Question

We are evaluating a project that costs $1,920,000, has a 6-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 94,500 units per year. Price per unit is $38.43, variable cost per unit is $23.60, and fixed costs are $839,000 per year. The tax rate is 23 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.) Best case NPV/ Worst case NPV?

Answer 1

Initial Investment = $1,920,000
Useful Life = 6 years

Annual Depreciation = Initial Investment / Useful Life
Annual Depreciation = $1,920,000 / 6
Annual Depreciation = $320,000

Best Case:

Annual OCF = [(Selling Price per unit - Variable Cost per unit) * Sales Volume - Fixed Costs] * (1 - tax) + tax * Depreciation
Annual OCF = [($42.273 - $21.240) * 103,950 - $755,100] * (1 - 0.23) + 0.23 * $320,000
Annual OCF = $1,431,280.35 * 0.77 + 0.23 * $320,000
Annual OCF = $1,175,685.8695

NPV = -$1,920,000 + $1,175,685.8695 * PVA of $1 (12%, 6)
NPV = -$1,920,000 + $1,175,685.8695 * 4.111407
NPV = $2,913,723.11

Worst Case:

Annual OCF = [(Selling Price per unit - Variable Cost per unit) * Sales Volume - Fixed Costs] * (1 - tax) + tax * Depreciation
Annual OCF = [($34.587 - $25.960) * 85,050 - $922,900] * (1 - 0.23) + 0.23 * $320,000
Annual OCF = -$189,173.65 * 0.77 + 0.23 * $320,000
Annual OCF = -$72,063.70105

NPV = -$1,920,000 - $72,062.7105 * PVA of $1 (12%, 6)
NPV = -$1,920,000 - $72,062.7105 * 4.111407
NPV = -$2,216,283.24