Capital Budgeting Under
Uncertainty
The Cost of Capital and Capital
Budgeting: Some Questions


Firms usually spend money on projects that are
not risk free. How do we find the proper discount
rate when projects are risky?
Firms can raise funds for investment by retaining
earnings, selling debt or selling equity. Does it
make any difference how the firm raises money in
determining the cost of capital?
– How can we determine the proper discount rate when
the firm uses both debt and equity?
– How do we do capital budgeting when the project has
different risk and/or a different capital structure than
does the firm as a whole?
Capital Budgeting Complexities


Our analysis of risk and return, as summarized by the
SML, can be extended to capital budgeting decisions.
If the firm uses no debt in its capital structure,
– the same is planned for the project,
– and the project has the same systematic risk (beta) as the
firm’s existing assets,
– then the expected return required on the firm’s equity is the
appropriate discount rate for the project.

If the project’s systematic risk (beta) differs from the
firm’s systematic risk then use a measure of the
project’s beta to determine the discount rate.
– First we’ll talk about: Why?
– Then we ask: How can this be estimated?
Project vs. Firm Risk (All Equity Firm)
Expected Return
SML
project cost
of capital
firm’s cost
of capital
•
•
project cost
of capital
Rf
Beta
Project
Beta – Low
Firm
Beta
Project
Beta – High
Cost of Capital for a Project

Ralph’s firm is an all equity financed firm in the
fast food industry. Ralph is considering a project
in the Bio-tech industry.
–
–
–
–

The 10 year risk free rate is currently 4%.
The historical average risk premium is 7%.
The beta of Ralph’s firm = 1.1.
The beta of Genzyme (an all equity firm) = 0.61.
The cost of capital for the new investment is
correctly calculated as:
– E(RP) = rs = 4% + 0.61 (7%) = 8.27%
– Not as: E(RP) = 4% + 1.1 (7%) = 11.7%. Why not?
– If it is, what mistake might the firm make?
Project Beta: How do you estimate it?


In evaluating a project, you want to know the risk
of that “enterprise.” What would its beta be if it
were a firm?
It is easy if the project falls neatly into an industry
in which there are publicly traded firms.
– Find the enterprise or asset betas of a set of firms in the
industry that closely resemble the project and take an
average (why?).

In the case of a new project that looks nothing like
existing enterprises it gets squishy.
– Do a comparable firm analysis (when possible).
– Evaluate the cyclicality of its revenues and its operating
leverage.
Capital Budgeting Complexities

If a project will be financed using both debt and
equity, adjustments to the discount rate are
required.
– Financial leverage increases the equity beta
relative to the asset beta.
» Which of these would be estimated using the
regression technique we discussed earlier?
– Interest is tax deductible.
» When you calculate NPV we must either allow for
this in the estimated cash flows or alter the discount
rate to reflect the presence of debt.
» We first consider adjusting the discount rate.
The Weighted Average Cost Of Capital
(WACC)
• When a project uses both debt and equity financing,
the most frequent recommendation is to use the
project’s weighted average cost of capital (WACC or
rWACC) as the discount rate:
rWACC 
S
B
rS 
rB (1  TC )
S B
S B
• where
– S is the market value of the equity
– B is the market value of the debt
– rS is the required rate of return on the equity
– rB is the required before tax rate of return on the debt
– TC is the marginal tax rate
WACC


Fundamentally, the WACC is, just what its name
suggests, an average of two costs of capital (the
costs of debt and equity capital) weighted by the
relative amounts of each security used.
If I raise a dollar by selling 25¢ of debt and 75¢ of
equity, and debt costs me 4% while equity costs
me 8%, what is the total cost per dollar?
– Simple: (0.04)(0.25) = 0.01 for the debt and
(0.08)(0.75) = 0.06 for the equity. The sum of these is
0.01 + 0.06 = 0.07 or 7¢ per dollar raised in this way.
$0.75
0.08  $0.25 0.04  $0.07  0.07  7%
$1
$1
$1
The Weights





The two weights in the “weighted average” are
just the relative amounts of borrowing represented
by the different securities.
Recall S+B is total value.
S/(S+B) is the percent of value that is represented
by equity.
B/(S+B) is the percent of value that is represented
by debt.
Any time this calculation is done the current
market values of these securities should be used in
the calculation.
Calculating the Cost of Equity (rS)
• The cost of equity can be calculated using the Security
Market Line (SML) from the CAPM.
rS = Rf + bS(E[RM] – Rf)
Some choices:
– Use of long-term versus short-term rate for Rf.
• Practitioners usually favor the long-term rate.
• The “first” Rf must be a current risk free rate.
• Make sure you adjust the risk-premium accordingly.
– Beta.
• Our own regression or published.
• Need to adjust the equity beta for differing capital structures.
Calculation of the Cost of Debt (rDebt)


The before tax cost of debt can be calculated as
the yield to maturity on the firm’s existing debt.
Can also be found from bond ratings of companies
with comparable financial structure in the same or
related industries.
– 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.
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
Suppose ΔNWC, Depr, and Cap Ex are zero in each
scenario so net income is cash flow.
In A, the firm can distribute a total of $600 to stakeholders.
In B, the firm can distribute $100 (interest) + $540=$640.
The tax shield from debt gives the firm $40 more to
distribute to stakeholders. This tax shield lowers the
effective interest payment on debt to $60=$100(1 - 0.4) or
an “after tax” 6% coupon rate.
WACC Example

Gamma airlines is financed with 60% debt and 40% equity.
Currently the YTM on Gamma bonds is 9%, and Gamma
has estimated its cost of equity to be 14.5%. Gamma’s
corporate tax rate is 40%. What is Gamma’s WACC?
WACC = .40(14.5%) + .60(9%)(1-.40) = 9.04%.

Issues:
– What if the risk of the project at hand differs from that
of Gamma’s past projects?
– What if risk of this project is similar to that of Delta
Airlines’ projects, and the 14.5% cost of equity figure
was actually obtained for Delta (bS = 1.215). However,
Delta’s capital structure differs from Gamma’s.
Betas and Leverage
• We noted earlier that the beta of a portfolio is the
average of the component betas. We can think of
the firm’s assets as a portfolio of the debt and
equity claims. From these insights it follows that:
 S 
 B 
b Assets  
 b Equity  
 b Debt
S B
S B
• Where S is the market value of the stock (equity), B is the
market value of debt (bonds), and Tc is the tax rate.
• Think of the “balance sheet” representation of the firm.
• The asset beta is the fundamental reflection of business risk.
Beta Under Different Capital Structures
• In this analysis it is often assumed that the debt has a
zero beta (sometimes a big simplification). Then:
b Assets
 S 

 b Equity
S B
• When taxes are explicitly accounted for, the
understanding is the same, but the math becomes more
complicated. The result is (sec 17.7 RWJ):
b Assets


S
 b Equity
 
 S  B(1  Tc ) 
Beta Under Different Capital Structures
Example: Gamma airlines’ equity beta is observed to be
1.31. Its equity is worth 25.0 million while its debt is
worth 15.0 million and its tax rate is 40%. What is the
beta of its underlying assets?
bAssets
25



 1.31  0.96
 25  15(1.4) 
Equity Betas and Leverage


If the firm uses no debt (B=0) the equity beta and the asset
beta are equal.
If the firm uses debt, the equity beta is higher than the asset
beta (since debt is first in line, levered equity is riskier than
the firm’s underlying assets):
b Equity
B (1  TC ) 

 b Assets 1 

S


 The formula implies:
(1) As we add more debt, equity holders will demand a
higher rate of expected return.
(2) When comparable firms are used to estimate beta,
adjustments for differing capital structures may be
needed.
Why does beta increase with
financial leverage?


Leverage increases the volatility of the equity cash
flow:
Numerical Illustration:
Outcome
EBI
Interest
Income
Good
125
50
75
Bad
100
50
50
% Ch.
-20%
0%
-33.3%
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 target
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/assets.
– Obtain the unlevered (asset) beta of the comparable
company by transforming its equity beta.
– Obtain the corresponding project equity beta, reflecting
the capital structure to be used by the project.
– Obtain the cost of equity and cost of debt for this
project at your firm.
– Calculate the WACC for the project and perform NPV
analysis.
Example: “Un-levering” and “Re-levering” b

In the process of evaluating Gamma Airlines you find:
– Delta Airlines has an Equity beta of 1.215, Tc = 40%.
– Delta uses 70% equity and 30% debt financing.

Find the asset beta of Delta:
b Assets


.70

1.215  0.966

 .70  .30(1  .4) 
– This will reflect the risk of the assets of Gamma Air’s project.

Now find the equity beta of Gamma Air
 .60(1  .40) 
1.835  0.9661 

.40


– This will reflect the risk of the equity of Gamma Air’s project.

If Delta’s and Gamma’s capital structures are different,
their costs of equity will be different.
Example: BK Industries
If you recall, BK was evaluating a project in a very different
industry from its own with the following incremental cash
flows (FCF). At 10% we found an NPV of $5.2 million.
($ Millions)
Year 0 Year 1 Year 2
2000
2001
2002
(A) Cash Flow
From Investment
(B) Cash Flow
From Operations
Project Cash
Flow [(A) + (B)]
-26.0
0.0
-0.632 -0.865 0.375
19.298
0.0
3.98
6.051
7.550
5.615
3.167
5.42
6.69
5.99
22.46
-26.00 3.98
Year 3
2003
Year 4 Year 5
2004
2005
Example: BK Industries Revisited


BK Industries is a conglomerate company with
operations in marine power, pleasure boating,
defense, and fishing tackle. BK’s 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, and a marginal tax rate
of 45% (as does BK).
Levered Betas using debt/equity ratios

The formulas for obtaining asset betas from equity
betas and vice versa provided earlier required
dollar values for debt (B) and equity (S). What if
you are only given the leverage ratio, L = B/S?
The formulas are easily restated as:
b Assets


1

 b Equity
 1  L(1  TC ) 
b Equity  b Assets (1  L(1  TC ))
“Unlever” Latec’s Beta to obtain
the Beta of Text-Editing Assets:

Latec has L = B/S = 0.75, TC = .45, and an equity
beta of 1.35.
b Assets
1



1.35  0.955
 1  0.75(1  0.45) 
“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  0.9551  1(1  .45)   1.48
•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%. Then the required equity return on BK’s
project is:
rS  RF  b ( E[ RM ]  RF )  8%  1.48 * 7%  18.36%
The weighted average cost of capital for the text
editing venture (using the fact that B/S = 1) is:
S
B
WACC 
rS 
rB (1  TC )
SB
SB
1
1
= 18.36%  8%(1  0.45)  11.38%
2
2

Finally, we can evaluate the NPV of the text editing
venture using the WACC that reflects the risk
associated with this particular business. Using the cash
flow estimates obtained earlier:
3.980
5.419
6.685
5.990
22.465




(1.1138) (1.1138) 2 (1.1138)3 (1.1138) 4 (1.1138)5
 $3.78 Million
NPV  26.0 
• The NPV is positive, so proceed with the text editing business.
• Note also that the total value of the project will be $29.78 M.
• Notice that the selected discount rate of 11.38% reflects:
 The risk (beta) of text editing businesses, not BK’s existing
businesses.
 BK’s capital structure (which will be used for the project),
not that of the comparable firm.
Questions

BK Industries’ debt to equity ratio is 1.0 as
it is for the project. BK’s equity beta prior
to starting the text editing business was 1.0
(levered beta).
– What will happen to the beta of BK Industries after
starting the text editing business?
– Suppose that BK uses its firm cost of capital to evaluate
the text business? Would this favor undertaking the
investment?
– Does BK diversifying into the text editor business help
shareholders by providing them a more “diversified
portfolio”?