Question

We are evaluating a project that costs $739,600, 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 $49, variable cost per unit is $34, and fixed costs are $735,000 per year. The tax rate is 23 percent, and we require a return of 9 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.)

Answer 1

Initial Investment = $739,600
Useful Life = 8 years

Annual Depreciation = Initial Investment / Useful Life
Annual Depreciation = $739,600 / 8
Annual Depreciation = $92,450

Best Case:

Annual Operating Cash Flow = [(Selling Price per unit - Variable Cost per unit) * Units Sold - Fixed Costs] * (1 - tax) + tax * Depreciation
Annual Operating Cash Flow = [($53.90 - $30.60) * 88,000 - $661,500] * (1 - 0.23) + 0.23 * $92,450
Annual Operating Cash Flow = $1,388,900 * 0.77 + 0.23 * $92,450
Annual Operating Cash Flow = $1,090,716.50

Required Return = 9%

Net Present Value = -$739,600 + $1,090,716.50 * PVA of $1 (9%, 8)
Net Present Value = -$739,600 + $1,090,716.50 * 5.534819
Net Present Value = $5,297,318.41

Worst Case:

Annual Operating Cash Flow = [(Selling Price per unit - Variable Cost per unit) * Units Sold - Fixed Costs] * (1 - tax) + tax * Depreciation
Annual Operating Cash Flow = [($44.10 - $37.40) * 72,000 - $808,500] * (1 - 0.23) + 0.23 * $92,450
Annual Operating Cash Flow = -$326,100 * 0.77 + 0.23 * $92,450
Annual Operating Cash Flow = -$229,833.50

Required Return = 9%

Net Present Value = -$739,600 - $229,833.50 * PVA of $1 (9%, 8)
Net Present Value = -$739,600 - $229,833.50 * 5.534819
Net Present Value = -$2,011,686.82