We are evaluating a project that costs $1,582,000, has a seven-year life, and ha
ID: 2711799 • Letter: W
Question
We are evaluating a project that costs $1,582,000, has a 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 87,100 units per year. Price per unit is $34.30, variable cost per unit is $20.55, and fixed costs are $751,000 per year. The tax rate is 30 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 ±10 percent. Calculate the best-case and worst-case NPV figures.
We are evaluating a project that costs $1,582,000, has a 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 87,100 units per year. Price per unit is $34.30, variable cost per unit is $20.55, and fixed costs are $751,000 per year. The tax rate is 30 percent, and we require a return of 12 percent on this project.
Explanation / Answer
Best case NPV
Initial Investment = 1582000
Annual Depreciation = Initial Investment /Useful Life
Annual Depreciation = 1582000/7
Annual Depreciation = 226000
Sales Quantity = 87100*(1+10%) = 95810
Price per unit = 34.30*(1+10%) = $ 37.73
variable cost per unit = 20.55*(1-10%) = $ 18.495
Fixed Cost = 751000*(1-10%) = $ 675900
Tax rate = 30%
Required rate of return = 12%
Annual Cash Flow = ((Price-Variable cost per unit)*Sales Quantity - Fixed Cost)*(1-tax rate) + Annual Depreciation *tax rate
Annual Cash Flow = ((37.73-18.495)*95810 - 675900)*(1-30%) + 226000*30%
Annual Cash Flow = $ 884,703.745
Best case NPV = -Initial Investment + Annual Cash Flow*(1-(1+r)^-n)/r
Best case NPV = -1582000 + 884703.745*(1-(1+12%)^-7)/12%
Best case NPV = $ 2,455,572.50
Worst case NPV
Initial Investment = 1582000
Annual Depreciation = Initial Investment /Useful Life
Annual Depreciation = 1582000/7
Annual Depreciation = 226000
Sales Quantity = 87100*(1-10%) = 78390
Price per unit = 34.30*(1-10%) = $ 30.87
variable cost per unit = 20.55*(1+10%) = $ 22.605
Fixed Cost = 751000*(1+10%) = $ 826100
Tax rate = 30%
Required rate of return = 12%
Annual Cash Flow = ((Price-Variable cost per unit)*Sales Quantity - Fixed Cost)*(1-tax rate) + Annual Depreciation *tax rate
Annual Cash Flow = ((30.87-22.605)*78390 - 826100)*(1-30%) + 226000*30%
Annual Cash Flow = $ -56944.655
Worst case NPV = -Initial Investment + Annual Cash Flow*(1-(1+r)^-n)/r
Worst case NPV = -1582000 -56944.655*(1-(1+12%)^-7)/12%
Worst case NPV = $ -1,841,881.54
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