,000)(1 – 0.35)] / 0.11
=
$5,909,091
The value of Firm A is $5.91 million.
16.18
a.
According to the Miller Model, in equilibrium:
r
B
(1 – T
C
) = r
S
where
r
B
= the pretax cost of debt (the interest rate)
T
C
= the corporate tax rate
r
S
= the required return on a firm’s equity
In this problem:
T
C
= 0.35
r
S
= 0.081
Therefore:
r
B
(1 – T
C
) = r
S
r
B
(1 – 0.35) = 0.081
r
B
= 0.081 / (1 – 0.35)
=
0.1246
The equilibrium market rate of interest is 12.46%.
b.
In order to determine whether each group would prefer to hold debt or equity, compare the
afterpersonal tax interest rate on debt to the required return on unlevered equity for each of
the three groups of investors. A group of investors will prefer to hold the security that offers
them the highest rate of return.
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 Summer '06
 TimothyDreyer
 Finance, Debt, Interest, Interest Rate

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