Integrating Real Options with Managerial Cash Flow Estimates

Abstract

This article presents a real options model that fits managerial cash flow estimates (optimistic, likely, and pessimistic projections) to a continuous geometric Brownian motion (GBM) cash flow process with changing growth and volatility parameters. The cash flows and the value of a project are correlated to a traded asset, so the real option is priced under the risk-neutral measure with a closed-form solution. The analysis is extended to a sequential compound call option for investments over multiple periods. If the project is correlated to the market, then some of the risk may be mitigated by a delta-hedging strategy. A numerical example shows that the effect of the correlated asset on the real option value is significant, and the relationship between the volatility of the project and the real option value is not analogous to the typical relationship found in financial option pricing. Integrating the expertise and industry knowledge of management, this approach makes possible a more rigorous estimation of model inputs for real option pricing.

Notes

Investors or managers expect to be compensated for taking on greater risk and therefore discount future cash flows of an investment at the risk-free rate plus an added premium. However, mathematically, it is more difficult to deduce the appropriate discount rate for assets, such as options, derived from traded asset, and instead options are typically valued using the risk-neutral measure and discounted at the risk-free rate. Essentially, the risk-neutral measure uses risk-adjusted probabilities so that assets can be valued using the risk-free rate. It should be emphasized that discounting future cash flows using the real-world measure and an appropriate discount factor will lead to the same result as discounting the same future cash flows at the risk-free rate under the risk-neutral measure. For additional details refer to Hull (2009).