Question

We are evaluating a project that costs $827,000, has an seven-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 103,000 units per year. Price per unit is $35, variable cost per unit is $22, and fixed costs are $831,135 per year. The tax rate is 38 percent, and we require a 16 percent return on this project. The projections given for price, quantity, variable costs, and fixed costs are all accurate to within +/- 13 percent. Calculate the best-case NPV. Calculate the worst-case NPV.

Answer 1

Initial Investment = $827,000
Useful Life = 7 years

Annual Depreciation = Initial Investment / Useful Life
Annual Depreciation = $827,000 / 7
Annual Depreciation = $118,142.86

Required Return = 16%
Tax Rate = 38%

Answer a.

Annual OCF = [(Selling Price - Variable Costs per unit)*Sales Unit - Fixed Costs]*(1 - tax) + tax * Depreciation
Annual OCF = [($39.55 - $19.14)*116,390 - $723,087.45] * (1-0.38) + 0.38 * $118,142.86
Annual OCF = $1,652,432.45 * 0.62 + 0.38 * $118,142.86
Annual OCF = $1,069,402.41

NPV = -$827,000 + $1,069,402.41 * PVIFA(16%, 7)
NPV = -$827,000 + $1,069,402.41 * (1 - (1/1.16)^7) / 0.16
NPV = -$827,000 + $4,318,851.61
NPV = $3,491,851.61

Answer b.

Annual OCF = [(Selling Price - Variable Costs per unit)*Sales Unit - Fixed Costs]*(1 - tax) + tax * Depreciation
Annual OCF = [($30.45 - $24.86)*89,610 - $939,182.55] * (1-0.38) + 0.38 * $118,142.86
Annual OCF = -$438,262.65 * 0.62 + 0.38 * $118,142.86
Annual OCF = -$226,828.56

NPV = -$827,000 - $226,828.56 * PVIFA(16%, 7)
NPV = -$827,000 - $226,828.56 * (1 - (1/1.16)^7) / 0.16
NPV = -$827,000 - $916,061.98
NPV = -$1,743,061.98