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Homework answers / question archive / A firm is considering the purchase of a fixed asset that costs $800
A firm is considering the purchase of a fixed asset that costs $800. has a five-year life, and no salvage value The asset is depreciated straight line to zero over its lite. The firm projects the following price per unit 515. quantity - 50 units, variable cost per unit = 56 and fixed costs $30. The required return on the project Is 104 and the tax rate is 15%. Find the sensitivity of net present value to changes in the number of units cold, 522 525 523 524
Answer is $22
Annual Depreciation = Initial Investment / Useful Life
Annual Depreciation = $800 / 5
Annual Depreciation = $160
If units sold is 50 units:
Annual OCF = [(Price per unit - Variable Cost per unit) * Quantity - Fixed Costs] * (1 - Tax Rate) + Tax Rate * Depreciation
Annual OCF = [($15 - $6) * 50 - $30] * (1 - 0.35) + 0.35 * $160
Annual OCF = $420 * 0.65 + 0.35 * $160
Annual OCF = $329
NPV = -$800 + $329/1.10 + $329/1.10^2 + $329/1.10^3 + $329/1.10^4 + $329/1.10^5
NPV = $447
If units sold is 51 units:
Annual OCF = [(Price per unit - Variable Cost per unit) * Quantity - Fixed Costs] * (1 - Tax Rate) + Tax Rate * Depreciation
Annual OCF = [($15 - $6) * 51 - $30] * (1 - 0.35) + 0.35 * $160
Annual OCF = $429 * 0.65 + 0.35 * $160
Annual OCF = $334.85
NPV = -$800 + $334.85/1.10 + $334.85/1.10^2 + $334.85/1.10^3 + $334.85/1.10^4 + $334.85/1.10^5
NPV = $469
Sensitivity of NPV = Change in NPV / Change in Quantity
Sensitivity of NPV = ($469 - $447) / (51 – 50)
Sensitivity of NPV = $22
