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 )
EPD
EPD
EPD
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 )
EPD
EPD
EPD
= (.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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