The project will cost $990,000, have a four-year life, and have no salvage value
ID: 2426933 • Letter: T
Question
The project will cost $990,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 320 units per year; price per unit will be $19,400, variable cost per unit will be $15,900, and fixed costs will be $330,000 per year. The required return on the project is 14 percent, and the relevant tax rate is 30 percent. Requirement 1: Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within ±10 percent. (a) What are the best and worst case NPVs with these projections?
Explanation / Answer
Best Case NPV
Initial Investment = 990000
Salvage Value = 0
Useful Life = 4
Annual Depreciation = (Cost-Salvage Value)/useful life
Annual Depreciation = (990000-0)/4
Annual Depreciation = 247500
Unit Sales = 320*(1+10%) = 352
Price per unit = 19400
variable cost per unit = 15900*(1-10%) = 14,310
fixed cost = 330000*(1-10%) = 297000
Required Return = 14%
Tax rate = 30%
Annual Cash Flow = (Unit Sales*(Price per unit - variable cost per unit)-Fixed Cost)*(1-tax rate) + Annual Depreciation*tax rate
Annual Cash Flow = (352*(19400-14310)-297000)*(1-30%) + 247500*30%
Annual Cash Flow = 1120526
NPV = -Initial Investment + Annual Cash Flow *(1-(1+r)^-n)/r
NPV = -990000 + 1120526*(1-(1+14%)^-4)/14%
NPV = $ 2,274,890.39
Worst Case NPV
Initial Investment = 990000
Salvage Value = 0
Useful Life = 4
Annual Depreciation = (Cost-Salvage Value)/useful life
Annual Depreciation = (990000-0)/4
Annual Depreciation = 247500
Unit Sales = 320*(1-10%) = 288
Price per unit = 19400
variable cost per unit = 15900*(1+10%) = 17,490
fixed cost = 330000*(1+10%) = 363000
Required Return = 14%
Tax rate = 30%
Annual Cash Flow = (Unit Sales*(Price per unit - variable cost per unit)-Fixed Cost)*(1-tax rate) + Annual Depreciation*tax rate
Annual Cash Flow = (288*(19400-17490)-363000)*(1-30%) + 247500*30%
Annual Cash Flow = 205206
NPV = -Initial Investment + Annual Cash Flow *(1-(1+r)^-n)/r
NPV = -990000 + 205206*(1-(1+14%)^-4)/14%
NPV = $ - 392,089
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