Capital Budgeting Under
Uncertainty
The Cost of Capital and Capital
Budgeting: Some Questions


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 in determining the cost of capital?
– What is the proper discount rate when the firm uses
both debt and equity?

How do we find the proper discount rate when
projects are risky?
– 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 has no debt in its capital structure and the
project being evaluated has the same (beta) systematic
risk as the firm’s existing projects, then the expected
return on the firm’s equity is the appropriate discount
rate for the project.
If the project beta differs from the firm beta then use
the project beta.
– Why?
– How can this be estimated?
Project vs. Firm Risk (All Equity Firm):Why?
Expected Return
project cost
of capital
SML
•
firm cost
of capital
•
Rf
Beta
Firm
Beta
Project
Beta
Project Beta: How do you estimate it?


In evaluating a project, you want to know the total risk of
that “enterprise.”
The easiest way is if it falls neatly into an industry in
which there are publicly traded firms.
– In this case find the enterprise or asset betas of a set of firms in the
industry that most closely resemble the project, and take an
average of these betas.

In the case of a new project that looks nothing like existing
enterprises it gets squishy.
– Evaluate the cyclicality of its revenues and its operating leverage.
– Do a comparable firm analysis.
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 bond rate is currently 4%.
The historical average risk premium is 7%.
The beta of Ralph’s firm = 1.1.
The beta of Genzyme (GENZ) an all equity firm = 0.61.
Cost of capital for the new investment is correctly
calculated as:
– E(RP) = 4% + 0.61 (7%) = 8.27%
– Not as E(RP) = 4% + 1.1 (7%) = 11.7%
Capital Budgeting Complexities

If the firm has debt in the capital structure,
adjustments are required.
– Interest is tax deductible. Either allow for this
in cash flows or alter the discount rate to reflect
the presence of debt.
– Financial leverage increases equity betas
relative to the firm’s beta.
» Which of these is estimated by the regression
technique we discussed earlier?
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 or rWACC):
WACC 
S
B
rS 
rB (1  TC )
S B
S B
• where
– S is the market value of the firm’s stock
– B is the market value of the firm’s debt
– rS is the required rate of return on the firm’s stock
– rB is the required before tax rate of return on the firm’s debt
– TC is the firm’s marginal tax rate
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.
– 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.
Calculation of the cost of equity (rEquity)
• The cost of equity can be calculated using the Security
Market Line (SML) from the CAPM.
• rS= Rf+ b (E[RM]- Rf)
Some choices:
– Use of long-term versus short-term rate for Rf.
• Practitioners usually favor the long-term rate.
• Make sure you adjust the risk-premium accordingly.
– Beta.
• Regression or beta book.
• Need to adjust the equity beta for different capital
structures.
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. 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 (borrowings), and Tc is the tax rate.
• Think of the “balance sheet” representation of the firm.
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 considered, the understanding
remains the same, but the math becomes more
complicated. The result is (see sec 17.7 in RWJ):
b Assets


S


 S  (1  T ) B  b Equity
c


Points to Notice Regarding 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, equity is riskier than the
overall firm):
b Equity
B (1  TC ) 

 b Assets 1 

S


 implies:
– (1) equity holders will require a higher rate of return,
– (2) when surrogate firms are used to estimate beta,
adjustments for differing capital structures are needed.
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.
– Obtain the unlevered (asset) beta of the comparable.
– Obtain the corresponding project equity beta, reflecting
your firm’s capital structure.
– 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

To 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.

Now find the equity beta of Gamma Air
 .60(1  .40) 
1.835  0.9661 

.40



If Delta’s and Gamma’s capital structures are different,
their costs of equity will be different: 18.85% not 14.5%.
Summary: Risk, Return, and Discount Rates

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Some risk can be diversified, some cannot.
‘Beta’ coefficients measure systematic risk.
We expect systematic risk to earn a risk premium
in equilibrium but that diversifiable risk will not.
The CAPM (and particularly the SML) is a simple
model capturing important insights regarding risk
and diversification.
Discount rates for projects should reflect the
systematic risk of the project (not necessarily that
of the firm) and the capital structure of the firm or
division (not necessarily the financing of the
project itself).