We are evaluating a project that costs $768,000, has a six-year life, and has no
ID: 2653068 • Letter: W
Question
We are evaluating a project that costs $768,000, has a six-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 57,000 units per year. Price per unit is $60, variable cost per unit is $35, and fixed costs are $770,000 per year. The tax rate is 35 percent, and we require a return of 15 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
We are evaluating a project that costs $768,000, has a six-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 57,000 units per year. Price per unit is $60, variable cost per unit is $35, and fixed costs are $770,000 per year. The tax rate is 35 percent, and we require a return of 15 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.
Best Case NPV
Sales Quantity = 57000 + 10% * 57000 = 62700
Sales Price per unit = 60 + 10% * 60 = $ 66
variable cost per unit = 35 - 10%*35 = $ 31.5
Fixed Cost = 770000 - 10%*770000 = 693000
Annual Depreciation = 768000/6 = 128000
Initial Investment = 768000
Require a return = 15%
Tax rate = 35%
Annual cash Flow =( (Sales Price per unit -variable cost per unit )*Sales Quantity - Fixed Cost)*(1-tax rate) + Annual Depreciation * tax rate
Annual cash Flow = ((66-31.5)*62700 - 693000)*(1-35%) + 128000*35%
Annual cash Flow = $ 1000397.50
Best Case NPV = -Initial Investment + cash Flow 1/(1+r)+ cash Flow 2/(1+r)^2 + cash Flow 3/(1+r)^3 + cash Flow 4/(1+r)^4 + cash Flow 5/(1+r)^5 + cash Flow 6/(1+r)^6
Best Case NPV = -768000 + 1000397.50 /(1+15%)+ 1000397.50 /(1+15%)^2 + 1000397.50 /(1+15%)^3 + 1000397.50/(1+15%)^4 + 1000397.50/(1+15%)^5 + 1000397.50/(1+15%)^6
Best Case NPV = $ 3,017,987.03
Worst Case NPV
Sales Quantity = 57000 - 10% * 57000 = 51300
Sales Price per unit = 60 - 10% * 60 = $ 54
variable cost per unit = 35 + 10%*35 = $ 38.50
Fixed Cost = 770000 + 10%*770000 = 847000
Annual Depreciation = 768000/6 = 128000
Initial Investment = 768000
Require a return = 15%
Tax rate = 35%
Annual cash Flow =( (Sales Price per unit -variable cost per unit )*Sales Quantity - Fixed Cost)*(1-tax rate) + Annual Depreciation * tax rate
Annual cash Flow = ((54-38.5)*51300 - 847000)*(1-35%) + 128000*35%
Annual cash Flow = $ 11097.50
Worst Case NPV = -Initial Investment + cash Flow 1/(1+r)+ cash Flow 2/(1+r)^2 + cash Flow 3/(1+r)^3 + cash Flow 4/(1+r)^4 + cash Flow 5/(1+r)^5 + cash Flow 6/(1+r)^6
Worst Case NPV = -768000 + 11097.50 /(1+15%)+ 11097.50 /(1+15%)^2 + 11097.50 /(1+15%)^3 + 11097.50/(1+15%)^4 + 11097.50/(1+15%)^5 + 11097.50/(1+15%)^6
Worst Case NPV = - $ 726,001.70
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