W E B E X T E N S I O N
11A
Certainty Equivalents
and RiskAdjusted
Discount Rates
T
wo alternative methods have been developed for incorporating project risk
into the capital budgeting decision process. One is the
certainty equivalent
method
, in which the expected cash flows are adjusted to reflect project risk:
Risky cash flows are scaled down because the riskier the flows, the lower their certainty
equivalent values. The second is the
riskadjusted discount rate method
, where differ
ential project risk is dealt with by changing the discount rate: Averagerisk projects are
discounted at the firm
’
s corporate cost of capital, aboveaveragerisk projects are
discounted at a higher cost of capital, and belowaveragerisk projects are discounted at
a rate below the corporate cost of capital. The riskadjusted discount rate method is used
by most companies, so we focused on it in earlier chapters. However, the certainty equiv
alent approach does have some advantages, so financial managers should be familiar with
it as well.
It is not always possible to find existing models for financial options that corre
spond to all real options. In such a situation, the analyst must use financial engineer
ing techniques. One technique,
riskneutral valuation
, is analogous to the certainty
equivalent method, except it is applied using simulation.
11.1 T
HE
C
ERTAINTY
E
QUIVALENT
M
ETHOD
The certainty equivalent (CE) method follows directly from the concept of utility
theory. Under the CE approach, the decision maker must first evaluate a cash flow
’
s
risk and then specify how much money, to be received with certainty, will make him
indifferent between the riskless and the risky cash flows. To illustrate, suppose a rich
eccentric offered you the following two choices:
1.
Flip a fair coin. If heads comes up you receive $1 million, but if tails comes
up you get nothing. The expected value of the gamble is (0.5)($1,000,000) +
(0.5)($0) = $500,000, but the actual outcome will be either $0 or $1 million,
so this choice is risky.
2.
Do not flip the coin and simply pocket $300,000 cash.
If you find yourself indifferent between the two alternatives, then $300,000 is your
certainty equivalent for this particular risky $500,000 expected cash flow. The certain
(or riskless) $300,000 thus provides you with the same
utility
as the risky $500,000
expected return.
Now ask yourself this question: In the preceding example, exactly how much cash
inhand would it actually take to make you indifferent between a certain sum and the
risky $500,000 expected return? If you are like most people, your certainty equivalent
would be significantly less than $500,000, indicating that you are risk averse. In
1
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general, people are risk averse, and the lower the certainty equivalent, the greater the
decision maker
’
s risk aversion.
The certainty equivalent concept can be applied to capital budgeting decisions, at
least in theory, in the following way.
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 Spring '10
 MR.Wroshr
 Corporate Finance, Net Present Value, Expected utility hypothesis

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