Question

We are evaluating a project that costs $800,000, has an eight-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 60,000 units per year. Price per unit is $40, variable cost per unit is $20, and fixed costs are $800,000 per year. The tax rate is 35 percent, and we require a return of 10 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. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and round your final answers to 2 decimal places, e.g., 32.16.)

NPV Best-case $

Worst-case $

Answer 1

Initial Investment = $800,000
Useful Life = 8 years

Annual Depreciation = Initial Investment / Useful Life
Annual Depreciation = $800,000 / 8
Annual Depreciation = $100,000

Base Case:

Annual OCF = [(Selling Price per unit - Variable Cost per unit) * Sales Volume - Fixed Costs] * (1 - tax) + tax * Depreciation
Annual OCF = [($44.00 - $18.00) * 66,000 - $720,000] * (1 - 0.35) + 0.35 * $100,000
Annual OCF = $996,000 * 0.65 + 0.35 * $100,000
Annual OCF = $682,400

Required Return = 10%

NPV = -$800,000 + $682,400 * PVA of $1 (10%, 8)
NPV = -$800,000 + $682,400 * 5.33493
NPV = $2,840,556.23

Worst Case:

Annual OCF = [(Selling Price per unit - Variable Cost per unit) * Sales Volume - Fixed Costs] * (1 - tax) + tax * Depreciation
Annual OCF = [($36.00 - $22.00) * 54,000 - $880,000] * (1 - 0.35) + 0.35 * $100,000
Annual OCF = -$124,000 * 0.65 + 0.35 * $100,000
Annual OCF = -$45,600

Required Return = 10%

NPV = -$800,000 - $45,600 * PVA of $1 (10%, 8)
NPV = -$800,000 - $45,600 * 5.33493
NPV = -$1,043,272.81