774  Flexibility be further off or closer to the ROV mark, depending on the project’s payoffs and risks. This example does not mean that ROV is always the best approach to valu- ing managerial flexibility. The stylized example did not take into account two important aspects of real-life investment decisions: the type of prevailing risk and the availability of data on the value and variance of cash flows from the un- derlying asset. Exhibit 39.8 identifies when each method is most suitable. As we explain next, the more straightforward DTA is often the better approach because in practice (most of) the underlying risk is diversifiable or because only rough estimates are available for required inputs such as the underlying asset value and variance. In addition, DTA is easier to use and understand. ROV works best only when the future cash flows are closely linked to traded commodities, secu- rities, or currencies. Not surprisingly, real-option valuations are most often used for commodity-linked investments, such as in the mining and oil industries. Prevailing Risk: Diversifiable and Nondiversifiable  Investment projects can be exposed to a wide range of risks, such as product price and demand risk, interest and currency risks, technological risk, and political risk. The question is which particular risk (or group of risks) is prevailing—in other words, which risk could affect a project’s cash flow to such an extent that it would change management’s future decisions. The following examples of prevailing risks describe whether the risks are diversifiable and how this affects the choice of a valuation tool: • If commodity prices (as in mining, the oil industry, or power generation) or currency and interest rates are keys to future investment decisions, the prevailing risk is not diversifiable, and only ROV leads to the theo- retically correct valuation. This was illustrated in the previous example EXHIBIT 39.8  Application Opportunities for Real-Option Valuation vs. Decision Tree Analysis Underlying risk Nontraded assets Nondiversifiable Diversifiable Traded assets Decision tree analysis Decision tree analysis Decision tree analysis, real-option valuation Real-option valuation Available data Methods for Valuing Flexibility  775 in this chapter, where the difference in mining payoffs stemmed from changes in the mineral price. The DTA approach could not provide a correct value, although it was quite close in that particular case. • If technological risks (such as customer preferences, technological inno- vations, drug trial outcomes, or geological survey results) are critical to future investment decisions, the prevailing risk is diversifiable, and both ROV and DTA are effective tools for valuing flexibility. In our experience, this is the more common case for prevailing risk. Applying DTA, it is possible to discount the project’s payoffs in each scenario at the cost of capital of the underlying asset and discount the investment requirements at the risk-free rate (see Equation 39.1 in the example of the pharmaceuti- cal drug company presented near the beginning of the chapter).12 Let’s illustrate how you can apply ROV and DTA, depending on which group of risks dominates in a more complex version of the mining example from the previous section. In addition to price risk, there is now also uncertainty about the size of the reserves found (see Exhibit 39.9, Example 1). The mine is either very large, with reserves at 2.50 times the expected level, or very small, at 0.26 times the expected level. The probability of very large mining reserves is 33 per- cent, versus a probability of 67 percent for very small reserves. This implies that there are not just two but four possible outcomes to the initial investment, with cash flows ranging from $375 in the large-mine and high-mineral-price scenario ($150 × 2.50) to $13 in the small-mine and low-price scenario ($50 × 0.26). As the conditional payoffs in the exhibit reflect, the rational decision is to start produc- tion only if the mine turns out to be large, regardless of the commodity price. For a small mine, even the high-price scenario does not justify production, as the investment requirements ($105) exceed the cash flow ($39 = $150 × 0.26). To use the ROV approach to derive the valuation results, multiply the con- ditional payoffs by the risk-neutral (pseudo-)probabilities for the price scenar- ios and the normal probabilities for the quantity scenarios, and then discount at the risk-free rate.13 For example, for the large-mine, high-price scenario: 0 45 0 33 270 1 5 38 6 . . $ % $ . × × + = 13 We can use the risk-neutral probabilities from the original example because the mineral price risk has not changed. For the quantity risk, no risk adjustment to the probabilities is needed because it is diversifiable. We used the risk-neutral probability approach for the ROV valuation because it is more straightforward to apply here; of course, the replicating portfolio approach leads to an identical value. 12 To value the drug development project with an ROV approach, we build a replicating portfolio. As- sume a twin security exists whose payoffs are perfectly correlated with the outcome of the drug trial, generating $52.50 when the outcome is favorable and $10.50 when it is unfavorable. Because its cash flows are driven by technological risk only, the security’s market beta is zero, and its present value must be $30. A replicating portfolio consists of a long position of 107.1 of these securities and a short position of $1,071.40 in risk-free bonds. The ROV is therefore 107.1($30) – $1,071.4(1) = $2,143. See also Dixit and Pindyck, Investment under Uncertainty, 30–32, for a similar proof.