You are the head of finance department in XYZ Company. You are considering addin

Question

You are the head of finance department in XYZ Company. You are considering adding a new machine to your production facility. The new machine’s base price is $10,800.00, and it would cost another $3,400.00 to install it. The machine falls into the MACRS 3-year class (the applicable MACRS depreciation rates are 33.33%, 44.45%, 14.81%, and 7.41%), and it would be sold after three years for $2,350.00. The machine would require an increase in net working capital (inventory) of $780.00. The new machine would not change revenues, but it is expected to save the firm $38,285.00 per year in before-tax operating costs, mainly labor. XYZ's marginal tax rate is 38.00%. If the project's cost of capital is 14.20%, what is the NPV of the project?

Explanation / Answer

Net Cost of Equipment = Cost of Equipment + Installation Cost
Net Cost of Equipment = $10,800 + $3,400
Net Cost of Equipment = $14,200

Depreciation Year 1 = $14,200 * 33.33% = $4,732.86
Depreciation Year 2 = $14,200 * 44.45% = $6,311.90
Depreciation Year 3 = $14,200 * 14.81% = $2,103.02

Book Value at the end of Year 3 = $14,200 - $4,732.86 - $6,311.90 - $2,103.02
Book Value at the end of Year 3 = $1,052.22

After-tax Salvage Value = Salvage Value - (Salvage Value - Book Value) * tax
After-tax Salvage Value = $2,350 - ($2,350 - $1,052.22) * 0.38
After-tax Salvage Value = $1,856.84

Initial NWC required = $780
NWC recovered = $780

OCF Year 1 = Pre-tax Cost Saving * (1 - tax) + Depreciation * tax
OCF Year 1 = $38,285 * (1 - 0.38) + $4,732.86 * 0.38
OCF Year 1 = $25,535.19

OCF Year 2 = Pre-tax Cost Saving * (1 - tax) + Depreciation * tax
OCF Year 2 = $38,285 * (1 - 0.38) + $6,311.90 * 0.38
OCF Year 2 = $26,135.22

OCF Year 3 = Pre-tax Cost Saving * (1 - tax) + Depreciation * tax
OCF Year 3 = $38,285 * (1 - 0.38) + $2,103.02 * 0.38
OCF Year 3 = $24,535.85

NPV = -$14,200 - $780 + $25,535.19/1.142 + $26,135.22/1.142^2 + $24,535.85/1.142^3 + $780/1.142^3 + $1,856.84/1.142^3
NPV = $45,664.49

So, NPV of this project is $45,664.49

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