Transcript Chapter 11

Calculating the Cost of Capital
Chapter 11
Fin 325, Section 04 – Spring 2010
Washington State University
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Weighted Average Cost of Capital
 The WACC formula
WACC 
E
P
D
iE 
iP 
iD  (1  TC )
EPD
EPD
EPD
 E, P, D are market value of equity, preferred stock,
and debt, respectively.
 iE , iP , iD are cost of equity, cost of preferred
stock, and cost of debt.
 TC is the appropriate corporate tax rate.
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Cost of Equity
 Two methods for calculating the cost of equity:
1.
CAPM
iE  i f   E [ E(iM )  i f ]
2. Constant Growth Model
D1
iE 
g
P0
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Which Model is Better?
 In the CAPM, βE estimates future systematic risk, but
we calculate it based on historic data
 Needs sufficient historic information
 Past level of systematic (market) risk is a good
indicator of future risk
 Applies more accurately in most cases
 The constant growth model assumes constant
perpetual growth in dividends
 Some type of simple or weighted average of the two
methods might be appropriate
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Example
 Calculate the cost of equity for ADK
Industries given the following information:
 ADK common stock price = $32.75
 The next dividend is expected to be $1.54 per
share
 ADK expects future dividends to grow by 6
percent per year indefinitely
 The risk-free rate is 3 percent
 The expected return on the market is 9 percent
 ADK has a beta of 1.3
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Solution
 CAPM method:
iE = if + βE[E(iM) – if ]
= .03 + 1.3[.09 - .03]
= 10.80%
 Constant growth model:
 iE = D1/P0 + g
= $1.54/$32.75 + .06
= 10.70%
 The best estimate is
(10.80%+ 10.70%)/2 = 10.75%
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Cost of Preferred Stock
 Preferred stock pays constant dividends forever,
and so it can be valued as a perpetuity
 We can rearrange the perpetuity model to solve
for iP:
iP 
D
P0
 Note: this is the same as the constant growth
model in which the value of the constant growth
is g = 0
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Example
 ADK has one million shares of preferred stock
outstanding, which pays dividend of $7 per
year and currently trades at $72 per share.
What is ADK’s cost of preferred equity?
iP = D/P0
= $7 / $72
= 9.72%
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Cost of Debt
 We estimate the before-tax cost of debt, and then
calculate the after-tax cost of debt
 Note that interest paid on debt is tax deductible
 To find the before-tax cost of debt we find the
Yield to Maturity on the firm’s existing debt
 YTM takes into account both the interest cash
flows and the principal, and reflects
debtholders’ required rate of return
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Example
 ADK has 30,000 20-year, 8 percent bonds
outstanding. If the bonds currently sell for
97.5 percent of par and the firm has a marginal
tax rate of 35.92 percent, what is the cost of
debt for ADK? (assuming annual compounding)
Input
Output
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N
I
8.26
-975
PV
80
PMT
1000
FV
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 If the before-tax cost of debt is 8.26 percent, then
the after-tax cost of debt is:
8.26% (1 - .3592) = 5.293%
 What tax rate do we use in the WACC
calculation?
 We use the marginal rate.
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Calculating the Weights
 We need to use the relevant market values of
equity, preferred stock, and debt, represented by
E, P, and D
 In the ADK example, the firm has 3 million share
of common stock outstanding, one million
shares of preferred stock, and 30,000 bonds.
 What are the relevant weights for ADK?
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 Equity has a total market value of
3,000,000 x $32.75 = $98,250,000
 Preferred stock has a market value of
1,000,000 x $72 = $72,000,000
 Debt has a market value of
30,000 x $975 = $29,250,000
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 For common equity:
E/(E+P+D) = $98,250,000 / $199,500,000
= 49.25%
 For preferred stock:
P/(E+P+D) = $72,000,000 / $199,500,000
= 36.09%
 For debt:
D/(E+P+D) = $29,250,000 / $199,500,000
= 14.66%
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 The WACC for ADK Industries:
E
P
D
WACC 
iE 
iP 
iD  (1  TC )
EPD
EPD
EPD
= (.4925 x 10.75%) + (.3609 x 9.72%) + (.1466 x 8.26%)(1 - .3592)
= 9.58%
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Firm WACC vs. Project WACC
 We have calculated the firm’s overall weighted
average cost of capital
 This WACC will be appropriate to use in
evaluating “typical” projects
 If a new project is similar enough to existing
projects, then the firm’s WACC is appropriate
 If the new project is riskier than the firm’s average
project, then a higher cost of capital should be used
 If the new project is safer, then a lower cost of
capital should be used to evaluate the project
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Divisional WACC
 Ideally, firms would calculate a risk-
appropriate WACC for every new project under
consideration
 Time consuming
 Managers must often consider hundreds of
new projects each year
 Instead, large firms often calculate a divisional
WACC, which consumes less time and
resources but achieves many of the benefits of
project-specific WACCs
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 Why not use a firm-wide WACC to evaluate all
projects
 Incorrect reject / accept decisions
 Reject most low-risk projects, both good
and bad
 Firm becomes riskier over time
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 Subjective vs. Objective Approaches to
Calculating Divisional WACCs
 Subjective approach



If the projects are riskier than the firm average, adjust
the WACC upward
If the projects are safer than the firm average, adjust the
WACC downward
Biggest disadvantage: the amount of the adjustment is
subjective
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 Objective approach:
 Compute the average beta per division, and use the
CAPM to calculate the cost of equity for each
division
 Use the divisional iE to calculate the divisional
WACCs
 The subjective approach is used more often than
the objective approach because it is easier to
implement
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