## Cost of Delay and Early Exercise

For typical listed options on financial assets, it is argued that early exercise is almost never optimal. Is this true for real options as well?

Illustration 6.10: Valuing a patent

Assume that a pharmaceutical company has been approached by an entrepreneur who has patented a new drug to treat ulcers. The entrepreneur has obtained FDA approval and has the patent rights for the next 17 years. While the drug shows promise, it is still

6 A value-creating cashflow is one that adds to the net present value because it is in excess of the required return for investments of equivalent risk.

very expensive to manufacture and has a relatively small market. Assume that the initial investment to produce the drug is \$ 500 million and the present value of the cash flows from introducing the drug now is only \$ 350 million. The technology and the market is volatile, and the annualized standard deviation in the present value, estimated from a simulation is 25%.7

While the net present value of introducing the drug is negative, the rights to this drug may still be valuable because of the variance in the present value of the cash flow. In other words, it is entirely possible that this drug may not only be viable but extremely profitable a year or two from now. To value this right, we first define the inputs to the option pricing model:

Value of the Underlying Asset (S) = PV of Cash Flows from Project if introduced now

Strike Price (K) = Initial Investment needed to introduce the product = \$ 500 million Variance in Underlying Asset's Value = (0.25)2 = 0.0625 Time to expiration = Life of the patent = 17 years Dividend Yield = 1/Life of the patent = 1/17 = 5.88%

Assume that the 17-year riskless rate is 4%. The value of the option can be estimated as follows:

Call Value= 350 exp(-00588)(17) (0.5285) -500 (exp(-004)(17) (0.1219)= \$ 37.12 million Thus, this ulcer drug, which has a negative net present value if introduced now, is still valuable to its owner.

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