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The standard net present values (NPV) analysis of capital budgeting values a project by discounting its expected cash flows at a risk-adjusted cost of capital. This technique is by far the most widely used technique for evaluating capital projects. However, standard NPV analysis does not take account of the flexibility inherent in the capital budgeting process. Part of the complexity of the capital budgeting process is that we can change our decision dynamically, depending on the circumstances. Many of the most important decisions that firms make concern real assets, a term that broadly encompasses factories, mines, office buildings, research and development, and other nonfinancial firm assets. We will see that it is possible to analyze investment and operating decisions for real assets using pricing models developed for financial options. To illustrate how it can be possible to evaluate an investment decision as an option, consider a firm that is deciding whether or not to build a factory. Compare the following two descriptions:

* A call option is the right to pay a strike price to receive the present value of a stream of future cash flows (represented by the price of underlying asset). * An investment project is the right to pay an investment cost to receive the present value of a stream of future cash flows (represented by the present value of the project).

So we have:

Investment Project| | Call Option|

Investment Cost| =| Strike Price|

Present Value of The Project| =| Price of Underlying Asset|

This comparison suggests that we can view any investment project as a call option, with the investment cost equal to the strike price and the present value of cash flows equal to the asset price. The exploitation of this and other analogies between real investment projects and financial options has come to be called real options, which we define as the application of derivatives theory to the operation and valuation of real investment projects. Note the phrase "operation and valuation." We will see in this chapter that you cannot value a real asset without also understanding how you will operate it. We have encountered this link before: You cannot value any option without understanding when you will exercise it.

Option to Choose

Suppose a large manufacturing firm decides to hedge itself through the use of strategic options. Specifically it has the option to choose among three strategies: expanding its current manufacturing operations, contracting its manufacturing operations, or completely abandoning its business unit at any time within the next five years. Suppose the firm has a current operating structure whose static valuation of future profitability using a discounted cash flow model (that is, the present value of the future cash flows discounted at an appropriate market risk-adjusted discount rate) is found to be $100 million. Possible strategic decisions that the firm can choose in the future can be summarized as the following real options:

* Option to Expand: The expansion option will increase the firm’s operations by 30 percent with a $20 million implementation cost. * Option to Contract: The firm has the option to contract 10 percent of its current operations at any time over the next five years, thereby creating an additional $25 million in savings after this contraction. * Option to Abandon: By abandoning its operations, the firm can sell its business for $100 million.

The most commonly used model for valuing real options is binomial lattice valuation constructed by Cox-Ross-Rubinstein method. Suppose we come up with the following parameters needed for construction of binomial tree:

S0 – current price of underlying asset, i.e. current value of the firm, $100 million

volatility of the logarithmic returns on the projected future cash flows, 15%

r – risk free rate for the next five years, 5%

T – expiration of the options, 5...