Question

We are examining a new project. We expect to sell 5,000 units per year at $64 net cash flow apiece for the next 10 years. In other words, the annual cash flow is projected to be $64 × 5,000 = $320,000. The relevant discount rate is 13 percent, and the initial investment required is $1,610,000. After the first year, the project can be dismantled and sold for $1,210,000. Suppose you think it is likely that expected sales will be revised upward to 8,000 units if the first year is a success and revised downward to 3,600 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 only be desirable if the project were a success. This implies that if the project is a success, projected sales after expansion will be 16,000 units. Note that abandonment is an option if the project is a failure.

A) If success and failure are equally likely, what is the NPV of the project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

B) What is the value of the option to expand? (value at time 0) (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

a)
If the project is a success, present value of the future cash flows
PV future CFs = $64 x 16000 units x PVIFA (13%, 9)
PV future CFs =$1,024,000 x 3.0040	$3,076,096.00
NPV Success	$3,076,096.00
The project has an equal likelihood of success or failure in one year, the expected value of the project in one year =
Expected value of project at year 1 = (NPV success + Market value/2 )+ $64 x base units
Expected value of project at year 1 =($3076096 + $1,210,000/2)+($64 x 5000 units)	$4,606,096.00
NPV = present value of the expected value in one year + cost of the equipment
NPV = $4,606,096/(1+13%)^1 -$1,610,000	$2,466,191.15
b)
Gain from option to expand = $64 x 8000 x (PVIFA13%,9)	$1,538,048.00
Option value = (.50)($1538048)/1.13	$680,552.21