We are evaluating a project that costs $1,180,000, has a five-year life, and has

Question

We are evaluating a project that costs $1,180,000, has a five-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 88,100 units per year. Price per unit is $34.80, variable cost per unit is $21.05, and fixed costs are $761,000 per year. The tax rate is 40 percent, and we require a return of 10 percent on this project.

Required: 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.

Explanation / Answer

Best case Time line 0 1 2 3 4 5 Project cost -1180000 +Increase in working capital 0 =Initial Investment outlay -1180000 Sales 1.1*No. of units*(1.1*selling price - 0.9*variable cost) 1873755 1873755 1873755 1873755 1873755 -Fixed cost =0.9*fixed cost -684900 -684900 -684900 -684900 -684900 -Depreciation (cost of equipment and plant)/5 -236000 -236000 -236000 -236000 -236000 = 952854.9 952854.9 952854.9 952854.9 952854.9 -taxes =(net sales - fixed cost - depreciation)*(1-tax) 571712.9 571712.9 571712.9 571712.9 571712.9 +Depreciation 236000 236000 236000 236000 236000 =after tax operating cash flow 807712.9 807712.9 807712.9 807712.9 807712.9 Reversal of Increase in working capital 0 = Terminal year after tax non operating CF 0 Total Cash flow -1180000 807712.9 807712.9 807712.9 807712.9 807712.9 Cost of capital = 10% Discount factor = (1 + cost of capital) ^ corresponding period 1 1.1 1.21 1.331 1.4641 1.61051 Discounted cashflow = total cash flow/discount factor -1180000 734284.5 667531.3 606846.7 551678.8 501526.2 NPV= Sum of discounted cash flow = 1881867 Worst case Time line 0 1 2 3 4 5 Project cost -1180000 +Increase in working capital 0 =Initial Investment outlay -1180000 Sales 0.9*No. of units*(0.9*selling price - 1.1*variable cost) 647402.9 647402.9 647402.9 647402.9 647402.9 -Fixed cost =1.1*fixed cost -837100 -837100 -837100 -837100 -837100 -Depreciation (cost of equipment and plant)/5 -236000 -236000 -236000 -236000 -236000 = -425697 -425697 -425697 -425697 -425697 -taxes =(net sales - fixed cost - depreciation)*(1-tax) -255418 -255418 -255418 -255418 -255418 +Depreciation 236000 236000 236000 236000 236000 =after tax operating cash flow -19418.3 -19418.3 -19418.3 -19418.3 -19418.3 Reversal of Increase in working capital 0 = Terminal year after tax non operating CF 0 Total Cash flow -1180000 -19418.3 -19418.3 -19418.3 -19418.3 -19418.3 Cost of capital = 10% Discount factor = (1 + cost of capital) ^ corresponding period 1 1.1 1.21 1.331 1.4641 1.61051 Discounted cashflow = total cash flow/discount factor -1180000 -17653 -16048.2 -14589.2 -13263 -12057.2 NPV= Sum of discounted cash flow = -1253611

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