Question

We are evaluating a project that costs $735,200, 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 80,000 units per year. Price per unit is $48, variable cost per unit is $33, and fixed costs are $730,000 per year. The tax rate is 22 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 = $735,200
Useful Life = 8 years

Annual Depreciation = Initial Investment / Useful Life
Annual Depreciation = $735,200 / 8
Annual Depreciation = $91,900

Best Case:

Annual Operating Cash Flow = [(Price per unit - Variable Cost per unit) * Sales Quantity - Fixed Costs] * (1 - Tax Rate) + Tax Rate * Depreciation
Annual Operating Cash Flow = [($55.20 - $28.05) * 92,000 - $620,500] * (1 - 0.22) + 0.22 * $91,900
Annual Operating Cash Flow = $1,877,300 * 0.78 + 0.22 * $91,900
Annual Operating Cash Flow = $1,484,512

Required Return = 12%

Net Present Value = -$735,200 + $1,484,512 * PVIFA(12%, 8)
Net Present Value = -$735,200 + $1,484,512 * 4.967640
Net Present Value = $6,639,321.19

Worst Case:

Annual Operating Cash Flow = [(Price per unit - Variable Cost per unit) * Sales Quantity - Fixed Costs] * (1 - Tax Rate) + Tax Rate * Depreciation
Annual Operating Cash Flow = [($40.80 - $37.95) * 68,000 - $839,500] * (1 - 0.22) + 0.22 * $91,900
Annual Operating Cash Flow = -$645,700 * 0.78 + 0.22 * $91,900
Annual Operating Cash Flow = -$483,428

Required Return = 12%

Net Present Value = -$735,200 - $483,428 * PVIFA(12%, 8)
Net Present Value = -$735,200 - $483,428 * 4.967640
Net Present Value = -$3,136,696.27