Question

A machine costs $17,026 and is expected to have a scrap value of $2,432 whenever it is retired. Operating and Maintenance costs are $1,268 for the first year and expected to increase by $1,784 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 5 year because cost is continuously increasing while salvage value is constant

Associated EUAC is 8681.61

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 (1268(P/A, 11%, 3) + 1784(P/G, 11%, 3)) = 7155.46

PV of salvage value for n = 3 = 2432 (P/F, 11%, 3) = 1778.26

NPV = 17026 + 7155.46 - 1778.26 = 22403.20

EUAC = 22403.20(A/P, 11%, 3) = 9167.68

Year	Annual cost	Salvage value	PV of the annual cost	PV of the market value	Net present value	EUAC
1	1268	2432	1142.34	2190.99	15977.35	17734.86
2	3052	2432	3619.41	1973.87	18671.55	10902.95
3	4836	2432	7155.46	1778.26	22403.20	9167.68
4	6620	2432	11516.25	1602.03	26940.22	8683.54
5	8404	2432	16503.62	1443.27	32086.35	8681.61