Question

A company is considering the purchase of a large stamping machine that will cost $145,000, plus $6,300 transportation and $11,700 installation charges. It is estimated that, at the end of five years, the market value of the machine will be $48,000. The IRS has established that this machine will fall under a three-year MACRS class life category. The justifications for the machine include $34,000 savings per year in labor and $44,000 savings per year in reduced materials. The before-tax MARR is 20% per year, and the effective income tax rate is 40%. What is the after-tax equivalent annual worth of this investment over the five year period which ends with the sale of the machine?    (Do not enter a dollar sign $ with your answer.)

Answer 1

Total Initial Cost = $145,000 + $6,300 + $11,700 = $163,000

Salvage Value = $48,000

Depreciation is counted only on the purchase price of $145,000. Transportation and Installation costs will not be considered. Since the Machine is in the 3year MACRS category, the yearly depreciation will be

Year 1; 33.33% of $145,000 = $48328.50

Year 2: 44.45% of $145,000 = $6445.20

Year 3: 14.81% of $145,000 = $21474.50

Year 4: 7.41% of $145,000 = $10744.50

Annual Savings which can be shown as a positive cashflow = $34,000 + $44,000 = $78,000

Before Tax MARR = 20%

Tax Rate = 40%

After Tax MARR = 20%*(1-40%) = 12%

Now the cashflow table can be made as below

End of Year	Investment / Salvage Value	Annual Savings	Depreciation	Net Income	Taxes	After Tax Cash Flow	After Tax MARR	PV of Cashflow
A	B	C	D	E=C-D	F=0.4*E	G=B+C-F	H	I=G/(1+H)^A
0	-163000					-163000	12%	-163000.00
1		78000	48328.5	29671.5	11868.6	66131.4	12%	59045.89
2		78000	64452.5	13547.5	5419	72581	12%	57861.13
3		78000	21474.5	56525.5	22610.2	55389.8	12%	39425.37
4		78000	10744.5	67255.5	26902.2	51097.8	12%	32473.58
5	48000	78000		78000	31200	94800	12%	53792.07
							Total	79598.03

Let the equivalent Annual Worth after Tax be x

So PV of the Annual Worth = x/1.12^1 + x/1.12^2 + x/1.12^3 + x/1.12^4 + x/1.12^5 = 3.605x

So 3.605x = 79598.03

or x = 22079.90

So the equivalent after tax annual worth over the 5 years is $22079.50

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