764  Flexibility The contingent NPV of $2,143 is considerably higher than the $286 NPV of committing today. Therefore, the best alternative is to defer a decision until the trial outcomes are known. The value of the option to defer investment is the difference between the value of the project with flexibility and its value without flexibility: $2,143 – $286 = $1,857. Based on this example, it is possible to summarize the distinction between the standard and contingent NPVs. The standard NPV is the maximum, de- cided today, of the expected discounted cash flows or zero: Standard NPV Max Expected Cash Flows Cost of Capital 0 =       = t 0 ( ) , The contingent NPV is the expected value of the maximums, decided when information arrives, of the discounted cash flows in each future state or zero: Contingent NPV Expected Max Cash Flows Contingent on Informat = × = t 0 ion Cost of Capital 0,               These two NPV approaches use information quite differently. Standard NPV forces a decision based on today’s expectation of future information, whereas contingent NPV permits the flexibility of making decisions after the informa- tion arrives. Unlike standard NPV, it captures the value of flexibility. A project’s contingent NPV will always be greater than or equal to its standard NPV. The value of flexibility is related to the degree of uncertainty and the room for managerial reaction (see Exhibit 39.3). It is greatest when uncertainty is high and managers can react to new information. In contrast, if there is little uncertainty, managers are unlikely to receive new information that would alter future decisions, so flexibility has little value. Similarly, if managers cannot act on new information that becomes available, the value of flexibility is low. Including flexibility in a project valuation is most important when the project’s standard NPV is close to zero—that is, when the decision whether to go ahead with the project is a close call. Sometimes senior management intuitively overrules standard NPV results and accepts an investment project for strategic reasons, for example, because the project creates an initial market position that can be expanded at a later stage if and when the company has EXHIBIT 39.2  Value of Flexibility to Defer Investment $ t = 0 Unsuccessful product Successful product 50% 50% p = 1 – p = t = 1 t = 2 . . . ? Cash flow 500 500 . . . 500 Investment (6,000) – . . . – Contingent NPV = 2,143 Cash flow 100 100 . . . 100 Cost of capital = 5% Investment (6,000) – . . . – Note: t = time, in years     p =  probability Uncertainty, Flexibility, and Value  765 the competitive products or services to offer. In these cases, the flexibility recognized in contingent valuation fits better with strategic intuition than do the rigid assumptions of standard NPV approaches. What Creates Flexibility Value To identify and value flexibility, you must understand where its value comes from. Consider what happens if the range of possible annual cash flow outcomes (originally $500 versus $100 per year) increases to $600 versus $0. Since expected cash flows and cost of capital remain unchanged, the standard NPV is the same ($286).5 However, the contingent NPV increases from its prior level of $2,143: NPV Max 0 = × − + ( )               + = ∞ ∑ 0 5 6 000 1 05 600 1 05 1 . $ , . $ . , t t 0 5 6 000 1 05 0 1 05 0 0 5 1 . $ , . $ . , . ($ × − + ( )               = = ∞ ∑ Max t t 6 286 0 5 0 3 143 , ) . ( ) $ , + = The contingent NPV of $3,143 is almost 50 percent greater at this higher level of uncertainty. Why? As in the original case, only the cash flows from the favorable outcome affect the contingent valuation. Since these cash flow projections have increased by 20 percent and the required investment has not changed, the contingent NPV increases substantially. The value of the deferral option rises from $1,857 to $2,857 (computed as $3,143 – $286). EXHIBIT 39.3  When Is Flexibility Valuable? Uncertainty, likelihood of receiving new information High High Low Low Moderate flexibility value Low flexibility value High flexibility value Moderate flexibility value Ability to respond, room for managerial flexibility 5 We assume that the trial outcome risk is uncorrelated with the overall economy.