## Obtaining The Inputs For Option Valuation

On the surface, the inputs needed to apply option pricing theory to valuing the option to delay are the same as those needed for any application: the value of the underlying asset; the variance in the value; the time to expiration on the option; the strike price; the riskless rate and the equivalent of the dividend yield. Actually estimating these inputs for product patent valuation can be difficult, however.

### Value Of The Underlying Asset

In the case of product options, the underlying asset is the project itself. The current value of this asset is the present value of expected cash flows fro initiating the project now, which can be obtained by doing a standard capital budgeting analysis. There is likely to be a substantial amount of noise in the cash flow estimates and the present value, however. Rather than being viewed as a problem, this uncertainty should be viewed as the reason for why the project delay option has value. If the expected cash flows on the project were known with certainty and were not expected to change, there would be no need to adopt an option pricing framework, since there would be no value to the option.

### Variance In The Value Of The Asset

As noted in the prior section, there is likely to be considerable uncertainty associated with the cash flow estimates and the present value that measures the value of the asset now, partly because the potential market size for the product may be unknown, and partly because technological shifts can change the cost structure and profitability of the product. The variance in the present value of cash flows from the project can be estimated in one of three ways. First, if similar projects have been introduced in the past, the variance in the cash flows from those projects can be used as an estimate. Second, probabilities can be assigned to various market scenarios, cash flows estimated under each scenario and the variance estimated across present values. Finally, the average variance in firm value of publicly traded companies which are in the business that the project will be in can be used. Thus, the average variance in firm value of bio-technology companies can be used as the variance for the option to delay a bio-technology project.

The value of the option is largely derived from the variance in cash flows - the higher the variance, the higher the value of the project delay option. Thus, the value of a option to do a project in a stable business will be less than the value of one in an environment where technology, competition and markets are all changing rapidly.

There is a data set on the web that summarizes, by sector, the variances in firm value and stock prices.

### Exercise Price On Option

A project delay option is exercised when the firm owning the rights to the project decides to invest in it. The cost of making this investment is equivalent to the exercise price of the option. The underlying assumption is that this cost remains constant (in present value dollars) and that any uncertainty associated with the product is reflected in the present value of cash flows on the product.

### Expiration Of The Option And The Riskless Rate

The project delay option expires when the rights to the project lapse; investments made after the project rights expire are assumed to deliver a net present value of zero as competition drives returns down to the required rate. The riskless rate to use in pricing the option should be the rate that corresponds to the expiration of the option.

### Dividend Yield

There is a cost to delaying taking a project, once the net present value turns positive. Since the project rights expire after a fixed period, and excess profits (which are the source of positive present value) are assumed to disappear after that time as new competitors emerge, each year of delay translates into one less year of value-creating cash flows.6 If the cash flows are evenly distributed over time, and the life of the patent is n years, the cost of delay can be written as:

Thus, if the project rights are for 20 years, the annual cost of delay works out to 5% a year.

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