W E B E X T E N S I O N
25B
RiskNeutral Valuation
T
his extension provides an introduction to a financial engineering technique
known as riskneutral valuation.
As we discussed in the chapter, decision trees will almost always give an inaccurate
estimate of a real option
’
s value because it is impossible to estimate the appropriate
discount rate. In many cases there is an existing model for a financial option that cor
responds to the real option in question. Sometimes, however, there isn
’
t such a
model, and then financial engineering techniques must be used. Many financial engi
neering methods are extremely complicated and are best left for an advanced finance
course. However, one method is reasonably easy to implement with simulation anal
ysis. This method is
riskneutral valuation
, and it is similar to the certainty equiva
lent method (discussed in Chapter 11) in that a risky variable is replaced with one
that can be discounted at the riskfree rate. We show how to apply this method to
the investment timing option presented in the chapter.
Recall that Murphy Software is considering a project with uncertain future cash
flows. Discounting these cash flows at a 14% cost of capital gives a present value of
$51.08 million. The cost of the project is $50 million, so it has an expected NPV of
$1.08 million. Given the uncertain market demand for the software, the resulting
NPV could be much higher or much lower.
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 Spring '10
 MR.Wroshr
 Net Present Value, Mathematical finance, riskneutral valuation

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