Question

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

Answer 1

Answer:

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