We are evaluating a project that costs $832,000, has an eight-year life, and has
ID: 2793282 • Letter: W
Question
We are evaluating a project that costs $832,000, 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 40,000 units per year. Price per unit is $40, variable cost per unit is $15, and fixed costs are $700,000 per year. The tax rate is 35 percent, and we require a return of 18 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.
Explanation / Answer
Initial cost of project = $832,000
Project life = 8 years
Projected sales = 40,000 units per year
Price per unit = $40
Vaiable cost per unit = $15
Fixed cost = $700,000
In best case scenario, all sales will increase by 10% and costs will decrease by 10%
For best case,
Sales = 40,000*(1.1) = 44,000
Price per unit = 40*1.1 = $44
Therefore Revenue = Sales*price per unit = 44000*44 = $1,936,000
Variable cost = 15*(0.9) = 13.5 per unit
Fixed cost = 700,000*0.9 = $630,000
Total Cost = (44000*13.5) + 630000 = 1224000
Depreciation = 832000/8 = 104000
Tax = 35%
Cash flow = (Revenue - cost - depreciation)*(1-tax) + depreciation = (1936000-1224000-104000)(1-0.35) + 104000 = 499200
NPV is sum of present value of cash flows
Present value = cash flow/(1+r)n, r is rate of return and n is number of years
r = 18%
NPV = -832,000 + 499200/(1.18)1 + 499200/(1.18)2 + ............................... +499200/(1.18)8 = $1,203,520.83
For worst case,
Sales = 40,000*(0.9) = 36,000
Price per unit = 40*0.9 = $36
Therefore Revenue = Sales*price per unit = 36000*36 = $1,296,000
Variable cost = 15*(1.1) = 16.5 per unit
Fixed cost = 700,000*1.1 = $770,000
Total Cost = (36000*16.5) + 770000 = 1364000
Depreciation = 832000/8 = 104000
Tax = 35%
Cash flow = (Revenue - cost - depreciation)*(1-tax) + depreciation = (1296000-1364000-104000)(1-0.35) + 104000 = -7800
NPV is sum of present value of cash flows
Present value = cash flow/(1+r)n, r is rate of return and n is number of years
r = 18%
NPV = -832,000 - 7800/(1.18)1 - 7800/(1.18)2 + ............................... - 7800/(1.18)8 = -$863,805.01
In best case, NPV = $1,203,520.83
In worst case, NPV = -$863,805.01
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