Question

We are evaluating a project that costs $756,000, has a life of 6 years, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 32,000 units per year. Price per unit is $60, variable cost per unit is $25, and fixed costs are $665,000 per year. The tax rate is 24 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 = $756,000
Useful Life = 6 years

Annual Depreciation = Initial Investment / Useful Life
Annual Depreciation = $756,000 / 6
Annual Depreciation = $126,000

Base Case:

Unit Sales = 32,000
Price per unit = $60
Variable Cost per unit = $25
Fixed Costs = $665,000

Best Case:

Unit Sales = 32,000 * 1.15 = 36,800
Price per unit = $60 * 1.15 = $69.00
Variable Cost per unit = $25 * 0.85 = $21.25
Fixed Costs = $665,000 * 0.85 = $565,250

Annual OCF = [(Price per unit – Variable Cost per unit) * Unit Sales - Fixed Costs] * (1 - tax) + tax * Depreciation
Annual OCF = [($69.00 - $21.25) * 36,800 - $565,250] * (1 - 0.24) + 0.24 * $126,000
Annual OCF = $1,191,950 * 0.76 + 0.24 * $126,000
Annual OCF = $936,122

NPV = -$756,000 + $936,122 * PVA of $1 (12%, 6)
NPV = -$756,000 + $936,122 * 4.11141
NPV = $3,092,781.35

Worst Case:

Unit Sales = 32,000 * 0.85 = 27,200
Price per unit = $60 * 0.85 = $51.00
Variable Cost per unit = $25 * 1.15 = $28.75
Fixed Costs = $665,000 * 1.15 = $764,750

Annual OCF = [(Price per unit – Variable Cost per unit) * Unit Sales - Fixed Costs] * (1 - tax) + tax * Depreciation
Annual OCF = [($51.00 - $28.75) * 27,200 - $764,750] * (1 - 0.24) + 0.24 * $126,000
Annual OCF = -$159,550 * 0.76 + 0.24 * $126,000
Annual OCF = -$91,018

NPV = -$756,000 - $91,018 * PVA of $1 (12%, 6)
NPV = -$756,000 - $91,018 * 4.11141
NPV = -$1,130,212.32