Question

One year​ ago, your company purchased a machine used in manufacturing for $95,000.vYou have learned that a new machine is available that offers many advantages and you can purchase it for $150,000 today. It will be depreciated on a​ straight-line basis over 10 years and has no salvage value. You expect that the new machine will produce a gross margin​ (revenues minus operating expenses other than​ depreciation) of $50,000 per year for the next 10 years. The current machine is expected to produce a gross margin of $21,000

per year. The current machine is being depreciated on a​ straight-line basis over a useful life of 11​ years, and has no salvage​ value, so depreciation expense for the current machine is $8,636 per year. The market value today of the current machine is $60,000. Your​ company's tax rate is 45%​, and the opportunity cost of capital for this type of equipment is 10%. Should your company replace its​ year-old machine?

The NPV of replacing the​ year-old machine is...

​

Answer 1

Tax rate		45%
Calculation of after-tax salvage value
Cost of machine			$             95,000
Depreciation			$               8,636
WDV			$             86,364
Sale price			$             60,000
Profit/(Loss)			$           (26,364)
Tax			$           (11,864)
Sale price after-tax			$            71,864
Calculation of initial investment
Cost of new machine			$          150,000
After tax sale price of old machine			$           (71,864)
Initial investment			$            78,136
Calculation of additional depreciation
		Old Machine	New Machine
Cost		$             95,000	$          150,000
Useful life		11.00	10.00
Annual Depreciation-Cost/Life		$                8,636	$             15,000
Additional depreciation		15000-8636
Additional depreciation		$                                               6,364
Calculation of annual incremental operating cash flow
		Year-1-10
Revenue from new machine		$             50,000
Less: Revenue from old machine		$             21,000
Contribution		$             29,000
Less: Incremental depreciation		$                6,364
Profit before tax		$             22,636
Tax@45%		$             10,186
Profit After Tax		$             12,450
Add Depreciation		$                6,364
Cash Profit after-tax		$             18,814
Calculation of NPV
						10.00%
Year		Capital		Operating cash	Annual Cash flow	PV factor	Present values
0		$            (78,136)			$            (78,136)	1.0000	$            (78,136)
1				$             18,814	$             18,814	0.9091	$             17,103
2				$             18,814	$             18,814	0.8264	$             15,548
3				$             18,814	$             18,814	0.7513	$             14,135
4				$             18,814	$             18,814	0.6830	$             12,850
5				$             18,814	$             18,814	0.6209	$             11,682
6				$             18,814	$             18,814	0.5645	$             10,620
7				$             18,814	$             18,814	0.5132	$                9,654
8				$             18,814	$             18,814	0.4665	$                8,777
9				$             18,814	$             18,814	0.4241	$                7,979
10		$                      -		$             18,814	$             18,814	0.3855	$                7,253
					Net Present Value of replaced machine		$             37,465