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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 are the time until making a decision (+), the costs of investment (–), the risk-free
3. Using the current liquidation value as an opportunity cost, the standard NPV is (0.6 *
higher because the managers can liquidate at $300.
$372.71.
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
(+57%) or down to 250 (–61%).
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
project with flexibility is greater than or equal to a project without flexibility, and the
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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
large level of commercial risk and assuming the other inputs remain constant (e.g., the
value of the completed drug), ROV NPV will be higher than ROV DTA since the lower
NPV? A trial-and-error search can find the value for volatility where the two estimates