Question

We are evaluating a project that costs $118,894, has a seven-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 4,101 units per year. Price per unit is $47, variable cost per unit is $30, and fixed costs are $82,846 per year. The tax rate is 36 percent, and we require a 12 percent return on this project. Suppose the projections given for price, quantity, variable costs, and fixed costs are all accurate to within +/-13 percent. What is the NPV of the project in best-case scenario?

Answer 1

Initial Investment = $118,894
Useful Life = 7 years

Annual Depreciation = Initial Investment / Useful Life
Annual Depreciation = $118,894 / 7
Annual Depreciation = $16,984.857

Base Case:

Units Sold = 4,101
Price per unit = $47.00
Variable Cost per unit = $30.00
Fixed Costs = $82,846

Best Case:

Units Sold = 4,101 + 13% * 4,101
Units Sold = 4,634

Price per unit = $47.00 + 13% * $47.00
Price per unit = $53.11

Variable Cost per unit = $30.00 - 13% * $30.00
Variable Cost per unit = $26.10

Fixed Costs = $82,846 - 13% * $82,846
Fixed Costs = $72,076.02

Annual OCF = [(Price per unit - Variable Cost per unit) * Units Sold - Fixed Costs] * (1 - Tax Rate) + Tax Rate * Annual Depreciation
Annual OCF = [($53.11 - $26.10) * 4,634 - $72,076.02] * (1 - 0.36) + 0.36 * $16,984.857
Annual OCF = $53,088.32 * 0.64 + 0.36 * $16,984.857
Annual OCF = $40,091.07332

Net Present Value = -$118,894 + $40,091.07332 * PVIFA(12%, 7)
Net Present Value = -$118,894 + $40,091.07332 * (1 - (1/1.12)^7) / 0.12
Net Present Value = -$118,894 + $40,091.07332 * 4.563757
Net Present Value = $64,071.92