The Datar–Mathews Method (DM Method) is a method for real options valuation. The method provides an easy way to determine the real option value of a project simply by using the average of positive outcomes for the project. The method can be understood as an extension of the net present value (NPV) multi-scenario Monte Carlo model with an adjustment for risk aversion and economic decision-making. The method uses information that arises naturally in a standard discounted cash flow (DCF), or NPV, project financial valuation. It was created in 2000 by Vinay Datar, professor at Seattle University; and Scott H. Mathews, Technical Fellow at The Boeing Company.
Method
The mathematical equation for the DM Method is shown below. The method captures the real option value by discounting the distribution of operating profits at R, the market risk rate, and discounting the distribution of the discretionary investment at r, risk-free rate, before the expected payoff is calculated. The option value is then the expected value of the maximum of the difference between the two discounted distributions or zero. Fig. 1.
is a random variable representing the future benefits, or operating profits at time T. The present valuation of uses R, a discount rate consistent with the risk level of R is the required rate of return for participation in the target market, sometimes termed the hurdle rate. is a random variable representing the strike price. The present valuation of uses r, the rate consistent with the risk of investment of In many generalized option applications, the risk-free discount rate is used. However other discount rates can be considered, such as the corporate bond rate, particularly when the application is an internal corporate product development project. is the real option value for a single stage project. The option value can be understood as the expected value of the difference of two present value distributions with an economically rational threshold limiting losses on a risk-adjusted basis. This value may also be expressed as a stochastic distribution.
The differential discount rate for R and r implicitly allows the DM Method to account for the underlying risk. If R > r, then the option will be risk-averse, typical for both financial and real options. If R < r, then the option will be risk-seeking. If R = r, then this is termed a risk-neutral option, and has parallels with NPV-type analyses with decision-making, such as decision trees. The DM Method gives the same results as the Black–Scholes and the binomial lattice option models, provided the same inputs and the discount methods are used. This non-traded real option value therefore is dependent on the risk perception of the evaluator toward a market asset relative to a privately held investment asset.
The DM Method is advantageous for use in real option applications because unlike some other option models it does not require a value for sigma (a measure of uncertainty) or for S0 (the value of the project today), both of which are difficult to derive for new product development projects; see further under real options valuation. Finally, the DM Method uses real-world values of any distribution type, avoiding the requirement for conversion to risk-neutral values and the restriction of a lognormal distribution; see further under Monte Carlo methods for option pricing.
Extensions of the method for other real option valuations have been developed such as contract guarantee (put option), Multi-Stage (compound option), Early Launch (American option), and others.
Implementation
The DM Method may be implemented using Monte-Carlo simulation, or in a simplified algebraic or other form (see the Range Option below).
Using simulation, for each sample, the engine draws a random variable from both calculates their present values, and takes the difference. Fig. 2A. The difference value is compared to zero, the maximum of the two is determined, and the resulting value recorded by the simulation engine. Here, reflecting the optionality inherent in the project, a forecast of a net negative value outcome corresponds to an abandoned project, and has a zero value. Fig. 2B. The resulting values create a payoff distribution representing the economically rational set of plausible, discounted value forecasts of the project at time T0.
When sufficient payoff values have been recorded, typically a few hundred, then the mean, or expected value, of the payoff distribution is calculated. Fig. 2C. The option value is the expected value, the first moment of all positive NPVs and zeros, of the payoff distribution.
A simple interpretation is: