Question

We are evaluating a project that costs $856,800, has a nine-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 90,000 units per year. Price per unit is $56, variable cost per unit is $40, and fixed costs are $770,000 per year. The tax rate is 25 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 ±15 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 = $856,800
Useful Life = 9 years

Annual Depreciation = Initial Investment / Useful Life
Annual Depreciation = $856,800 / 9
Annual Depreciation = $95,200

Best Case:

Annual OCF = [(Price per unit - Variable Cost per unit) * Sales Volume - Fixed Costs] * (1 - tax) + tax * Depreciation
Annual OCF = [($64.40 - $34.00) * 103,500 - $654,500] * (1 - 0.25) + 0.25 * $95,200
Annual OCF = $2,491,900 * 0.75 + 0.25 * $95,200
Annual OCF = $1,892,725

NPV = -$856,800 + $1,892,725 * PVIFA(12%, 9)
NPV = -$856,800 + $1,892,725 * 5.32825
NPV = $9,228,111.98

Worst Case:

Annual OCF = [(Price per unit - Variable Cost per unit) * Sales Volume - Fixed Costs] * (1 - tax) + tax * Depreciation
Annual OCF = [($47.60 - $46.00) * 76,500 - $885,500] * (1 - 0.25) + 0.25 * $95,200
Annual OCF = -$763,100 * 0.75 + 0.25 * $95,200
Annual OCF = -$548,525

NPV = -$856,800 - $548,525 * PVIFA(12%, 9)
NPV = -$856,800 - $548,525 * 5.32825
NPV = -$3,779,478.33