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Self-Study Problems
13.2 Berron Comics, Inc., has borrowed $100 million and is required to pay its lenders $8 million
in interest this year. If Berron is in the 35 percent marginal tax bracket, then what is the
after-tax cost of debt (in dollars as well as in annual interest) to Berron.
Solution:
Because Berron enjoys a tax deduction for its interest charges, the after-tax interest expense
for Berron is $8 million × (1 – 0.35) = $5.2 million, which translates into an annual interest
expense of $5.2/$100 = 0.052, or 5.2 percent.
13.3 Explain why the after-tax cost of equity (common or preferred) does not have to be
adjusted by the marginal income tax rate for the firm.
Solution:
The U.S. tax code allows a deduction for interest expense incurred on borrowing.
Preferred and common shares are not considered debt and, thus, do not benefit from an
interest deduction. As a result, there is no distinction between the before-tax and after-tax
cost of equity capital.
13.4 Mike’s T-Shirts, Inc., has debt claims of $400 (market value) and equity claims of $600
(market value). If the after-tax cost of debt financing is 11 percent and the cost of equity is
17 percent, then what is Mike’s weighted average cost of capital?
The Cost of Capital (WACC)
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Solution:
Mike’s T-Shirts’ total firm value = $400 + $600 = $1,000. Therefore,
Debt = 40 percent of financing
Equity = 60 percent of financing
WACC = xDebtkDebt(1-t) + xpskps + xcskcs
WACC = (0.4 × 0.11) + (0.6 × 0.17) = 0.146, or 14.6%
13.5 You are analyzing a firm that is financed with 60 percent debt and 40 percent equity. The
current cost of debt financing is 10 percent, but due to a recent downgrade by the rating
agencies, the firm’s cost of debt is expected to increase to 12 percent immediately. How
will this change the firm’s weighted average cost of capital if you ignore taxes?
Solution:
The pretax debt contribution to the cost of capital is xDebt × kDebt, and since the firm’s
pretax cost of debt is expected to increase by 2 percent, we know that the effect on WACC
(pretax) will be 0.6 × 0.02 = 0.012, or 1.2 percent. Incidentally, if we assume that the firm
is subject to the 40 percent marginal tax rate, then the after-tax contribution to the cost of
capital for the firm would be 0.012 × (1 – 0.4) = 0.0072, or 0.72 percent.
Questions and Problems
13.2 WACC: What is the weighted average cost of capital?
LO 4
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Solution:
The weighted average cost of capital (WACC) is the weighted average of the costs to the
different sources of capital used to fund a firm, The WACC is often used as an estimate
of the cost of financing a new project given the firm’s current mix of debt and equity.
13.10 WACC: Describe the alternatives to using a firm’s WACC as a discount rate when
evaluating a project.
LO 4
Solution:
There are two major reasons why WACC may not be used to discount new projects:
1. It is not appropriate to use a firm’s WACC to discount a project’s free cash flows if the
systematic risk of the project is very different from the systematic risk of the firm. To
account for this potential problem, some firms estimate discount rates that directly reflect
the risk involved in the project’s cash flows. For example, a risky project might be
assigned a discount rate that is significantly higher then the firm’s WACC.
2. It is not appropriate to use a firm’s WACC when a project that has the same systematic
risk as the firm is not being financed using the same mix of debt and equity as the firm—
for example, if a project will be financed entirely with equity. The project’s cash flows
should be discounted using the cost of equity rather than the firm’s WACC. These two
rates will be the same only if the firm has no debt.
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13.11 WACC for a firm: Capital Co. has a capital structure, based on current market values,
that consists of 50 percent debt, 10 percent preferred shares, and 40 percent common
shares. If the returns required by investors are 8 percent, 10 percent, and 15 percent for
debt, preferred equity, and common stock, respectively, what is Capital’s after-tax
WACC? Assume that the firm’s marginal tax rate is 40 percent.
LO 4
Solution:
cscspspsdebtdebt
kxkxtkxWACC ++−= )1(
=
WACC=0.5×0.08×(1-0.4)+0.1×0.10+0.4×0.15=0.094, or 9.4%
13.18 Taxes and the cost of debt: Holding all other things constant, does a decrease in the
marginal tax rate for a firm provide incentive for the firm to increase or decrease its use
of debt?
LO 2
Solution:
The after-tax cost of debt for the firm is equal kDebt x (1 – t). We can then calculate the
tax benefit to using debt to be kDebt x t. Therefore, the value of the tax benefit to debt
increases with the marginal tax rate. If the marginal tax rate decreases, then the tax
benefit to debt decreases as well. Therefore, the incentive to borrow actually decreases
with a decrease in the marginal tax rate.
