Using the WACC to Value Real Options

Use of the weighted-average cost of capital (WACC) in real-option valuation is an alternative to using risk-neutral real-option valuation. Using the WACC involves a marginal increase in mathematical complexity, but the method is easy to implement in a spreadsheet and easy to present to company managers, clients, and colleagues. Because real-option valuation is immune to choices of admissible discount rates, however, the critical issue is correct estimation of volatility, not choice of discount rate. We also point out that the natural and conservative tendency to overestimate risk is anything but conservative in a real-option valuation. Two problems obstruct the wider use of real-option analysis: a lack of understanding of risk-neutral valuation and an inability to question a given constant discount rate for a project. We demonstrate how to overcome these problems by using the weighted-average cost of capital (WACC) to perform real-option valuation. Our argument relies on the immunity of option valuation to choice of admissible discount rates; that is, different admissible discount rates must lead to identical option valuations. The WACC valuation is marginally more mathematically complex than risk-neutral valuation, but it is easy to implement in a spreadsheet.We begin by deriving the generalized one-period option-pricing (GOPOP) model as a generalized risk-adjusted version of the Cox–Ross–Rubinstein (CRR) one-period binomial tree model. The GOPOP model allows any admissible risk-adjusted discount rate for the underlying asset to be used in option valuation. Admissibility is determined by arbitrage or equilibrium considerations.We use the GOPOP model to value a simple real option with the WACC as the discount rate for the underlying asset. We show that the valuation is identical to that obtained using CRR risk-neutral valuation. We then distinguish between the discount rate on the underlying asset and the discount rate on the real-option project itself. The discount rate on the real-option project changes as one steps through a multiperiod tree; the discount rate on the underlying asset does not. The WACC, however, applies properly to the real-option project, not the underlying asset. We show that using the WACC for option pricing is feasible and produces a final result identical to the results of the two earlier option value calculations. We argue, however, that forcing the underlying discount rate to change from period to period so as to maintain a constant project WACC is unduly artificial.We then ask: If real-option valuation is immune to assumptions about the discount rate—in which case, questions about the legitimacy of risk-neutral valuation are irrelevant—what is the critical parameter for real-option valuation?To answer this question, we show that even if one knows the payoffs to the option one period ahead and the real-world probabilities with which they will occur, one cannot value the option without an estimate of volatility. Thus, volatility estimation is the critical ingredient of real-option valuation. If one is using risk-neutral valuation (CRR), one still needs the risk-neutral probabilities before discounting, and one cannot find these probabilities without an estimate of volatility; if one is using non-risk-neutral valuation (GOPOP), then even if one has the non-risk-neutral probabilities, one still needs the discount rate, which is a function of volatility.Finally, we note that an overestimate of risk can make one too conservative in net present value (NPV) analysis but an overestimate of risk can make one very daring in real-option analysis because option values increase with volatility. A sensitivity analysis with regard to volatility is thus crucial in making project decisions in real-option analysis.