Real Option Valuation

Real options valuation is a financial technique for evaluating investments under conditions of uncertainty, particularly uncertainty associated with market variables such as future product demand or the future value of an asset. Option pricing is a well-developed area of financial engineering, dealing with the valuation of puts, calls, and more complex derivatives, but when applied to non-financial assets, the term “real options” is used. In real options valuation, the general ideas from financial options pricing theory are used along with some of the mathematics.

Real option valuation has already been applied to a variety of investment decisions by industry, and is widely taught as part of a modern curriculum in business investment analysis. Only recently, though, has real options modeling and analysis have been applied to space systems3 and NASA investments.4

Basically, real options valuation is a way of capturing value that goes unrecognized in traditional NPV analysis. In particular, when the future is uncertain, there is a value in having the flexibility to decide what to do after some of that uncertainty has been resolved. The managerial flexibility to wait, abandon, or expand on an investment opportunity is captured in a real option. The real option value of the investment opportunity, then, is what a value-maximizing firm would pay for the right to undertake the investment project with its inherent decision points.

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Calculating the Value of a Real Option

The value v of a real (non-income producing) option that pays

off W(T) at future time T is given by the general formula:

v(t,T) = exp( –r (T – t)) E[ max(0, W(T))]

where t is current time, E denotes the risk-neutral expected value, and r is the riskless discount rate.

The expected value of the truncated payoff function, W( ), rarely can be computed analytically. Generally, W( ), or an argument of it, is assumed to follow a stochastic Ito process, and methods such as Monte Carlo simulation can be employed to approximate its full probability distribution at time T. The simulated payoffs can then be averaged and discounted to obtain the option value.

Examples

Consider, for example, an R&D investment or pilot project to develop a lower-cost technological process. The present

value of the cost of the R&D or pilot project is C. Such a

strategic investment opportunity can be viewed as a call

option, having as [its] underlying asset the present value of

the expected cash inflows from the completed and operating follow-on project, VT, with [the] exercise price being the

necessary investment outlay, I.

The ability to defer (for T – t periods) investment in the

follow-on project under market demand uncertainty creates valuable flexibility for management. If, during the later stages, market demand develops favorably, the firm can make the

follow-on investment and obtain the project’s net present

value at that time, NP VT = VT – I [º W(T)]. If, however, market demand is weak, management can decide not to invest and its value would be truncated to 0.

In option pricing thinking, the entire investment program is worth –C + the value of

the call option on the follow-on project, namely, –C + v(t,T) = –C + exp( –r (T – t))

E[ max(0, NP VT)].

More Information

Numerous books and articles have been published on

real options topics. For a very simple exposition of real options and their valuation, including what makes option value different from NPV, see:

Timothy A. Luehrman, “Investment Opportunities

as Real Options: Getting Started on the Numbers”,

Harvard Business Review, July-August 1998.

Timothy A. Luehrman, “Strategy as a Portfolio of

Real Options”, Harvard Business Review,

September-October 1998.

For more advanced reading, see:

Avinash K. Dixit and Robert Pindyck, Investment Under Uncertainty,

Princeton University Press, Princeton, NJ, 1994.

Lenos Trigeorgis, Real Options: Managerial Flexibility and Strategy in

Resource Allocation, MIT Press, Cambridge, MA, 1996.

Eduardo S. Schwartz and Lenos Trigeorgis, eds., Real Options and

Investment Under Uncertainty: Classical Readings and Recent Contributions, M.I.T. Press, Cambridge, MA, 2001.

3 Saleh, Joseph H., Lamassoure, Elizabeth, and Hastings, Daniel E., “Space Systems Flexibility Provided by On-Orbit Servicing: Part 1”, Journal of Space Cost Estimating Community Spacecraft and Rockets, July-August 2002, 39(4), pp. 551-560; and Lamassoure, Elizabeth, Saleh, Joseph H., and Hastings, Daniel E., Space Systems Flexibility Provided by On-Orbit Servicing: Part 2”, Journal of Space Cost Estimating Community Spacecraft and Rockets, July-August 2002, 39(4), pp. 561-570.

4 Shishko, Robert, Ebbeler, Donald H. and Fox, George, “NASA Technology Assessment Using Real

Options Valuation”, Systems Engineering, 2003, 6(4), pp. 224-234.