Question

We are evaluating a project that costs $908,000, has a four-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 87,200 units per year. Price per unit is $34.35, variable cost per unit is $20.60, and fixed costs are $752,000 per year. The tax rate is 30 percent, and we require a return of 12 percent on this project. Suppose the projections given for price, quantity, variable costs, and fixed costs are all accurate to within ±10 percent. Calculate the best-case and worst-case NPV figures. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g. 32.16.)?

Answer 1

Initial Investment = $908,000
Useful Life = 4 years

Annual Depreciation = Initial Investment / Useful Life
Annual Depreciation = $908,000 / 4
Annual Depreciation = $227,000

Worst Case:

Annual OCF = [(Price per unit - Variable Cost per unit) * Sales Quantity - Fixed Costs] * (1 - Tax Rate) + Tax Rate * Depreciation
Annual OCF = [($30.915 - $22.660) * 78,480 - $827,200] * (1 - 0.30) + 0.30 * $227,000
Annual OCF = -$179,347.60 * 0.70 + 0.30 * $227,000
Annual OCF = -$57,443.32

Net Present Value = -$908,000 - $57,443.32 * PVIFA(12%, 4)
Net Present Value =-$908,000 - $57,443.32 * (1 - (1/1.12)^4) / 0.12
Net Present Value = -$908,000 - $57,443.32 * 3.037349
Net Present Value = -$1,082,475.41

Best Case:

Annual OCF = [(Price per unit - Variable Cost per unit) * Sales Quantity - Fixed Costs] * (1 - Tax Rate) + Tax Rate * Depreciation
Annual OCF = [($37.785 - $18.540) * 95,920 - $676,800] * (1 - 0.30) + 0.30 * $227,000
Annual OCF = $1,169,180.40 * 0.70 + 0.30 * $227,000
Annual OCF = $886,526.28

Net Present Value = -$908,000 + $886,526.28 * PVIFA(12%, 4)
Net Present Value =-$908,000 + $886,526.28 * (1 - (1/1.12)^4) / 0.12
Net Present Value = -$908,000 + $886,526.28 * 3.037349
Net Present Value = $1,784,689.71