Technical note: waiting cost models for real options.

INTRODUCTION

The simplest form of real options is the deferral or delay option. The mathematics used are based on the financial call option. For that financial case, if the purchase of a stock is delayed and an option is purchased instead, then any dividend is lost since the stock is not owned. For real options, project delays may carry a benefit but most delays also involve a cost. The dividend model has been used to determine the option value of both financial and real options. However, real options must consider a much broader array of possibilities.

Let us begin with three examples of why real options may be useful in evaluating potential delays in projects that engineering economists must evaluate. First, potentially higher future market prices for the output of a mining or petroleum project may well justify continuing to make lease payments for a tract whose development is currently uneconomic. Second, possible advances in uncertain technological capabilities may justify continuing R&D for a project that is "on hold" rather than being terminated. Third, a pharmaceutical firm might be evaluating whether to proceed with plant construction while waiting for regulatory approval.

The common thread in these examples and all real delay options is that something may change the project economics during the delay period, so that the project becomes worthwhile. European-style real options include projects that are waiting for an event to happen, such as regulatory approval. American-style real options tend to be situations where the firm is waiting for conditions to improve, such as higher oil prices making previously uneconomical oil fields become economically attractive. Given that expected value decision-making is often used, the change may simply be a shift in the probability distribution for key project elements.

While many authors point out the possible advantages of delaying a decision, we have found few that point out that there are potential costs associated with that delay. Proceeding immediately starts the cash flow or benefit stream as soon as possible, while delay in the decisions means those cash flows are lost or delayed.

There are a number of possible models for the costs of a delay associated with a real deferral option. These are summarized with a title that suggests the basis for the model. These include:

* No cost associated with delay (or cost is ignored)