Valuation: Measuring and Managing the Value of Companies, Fifth Edition
Chapter 32 Solutions
Valuing Flexibility
1. Standard NPV analysis considers one possible set of cash flows. Contingent NPV
2. Flexibility is the main driver of value in the real-option approach, and several inputs
determine the value of the option. Those drivers and their effect on the value of the option
higher because the managers can liquidate at $300.
The ROV NPV is found by first computing the risk-neutral probabilities: u =
ROV gives a higher value because flexibility lowers risk so the cost of capital for a
project with downside protection from the put option should be lower than k = 10%. The
lower risk from flexibility can be seen by comparing the potential values in the ROV
model to those of the DCF model. The ROV value can go up from 657 to 1,000 (+52%)
The implied cost of capital when there is flexibility is the value that makes the expected
value in the ROV model equal to the project value, that is, the solution for k in the
Since this is less than 10 percent, there is an underestimation of project value with
flexibility (although the difference is small).
4. The standard NPV approach applies in a case where there is low uncertainty and/or
managers do not have the ability to make major decisions such as expansions or
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5. These two options mean the manager can significantly reduce the probability of negative
6. The cost of capital for a project using ROV can be higher than that using NPV because
7. The expected cash flows provide an estimate of the present value of the project, which is
8. Since the nondiversifiable commercial risk was relatively small in the example, the two
approaches delivered the same estimate of NPV = $120 million. For some sufficiently
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