Masters Machine Shop is considering a four-year project to improve its production efficiency. Buying a new machine press for $410,000 is estimated to result in $160,000 in annual pretax cost savings. The press falls in the MACRS five-year class, and it will have a salvage value at the end of the project of $60,000. The press also requires an initial investment in spare parts inventory of $25,000, along with an additional $3,350 in inventory for each succeeding year of the project. The shop's tax rate is 25 percent and its discount rate is 12 percent. Calculate the NPV of this project

NPV = $49,528.87

Explanation:

The NPV is calculated systematically as follows:

The Initial Investment = $410,000

Useful Life = 4 years

Step 1) Begin by calculating the yearly Depreciation figures

Depreciation for Year 1 = 0.20 x $410,000

Depreciation for Year 1 = $82,000

Depreciation for Year 2 = 0.32 x $410,000

Depreciation Year 2 = $131,200

Depreciation for Year 3 = 0.192 x $410,000

Depreciation for Year 3 = $78,720

Depreciation for Year 4 = 0.1152% x $410,000

Depreciation Year 4 = $47,232

Therefore, calculate the Book Value at the end of the 4th year by subtracting all depreciation figures from the Initial Value as follows: $410,000 - $82,000 - $131,200 - $78,720 - $47,232 = $70,848

Step 2: Calculate the After tax Salvage Value as follows:

= Salvage value - (Book Value - Salvage Value) x the tax rate

$60,000 - ($70,848-$60,000) x 0.25

After-tax Salvage Value = $62,712

Step 3: Begin the Calculation of the Net Cash Flow (NCF) Per Year from Year O

Year 0:

NCF = Initial Investment + Initial Investment in NWC

= - $410,000 - $25,000

= - $435,000

Year 1:

Operating Cash Flow (OCF)

= The Pre-tax Cost Saving x * (1 - tax) + tax x Depreciation

= $160,000 x (1 - 0.25) + 0.25 x $82,000

= $140,500

Net Cash flow = OCF - Investment in NWC = $140,500 - $3,350 = $137,150

Year 2:

Operating Cash Flow (OCF) =

$160,000 * (1 - 0.25) + 0.25 * $131,200

=$152,800

Net Cash flow = $152,800 - $3,350 = $149,450

Year 3:

Operating Cash Flow = $160,000 * (1 - 0.25) + 0.25 * $78,720

= $139,680

Net Cash Flows = $139,680 - $3,350 = $136,330

Year 4:

Operating Cash Flow = $160,000 * (1 - 0.25) + 0.25 * $47,232

=$131,808

Net Cash Flows = Operating Cash Flow + NWC recovered + After-tax Salvage Value

= $131,808 + $35,050 + $62,712

= $229,570

Step 4: Now Calculate the Net Present Value using the Required rate of return of 12%

Net Cash Flow (year 0) + Net Cash Flow Years 1-4 / 1+r^n

=-$435,000 + $137,150/1.12 + $149,450/1.12^2 + $136,330/1.12^3 + $229,570/1.12^4

NPV = $49,528.87