Geary Machine Shopis considering a fouryear project to impro

Geary Machine Shopis considering a four-year project to improve its production efficency Buying a new machine press for $940 800 is estimated to result in $313 600 In annual pretex cost savings. The press falls in the MACRS five- year class (MACRS Table, and it will have a salvage value at the end of the project of $137.200 The press also requires an intial Investment in spare parts Inventory of $39.200, along with an edditional $5 880 in inventory for ech succeeding year of the projec. Required If the shop\'s tax rate is 31 percent and its discount rate is 16 percent what is the NPV for this project? (Do not round your Intermedlate calculations) O $-102142 21 ?$98.67879 O $-192.00260 ?$-10724932 O $-9703510

Solution

Step 1: Calculate Annual Cash Flows

The annual cash flows are calculated as below:

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Notes:

1) The after-tax salvage value is calculated as below:

Book Value of Machinery after 4 Years = Cost - Depreciation for Year 1 - Depreciation for Year 2 - Depreciation for Year 3 - Depreciation for Year 4 = 940,800 - 188,160 - 301,056 - 180,633.60 - 108,380.16 = $162,570.24

Loss on Sale of Machinery = Book Value - Sales Value = 162,570.24 - 137,200 = $25,370.24

Tax Savings = Loss on Sale of Machinery*Tax Rate = 25,370.24*31% = $7,864.77

After-Tax Salvage Value = Sales Value + Tax Savings = 137,200 + 7,864.77 = $145,064.77

2) The amount of working capital required for year 4 is not deducted from operating cash flow as it will get recovered the same year.

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Step 2: Calculate NPV

The NPV is calculated with the use of following formula:

NPV = -Initial Investment - Initial Investment in Working Capital + Cash Flow Year 1/(1+Discount Rate)^1 + Cash Flow Year 2/(1+Discount Rate)^2 + Cash Flow Year 3/(1+Discount Rate)^3 + Cash Flow Year 4/(1+Discount Rate)^4

Substituting values in the above formula, we get,

NPV = -940,800 - 39,200 + 268,833.60/(1+16%)^1 + 303,831.36/(1+16%)^2 + 266,500.42/(1+16%)^3 + 451,886.62/(1+16%)^4 = -$102,142.21 (which is Option A)

	Cash Flow
	Year
	1	2	3	4
Annual Cost Savings	313,600.00	313,600.00	313,600.00	313,600.00
Less Depreciation	188,160.00 (940,800*20%)	301,056.00 (940,800*32%)	180,633.60 (940,800*19.20%)	108,380.16 (940,800*11.52%)
EBT	125,440.00	12,544.00	132,966.40	205,219.84
Less Taxes (EBT*31%)	38,886.40	3,888.64	41,219.58	63,618.15
EAT	86,553.60	8,655.36	91,746.82	141,601.69
Add Depreciation	188,160.00	301,056.00	180,633.60	108,380.16
Operating Cash Flow	274,713.60	309,711.36	272,380.42	249,981.85
Less Investment in Working Capital	5,880.00	5,880.00	5,880.00	0.00
Add Recovery of Working Capital (39,200 + 3*5,880)	0.00	0.00	0.00	56,840.00
After-Tax Salvage Value	0.00	0.00	0.00	145,064.77
Annual Cash Flow	$268,833.60	$303,831.36	$266,500.42	$451,886.62