Question

We are evaluating a project that costs $709,000, has a life of fifteen years, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 96,000 units per year. Price per unit is $43, variable cost per unit is $21, and fixed costs are $723,889 per year. The tax rate is 23 percent, and we require a return of 16 percent on this project. The projections given for price, quantity, variable costs, and fixed costs are all accurate to within +/- 16 percent.

a. Calculate the best-case NPV.

b. Calculate the worst-case NPV.

Answer 1

Initial Investment = $709,000
Useful Life = 15 years

Annual Depreciation = Initial Investment / Useful Life
Annual Depreciation = $709,000 / 15
Annual Depreciation = $47,266.67

Best Case:

Annual OCF = [(Price per unit - Variable Cost per unit) * Units Sold - Fixed Costs] * (1 - tax) + tax * Depreciation
Annual OCF = [($49.88 - $17.64) * 111,360 - $608,066.76] * (1 - 0.23) + 0.23 * $47,266.67
Annual OCF = $2,982,179.64 * 0.77 + 0.23 * $47,266.67
Annual OCF = $2,307,149.66

Net Present Value = -$709,000 + $2,307,149.66 * PVA of $1 (16%, 15)
Net Present Value = -$709,000 + $2,307,149.66 * 5.575456
Net Present Value = $12,154,411.39

Worst Case:

Annual OCF = [(Price per unit - Variable Cost per unit) * Units Sold - Fixed Costs] * (1 - tax) + tax * Depreciation
Annual OCF = [($36.12 - $24.36) * 80,640 - $839,711.24] * (1 - 0.23) + 0.23 * $47,266.67
Annual OCF = $108,615.16 * 0.77 + 0.23 * $47,266.67
Annual OCF = $83,645.15

Net Present Value = -$709,000 + $83,645.15 * PVA of $1 (16%, 15)
Net Present Value = -$709,000 + $83,645.15 * 5.575456
Net Present Value = -$242,640.17