We have yet to take into consideration market risk. Using a Black-Scholes model, a volatility of 50 percent (characteristic of DuPont and Dow stock today), and an overall chance of success of 10.4 percent, the value of the Polyarothene project is $3.57 million versus $1.67 million based on the decision tree alone.
This result does not consider the option to abandon at each of four stages; it is based on a straight 10.4 percent unique risk. So it is the rifle shot, but it takes into account the volatility of the marketplace. This result is also interesting—because of market volatility alone, it might still pay to do this rifle shot project, just as it would pay to drill the exploratory well in Chapter 5. NPV gave the wrong answer for another reason!
Of course, we should take into account both kinds of risk.
This requires us to work backward from the end result, using the probabilities of success cited in the previous section. First, value an option of entering stage 4 with an 83 percent chance of successful commercialization, using Black-Scholes. With this value in hand, go back a stage: Value the option of entering stage 3 with a 75 percent success rate and the reward (underlying security) being the value of the stage 4 option, discounted for the probability of success.
Do it twice more until you are back to the beginning of the process, stage 1. We have created a series of linked, nested, compound options. Although the detailed calculations are beyond the scope of this book, the result is interesting: $4.75 million.
In effect, we have now moderated the negative impacts associated with unique risk using multiple options to abandon and have taken full advantage of the positive values associated with market risk.
To summarize, without the option to abandon, the project has an NPV of –$2.60 million. With four options to abandon, which relate only to unique risk, it is worth $1.67 million. Adding market risk to the equation improves the value to $4.75 million. In relative terms, each step in risk management represents an enormous increment in value. Note also that these results depend critically on the systematic reduction of risk at each stage and the acceleration of costs from stage to stage. But that is how R&D should be managed.