Chapter 11: Cost of Capital
Chapter 11
Cost of Capital
Discussion Questions
11-1.
Why do we use the overall cost of capital for investment decisions even when
only one source of capital will be used (e.g., debt)?
Though an investment financed by low-cost debt might appear acceptable at first
glance, the use of debt could increase the overall risk of the firm and eventually
make all forms of financing more expensive. Each project must be measured
against the overall cost of funds to the firm.
11-2.
How does the cost of a source of capital relate to the valuation concepts presented
previously in Chapter 10?
The cost of a source of financing directly relates to the required rate of return for
that means of financing. Of course, the required rate of return is used to establish
valuation.
11-3.
In computing the cost of capital, do we use the historical costs of existing debt
and equity or the current costs as determined in the market? Why?
In computing the cost of capital, we use the current costs for the various sources
of financing rather than the historical costs. We must consider what these funds
will cost us to finance projects in the future rather than their past costs.
11-4.
Why is the cost of debt less than the cost of preferred stock if both securities are
priced to yield 10 percent in the market?
Even though debt and preferred stock may be both priced to yield 10 percent in
the market, the cost of debt is less because the interest on debt is a tax-deductible
expense. A 10 percent market rate of interest on debt will only cost a firm in a
35 percent tax bracket an aftertax rate of 6.5 percent. The answer is the yield
multiplied by the difference of (one minus the tax rate).
11-5.
What are the two sources of equity (ownership) capital for the firm?
The two sources of equity capital are retained earnings and new common
stock.
Chapter 11: Cost of Capital
11-6.
Explain why retained earnings have an associated opportunity cost?
Retained earnings belong to the existing common stockholders. If the funds are
paid out instead of reinvested, the stockholders could earn a return on them. Thus,
we say retaining funds for reinvestment carries an opportunity cost.
11-7.
Why is the cost of retained earnings the equivalent of the firm’s own
required rate of return on common stock (Ke)?
Because stockholders can earn a return at least equal to their present
investment. For this reason, the firm’s rate of return (Ke) serves as a means
of approximating the opportunities for alternate investments.
11-8.
Why is the cost of issuing new common stock (Kn) higher than the cost of
retained earnings (Ke)?
In issuing new common stock, we must earn a slightly higher return than
the normal cost of common equity in order to cover the distribution costs
of the new security. In the case of the Baker Corporation, the cost of new
common stock was six percent higher.
11-9.
How are the weights determined to arrive at the optimal weighted average
cost of capital?
The weights are determined by examining different capital structures and
using that mix which gives the minimum cost of capital. We must solve a
multidimensional problem to determine the proper weights.
11-10.
Explain the traditional, U-shaped approach to the cost of capital.
The logic of the U-shaped approach to cost of capital can be explained
through Figure 11-1. It is assumed that as we initially increase the
debt-to–equity mix the cost of capital will go down. After we reach an
optimum point, the increase use of debt will increase the overall cost of
financing to the firm. Thus we say the weighted average cost of capital
curve is U-shaped.
11-11.
It has often been said that if the company can’t earn a rate of return greater
than the cost of capital it should not make investments. Explain.
If the firm cannot earn the overall cost of financing on a given project, the
investment will have a negative impact on the firm‘s operations and will
lower the overall wealth of the shareholders.
Clearly, it is undesirable to invest in a project yielding 8 percent if the
financing cost is 10 percent.
Chapter 11: Cost of Capital
11-12.
What effect would inflation have on a company’s cost of capital? (Hint:
Think about how inflation influences interest rates, stock prices, corporate
profits, and growth.)
Inflation can only have a negative impact on a firm‘s cost of capital-forcing
it to go up. This is true because inflation tends to increase interest rates and
lower stock prices, thus raising the cost of debt and equity directly and the
cost of preferred stock indirectly.
11-13.
What is the concept of marginal cost of capital?
The marginal cost of capital is the cost of incremental funds. After a firm
reaches a given level of financing, capital costs will go up because the firm
must tap more expensive sources. For example, new common stock may be
needed to replace retained earnings as a source of equity capital.
Appendix A
Discussion Questions
11A-1.
How does the capital asset pricing model help explain changing costs of
capital?
The capital asset pricing model explains the relationship between risk and
return, and the price adjustment of capital assets to changes in risk and return.
As investors react to their economic environment and their willingness to take
risk, they change the prices of financial assets like common stock, bonds, and
preferred stock. As the prices of these securities adjust to investors’ required
returns, the company’s cost of capital is adjusted accordingly.
Chapter 11: Cost of Capital
11A-2.
How does the SML react to changes in the rate of interest, changes in the rate of
inflation, and changing investor expectations?
The SML, Security Market Line, reflects the risk-return tradeoffs of securities.
As interest rates increase, the SML moves up parallel to the old SML. Now
investors require a higher minimum return on risk free assets and an equally
higher rate for all levels of risk. A change in the rate of inflation has a similar
impact. The risk free rate goes up to provide the appropriate inflation premium
and there is an upward shift in the SML.
In regard to changing investor expectations, as investors become more risk
averse, the SML increases its slope. The more risk taken, the greater the return
premium that is desired (see figure 11A-4).
Chapter 11
Problems
1. Cost of capital (LO2) In March 2010 Hertz Pain Relievers bought a massage machine that
provided a return of 8 percent. It was financed by debt costing 7 percent. In August 2010,
Mr. Hertz came up with a heating compound that would have a return of 14 percent.
The Chief Financial Officer, Mr. Smith, told him it was impractical because it would
require the issuance of common stock at a cost of 16 percent to finance the purchase.
Is the company following a logical approach to using its cost of capital?
11–1. Solution:
No, each individual project should not be measured against the
determined, the “heating compound” yielding 14 percent is much
more likely to be accepted than the “massage machine” only
yielding 8 percent.
Chapter 11: Cost of Capital
2. Cost of capital (LO2) Speedy Delivery Systems can buy a piece of equipment that is
anticipated to provide an 8 percent return and can be financed at 5 percent with debt. Later
in the year, the firm turns down an opportunity to buy a new machine that would yield a 15
percent return but would cost 17 percent to finance through common equity. Assume debt
and common equity each represent 50 percent of the firm’s capital structure.
a. Compute the weighted average cost of capital.
b. Which project(s) should be accepted?
11–2. Solution:
Speedy Delivery Systems
Weighted
a.
Cost
Weights
Cost
Debt
5%
50%
2.5%
Common equity
17%
50%
8.5%
Weighted average cost of
capital
11%
b.
Only the new machine with a return of 17 percent.
The return exceeds the weighted average cost of capital of
11.0 percent.
3. Effect of discount rate (LO2) A brilliant young scientist is killed in a plane crash. It is
anticipated that he could have earned $200,000 a year for the next 40 years. The attorney
for the plaintiff’s estate argues that the lost income should be discounted back to the
present at four percent. The lawyer for the defendant’s insurance company argues for
discount rate of 12 percent. What is the difference between the present value of the
settlement at four percent and 12 percent? Compute each one separately.
11-3. Solution:
Chapter 11: Cost of Capital
11-6
Law Suit Settlement
Present Value at 4%
PVA = A × PVIFA (4 percent, 40 periods) Appendix D
Present Value at 12%
PVA = A × PVIFA (12 percent, 40 periods) Appendix D
4. Aftertax cost of debt (LO3) Telecom Systems can issue debt yielding 8 percent. The
company is in a 35 percent bracket. What is its aftertax cost of debt?
11–4. Solution:
Telecom Systems
Kd = Yield (1 – T)
5. Aftertax cost of debt (LO3) Calculate the aftertax cost of debt under each of the following
conditions.
Yield
Corporate Tax Rate
a. 6.0%
16%
b. 12.6
35
c. 9.4
24
11–5. Solution:
Chapter 11: Cost of Capital
11-7
Kd = Yield (1 – T)
Yield (1 – T) Yield (1 – T)
a. 6.0% (1 – .16) 5.04%
6. Aftertax cost of debt (LO3) Calculate the aftertax cost of debt under each of the following
conditions.
Yield
Corporate Tax Rate
a.
8.0%
28%
b.
11.4
40
c.
7.5
0
11–6. Solution:
Kd = Yield (1 – T)
Yield (1 – T) Yield(1 – T)
a. 8.0% (1 – .28) 5.76%
7. Aftertax cost of debt (LO3) The Goodsmith Charitable Foundation, which is tax-exempt,
issued debt last year at 8 percent to help finance a new playground facility in Los Angeles.
This year the cost of debt is 20 percent higher; that is, firms that paid 10 percent for debt
last year will be paying 12 percent this year.
a. If the Goodsmith Charitable Foundation borrowed money this year, what would the
aftertax cost of debt be, based on their cost last year and the 20 percent increase?
b. If the receipts of the foundation were found to be taxable by the IRS (at a rate of 35
percent because of involvement in political activities), what would the aftertax cost of
debt be?
11–7. Solution:
Chapter 11: Cost of Capital
11-8
Goodsmith Charitable Foundation
a. Kd = Yield (1 – T)
Yield = 8% × 1.20 = 9.6%
8. Aftertax cost of debt (LO3) Royal Jewelers Inc., has an aftertax cost of debt of 6 percent.
With a tax rate of 40 percent, what can you assume the yield on the debt is?
11–8. Solution:
Regal Jewelers, Inc.
( )
( )
( )
d
d
K Yield 1 T
K
Yield = 1T
6% 6%
Yield = 10%
1 .40 .60
=−
−
==
−
9. Approximate yield to maturity and cost of debt (LO3) Airborne Airlines, Inc., has a
$1,000 par value bond outstanding with 25 years to maturity. The bond carries an annual
interest payment of $78 and is currently selling for $875. Airborne is in a 30 percent tax
bracket. The firm wishes to know what the aftertax cost of a new bond issue is likely to be.
The yield to maturity on the new issue will be the same as the yield to maturity on the old
issue because the risk and maturity date will be similar.
a. Compute the approximate yield to maturity (Formula 11-1) on the old issue and use
this as the yield for the new issue.
b. Make the appropriate tax adjustment to determine the aftertax cost of debt.
11–9. Solution:
Chapter 11: Cost of Capital
Airborne Airlines, Inc.
a.
payment) (Principal .4 bond) of (Price .6
maturity toyears ofNumber
bond theof Pricepayment Principal
paymentinterest Annual
Y’ +
−
+
=
( ) ( )
$1,000 $875
$78 25
.6 $875 .4 $1,000
$125
$78 25
$525 $400
$78 $5
$925
$83 8.97%
$925
−
+
=+
+
=+
+
=
==
b. Kd = Yield (1 – T)
10. Approximate yield to maturity and cost of debt (LO3) Russell Container Corporation
has a $1,000 par value bond outstanding with 20 years to maturity. The bond carries an
annual interest payment of $95 and is currently selling for $920 per bond. Russell Corp. is
in a 25 percent tax bracket. The firm wishes to know what the aftertax cost of a new bond
issue is likely to be. The yield to maturity on the new issue will be the same as the yield to
maturity on the old issue because the risk and maturity date will be similar.
a. Compute the approximate yield to maturity (Formula 11-1) on the old issue and use
this as the yield for the new issue.
b. Make the appropriate tax adjustment to determine the aftertax cost of debt.
Chapter 11: Cost of Capital
Russell Container Corporation
a.
payment) (Principal .4 bond) of (Price .6
maturity toyears ofNumber
bond theof Pricepayment Principal
paymentinterest Annual
Y’ +
−
+
=
( ) ( )
$1,000 $920
$95 20
.6 $920 .4 $1,000
$80
$95 20
$552 $400
$95 $4
$952
$99 10.40%
$952
−
+
=+
+
=+
+
=
==
b. Kd = Yield (1 – T)
11. Changing rates and cost of debt (LO3) For Russell Container Corporation, described in
problem 10, assume that the yield on the bonds goes up by 1 percentage point and that the
tax rate is now 35 percent.
a. What is the new aftertax cost of debt?
b. Has the aftertax cost of debt gone up or down from problem 10? Explain why.
11–11. Solution: