In the section “Valuation Models: Traditional versus Real Options,” we examined a company called the Hokie Company, which is considering investing $10 million in a three-year research and development (R&D) program that has a 0.7 probability of leading to a marketable product. If at the end of the third year a product is successfully developed, the Hokie Company must then decide whether to invest $80 million in the production and sale of the product. If the Hokie Company proceeds with this investment, it will generate perpetual after-tax cash flows of $30 million a year with a probability of 0.4 and $15 million a year with a probability of 0.6. The risk-free rate is 4 percent, and the cost of capital is 20 percent. In this application, we shall illustrate the problem with a binomial tree.

In an actual situation, the probability distributions are not likely to be specified in the manner we have done here. The distribution of cash flows if the product is developed is not likely to be as simple as $30 million with a probability of 0.4 and $15 million with a probability of 0.6. Also, the outcome of the R&D process is not likely to be simply a 0.7 chance of developing a product and a 0.3 chance of coming up with nothing. Instead, these uncertainties would be reflected in a measure of volatility. Because the option is whether to invest $80 million in the product, given the success of the R&D process, the volatility ...

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