Question

Jackson & Sons uses packing machines to prepare its products for shipping. One machine costs $397,500 and lasts 5 years before it needs replaced. The machine will be worthless after the 5 years. The annual after-tax operating cost per machine is $38,400.   
What is the equivalent annual cost of one machine if the required rate of return is 16 percent?

Answer 1

Machine's costs = $397,500

Annual after-tax operating cost per machine for 5 years is $38,400

calculating the Net Present Value of Machine:-

Year	Cash Flow of Machine ($) (a)	PV Factor @11%  (b)	Present Value of Machine ($)  [(a)*(b)]
0	(397,500.00)	1.00000	(397,500.000)
1	38,400.00	0.86207	33,103.448
2	38,400.00	0.74316	28,537.455
3	38,400.00	0.64066	24,601.255
4	38,400.00	0.55229	21,207.978
5	38,400.00	0.47611	18,282.740
			(271,767.12)

So, NPV of Machine is -$271,767.12

Note- PV Factor@16% can be taken from PVAF Table or calculated using this formula which is = 1/(1+0.16)^n

where, n = Respective year.

For example, PV Factor@16% of 2nd year = 1/(1+0.16)^2 = 1/1.3456 = 0.74316

Calculating Equivalent Annual Cost(EAC) of one Machine:-

where, r = Interest rate = 16%

n = no of years = 5

EAC = $83,000.23

So, the the equivalent annual cost of one machine is $83,000.23

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