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FIN 40153: Advanced Corporate Finance
THE WEIGHTED AVERAGE COST OF
CAPITAL
(BASED ON RWJ CHAPTER 13)
The Cost of Capital and Valuation
 Debt and Equity
 A company can get cash for investment by
retaining earnings or selling either debt or
equity.
 Does it make any difference how the firm
raises money?
 What is the proper discount rate when the firm
uses both debt and equity?
 How do we perform capital budgeting/valuation
when the project has different risk and/or capital
structure than the firm as a whole?
Setting the stage
Cash
Flows
Debt
Assets
Produce Cash Flows
That Create Value
Equity
The firm’s assets are a portfolio of the debt and equity.
Debt and equity just divide up the cash flows (value) of the firm.
The Weighted Average Cost Of Capital
(WACC)
• When a firm has both debt and equity in its capital
structure, the most frequent recommendation is to base
the project discount rate on the weighted average cost
of capital (WACC):
E
D
WACC 
rE 
rD (1  TC )
ED
ED
• where
– E is the market value of the firm’s stock
– D is the market value of the firm’s debt
– rE is the required rate of return on the firm’s stock
– rD is the required before tax rate of return on the firm’s debt
– TC is the firm’s marginal tax rate
Why Is There A Tax Adjustment For
Debt?
 Consider a firm that has earnings before
interest and taxes each period of $1000.
Under scenario A, the firm is all equity
financed; under scenario B, the firm has
issued debt with a face value of $1000 and a
coupon rate of 10%. The firm has a 40%
marginal tax rate.
Why Is There A Tax Adjustment For Debt?
A
EBIT
Interest
$1000
$0
______
EBT
$1000
Tax (40%) $(400)
______
Net Inc
$600
B
$1000
$(100)
______
$900
$(360)
______
$540
 In A, the firm can distribute a total of $600 to stakeholders.
 In B, the firm can distribute $100+$540=$640 to
stakeholders.
 The tax shield from debt gives the firm $40 more to
distribute. This tax shield lowers the effective interest
payment on debt to $60=$100(1-0.4) or 6% coupon rate.
Calculation of the cost of debt (RDebt)
 The before tax cost of debt can be calculated as the yield
to maturity (YTM) on the firm’s existing debt.
 Much debt is not publicly traded, so you do not have the
current price to compute the YTM.
 YTM is basically the IRR of the debt.
 Can also be determined using the current interest rates
applicable to bonds of companies with comparable
financial structure and bond ratings.
 Wall Street Journal
 Moody’s
 The after tax cost of debt is the before tax cost of debt
multiplied by (1-Tc), where Tc is the firm’s effective
marginal tax rate.
Bond Ratings and Bond Yields
So on 3/1/2006 10 year AAA bonds pay 68 basis points
higher than 10 year than Treasuries, 4.59% + 0.68% =
5.27%
High Yield Bond Quotes
For Intelsat if the face a corporate tax rate of 35% their after
tax cost of debt would be 9.467(1 – 0.35) = 6.154%
Calculation of the cost of equity (rEquity)
 The cost of equity can be calculated using the
Security Market Line (SML) from the CAPM.
 rE= Rf+ b (E[RM]- Rf)
 Three inputs are required
 Firm Beta
 Risk free rate
 Market risk premium
Applying the CAPM
 (i) An estimate of the risk free interest rate.
 Practitioners tend to favor the current yield on longer-term
treasury bonds but adjust according to projects maturity.
 Remember to adjust the market risk premium accordingly.
 (ii) An estimate of the market risk premium, E(Rm rf), the extra return investors expect to earn from
holding the market instead of the risk-free bond.
 The theory calls for a forward looking measure (expected)
 Expectations are not observable.
 Generally use a historically estimated value.
 (iii) An estimate of beta. Is the project or a surrogate
for it traded in financial markets? If so, gather data
and run an OLS regression.
How To Obtain Beta.
 Estimate beta from a regression equation.
 In practice, generally use last five years of
monthly data. Some companies publish beta
estimates on a regular basis:
 Value Line
 Merrill Lynch Beta Book
 Internet Finance Websites
 What if the company is not publicly traded?
 Find a comparable company that is traded.
 Use accounting data (ROE) instead of stock returns
 Reason it out.
Microsoft Return Versus S&P 500
RMicrosoft
RS&P
Estimating Microsoft’s Beta
Regression Results of Microsoft
Return on S&P 500 Return 20012004
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.598458926
R Square
0.358153086
Adjusted R Square
0.34708676
Standard Error
0.099420174
Observations
60
ANOVA
df
Regression
Residual
Total
Intercept
X Variable 1
1
58
59
SS
0.319900025
0.573293522
0.893193547
MS
0.319900025
0.009884371
Coefficients Standard Error
t Stat
-0.000268979
0.012848137 -0.020935275
1.563925441
0.274905499 5.688956548
This is Microsoft’s Beta
F
Significance F
32.36422661
4.41249E-07
P-value
0.983369144
4.41249E-07
Lower 95%
Upper 95% Lower 95.0% Upper 95.0%
-0.025987299 0.025449341 -0.025987299 0.025449341
1.013642709 2.114208173 1.013642709 2.114208173
What Determines Beta?




Beta is a measure of sensitivity to the
market.
Companies with cyclical cash flows will
tend to have higher betas.
Higher operating leverage implies higher
betas.
 operating leverage is the ratio of fixed
costs to variable costs.
Higher financial leverage also means higher
equity beta.
The Market Risk Premium


The market risk premium measures the additional return that an
investor needs to hold risky assets (i.e. stocks) rather than riskfree assets (treasuries).
The Market Risk Premium is defined as:
[E[R M ]  R F ]


Ideally, the MRP would be based on expectations of investors
about the future. However, expectations are not observable.
We can observe what has actually happened based on historical
data.
The Market Risk Premium (Excess Returns)
 Excess Returns
 The difference between the average return for an
investment and the average return for a risk-free asset
 The extra return earned for holding a risky investment
 For U.S. data from 1928 to 2007
The Market Risk Premium







Recall that the standard deviation of returns on the S&P 500 is
approximately 20% per year.
If we use data from 1928-2007 we have 80 years of data.
The standard error of the risk premium estimate is about
0.20/sqrt(80)=0.022
This implies that our estimate of the risk premium is not very
precise. The 95% confidence interval is:
0.078 ± 2 x 0.022
The risk premium is between 3.3% and 12.2%
Note that these calculations assume that the process generating
stock returns is stationary over time.
 What if it is not?
The Market Risk Premium [E[R M ]  R F ]





Should we use a longer sample?
Some researchers have now been able to get U.S. stock return data
back to the early 1800s. See for example “Stocks for the Long Run”
by Jeremy Siegel http://www.wharton.edu/research/1998.html
Also, do we want to create our sample estimate using only data from
U.S. markets?
The U.S. “won” the major wars, avoided communism or other major
social upheaval. Could the U.S. market outcomes reflect what was
expected, plus a “bonus” for doing so well?
Lets look at some data from “A Century of Global Stock Market
Returns” provided by William Goetzmann, Yale University.
Fig.1. Real Returns on Global Stock Markets
6 Percent
Sorted by Years of Existence: 1921-1996
5
The US is clearly not typical
4
Czechoslovakia
•
3
Hungary
US
Sweden
Switzerland
Israel
Uruguay
Canada
Norway
Chile*
UK
Mexico
Denmark
Finland
Germany*
Netherlands
Ireland
Austria
Australia
France
2
1
0
Brazil
-1
Pakistan
-2
Italy
New Zealand
Portugal*
South Africa
Venezuela
India
Belgium
Japan*
Spain
Egypt
-3
-4
Poland
Philippines
Colombia
Argentina*
-5
Peru*
Greece
-6
0
20
40
60
80
Years of Existence since 1921 (* indicates a long-term break)
100
Country Risk Premiums
How do estimates of the market risk premium
change?
 If we add additional years to the sample using the Siegel data
it suggests a risk premium relative to short-term treasuries of
perhaps 6% per year (compared to 7.78%).
 The Goetzmann data suggest that the average U.S. stock return
exceeds average world returns by about 2% per year.
 These findings suggest estimates of:
 6.0% relative to short-term treasuries.
 4.5% relative to long-term treasuries .
 Finally, might the risk premium change over
time -- higher at some points, lower at others?
 If the risk premium is not stationary then using a longer sample will not
provide an accurate estimate of current expectations.
 But using only recent data increases the estimation error.
Betas and Leverage
• We noted earlier that the beta of a portfolio is the
average of the component betas. Also, we can
think of the firm’s assets as a portfolio of the debt
and equity claims. From these insights it follows
that:
 E 
 D 
b Assets  
 b Equity  
 b Debt
ED
ED
• Where E is the market value of the stock (equity) and D is the
market value of debt (borrowings).
Risk of Debt and Equity
Assets
Produce Cash Flows
That Create Value
(Asset Beta)
Cash
Flows
Debt
(Debt Beta)
Equity
(Equity Beta)
The firm’s assets are a portfolio of the debt and equity.
Debt and equity just divide up the cash flows (value) of the firm.
Beta and Leverage
 This formula can be used to find the asset beta given the equity
and debt betas or to find the equity beta, given the asset and debt
betas. Rearranging the formula gives:
D
b Equity  b Assets  ( b Assets  b Debt )
E
 Note that the equity beta increases as leverage (D/E) increases.
 It is often assumed that the debt has a zero beta (a big
simplification). Then:
b Assets
 E 
 b Equity 

E

D


b Equity  b Assets 1 

D

E
Beta and Leverage
 This formula can be used to find the asset beta given the equity
and debt betas or to find the equity beta, given the asset and debt
betas.
 For firms with risky debt (i.e., below investment grade), in
practice it is often assumed that the debt beta is 0.25 to 0.30.
b Equity  b Assets
b Assets
D
 ( b Assets  b Debt )
E
 E 
 D 

 b Equity  
 b Debt
 E  D
 E  D
Adjusting beta for different capital
structures
 Example: Gamma airlines’ equity beta is observed to be 1.31.
It’s equity is worth 25.0 million while its debt is worth 15.0
million. What is the beta of the underlying assets assuming a
debt beta of zero?
b Assets  
25 
1.31  0.819
 25  15 
 Note: The asset beta is always less than or equal to the equity
beta.
Points to Note Regarding Beta and Leverage
 If the firm uses no debt (D=0) the equity beta and the asset
beta are equal.
 If the firm uses debt, the equity beta is increased relative to
the asset beta:
b Equity

 D
 b Assets 1  
E

implies:


(1) equity holders will require a higher rate of return,
(2) when comparable firms are used to estimate beta, allowances
for differing capital structures will be required.
How to use the set of tools developed here to select
discount rates for capital budgeting.
 The cost of capital for each project should reflect
the systematic risk of that project and the capital
structure of the firm (or division) taking the
project. So,
 Select a publicly traded company that is comparable in terms of the
risk of the underlying business (i.e., the asset beta).
 Obtain the unlevered (asset) beta of the comparable.
 Obtain the corresponding project equity beta for your firm,
reflecting your firm’s capital structure.
 Obtain the cost of equity and cost of debt for this project reflecting
your firm’s capital structure.
 Calculate the WACC for the project and perform NPV analysis
based on the expected cash flows with no leverage.
EXAMPLE
The Story For BK Industries
 Remember BK Industries has been producing
publishing equipment for some time now and the
CEO believes that he has stumbled upon a
valuable product innovation that embeds new
features in text editing systems. BK’s cost
advantages and vast skill in marketing mean it
would be difficult for competitors to undertake
such a project.
BK Industries
Incremental Cash Flows
 Suppose that BK forecasts the following cash
flows from operating a text editing business ($
millions).
Year 0
Year 1
Year 2
Year 3
Year 4
Year5
-26.00
3.98
5.42
6.69
5.99
22.46
BK Industries Net Present Value (NPV)

BK has estimated its company cost of capital to be
10%. What is the NPV of the text editing business?

NPV (@ r=10%) =
-26.00 + 3.98/(1.10) + 5.42/(1.10)2 + 6.69/(1.10)3 +
5.99/(1.10)4 + 22.46/(1.10)5 = $5.159 Million

The NPV is greater than zero, so BK should proceed
with the project.
Example: BK Industries Revisited
 Suppose that BK Industries is a conglomerate
company with operations in a number of other
products lines with no text editing business. Also
suppose BK’s current equity beta is 1.0. BK has
and will maintain a debt/equity ratio of 1.0.
 Can we use the company cost of capital to
value the text editing project?
 Latec Inc. is a firm that makes only text editing
systems. Latec’s equity beta is 1.35. Latec has a
debt to equity ratio of 0.75.
Delevered Betas with debt/equity ratios
• The formulas for obtaining asset betas from equity
betas and vice versa provided earlier required
dollars values for debt (D) and equity (E). What if
you are only given the leverage ratio, L = D/E?
The formulas are restated as:
 1 
b Assets  
b Equity
1 L 
b Equity  b Assets (1  L)
Delever Latec’s Beta to obtain
the Beta of text-editing assets:
• Latec has L =0.75and an equity beta of 1.35.
b Assets
 1 

1.35  0.77
 1  0.75 
Relever the asset Beta to reflect
BK’s capital structure:
Recalling that BK will keep its debt/equity
ratio equal to one, we can get:
b Equity  0.77  1  1  1.54
This is the beta for a BK equity position in a text
 editing asset.
Why is this equity beta greater than Latec’s?
BK Industries, Cont.
 Assume that the risk free rate is 8% and that BK’s
cost of debt is also 8%. The market risk premium
is 7% and the marginal tax rate is 45%. The
required return on BK’s equity is:
requity  RF  b (E[RM ]  RF )  8% 1.54 7%  18.78%
The weighted average cost of capital for the text editing
venture (using the fact that D/E = 1 here) is:
E
D
WACC 
rE 
rD (1  TC )
ED
ED
1
1
=
18.78% 
8%(1  0.45)  11.59%
1+1
1 +1
 Finally, we can evaluate the NPV of the text editing
venture using the WACC that reflects the risk
associated with this particular business.
 The NPV of the text editing project is -$21,329
 Notice that the selected discount rate of 11.59% reflects:

The risk (beta) of text editing businesses, not BK’s existing
businesses.

BK’s capital structure, not that of the surrogate firm.
COMPANY COST OF CAPITAL AND
PROJECT COST OF CAPITAL
Required return
Security market line showing
required return on project
Risky Project
Safe Project
Company cost of capital
Average beta
of firm's assets
Project beta
Some Common Errors to Avoid
 Using book value weights in the WACC.
 The weights should be based on market values
 The weights should reflect the firm’s target
capital structure.
 Using incorrect leverage ratios for levering
and unlevering betas and computing
WACC.
 D/E versus D/(D+E).
 Know which one you are using.
Some Common Errors to Avoid
 Subtracting the current risk-free rate from the
historical average market return to get the
market-risk-premium.
 The MRP estimate should be based on the
difference between the historical average of the
market return and the historical average return on
the risk-free bond.
 The current risk-free rate is used for the standalone Rf if the SML equation.
E[R i ]  R F  b i [E[R M ]  R F ]
Current-Value
Historical difference between return on the
market and return on the risk-free bond