Question

Emotion Cosmetics is considering whether to replace one of its manufacturing machines with a new one that will increase operating income (excluding depreciation) by $14,300 per year for the next three years. The new machine costs $37,500, and it falls in the MACRS 3-year class. If the new machine is purchased, the old machine, which has a current book value equal to $8,300, will be sold for $5,000. If the old machine is kept, it will continue to be depreciated on a straight-line basis at $2,300 per year, and then it will be sold in three years for $2,000. If the new machine is purchased, Emotion plans to sell it in three years for $6,000. The firm’s marginal tax rate is 40, and its required rate of return is 11 percent. Should the old machine be replaced?

Answer 1

Incremental Investment	$
Cost of new machine	37,500
(-) Sale of old machine	-5,000
(-) tax saved on loss on sale = 0.40( 8300 - 5000)	-1,320
	31,180

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Annual cash in flow	YEAR -1   ($)	YEAR - 2   ($)	YEAR - 3   ($)
Increase in operating income	14,300.00	14,300	14,300
(-) Increased Depreciation charges	10,198.75	14,368.75	3,253.75
Income before tax	4,101.25	-68.75	11,046.25
(-) tax @ 0.40	1,640.50	-27.50	4,418.50
Income after tax	2,460.75	-41.25	6,627.75
(+) increased Depreciation charges	10,198.75	14,368.75	3,253.75
Cash flow after tax	12,659.50	14,327.50	9,881.50
(+) Additional scrap realised 6000 - 2000			4,000.00
Profit on sale of new machine =6000-(37500-34721.25)= 3221.25
Profit on sale of old machine =2000 - (8300 - 6900)= 600
Tax payable on differencial gain =(3221.25 - 600)*0.40 =1048.5			1,048.50
			14,930.00

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Calculation of NPV
Year	Cash Flow	PV Factor (11%)	Present Value
1	12,659.50	0.901	11,404.96
2	14,327.50	0.812	11,628.51
3	14,930.00	0.731	10,916.68
	Total		33,950.15
	(-) Incremental Investment	31,180.00
		NPV	2,770.15

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MACRS - 3 years class depreciation rate
Year	Dep rate
1	33.33%
2	44.45%
3	14.81%
4	7.41%

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Depreciation
Year	New Machine	Old Machine	Increased Depreciation
1	12,498.75	2300	10,198.75
2	16,668.75	2300	14,368.75
3	5,553.75	2300	3,253.75
	34,721.25	6,900.00

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Hope you understood.