ESTIMATING THE WEIGHTED-AVERAGE COST OF CAPITAL
By L. Schall
This note explains how to estimate the discount rate (weighted average cost of capital,
or WACC) for a firm or for a particular investment (e.g., a machine). Section I discusses the
estimation of the WACC for a publicly traded company for which the analyst believes that the
observable market value equals intrinsic value. In this case, the purpose of estimating the
WACC is to determine the discount rate for computing the NPVs of newly proposed
investments that have risk and financing similar to the existing company. Section II explains
how to estimate the firm’s WACC if the purpose is to value a publicly traded company for
which market value may significantly differ from intrinsic value, or to value a privately held
company for which there is no observable market price. In this case, comparables (firms
similar to the one being valued) are employed in the estimation procedure. Section III
discusses the estimation of the WACC to be used as the discount rate to value a new project
that has a risk that differs from that of the firm as a whole.
Part of the WACC estimation process involves the estimation of beta, a measure of a
stock’s (or any asset’s) risk. In most cases, the beta for a stock should be obtained from an
outside source that specializes in risk analysis and beta estimation (such as Bloomberg,
BARRA, or Ibbotson Associates). In fact, a cost of capital estimate can also be purchased
(for example, from Ibbotson Associates). Why then should a financial manager be concerned
with the WACC estimation process? There are at least three reasons. First, most companies
compute their own discount rates, depending on an external information source largely to
obtain market betas and interest rates. It is the job of the company’s finance staff to use these
data to compute discount rates for valuation purposes. This note explains how that is done.
Second, a company’s management should be the most informed about the drivers of the firm’s
business risk.
Even if an outside consultant computes the company’s cost of capital,
management will have to provide relevant information to enable that estimate. A financial
manager who does not understand what a WACC is and how it is estimated will be at a loss in
providing the key information required to generate a defensible WACC estimate. Third,
knowledge of what constitutes “risk,” how it arises, and how it affects value (the WACC is a
risk-adjusted discount rate for computing value), is essential in managing and controlling risk
so that equity value is maximized.
1
I.
THE WACC OF A CORRECTLY VALUED PUBLICLY TRADED FIRM
Suppose that management wants to compute the after-tax WACC for the company in
order to evaluate new investments that will have similar business risk and financing as the
company as it currently exists. Management believes that the prevailing market values of the
company’s traded securities (equity, debt, etc.) are close to their intrinsic values.
after  tax
The after-tax WAAC, rWACC
, is defined as:
After - tax weighted - average
 cost of capital r after-tax under
WACC

assumption
s
[1] and [2]


 =  E 0  r   D 0  r (1  T) +  CFin 0  r
  E   D

 CFin

 V0 
 V0 
 V0 

[1]
E 0 , D 0 , CFin 0 are the current market values of the firm’s equity, debt and complex
financing, respectively; and rE , rD , rCFin and T are the equity cost of capital (equity discount
rate), the debt cost of capital (debt discount rate), the complex financing cost of capital
(complex financing discount rate), and the firm’s tax rate, respectively. The firm’s tax rate T
can often be determined from the company’s annual report or 10-K. If not, the tax rate could
likely be obtained from an investment bank that follows the company, or from the company
itself. In Sections I.1 and I.2 we discuss the estimation of the other terms in equation [1].
I.1.
Determining the E 0 , D 0 , and CFin 0 : Market value data for the firm’s publicly
traded securities are readily available by simply obtaining the market quotes and multiplying
by the quantity of the security that is outstanding. If all the company’s securities are publicly
traded, E 0 , D 0 , and CFin 0 are therefore easily computed quantities.
Valuing securities that are not publicly traded is more difficult. For securities that do
not have option characteristics (convertible securities, for example, have embedded options),
the valuation is a fairly straightforward exercise. For example, valuing a particular issue of
non-traded non-convertible debt can be performed as follows. [a] Analyze the debt’s risk
level by studying the underlying business risk and financial structure (debt to assets level) of
the company, and the specific provisions in the debt agreement (priority, nature of collateral,
etc.). Financial ratios are often used in such an analysis. [b] Given the findings in [a], rate the
debt (e.g., comparable to Standard and Poor’s A or BBB) and determine the yield to maturity
on debt with that rating and a similar term to maturity and pattern of interest and principal
payments, where yields to maturity can be obtained from Bloomberg and various other
sources. [c] Value the debt by discounting the debt’s promised future interest and principal
2
payments using the yield to maturity estimated in [b]. To illustrate, suppose that the firm has
a debt issue X that would justify a Standard & Poor’s rating of A, that matures in 5 years, and
that pays interest semi-annually and all principal in 5 years. Assume that such debt would
have a current yield to maturity of 8 percent. To value the X-debt, the debt’s promised
interest and principal would be discounted using a discount rate of 8 percent.
The valuation of non-traded complex financing (financing other than common stock
and non-convertible debt) depends on the type of financing. For example, preferred stock is
rated very much the way debt is rated. So, imagine a non-callable, non-convertible preferred
stock issue paying a fixed dividend and justifying a BB rating, and assume that a BB rating
implies a prevailing market dividend yield (dividend/price) of 6 percent. The estimated value
of the preferred would be the present value of the forecasted future dividend discounted at a 6
percent rate (price = [annual dividend/.06]).
Financing with option properties (convertibles, warrants, firm issued puts, etc.) must
be valued using an option-pricing model. Option valuation will not be covered here.
I.2.
Determining the Costs of Capital rE , rD and rC Fin
Estimating Equity Rate rE : Equity discount rate (cost of capital) rE is typically
estimated using the CAPM. The CAPM equation for the equity cost of capital for firm X is:
X
rEX = rRF + equity
[ r M  rRF ]
[2]
Rate rM is the market rate of return over the coming time period (e.g., a year), which is
unknown now and has a probability distribution. Quantity r M in [2] is the mean of the
probability distribution of rM ; r M is the “expected rate of return on the market.” Rate rRF is
the risk-free rate (usually estimated using the rate on a U.S. Government security). Parameter
X
is the risk parameter (the beta) for stock X; it indicates the stock’s risk from an investor
equity
X
portfolio standpoint. Beta equity
reflects the degree to which firm X’s stock moves with the
overall stock market. Quantity [ r M  rRF ] in [2] is referred to as the “equity premium.” The
equity premium is the amount by which the expected return on the entire market of risky
securities exceeds the rate on a “riskless” asset (such as a U.S. Government security).
X
A publicly traded firm’s stock beta ( equity
), and the rates on U.S. Government
securities, can be obtained from Bloomberg, Value Line, Standard & Poor’s, and other
sources. The equity premium ([ r M  rRF ]) can be obtained from Ibbotson Associates (and
other data services). So, for a given publicly traded stock, equation [2] is readily solved.
3
Stock betas are estimated using historical (past) stock price data. As a word of
caution, the beta estimate for a particular firm’s stock (e.g., Intel common stock) will differ
among information services that provide betas.
This is because the services use different
stock portfolios to represent the market (the S&P 500, the Wilshire 5000, the Value Line
stock universe, etc.) and use different historical time periods to estimate betas.
Estimating Debt Rate rD : Rate rD is the interest rate that the company would have to
pay on incremental borrowing (if there are multiple issues of debt, it is a value-weighted
average of the incremental rate on each issue of debt). The rate on incremental debt of a
particular debt issue is the yield to maturity on that debt. If the debt is publicly traded, that
rate is observable. If the debt is not publicly traded, then an appropriate procedure would be
the one described in Section I.1 above (rating the debt based on the company’s business risk
and financing, and the debt’s particular characteristics, and then determining the prevailing
yield to maturity on similar debt). The debt cost of capital can also be estimated using the
CAPM (estimate the debt’s beta and plug into the CAPM formula).
Estimating Other Financing Rate rCFin : The procedure for estimating the cost of
capital on complex financing depends on the nature of the complex financing.
For non-
callable, non-convertible preferred with a constant dividend, [dividend/market price] is the
cost of capital. Complex financing with option characteristics (convertibles, etc.) should be
evaluated using an option-pricing model. An investment or commercial bank can assist in
estimating the incremental cost of a given type of complex financing.
I.3.
Illustration
Main Corporation’s management wants to estimate the company’s after-tax WACC.
Main is publicly traded and management believes that the market prices of the firm’s
securities approximate their intrinsic values. Main’s financing (using market values) is E 0 =
$300 million, D 0 = $150 million, and CFin 0 = $50 million. It is expected that the firm’s
financial structure (financing proportions), capital costs, and tax rate (T) will not change
significantly over time. Main’s marginal borrowing rate is 8% (so let rD = 8%), and the cost
of capital for Main’s complex financing is 12% ( rCFin = 12%). The beta on the company’s
Main
stock, equity
, equals 1.4. Suppose that the risk-free rate (based on U.S. Government treasury
bills) is rRF = 4%; and the equity premium [ r M  rRF ] = 8%. Main’s corporate tax rate T is
after tax
34%. What is Main’s after-tax WACC, rWACC
?
4
Solution: All of the needed data were provided above. We begin by computing the
equity cost of capital rE using equation [2].
Main
[ r M  rRF ]
rE = rRF + equity
= 4% + 1.4 [8%]
= 15.2%
[3]
By definition, the value of the firm, V0 , equals the sum of the value of all the firm’s
securities. Therefore, V0 = E 0 + D 0 + CFin 0 = $300 million + $150 million + $50 million
= $500 million. Using the information in Exhibit 1 below, we have:
E 
D 
 CFin 0 
after tax
=  0  rE   0  rD (1  T) + 
rWACC
 rCFin
 V0 
 V0 
 V0 
 $300 
 $150 
 $50 
= 
15.2% + 
8% (1  .34) + 
12%


 $500 
 $500 
 $500 
= 11.904%
[4]
Exhibit 1. Main, Inc. Financial Data
Equity market value ( E 0 )
Debt market value ( D 0 )
Complex financing market value ( CFin 0 )
Firm value ( V0 )
Equity cost of capital ( rE )
Debt cost of capital ( rD )
Complex financing cost of capital ( rCFin )
Corporate tax rate
5
$300 million
$150 million
$50 million
$500 million
15.2%
8%
12%
34%
II.
ESTIMATING THE WACC TO VALUE A FIRM
Section I explained how to estimate the WACC for a firm that has publicly traded
common stock that is assumed to be fairly valued in the market (i.e., market value is close to
intrinsic value, so there is no need to estimate the stock’s intrinsic value). This section
explains how to estimate the WACC if the intrinsic value of the common stock is assumed not
to be known. This is a common problem for privately-held companies (for which there is no
quoted stock price), and also for publicly traded firms in cases in which the analyst (appraiser)
believes that the equity market value may be significantly different from intrinsic value.
Business acquisitions often involve this issue (both buyer and seller will want an intrinsic
value estimate) whether the acquired company is publicly-held or privately-held.
The approach for estimating the after-tax WACC presented here parallels that in
Chapter 19 of Brealey & Myers 7th edition. To tie this discussion to that in Brealey & Myers,
we assume a firm (Olive Corporation) that plans to have only debt and equity in its capital
structure (no “complex financing”). Define E Olive
, D Olive
, CFin 0 as the current market values
0
0
of Olive’s equity, debt and complex financing, respectively; and define r EOlive , r DOlive , and
Olive
as Olive’s equity cost of capital, debt cost of capital, and the complex financing cost of
rCFin
capital, respectively. Rate r Olive signifies Olive’s opportunity cost of capital. T is Olive’s
marginal corporate tax rate. The approach presented here entails the following three steps.
Step 1: Estimate Olive’s opportunity cost of capital. To do this, identify publicly
traded companies that have an underlying business risk like that of Olive. We refer to
these similar business risk companies as “comparables.” From data about Olive’s
comparables, we infer Olive’s opportunity cost of capital ( r Olive ), which is the cost of
capital that is appropriate to the underlying business risk of Olive and its comparables.
Step 2: Determine Olive’s target capital structure and debt cost of capital ( r DOlive ) and,
using that information and the estimated r Olive from Step 1, determine Olive’s equity
cost of capital ( r EOlive ).
after tax
Step 3: Use the data from Steps 1 and 2 to compute Olive’s rWACC
.
We will now discuss each of the three above steps in detail, using Olive to illustrate the
concepts.
6
STEP 1:
ESTIMATE OLIVE’S OPPORTUNITY COST
OF
CAPITAL r.
Olive’s
opportunity cost of capital, r, is defined as:
r
Olive

 E Olive
 Olive  D Olive
 Olive  CFin Olive
Olive
0
0
0
 r CFin
=  Olive  r E   Olive  r D + 
Olive
V
V
 V 0

 0 
 0 
[5]
Rate r Olive is not the same as the after-tax WACC (in [1] above) because the (1  T) is absent
in [5]. The Modigliani-Miller analysis implies that, for a given firm, r is independent of the
firm’s capital structure (i.e., r Olive is the same for any financing proportions [ E Olive
/ V0Olive ],
0
/ V0Olive ] ). So, r Olive depends on Olive’s business risk, not its
[ D Olive
/ V0Olive ], and [ CFin Olive
0
0
financing method. The higher is Olive’s business risk, the higher is r Olive . The underlying
business risk is determined by the probability distribution of Olive’s free cash flow (FCF).
Since we are unsure of the intrinsic market values of Olive’s equity and debt, we
cannot at this point compute the proportions in [5]. So, what we do is to examine publicly
traded firms that have the same underlying business risk as does Olive, and then use the data
about these comparable firms to estimate r Olive .
Suppose that we identify three other
companies (A, B, and C) that we regard as Olive’s comparables in terms of underlying
business risk (you would prefer more than three if you can find them). Firms A, B and C have
the characteristics shown in Exhibit 2 below. The estimate of r Olive is the average of the
comparables’ r magnitudes. This average is r Olive = 12.2%.
To compute a comparable’s r (the last column in Exhibit 2), we use the approach
described in Section I for publicly traded companies to determine each comparable’s
[ E 0 / V0 ], [ D 0 / V0 ], [ CFin 0 / V0 ], rE , rD , and rCFin . (As shown below, to determine a
comparable’s rE we use its  equity and the CAPM.) We then substitute those six quantities
into equation [5] to solve for that comparable’s r. Thus, using the data in Exhibit 2, we have:
 E 0A  A  D 0A  A  CFin 0A  A
=  A  rE   A  rD + 
= [.8] 12% + [.2] 8% + 0 = 11.2%
r
A  CFin
 V0 
 V0 
 V0 
[6a]
 E 0B  B  D 0B  B
 CFin 0B  B
= [.6] 14% + [.4] 10% + 0 = 12.4%
r =  B  rE   B  rD + 
r
B  CFin
 V0 
 V0 
 V0 
[6b]
r
A
B
 E C0  C  D C0  C
 CFin C0  C
= [.5] 16% + [.4] 9% + [.1] 14% = 13% [6c]
r =  C  rE   C  rD + 
r
C  CFin
 V0 
 V0 
 V0 
C
7
Notice from Exhibit 2 that Firms A, B and C do not have the same r, which they
would if their business risk were identical. In practice, the best that we can usually do is to
identify comparables with similar, but not identical, risk. That is what we are assuming here.
Exhibit 2. Data on Olive Corporation Comparables
[ E 0 / V0 ] [ D 0 / V0 ] [ CFin 0 / V0 ]  equity
rE
rD
Firm A
.8
.2
0
Firm B
.6
.4
0
Firm C
.5
.4
.1
Average*
* 12.2% = (11.2% + 12.4% + 13.0%)/3.
1.00
1.25
1.50
12%
14%
16%
8%
10%
9%
rCFin
r
n/a
n/a
14%
11.2%
12.4%
13.0%
12.2%
Above we showed how to each comparable’s opportunity cost of capital using the
market data, and the estimated betas, shown in Exhibit 2. We did not address the issue of how
one finds comparables, and we brushed over the determination of each comparable’s
[ E 0 / V0 ], [ D 0 / V0 ], [ CFin 0 / V0 ], rE , rD , and rCFin . Let’s fill in some of these details.
Finding and Analyzing Comparables: For purposes here, a comparable is a publicly
traded company that is very similar to Olive in terms of underlying business risk. Business
risk is measured by the firm’s free cash flow (FCF) probability distribution. To identify
comparables, a good place to start is Olive’s industry, since firms in a given industry are
subject to similar supply and demand forces. We would also consider other industries with
risk characteristics like Olive’s industry. For example, the sales of consumer products that are
income sensitive and also appeal to consumers in the same income category may be highly
correlated. The FCFs of some producers’ goods manufacturers are highly correlated because
they depend on the general economy in similar ways.
Keep in mind that we want to estimate the discount rate (WACC) to discount Olive’s
future FCF. This means that we want each comparable to have a future like that of Olive (not
simply a similar past history). Current market values and discount rates for a comparable
reflect investors’ perceptions about the comparable’s anticipated future performance.
Estimating a Comparable’s Capital Structure Parameters: Since the comparables
are publicly traded, obtaining their E 0 , D 0 , and CFin 0 will not be difficult. Debt and
complex financing that is not publicly traded can be valued on the basis of the firm’s business
risk, capital structure, rating of the security (e.g., bond rating), and provisions in the financing
agreement. On this, see Section I.1 above.
8
Estimating a Comparable’s rE , rD and rOF : We can apply the procedures that were
presented in Section I.1 here, including the use of the CAPM to estimate each comparable’s
equity cost of capital rE . So, the equity cost of capital rates rEA , rEB , and rEC for firms A, B
and C, respectively, would be computed in the following way. As in expression [3], assume
that risk-free rate rRF = 4% and equity premium [ r M  rRF ] = 8%. Assume that we also have
obtained from an external source (Bloomberg, Ibbotson Associates, etc.) the beta estimates
A
B
= 1.0, equity
= 1.25, and Cequity = 1.5; these quantities are shown in Exhibit 2. Using the
equity
CAPM, it follows that the equity rates for comparables A, B and C are calculated as shown in
equations [7a], 7b] and [7c].
A
[ r M  rRF ] = 4% + 1.00 [8%] = 12%
rEA = rRF + equity
[7a]
B
[ r M  rRF ] = 4% + 1.25 [8%] = 14%
rEB = rRF + equity
[7b]
rEC = rRF + Cequity [ r M  rRF ] = 4% + 1.50 [8%] = 16%
[7c]
STEP 2: DETERMINE OLIVE’S TARGET CAPITAL STRUCTURE, rD
AND
rE . We
assume that Olive plans to have only debt and equity in its capital structure. Therefore,
CFin Olive
= 0. Set CFin Olive
= 0 in [5] and rearrange the terms and it follows that:
0
0
/ E Olive
]
r EOlive = r Olive + ( r Olive  r DOlive )[ D Olive
0
0
[8]
Suppose that the target [ E Olive
/ V0Olive ] = .8 and [ D Olive
/ V0Olive ] = .2, which implies
0
0
[ D Olive
/ E Olive
] = .25 (observe that the denominator in the ratio in [8] is E Olive
and not V0Olive ).
0
0
0
[Note that we could not use [8] for the comparables because we did not have their r levels.]
Now to estimate r DOlive . To estimate r DOlive you can consult with a financing expert, or you can
do the research yourself. The appropriate expert is an investment banker or commercial bank
loan officer. You would provide information about Olive’s underlying business risk profile
and about Olive’s planned capital structure. The banker will be able to estimate, based on
data about similar business risks and financing, what the firm would have to pay, in terms of
interest rate, for borrowed funds. The banker could forecast the rating (e.g., bond rating) that
would apply to the company’s debt and the implied interest rate. Of course, you could do
your own research on all of this, but you probably will have other responsibilities where you
have more of a comparative advantage. Let’s assume that the interest rate on your debt will
be r DOlive = 10%.
9
We have determined that [ D Olive
/ E Olive
] = .25 and r DOlive = 10%, and that r = 12.2%
0
0
(from our comparables analysis; see Exhibit 2). Substitute these numbers into [8] and we get:
/ E Olive
] = 12.2% + (12.2%  10%) [.25] = 12.75% [9]
r EOlive = r Olive + ( r Olive  r DOlive )[ D Olive
0
0
So, rEOlive = 12.75%. In Step 3, we will use the above data to compute Olive’s WACC.
STEP 3: COMPUTE OLIVE’S WACC. The quantity that we are trying to estimate for
after  tax , Olive
Olive is rWACC
in equation [1]. In Step 2 we concluded that: [ E Olive
/ V0Olive ] = .8,
0
[ E Olive
/ V0Olive ] = .2, r DOlive = 10% and r EOlive = 12.75%. Suppose that T = 34%. Substituting
0
into [1], we have:
after  tax , Olive
WACC
r
 E Olive
 Olive  D Olive
 Olive
0
0
=  Olive  r E   Olive
 r D (1  T)
 V0 
 V0 
= (.8)(12.75%) + (.2)(10%)(.66) = 11.52%
[10]
after tax , Olive
The rWACC
= 11.52% would be used to discount Olive’s expected future free cash flow
to value Olive’s equity. If Olive is a privately held firm, we would then apply a liquidity
discount to the FCF discounted value to produce our estimate of Olive’s equity market value.
III.
ESTIMATING THE WACC FOR AN ASSET OR PROJECT OF THE FIRM
As a matter of normal operations, both publicly traded and privately held companies
value assets that are not publicly traded. Investment projects are valued (their NPVs are
computed) when they are considered for adoption. A project’s WACC is the discount rate
used to compute the project’s NPV. A project is of course not itself publicly traded; it is
within the firm. Similarly, a parent may value a division or subsidiary that is not publicly
traded, perhaps in preparation for a spinoff or other type of business reorganization. In all
these cases, a discount rate, or cost of capital, is used in estimating the asset’s market value.
In Brealey & Myers Chapter 9 (Section 9.1, page 222), the authors make the point that
an investment project of the company should be valued as though it were a “mini-firm” with
its own cost of capital (that cost of capital depends on the risk of the project). But the cost of
capital cannot be directly observed as for a publicly traded company. In that sense, estimating
10
the cost of capital for a project is conceptually very similar to estimating the cost of capital for
a company that is not publicly traded (see Section II above).
The financing weights used in Section II for a privately held company were the target
financing proportions for the company (see Step 2 on page 9).
For a single project of the
company, the financing weights to use in computing the project’s WACC are the targeted
incremental changes in the firm’s overall financing that will result from the project. To
illustrate the point, suppose that Todd, Inc. is evaluating Project Zed. Zed will be financed
with debt and equity capital. The value of the project equals the present value of the
project’s expected future FCF computed using the appropriate WACC (just as the value of
Olive in Section II was the present value of Olive’s expected future FCF using Olive’s
WACC). The NPV of the project is the value of the project minus the project’s initial outlay.
We will an example to illustrate the estimation procedure described here. Assume that
Todd Corporation is considering Project Zed and needs an appropriate WACC to discount
Project Zed’s cash flows in order to compute its NPV. [ E Zed
/ V0Zed ], [ D Zed
/ V0Zed ] and
0
0
[ CFin Zed
/ V0Zed ] are the market value financing proportions for project Zed. (we will assume
0
only equity and debt financing of Zed, so [ CFin Zed
/ V0Zed ] = 0). Define r Zed , r EZed , and r DZed as
0
Zed’s opportunity cost of capital, equity cost of capital, and debt cost of capital. Zed’s
opportunity cost of capital is signified by r Zed . The following three steps are involved in
estimating Zed’s WACC.
Step 1: Estimate Zed’s opportunity cost of capital. To do this, identify publicly traded
companies that have an underlying business risk like that of Zed. We refer to these
similar business risk companies as “comparables.”
From data about Zed’s
comparables, we infer Zed’s opportunity cost of capital ( r Zed ), which is the cost of
capital appropriate to the underlying business risk of Zed and its comparables.
Step 2: Determine Zed’s target market value financing proportions ([ E Zed
/ V0Zed ] and
0
[ D Zed
/ V0Zed ]) and debt cost of capital and, using that information and the estimated r
0
from Step 1, determine Olive’s equity cost of capital.
after tax
Step 3: Use the data from Steps 1 and 2 to compute Olive’s rWACC
.
The above three steps are very similar to Steps 1, 2, and 3 in Section I. We will now apply
the above three steps to estimate the WACC for Project Zed.
11
STEP 1: ESTIMATE ZED’S OPPORTUNITY COST
OF
CAPITAL r Zed . Project Zed’s
opportunity cost of capital, r, is defined as:
r
Zed
 E Zed 
 CFin 0Zed  Zed
 D Zed 
=  0Zed  rEZed   0Zed  rDZed + 
r
Zed  CFin
 V0

 V0 
 V0 
[11]
Notice that [11] has the same form as [5]. As for a privately held company in Section II, in
analyzing a single project we look for publicly traded assets (firms) that have the same
underlying business risk as does Zed. We then estimate the r for each of these “comparables”
and compute their average r and use this average as our estimate of Zed’s r. So, let Project
Zed be the production of a consumer electronics product, and that we identify three publicly
traded manufacturers (Miko Corporation, United Industries, and Cora, Inc.) of similarly risky
consumer electronic products. Miko, United, and Cora have the following characteristics.
Exhibit 3. Data on Zed’s Comparables
[ E 0 / V0 ] [ D 0 / V0 ] [ CFin 0 / V0 ]  equity
rE
rD
Miko
.4
.5
0.1
United
0.6
0.4
0
Cora
0.8
0.2
0
Average*
* 11.6% = (12.2% + 11.4% + 11.2%)/3.
1.375
1.125
1.000
15%
13%
12%
10%
9%
8%
rCFin
r
12%
N/a
N/a
12.2%
11.4%
11.2%
11.6%
Using the Miko, United and Cora comparable data, we estimate the opportunity cost of capital
for Zed to be r Zed = 11.6%.
United
Miko
Again let rRF = 4% and [ r M  rRF ] = 8%. Beta measures equity
= 1.375,  equity
=
1.125, and Cora
equity = 1.0 would be obtained from an external source (e.g., Bloomberg) and then
used by the analyst (appraiser) to compute the equity rates for the comparables.
The
computation of the comparables’ equity rates is shown in [12a], [12b] and [12c] below.
Miko
[ r M  rRF ] = 4% + 1.375 [8%] = 15%
rEMiko = rRF + equity
[12a]
United
rEUnited = rRF +  equity
[ r M  rRF ] = 4% + 1.125 [8%] = 13%
[12b]
rECora = rRF + Cora
equity [ r M  rRF ] = 4% + 1.0 [8%] = 12%
12
[12c]
STEP 2: DETERMINE ZED’S FINANCING PROPORTIONS, rD
AND rE .
Assume that the
target impact of Project Zed on the firm’s equity and debt market values (that is, the financing
proportions) are 60% equity, 40% debt, and no complex financing ([ E Zed
/ V0Zed ] = .6,
0
[ D Zed
/ V0Zed ] = .4, and CFin 0Zed = 0).
0
Set CFin 0Zed = 0 in [11], and then rearrange [11] to
obtain the following equation for Zed’s equity cost of capital:
/ E Zed
]
r EZed = r Zed + ( r Zed  r DZed )[ D Zed
0
0
[13]
Equation [13] has the same form as equation [8]. Letting V0Zed be the increase in the value of
the firm due to Project Zed, as noted above management has decided that [ E Zed
/ V0Zed ] = .6
0
and [ D Zed
/ V0Zed ] = .4, which implies [ D0Zed / E Zed
] = (2/3).
0
0
Now we must estimate r DZed . For the project, r DZed is the incremental interest that the
firm will have to pay per dollar of additional borrowing to finance Zed. The most practical
approach for doing this is to estimate the interest rate that the company would have to pay on
its incremental borrowing given that the project is adopted (that is, taking into account what
the project will do to the risk of the firm). Suppose that this rate is 8%; thus, let rDZed = 8%.
Substitute r Zed = 11.6%, [ D Zed
/ E Zed
]= (2/3), and r DZed = 8% into [13]. We find that:
0
0
/ E Zed
] = 11.6% + (11.6%  8%)[2/3] = 14%
r EZed = r Zed + ( r Zed  r DZed )[ D Zed
0
0
[14]
So, rEZed = 14%. Now to compute the after-tax WACC for Project Zed.
STEP 3: COMPUTE ZED’S WACC. From Steps 1 and 2 we have for Project Zed:
[ E Zed
/ V0Zed ] = .6, [ D Zed
/ V0Zed ] = .4, r DZed = 8% and r EZed = 14%. Assume that corporate tax
0
0
rate T = 30%. Substituting into cost of capital equation [1], we have:
after  tax , Zed
WACC
r
 E Zed
=  0Zed
 V0
 Zed  D Zed
0
 r E   Zed

 V0
 Zed
 r D (1  T) = (.6)(14%) + (.4)(8%)(.70) = 10.64% [15]

after tax , Zed
The rWACC
= 10.64% would be used to discount Project Zed’s expected future FCF to
compute the value of Project Zed, V0Zed .
V0Zed is the present value of the future free cash flow generated by Project Zed.
Project Zed’s NPV equals V0Zed minus the initial cost of Project Zed. [ E Zed
/ V0Zed ] = 60% is
0
the proportion of V0Zed going to shareholders, and [ D Zed
/ V0Zed ] = 40% is the proportion of
0
V0Zed . We will now put some numbers on the variables to clarify this.
13
EVALUATING PROJECT ZED (This Discussion of Steps 4 and 5 is Optional Reading)
after  tax , Zed
Once rWACC
has been estimated, two additional key steps in investment analysis
can be performed. The first is the computation of the Project Zed’s NPV (which we will call
Step 4); and the second is determining the method of financing Project Zed’s initial outlay so
that the target market value proportions assumed in the cost of capital estimation will be
achieved (Step 5). To examine this, assume the following definitions:
V0Zed = present value of the future free cash flow from Project Zed
I 0Zed = initial outlay for Project Zed
I 0Zed , Debt = portion of I 0Zed that is provided by new borrowing
I 0Zed , Equity = portion of I 0Zed that is provided by equity financing
We know that:
I 0Zed = I 0Zed , Debt + I 0Zed , Equity
[16]
NPV0Zed = V0Zed  I 0Zed
STEP 4. DETERMINING
[17]
THE
NPV
OF
PROJECT ZED. The NPV of Project Zed,
NPV0Zed , is expressed in [17]. To compute V0Zed , the free cash flow from Project Zed is
after  tax , Zed
forecasted and then discounted using the estimated rWACC
(= 10.64%) in [15]. Estimating
the initial outlay, I 0Zed , involves an analysis of the alternative methods, and the associated
costs, of implementing the project, and choosing the method that is most cost-effective. To
illustrate Steps 4 and 5, assume the following estimates:
V0Zed = $150 million
[18]
I
Zed
0
= $100 million
It follows that NPV0Zed equals:
NPV0Zed = V0Zed  I 0Zed = $150 million  $100 = $50 million
[19]
Project Zed is acceptable because NPV0Zed > 0. Project Zed is adopted if the choice is simply
whether to accept or reject Project Zed. If Project Zed is being compared with a mutually
exclusive alternative, the one with the higher positive NPV is adopted.
14
STEP 5. DETERMINING
THE
FINANCING
OF
PROJECT ZED’S INITIAL OUTLAY. The
financing proportions in [15] ([ E Zed
/ V0Zed ] and [ D Zed
/ V0Zed ]) are target market value
0
0
proportions set by the firm (Todd Corporation) for Project Zed; they are the fractions of the
value of Project Zed ( V0Zed ) going to the equity and to the debt, not the fractions of the cost of
Project Zed (initial outlay I 0Zed ) that will financed with debt and equity funds (the cost
fractions being [ I 0Zed , Debt / I 0Zed ] and [ I 0Zed , Equity / I 0Zed ]). These cost fractions are determined as
follows.
When the firm issues new debt to finance Project Zed, it receives an amount from the
lender that is equal to the present value of what the firm will pay to the lender in interest and
principal in the future. Borrowing is, at least approximately, a zero net present value activity
for the borrower and for the lender (in a competitive market, lenders earn just their cost of
capital, implying that lending for the lender is a zero NPV activity). The NPV of Project Zed
goes to the firm’s (Todd Corporation’s) shareholders. This means that the market value of the
additional debt issued to finance Project Zed, D 0Zed , equals the amount received by the firm to
finance the initial outlay; that is:
I 0Zed , Debt = D 0Zed
[20]
Since [ D Zed
/ V0Zed ] = .4 (see [15]) and V0Zed = $150 million (see [18]), it follows that:
0
D
Zed
0
 D Zed
0
=  Zed
V
 0
 Zed
 V0 = .4 ($150 million) = $60 million

[21]
Combining [20] and [21], we have:
I 0Zed , Debt = $60 million
[22]
Using [16]:
I 0Zed , Equity = I 0Zed  I 0Zed , Debt = $100 million  $60 million = $40 million
[23]
Thus, given that V0Zed = $150 million and I 0Zed = $100 million, in order to meet market value
target [ D Zed
/ V0Zed ] = .4, the funds to finance Project Zed’s initial cost ( I 0Zed = $100 million)
0
must be in the form of I 0Zed , Debt = $60 million and I 0Zed , Equity = $40 million.
15
ANOTHER ILLUSTRATION: Blarney Beer Corporation plans to introduce a new ale,
Debenture Ale. This project (Project Debenture) will require an initial outlay of $40 million,
and is judged by management to be significantly riskier than Blarney’s existing product line.
STEP 1: ESTIMATE PROJECT DEBENTURE ALE’S OPPORTUNITY COST OF CAPITAL
r De b : Project Debenture will be financed with additional Blarney Corporation debt and
equity; there will be no complex financing ( CFin 0Deb = 0). The opportunity cost of capital for
Debenture Ale is therefore defined as follows:
r
Deb
 E 0Deb  Deb  D 0Deb  Deb  CFin 0Deb  Deb  E 0Deb  Deb  D 0Deb  Deb
=  Deb  rE   Deb  rD + 
=  Deb  rE   Deb  rD
r
Deb  CFin
 V0
 V0 
 V0 
 V0 

 V0 
[24]
Blarney has identified four relatively small publicly traded breweries that have risks similar to
Project Debenture. They have the following financial characteristics.
Exhibit 4. Debenture Ale Comparables
[ E 0 / V0 ] [ D 0 / V0 ] [ CFin 0 / V0 ]  equity
rE
rD
Spike
.4
.5
.1
Bluebeard
.2
.8
0
Firebird
.7
.3
0
Gazelle
.5
.5
0
Average*
* 12.15 = (11.2% + 12.8+ 12.1% + 12.5%)/4.
1.25
1.50
1.125
1.25
14%
16%
13%
14%
8%
12%
10%
11%
rCFin
r
16%
n/a
n/a
n/a
11.2%
12.8%
12.1%
12.5%
12.15%
The last row in Exhibit 4 is the opportunity cost of capital computed using equation [9]. The
estimated opportunity cost of capital for Project Debenture is r De b = 12.15%.
The comparables’ equity rates (the rE ) are computed using the  equity shown in Exhibit
4. Assuming that rRF = 4% and [ r M  rRF ] = 8%, it follows that (using, from Exhibit 4, Spike
equity
Firebird
Bluebeard
= 1.25,  equity
= 1.50,  equity
= 1.125 and  Gazelle
equity = 1.25):
rESpike = rRF + Spike
equity [ r M  rRF ] = 4% + 1.25 [8%] = 14%
Bluebeard
[ r M  rRF ] = 4% + 1.5 [8%] = 16%
rEBluebeard = rRF +  equity
[25a]
[25b]
Firebird
rEFirebird = rRF +  equity
[ r M  rRF ] = 4% + 1.125 [8%] = 13%
[25c]
rEGazelle = rRF +  Gazelle
equity [ r M  rRF ] = 4% + 1.25 [8%] = 14%
[25d]
16
STEP 2: DETERMINE PROJECT DEBENTURE’S FINANCING PROPORTIONS, r DDe b
AND
r EDe b . Project Debenture will be financed with additional Blarney Corp. debt and equity;
there will be no complex financing ( CFin Deb
= 0). Therefore, analogous to [13], we have:
0
r EDeb = r Deb + ( r Deb  rDDeb )[ D 0Deb / E Deb
]
0
[26]
Let V 0Deb be the value of Project Debenture (the present value of Project Debenture’s
expected future FCF using the WACC in equation [28] below as the discount rate), and let
E Deb
and D 0Deb be the market values of the portions of Project Debenture’s cash flows going
0
to Blarney Beer’s equity and the added Blarney Beer debt, respectively. Thus, V 0Deb = E Deb
0
+ D 0Deb . Suppose that management has set at its target the market value financing proportions
b
/ E 0De b ] = (1/3).
at [ E Deb
/ V 0Deb ] = .75 and [ D 0Deb / V 0Deb ] = .25, which implies that [ D De
0
0
Next we must estimate rDDeb . For Project Debenture, rDDeb is the incremental interest
that Blarney Beer will have to pay per dollar of additional borrowing to finance Project
Debenture.
Suppose that Blarney Beer would have to pay 10% on its added borrowing if
Project Debenture were adopted (that is, taking into account what Project Debenture would do
to Blarney Beer’s risk). Thus, assume that, for Project Debenture, r DDe b = 10%.
Substituting r Deb = 12.15%, [ D 0Deb / E Deb
] = (1/3), and rDDeb = 10% into equation [26],
0
we have:
r EDeb = 12.15% + (12.15%  10%)[1/3] = 12.87%
[27]
STEP 3: COMPUTE PROJECT DEBENTURE’S WACC. From Steps 1 and 2 we have for
Project Debenture: [ E Deb
/ V 0Deb ] = .75, [ D 0Deb / V 0Deb ] = .25, rDDeb = 10% and r EDeb = 12.87%.
0
Assume that T = 34%. Substituting into cost of capital equation [1], we have:
after tax, Deb
rWACC
 E Deb 
 D Deb 
Deb
0
0
=  Deb  r E   Deb
 rDDeb (1  T)
 V0 
 V0 
= (.75)(12.87%) + (.25)(10%)(.66) = 11.3%
[28]
after tax , Deb
The rWACC
= 11.3% would be used to discount Project Debenture’s expected future FCF
to compute the value of Project Debenture. Project Debenture’s NPV would equal that
amount minus the $40 million initial cost of Project Debenture Ale.
17
EVALUATING PROJECT DEBENTURE (This Discussion of Steps 4 and 5 is Optional
Reading)
after tax, Deb
Rate rWACC
has been estimated to be 11.3 percent. The evaluation of Project
Debenture now requires the computation of the Project Debenture’s NPV (Step 4); and the
determination of the method of financing Project Debenture’s initial outlay so that the target
market value proportions assumed in the cost of capital estimation will be achieved (Step 5).
Paralleling the Project Zed analysis, define the following terms.
V 0Deb = present value of the future free cash flow from Project Debenture
I 0Deb = initial outlay for Project Debenture
I 0Deb , Debt = portion of I 0Deb that is provided by new borrowing
I 0Deb, Equity = portion of I 0Deb that is provided by equity financing
We know that:
I 0Deb = I 0Deb , Debt + I 0Deb, Equity
[29]
NPV0Deb = V 0Deb  I 0Deb
STEP 4. DETERMINING
THE
NPV, NPV0Deb , is shown in [30].
[30]
NPV
OF
PROJECT DEBENTURE. Project Debenture’s
Suppose that the present value (using discount rate
after tax, Deb
= 11.3%) of the forecasted Project Debenture free cash flow, V 0Deb , and the
rWACC
estimated initial outlay for Project Debenture ( I 0Deb ) are as indicated below.
V 0Deb = $60 million
[31]
I
Deb
0
= $40 million
It follows that NPV0Deb equals:
NPV0Deb = V 0Deb  I 0Deb = $60 million  $40 = $20 million
[32]
Project Debenture is acceptable because NPV0Deb > 0. Project Debenture is adopted if the
choice is to accept or reject Project Debenture. If Project Debenture is being compared with a
mutually exclusive alternative, the one with the higher positive NPV is adopted.
18
STEP 5. DETERMINING THE FINANCING OF PROJECT DEBENTURE’S INITIAL OUTLAY.
The financing proportions in [28] (([ E Deb
/ V0Deb ] and [ D Deb
/ V0Deb ]) are target market value
0
0
proportions established by the company for Project Debenture. Now we must determine the
Project Debenture initial outlay financing proportions ([ I 0Deb , Debt / I 0Deb ] and [ I 0Deb, Equity / I 0Deb ]).
Since the market value of the additional debt issued to finance Project Debenture,
D 0Deb ,
equals the amount received by the company to fund the Project Debenture initial
outlay, we know that:
I 0Deb , Debt = D 0Deb
[33]
Noting that [ D 0Deb / V 0Deb ] = .25 (see [28]) and V 0Deb = $60 million (see [31]), it follows that:
D 0Deb
 D Deb
 Deb
0
=  Deb
 V 0 = .25 ($60 million) = $15 million
V
 0 
[34]
Combining [33] and [34], we have:
I 0Deb , Debt = $15 million
[35]
Using [29]:
I 0Deb, Equity = I 0Deb  I 0Deb , Debt = $40 million  $15 million = $25 million
[36]
Therefore, given that V 0Deb = $60 million and I 0Deb = $40 million, in order to meet market value
target [ D 0Deb / V 0Deb ] = .25, the funds to finance Project Debenture’s initial cost ( I 0Deb = $40
million) must be from I 0Deb , Debt = $15 million and I 0Deb , Equity = $25 million.
10/21/2004
19