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146
CHAPTER 18
How Much Should a Firm Borrow?
Answers to Practice Questions
1.
a.
T
c
is the corporate tax rate, T
p
is the personal tax rate on interest income
and T
pE
is the effective personal tax rate on equity income.
In the U.K.,
T
c
= 30% and T
p
= 40%.
T
pE
is less than 40% because the effective
capital gains tax rate for the John Peel Group is zero.
If, for example,
T
pE
= 20%, then:
(1 – T
pE
) × (1 – T
c
) = 0.80 × 0.70 = 0.56
and: 1 – T
p
= 0.60
Here, a lower debt ratio reduces the sum of corporate and personal taxes.
If T
pE
= 14.3% then:
(1 – T
pE
) × (1 – T
c
) = 0.857 × 0.70 = 0.600
If the effective tax rate on equity income is 14.3% or higher, then a lower
debt ratio reduces the sum of corporate and personal taxes.
Since the
John Peel Group shareholders are in the top U.K. tax bracket, indicating
relatively high income, it seems likely that T
pE
is relatively high; the annual
allowance of £8,000 is relatively low for highincome taxpayers, so that the
bulk of their equity income is in the form of cash dividends.
b.
As discussed in Chapter 16, an increase in cash dividend payout, holding
capital investment and debt constant, must be financed by issuing new
shares; the capital loss to existing shareholders resulting from the new
issue exactly offsets the increased cash dividend.
For the John Peel
Group shareholders, the increased dividend is taxed at 40% but the
capital loss is apparently not tax deductible.
Therefore, an increase in
cash dividend payout increases the sum of corporate and personal taxes.
The John Peel Group should maintain a low dividend payout ratio and use
internally generated funds as its primary source of financing.
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View Full Document 147
2.
Consider a firm that is levered, has perpetual expected cash flow X, and has an
interest rate for debt of r
D
.
The personal and corporate tax rates are T
p
and T
c
,
respectively.
The cash flow to stockholders each year is:
(X  r
D
D)(1  T
c
)(1  T
p
)
Therefore, the value of the stockholders’ position is:
where r is the opportunity cost of capital for an allequityfinanced firm.
If the
stockholders borrow D at the same rate r
D
, and invest in the unlevered firm, their
cash flow each year is:
The value of the stockholders’ position is then:
The difference in stockholder wealth, for investment in the same assets, is:
V
L
– V
U
= DT
c
This is the change in stockholder wealth predicted by MM.
If individuals could not deduct interest for personal tax purposes, then:
Then:
So the value of the shareholders’ position in the levered firm is relatively greater
when no personal interest deduction is allowed.
)
T
(1
)
(r
)
T
(1
)
T
(1
D)
(
)
(r
)
T
(1
(r)
)
T
(1
)
T
(1
(X)
V
p
D
p
c
D
p
p
c
L
−
−
−
−
−
−
−
=
)]
T
(1
D)
(
)
T
(1
(r)
)
T
(1
)
T
(1
(X)
V
c
p
p
c
L
−
−
−
−
−
=
[
)]
T
(1
D)
(
)
r
(
)]
T
(1
)
T
(1
[(X)
p
D
p
c
−
−
−
−
[
)
T
(1
)
(r
)
T
(1
D)
(
)
(r
)
T
(1
(r)
)
T
(1
)
T
(1
(X)
V
p
D
p
D
p
p
c
U
−
−
−
−
−
−
=
D
)
T
(1
(r)
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This note was uploaded on 04/18/2010 for the course FINANCE 936116531 taught by Professor Wuyiling during the Spring '10 term at Nashville State Community College.
 Spring '10
 wuyiling
 Corporate Finance, Interest

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