Question

An industrial sewing machine costs $5,641 and is expected to have a scrap value of $3,792 whenever it is retired. Operating and Maintenance costs are $1,038 for the first year and expected to increase by $2,612 thereafter. If the MARR is 11%, determine the minimum equivalent uniform annual cost associated with the optimal economic life of the machine. The service life of this machine is 5 years.

Answer 1

The economic service life is 1 year because cost is continuously increasing while salvage value is constant

Associated EUAC is 3507.51

This is found by

• finding the present value of annual cost for n = 1 to 5 using P/A factor
• finding the present value of salvage value using P/F factor
• finding the net present value
• finding the EUAC using A/P factor

This is done in table below

For example, PV of annual cost for n = 3 is (1038(P/A, 11%, 3) + 2612(P/G, 11%, 3)) = 8476.28

PV of salvage value for n = 3 = 3792 (P/F, 11%, 3) = 2772.68

NPV = 5641 + 8476.28 - 2772.68 = 11344.60

EUAC = 11344.60(A/P, 11%, 3) = 4642.36

Year	Annual cost	Salvage value	PV of the annual cost	PV of the market value	Net present value	EUAC
1	1038	3792	935.14	3416.22	3159.92	3507.51
2	3650	3792	3897.56	3077.67	6460.88	3772.73
3	6262	3792	8476.28	2772.68	11344.60	4642.36
4	8874	3792	14321.86	2497.91	17464.95	5629.41
5	11486	3792	21138.24	2250.37	24528.87	6636.78