Question

1. Typical capital budgeting approaches does not account for the potential value of future expansion opportunities which may become available later in the life of the project.
   1. Provide an example of an expansion opportunity and discuss how it can be evaluated using the option pricing model.
   2. What are the parameters of the expansion option (underlying asset, exercise price, variance, risk-free rate, maturity)?

Answer 1

Solution:

The question is about real options.

Lets take an example.

Suppose a company ABC wants to replace its existing 6 machines with a new machines. The new machines cost $1,100 each and have a five-year life.

The company has estimated the incremental cash flows of replacing a single old machine with the new machine and include the after-tax savings from introducing new machines, the tax shield on incremental depreciation from replacing an old by a new machine, and the sale of the old machine.

The expected cash flows for the new machine are given below.

Year	0	1	2	3	4	5
CF of single machine	-1100	250	300	400	200	200

The risk adjusted cost of capital for the project is 12%. Therefore the NPV of the project is  -112.33.

It can be concluded that the replacement of the single old machine by new machine is unprofitable.

Now comes the twist. Remember, the cash flows are estimated and not actual. Let the standard deviation of the cash flows be 40%.

The owner of the company want to try single replacement first to check the true realizations of the cash flows in one year. If the experiment is successful, he will replace the balance 5 machines next year. The owner thus has an option of replacing the 5 more machines in one year. The option available to the owner is a CALL option.

The underlying assets are the cash flows from the machines. The current value of this underlying assets are

S=

S =  987.67

The exercise price is the purchase price of the machine which is $1100.

Assuming the risk free rate of 6%.

The value of the call option using the Black Scholes model is =   137.38

Project Value = NPV of the first machine + 5 options to acquire

=  -112.33 + 5 *  137.38 =  574.58

Including the option to expand, the project is profitable.

Excel calculations are below for reference.

-x-