Principles of Corporate Finance_ 12th Edition

452 Part Five Payout Policy and Capital Structure

bre44380_ch17_436-459.indd 452 10/05/15 12:52 PM

MM left us a simple message. When the firm changes its mix of debt and equity securities, the

risk and expected returns of these securities change, but the company’s overall cost of capital

does not change.

Now if you think that message is too neat and simple, you’re right. The complications are

spelled out in the next two chapters. But we must note one complication here: In the U.S.

and many other countries, interest paid on a firm’s borrowing can be deducted from taxable

income. Thus the after-tax cost of debt is rD(1 – Tc), where Tc is the marginal corporate tax

rate. So, when companies discount an average-risk project, they do not use the company cost

of capital as we have just computed it. Instead they use the after-tax cost of debt to compute

the after-tax weighted-average cost of capital or WACC:

After-tax WACC = rD(1 − Tc) D__

V

+ rE E__

V

We briefly introduced this formula in Chapter 9, where we used it to estimate the weighted-

average cost of capital for Union Pacific. In 2014, Union Pacific’s long-term borrowing rate

was rD = 4.2%, and its estimated cost of equity was rE = 9.8%. With a 35% corporate tax rate,

the after-tax cost of debt was rD(1 – Tc) = 4.2(1 – .35) = 2.7%. The ratio of debt to overall

company value was D/V = 9.4%. Therefore

After-tax WACC = rD(1 − Tc) __D

V

+ rE E__

V

= 4.2 × (1 − .35) × .094 + 9.8 × .906 = 9.1%

MM’s proposition 2 states that in the absence of taxes the company cost of capital stays the

same regardless of the amount of leverage. But if companies receive a tax shield on their interest

payments, then the after-tax WACC declines as debt increases. This is illustrated in Figure 17.4,

which shows how Union Pacific’s WACC changes as the debt–equity ratio changes.

Most large public corporations use an after-tax WACC to discount cash flows from pro-

posed investments. By doing so they are following MM’s proposition 1, except for using an

after-tax cost of debt.^12

(^12) They are also simplifying by using the promised rate of return on debt. Strictly speaking, MM would use the expected rate of return,
which is lower than the promised rate of return because of the risk of default. But promised and expected rates of return are usually
close for creditworthy companies.
17-4 A Final Word on the After-Tax Weighted-Average Cost of Capital
BEYOND THE PAGE
mhhe.com/brealey12e
Try It! Figure 17.4:
Changing leverage
and the cost of
capital
◗ FIGURE 17.4
Estimated after-tax WACC
for Union Pacific at differ-
ent debt–equity ratios. The
figure assumes rE = 9.8% at
a 9.4% debt ratio (equiva-
lent to a 10.4% debt–equity
ratio) and a borrowing rate
of rD = 4.2%. Notice that the
debt interest rate is assumed
to increase at higher debt
ratios. 2
0.00 0.06 0.12 0.19 0.25 0.31 0.37 0.44 0.50
3
4
5
6
7
8
9
10
11
12
Debt-equity ratio (D/E)
Return, %
After-tax WACC
Opportunity cost of capital (rA)
Cost of debt (rD )
Cost of equity (rE )