In a recent paper, Percival and Westerfield [2] suggested that the certainty equivalent (CE) and single certainty equivalent (SCE) approaches for analyzing capital budgeting problems each incorporate implicit assumptions regarding the intertemporal pattern of uncertainty resolution. PW concluded that differences in valuing cash-flow streams using these two methods result from these implicit assumptions. They provided an example to demonstrate this apparent difference [2, p. 350, fn. 51.Unfortunately, PW made a computational error in their example. In calculating the NPV using the CE method, they discounted the expected utility of the two outcomes and then applied the inverse utility transformation. To be consistent with their development of the CE method [2, p. 3491, the inverse utility transformation should have been performed before the discounting.The application of the correct CE valuation procedure to the PW example demonstrates that there is no difference in value between the CE and SCE methods.' Therefore, PW are in error when they state that "this equality will hold only if there is no risk adjustment (only time preference adjustments) after period 0" [2, p. 3501. The equality holds in their example, which includes uncertainty that is not resolved until afterperiod 0. In fact, it can be shown that in the decision environment assumed by PW, the CE and SCE methods will always yield the same valuations for certain forms of utility functions. In particular, the equality holds for the common utility functions U = ln(F), the form used by PW *The authors share equal responsibility for the content and any errors that may appear in this paper.'The correct CE procedure is to first calculate the expected utility of the two outcomes. u = . 5 ln(50)+.5 ln(25)=3.565 The inverse utlity transformation is then applied. U-' =antilog U = 35.35 This value is then discounted to yield the NPV. N P V = -35'35 --33.67 I .05Therefore, the correct CE procedure yields the same result as was obtained by P W for the SCE method.
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