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Cost of Capital
Author's Overview
Chapter 11 on "Cost of Capital" naturally follows Chapter 10 on "Valuation and Rates of
Return." The instructor should emphasize at the outset that the investors' required rate of return
translates into the cost of financing for the firm. There should be a dual emphasis on properly
determining the aftertax cost for each type of financing and on determining the appropriate
weights to be assigned to the various sources of financing.
The cost of debt and the cost of preferred stock are reasonably straightforward, but additional
guidance is required in determining the cost of common equity. The instructor should indicate
the firm's ability to acquire equity capital through retained earnings or through new common
stock and the associated cost of each. The cost of retained earnings should be explained as an
opportunity cost for the use of the stockholders' funds. For that reason, it is assumed the
stockholders can earn as much on these funds, if distributed, as they are currently earning in the
firm. Thus, the cost of retained earnings is also equal to Ke (the firm's return on common
equity).
After the various costs are computed, the instructor can direct more attention to the weighting
scheme given to the components in the capital structure. The instructor may wish to refer to
the authors' example in which the increased use of debt initially decreases the cost of capital,
but then ultimately increases it. The interdependent nature (of costs and weights) should be
stressed in discussing the optimal capital structure.
The instructor has the option of introducing the student to the capital asset pricing model in the
text and more fully in Appendix 11A. There the concepts of regression analysis, the beta
coefficient, and the security market line are introduced and related to previously discussed
material on the cost of capital. This chapter as well as subsequent chapters is fully
comprehensible without the use of this material. The appendix is available, however, for those
instructors who wish to go over the capital asset pricing model in detail.
Chapter Concepts
LO1. The cost of capital represents the weighted average cost of all sources of long-term
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Education.
11-1
11
financing to the firm.
LO2. The cost of capital is normally the discount rate to use in analyzing an investment.
LO3. The cost of capital is based on the valuation techniques from the previous chapter and is
applied to bonds, preferred stock and common stock.
LO4. A firm attempts to find a minimum cost of capital through varying the mix of its sources
of financing.
LO5. The cost of capital may eventually increase as larger amounts of financing are utilized.
Annotated Outline and Strategy
I. The Overall Concept
A. A business firm must strive to earn at least as much as the cost of the funds that
it uses.
B. Usually a firm has several sources of funds and each source may have a different
cost.
C. The overall cost of the funds employed is a proportionate average of the various
sources.
D. The firm's required rate of return that will satisfy all suppliers of capital is called
its cost of capital.
E. There are several steps in measuring a firm's cost of capital.
1. Compute the cost of each source of capital.
2. Assign weights to each source.
3. Compute the weighted average of the component costs.
PPT Cost of Capital—Baker Corporation (Table 11-1)
II. Cost of Debt
A. The basic cost of debt to the firm is the effective yield to maturity. The yield to
maturity is a market determined rate and can be found by examining the
relationships of security price, periodic interest payments, maturity value, and length
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Education.
11-2
of time to maturity. The yield to maturity for a corporate bond may be found by
solving for YTM in the following calculator keystrokes:
N Number of periods to maturity
PV Current price of the bond
PMT Periodic coupon payment
FV Maturity value of bond (usually $1000) Function
CPT
I/Y Yield to maturity
Table 11-2 on page 343 uses an Excel Spreadsheet to calculate the yield to
maturity using the RATE function.
B. Since interest is tax deductible, the actual cost of debt to the firm is less than the
yield to maturity
C. The after-tax cost of debt is:
(1 )
d
K Y T= -
Where:
Y = Yield to maturity
T = Firm’s effective tax rate
Thus the after-tax cost to a firm of bonds issued at par paying $100 annually in
interest would be 6.6 percent if the firm's marginal tax rate were 34 percent.
.10 (1 .34) .066
d
K = - =
D. The example of KeySpan Corporation in Table 11-3 on page 344 presents the
opportunity for the professor to expose the students to the information found in
the Standard & Poor’s Capital IQ Net Advantage.
Perspective 11-1: Explain that since the cost of preferred stock and common stock are
calculated on an aftertax basis, the cost of debt is adjusted for taxes so all three sources of
capital are on an aftertax cost basis.
III. Cost of Preferred Stock
A. Preferred stock is similar to debt in that the preferred dividend is fixed but
dissimilar in that dividends are not tax deductible.
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11-3
B. The cost of preferred stock to a firm may be determined by examining the
relationship of its annual (usually fixed) dividend and its market determined
price. Preferred stock, unlike debt, has no maturity and therefore the dividends
are expected to be perpetual.
C. The cost of preferred stock Kp is computed by dividing the annual dividend
payment by the net proceeds received by the firm in the sale of preferred stock.
where:
Kp= Cost of preferred stock
D= Preferred stock dividend
F= Flotation costs per share
Pp= Market price of preferred stock
IV. Cost of Common Equity
A. The basis of computation of the price of common stock is the Dividend
Valuation Model.
P0 = Price per share of stock at the beginning of the first year
D1 = Expected dividend at the end of the first year (or period)
Ke = Required rate of return
g = Constant growth rate in dividends
C. The equation for the cost of common equity Ke is equal to the total of the
dividend yield rate plus capital gains on the original investment. D1/P0
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Education.
11-4
( )
p
D
KP F
=-
(Formula 11-2)
1
0 ( )
e
D
Pg
K
=-
(Formula 10-8)
B. Assuming constant growth, the Dividend Valuation Model can be manipulated to
represent the required rate of return:
1
e
o
Dg
KP
= +
(Formula 11-3)
represents the dividend yield. Since the original investment must grow at the
same rate as the dividends, the capital gains on the investment is achieved by
adding g, the dividend growth rate.
D. Required Return on Common Stock Using the Capital Asset Pricing Model
(CAPM). The CAPM provides an alternative calculation of the required return on
common stock. See perspective 11-2 on the next page.
1. Under the CAPM, the required return for common stock can be described
by the following formula:
Where:
Kj= Required return on common stock
Rf= Risk-free rate of return; usually the current rate on
Treasury bill securities
= Beta coefficient. The beta measures the historical
volatility of an individual stock's return relative to a stock
market index. A beta greater than 1 indicates greater
volatility (price movements) than the market, while the
reverse would be true for a beta less than 1.
Km= Return in the market as measured by an appropriate index
2. Both Kj and Ke should be equal under the case of market equilibrium.
3. Appendix 11A presents the capital asset pricing model in more detail for
those who wish to expand the textbook coverage on this concept.
Perspective 11-2: It is helpful to point out that the Kj in the capital asset pricing model is
often used in the dividend valuation model because if you plug Ke from Formula 11-3 into the
dividend valuation model, you will always get the current price of the stock as the value. By
developing Ke (Kj) independently from the dividend valuation model, you eliminate using a
circular reference.
E. Cost of Retained Earnings: Common stock financing is available through the
retention of earnings belonging to current stockholders or by issuing new
common stock.
1. The cost of retained earnings is equivalent to the rate of return on the
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Education.
11-5
( )
j f m f
K R K R
b= + -
firm's common stock. This is the opportunity cost. Thus the cost of
common equity in the form of retained earnings is:
Where:
Ke = Required rate of return
D1 = Expected dividend at the end of the first year
P0 = Price per share of stock at the beginning of the first year
g = Constant growth rate in dividends
F. Cost of New Common Stock: The sale of new common stock has a higher cost
than the cost of retained earnings because the firm's proceeds from the sale of the
new stock are reduced by the flotation costs (F) paid to the investment banker.
The cost of new common stock, Kn is:
Where:
Kn = Required rate of return on new common shares
D1 = Expected dividend at the end of the first year first year
P0 = Price per share of stock at the beginning of the first year
g = Constant growth rate in dividends
F = Flotation costs per share
V. Optimal Capital Structure - Weighing Costs
A. The firm should seek to minimize its cost of capital by employing the optimal
mix of capital financing.
B. Weighted Average Cost of Capital can be calculated by the summation of the
product of each element of capital multiplied by its relative weight or mix.
C. The Baker Corporation example on page 349 and 350 demonstrates the concept
of weighted average cost of capital numerically while Figure 11-1 does so
graphically.
PPT Cost of Capital Curve (Figure 11-1)
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11-6
1
0
e
Dg
KP
= +
1
0
( )
n
Dg
KP F
= +
-
(Formula 11-6)
D. Although debt is the cheapest source of capital, there are limits to the amount of
debt capital that lenders will provide (recall the Debt/Equity (D/E) relationships
discussed in Chapter 3). The cost of both debt and equity financing rise as debt
becomes a larger portion of the capital structure.
E. Traditional financial theory maintains that the weighted average cost of capital
declines as lower costing debt is added to the capital structure. The optimum
mix of debt and equity corresponds to the minimum point on the average cost of
capital curve.
F. The optimal debt-to-equity mix varies among industries. The more cyclical the
business, the lower the D/E ratio would be required.
PPT Long-Term Debt as a Percentage of Total Assets (Table 11-4)
G. The weights applied in computing the weighted average cost should be market
value weights.
VI. Capital Acquisition and Investment Decision Making
A. The discount rate used in evaluating capital projects should be the weighted
average cost of capital.
B. If the cost of capital is earned on all projects, the residual claimants of the
earnings stream, the owners, will receive their required rate of return. If the
overall return of the firm is less than the cost of capital, the owners will receive
less than their desired rate of return because providers of debt capital must be
paid.
C. For most firms, the cost of capital is fairly constant within a reasonable range of
debt-equity mixes (flat portion of curve in Figure 11-2). Changes in money and
capital market conditions (supply and demand for money), however, cause the
cost of capital for all firms to vary upward and downward over time.
Perspective 11-3: Discuss the impact of economic cycles on the cost of capital. The shifts
that occur in costs of capital demonstrate that companies raise capital in an uneven fashion,
often raising capital before it is all needed in anticipation of rising costs. The low cost of debt
between 2008-2013 is a good example of a low interest rate environment.
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Education.
11-7
PPT Cost of Capital over Time (Figure 11-2)
D. Cost of Capital in the Capital Budgeting Decision
1. It is the current cost of each source of funds that is important.
2. The cost of each source of capital will vary with the amount of capital
derived from that source.
3. The required rate of return or discount rate for capital budgeting
decisions will be the weighted average cost of capital.
Perspective 11-4: Use Table 11-5 and Figure 11-3 together to show that not all projects can be
accepted and that only those projects with expected rates of return greater than the cost of
capital can be accepted as viable capital budgeting projects.
PPT Investment Projects Available to the Baker Corporation (Table 11-5)
PPT Cost of Capital and Investment Projects for the Baker Corporation
(Figure 11-3)
Finance In Action: Big Bond Are “Liquid” Bonds
Bond issues of $500 million or more may have a lower cost of debt than smaller bond issues.
$500 million seems to be the threshold for creating a market for a company’s bonds where there
are enough investors to create a continuous market of buyers and sellers. Smaller bond issues
carry what is called a liquidity risk because there is not an active market and bid and ask prices
can have wide spreads. The Dodd-Frank Act made it more difficult for U.S. banks to carry an
inventory of small bond issues and thus larger bond issues have become more common. Ventas,
a real estate investment trust, is used in to illustrate this new paradigm.
VII. Marginal Cost of Capital
A. The marginal cost of debt (the cost of the last amount of debt financing) will rise as
more debt financing is used. The marginal cost of equity also rises when the
shift from retained earnings to external (common stock) equity financing is
necessary.
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11-8
Perspective 11-5: Compare Table 11-6 and Table 11-7 to show how the cost of capital rises as
the Baker Corp. raises it first $39 million, its next $11 million and then the rising cost of funds
raised over the $50 million threshold. Figure 11-4 brings these tables together to show that the
marginal cost of capital rises and project E is now eliminated.
PPT Cost of Capital for Different Amounts of Financing (Table 11-6) and
PPT Cost of Capital for Increasing Amounts of Financing (Table 11-7)
PPT Marginal Cost of Capital and Baker Corporation Projects
(Figure 11-4)
VIII. Appendix 11A: Cost of Capital and the Capital Asset Pricing Model
A. The Capital Asset Pricing Model (CAPM) relates the risk-return tradeoffs of
individual assets to market returns.
B. The CAPM encompasses all types of assets but is most often applied to common
stock.
C. The basic form of the CAPM is a linear relationship between returns on
individual stocks and the market over time. Using least squares regression
analysis, the return on an individual stock Kj is:
where:
Kj = Return on individual common stock of company
= Alpha, the intercept on the y-axis
= Beta, the coefficient
Km = Return on the stock market (an index of stock returns is used,
usually the Standard & Poor's 500 Index)
e = Error term of the regression equation
PPT Performance of PAI and the Market (Table 11A-1)
PPT Linear Regression of Returns between PAI and the Market
(Figure 11A-1)
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11-9
j m e
K K
a b= + +
D. Using historical data, the beta coefficient is computed. The beta coefficient is a
measurement of the return performance of a given stock relative to the return
performance of the market.
E. The CAPM is an expectational model. There is no guarantee that historical data
will be repeated.
F. The CAPM evolved into a risk premium model.
1. Investors expect higher returns if higher risks are taken.
2. The minimum return expected by investors will never be less than can be
obtained from a riskless asset (usually considered to be U.S. Treasury
bills). The relationship is expressed as follows:
where:
Rf = Risk-free rate of return
= Beta coefficient from Formula 11A-1
Km = Return on the market index
Km - Rf = Premium or excess return of the market versus the risk-free
rate (since the market is riskier than Rf, the assumption is
that the expected Km will be greater than Rf)
(Km - Rf) = Expected return above the risk-free rate for the stock of
Company j, given the level of risk
3. Beta measures the sensitivity of an individual security's return relative to
the market.
a. By definition, the market beta = 1.
b. A security with a beta = 1, is expected to have returns equal to
and as volatile as the market. One with a beta of 2 is twice as
volatile (up or down).
4. Beta measures the impact of an asset on an individual's portfolio of assets.
G. A risk-return graph can be derived from the risk premium model. The graphed
relationship between risk (measured by beta) and required rates of return is
called the Security Market Line (SML).
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11-10
( - )
j f m f
K R K R
b= +
PPT The Security Market Line (SML) (Figure 11A-2)
H. Cost of capital considerations
1. If required returns rise, prices of securities fall to adjust to the new
equilibrium return level and as required returns fall, prices rise.
2. A change in required rates of return is represented by a shift in the SML.
PPT The Security Market Line and Changing Interest Rates (Figure
11A-3)
a. The new SML will be parallel to the previous one if investors
attempt to maintain the same risk premium over the risk-free rate.
b. If investors attempt to maintain purchasing power in an
inflationary economy, the slope of the new SML may be greater
than before due to an inflation premium.
c. An investor's required rate of return and thus a firm's cost of
capital will also change if investors risk preferences change. The
slope of the SML would change even if the risk-free rate remained
the same.
PPT The Security Market Line and Changing Investor Expectations
(Figure 11A-4)
Other Chapter Supplements
Cases for Use with Foundations of Financial Management
Case 16, Berkshire Instruments, (Cost of Capital)
Case 17, Galaxy Systems, Inc. (Divisional Cost of Capital)
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11-11
