Question

Suppose the chief engineer asks you to do a replacement analysis on an existing piece of equipment. (The defender) Because technology changes so rapidly, she does not want you to evaluate the equipment beyond 4 years since the equipment will be obsolete. The company uses a MARR of 8 percent.

The existing equipment was purchased 5-years ago for $175,000 but can be sold today (t = 0) for $30,000. The future salvage values of the equipment are expected to decrease by 20% per year. For the first year, (t=1) the firm will have to spend money on upgrading the equipment ($32,000) in addition to its operating costs ($8,000) The upgrading cost, the annual operating costs and salvage values are shown in the table below.

Year	Operating Cost and Upgrade	Salvage	AEC
0
1	40,000*	24,000
2	16,000	19,200
3	24,000	15,360
4	32,000	12,288

*$32,000 + $8,000 = $40,000

1. Calculate the economic service life of the equipment.
2. Suppose the firm keeps the defender for 3 years. Calculate the cost of keeping the equipment for one more year. (From year 3 to year 4)

Answer 1

a.

EUAC for 1 yr of operation = 30000*(A/P,8%,1) + 40000 - 24000*(A/F,8%,1)

= 30000*1.08 + 40000 - 24000

= 48400

EUAC for 2 yr of operation = 30000*(A/P,8%,2) + 16000 + 24000*(P/F,8%,1)*(A/P,8%,2) - 19200*(A/F,8%,2)

= 30000*0.560769 + 16000 + 24000* 0.925926*0.560769 - 19200*0.480769

= 36053.84

EUAC for 3 yr of operation = 30000*(A/P,8%,3) + 16000 + 24000*(P/F,8%,1)*(A/P,8%,3) + 8000*(A/F,8%,3) - 15360*(A/F,8%,3)

= 30000*0.388034 + 16000 + 24000* 0.92593*0.388034 + 8000*0.308034 - 15360*0.308034

= 33996.90

EUAC for 4 yr of operation = 30000*(A/P,8%,4) + 16000 + 24000*(P/F,8%,1)*(A/P,8%,4) + 8000*(F/P,8%,1)*(A/F,8%,4) + 16000*(A/F,8%,4) - 12288*(A/F,8%,4)

= 30000*0.301921 + 16000 + 24000*0.92593* 0.301921 + 8000*1.08*0.221921 + 16000*0.221921 - 12288*0.221921

= 34508.14

Minimum EUAC = 33996.90, ESL = 3 yrs

b.

Marginal cost of keeping equipment for 1 more yr = (15360 - 12288) + 0.08 * 15360 + 32000

= 36300.80