Question

The most likely outcomes for a particular project are estimated as follows:

Unit price:	$	80
Variable cost:	$	60
Fixed cost:	$	380,000
Expected sales:		37,000	units per year

However, you recognize that some of these estimates are subject to error. Suppose that each variable may turn out to be either 5% higher or 5% lower than the initial estimate. The project will last for 10 years and requires an initial investment of $1.7 million, which will be depreciated straight-line over the project life to a final value of zero. The firm’s tax rate is 21% and the required rate of return is 10%.

(For all the requirements, a negative amount should be indicated by a minus sign. Enter your answer in dollars not in millions. Do not round intermediate calculations. Round your answer to the nearest dollar amount.)

a. What is project NPV in the best-case scenario, that is, assuming all variables take on the best possible value?

b. What is project NPV in the worst-case scenario?

Answer 1

Initial Investment = $1,700,000
Useful Life = 10 years

Annual Depreciation = Initial Investment / Useful Life
Annual Depreciation = $1,700,000 / 10
Annual Depreciation = $170,000

Answer a.

Annual OCF = [(Unit Price - Variable Cost) * Expected Sales - Fixed Cost] * (1 - tax) + tax * Depreciation
Annual OCF = [($84.00 - $57.00) * 38,850 - $361,000] * (1 - 0.21) + 0.21 * $170,000
Annual OCF = $687,950 * 0.79 + 0.21 * $170,000
Annual OCF = $579,180.50

Net Present Value = -$1,700,000 + $579,180.50 * PVA of $1 (10%, 10)
Net Present Value = -$1,700,000 + $579,180.50 * 6.14457
Net Present Value = $1,858,815

Answer b.

Annual OCF = [(Unit Price - Variable Cost) * Expected Sales - Fixed Cost] * (1 - tax) + tax * Depreciation
Annual OCF = [($76.00 - $63.00) * 35,150 - $399,000] * (1 - 0.21) + 0.21 * $170,000
Annual OCF = $57,950 * 0.79 + 0.21 * $170,000
Annual OCF = $81,480.50

Net Present Value = -$1,700,000 + $81,480.50 * PVA of $1 (10%, 10)
Net Present Value = -$1,700,000 + $81,480.50 * 6.14457
Net Present Value = -$1,199,337