We are examining a new project. We expect to sell 8,000 units per year at $80 ne

Question

We are examining a new project. We expect to sell 8,000 units per year at $80 net cash flow a piece for the next 15 years. In other words, the annual operating cash flow is projected to be $80 × 8,000 = $640,000. The relevant discount rate is 16 percent, and the initial investment required is $2,740,000. The project can be dismantled after the first year and sold for $2,130,000. Suppose you think it is likely that expected sales will be revised upward to 9,600 units if the first year is a success and revised downward to 3,000 units if the first year is not a success. Suppose the scale of the project can be doubled in one year in the sense that twice as many units can be produced and sold. Naturally, expansion would be desirable only if the project is a success. This implies that if the project is a success, projected sales after expansion will be 19,200. Assume that success and failure are equally likely. Note that abandonment is still an option if the project is a failure. What is the value of the option to expand?

Explanation / Answer

The gain from the option to expand is the present value of the cash flows from the additional units sold, so:

Gain from option to expand        = $80 per unit (9,600 units)(PVIFA16%, 14)

                                                                = $80 * 9600 * 5.4675

= $4,199,062.39

We need to find the value of the option to expand times the likelihood of expansion.

We also need to find the value of the option to expand today, so:

Option value = (0.50) * ($4,199,062.39) / 1.16 = $1,809,941

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