Principles of Corporate Finance_ 12th Edition

Chapter 18 How Much Should a Corporation Borrow? 465

bre44380_ch18_460-490.indd 465 10/05/15 12:53 PM

This suggests two special cases. First, suppose that debt and equity income were taxed at the
same effective personal rate. With TpE = Tp, the relative advantage depends only on the cor-
porate rate:

Relative advantage =

1 − Tp

______________

(1 − TpE)(1 − Tc)

= ______^1

1 − Tc

In this case, we can forget about personal taxes. The tax advantage of corporate borrowing
is exactly as MM calculated it.^6 They do not have to assume away personal taxes. Their theory
of debt and taxes requires only that debt and equity income be taxed at the same rate.
The second special case occurs when corporate and personal taxes cancel to make debt
policy irrelevant. This requires

1 − Tp = (1 − TpE)(1 − Tc)

This case can happen only if Tc, the corporate rate, is less than the personal rate Tp and if TpE,
the effective rate on equity income, is small. Merton Miller explored this situation at a time
when U.S. tax rates on interest and dividends were much higher than now, but we won’t go
into the details of his analysis here.^7

◗ FIGURE 18.1

The firm’s capital structure

determines whether operating

income is paid out as inter-

est or equity income. Interest

is taxed only at the personal

level. Equity income is taxed

at both the corporate and

the personal levels. However,

TpE, the personal tax rate on

equity income, can be less

than Tp, the personal tax rate

on interest income.

Corporate tax None Tc

Income after

corporate tax $1.00 $1.00–Tc

Personal tax Tp TpE( 1.00–Tc )

1.00–Tc – TpE( 1.00–Tc )

Income after all taxes (1.00–Tp ) = (1.00 –TpE )(1.00–Tc )

Operating income

$1.00

Paid out as

interest

Or paid out as

equity income

To bondholder To stockholder

(^6) Personal taxes reduce the dollar amount of corporate interest tax shields, but the appropriate discount rate for cash flows after
personal tax is also lower. If investors are willing to lend at a prospective return before personal taxes of rD, then they must also be
willing to accept a return after personal taxes of rD(1 – Tp), where Tp is the marginal rate of personal tax. Thus we can compute the
value after personal taxes of the tax shield on permanent debt:
PV(tax shield) =
Tc × rDD × (1 − Tp)
_____r
D × (1 − Tp)
= TcD
This brings us back to our previous formula for firm value:
Value of firm = value if all-equity-financed + TcD
(^7) M. H. Miller, “Debt and Taxes,” Journal of Finance 32 (May 1977), pp. 261–276.