Question

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

Unit price:	$	50
Variable cost:	$	30
Fixed cost:	$	410,000
Expected sales:		40,000	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 10% higher or 10% lower than the initial estimate. The project will last for 10 years and requires an initial investment of $1.4 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 14%.

(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

A)
Unit Price = $50
Variable Cost = $30*90% = $27
Fixed Cost = $410,000
Expected Sales = 40,000 units

Initial Investment = $1,400,000
Useful Life = 10 years
Annual Depreciation = $1,400,000 / 10
Annual Depreciation = $140,000

OCF = (40,000*$50 - 40,000*$27 - 410,000)*(1-0.21) + 0.21*$140,000
OCF = $432,300

NPV = -$1,400,000 + $432,300*PVIFA(14%, 10)
NPV = -$1,400,000 + $432,300*5.2161
NPV = $854,920.03

B)

Unit Price = $50
Variable Cost = $30*110% = $33
Fixed Cost = $410,000
Expected Sales = 40,000 units

Initial Investment = $1,400,000
Useful Life = 10 years
Annual Depreciation = $1,400,000 / 10
Annual Depreciation = $140,000

OCF = (40,000*$50 - 40,000*$33 - 410,000)*(1-0.21) + 0.21*$140,000
OCF = $242,700

NPV = -$1,400,000 + $242,700*PVIFA(14%, 10)
NPV = -$1,400,000 + $276,000*5.2161
NPV = $39,643.6