A vision-based robotic system is being considered for acquisition at a cost of $30,000. Its annual maintenance cost for the first 5 years is estimated to be $1,000. Thereafter it will increase each year by $1,000. The cost of insurance and utilities for the first year is expected to be $2,000

Question

A vision-based robotic system is being considered for acquisition at a cost of $30,000. Its annual maintenance cost for the first 5 years is estimated to be $1,000. Thereafter it will increase each year by $1,000. The cost of insurance and utilities for the first year is expected to be $2,000, increasing thereafter by $750 each year. For 15% MARR, determine the asset’s marginal cost over its 10-year useful life if its estimated market values are:

Year	Market Value	Year	Market Value
0	$30,000(first cost)	6	$8,500
1	$24,000	7	$7,500
2	$19,000	8	$6,750
3	$15,000	9	$6,250
4	$12,000	10	$6,000
5	$10.000

Accepted Answer

Let us first gather the various costs of operating the asset, and post them in the previous table, as follows

Year	Market Value	Maint. Cost	Utility Cost
0	$30,000
1	$24,000	$1,000	$2,000
2	$19,000	$1,000	$2,750
3	$15,000	$1,000	$3,500
4	$12,000	$1,000	$4,250
5	$10,000	$1,000	$5,000
6	$8,500	$2,000	$5,750
7	$7,500	$3,000	$6,500
8	$6,750	$4,000	$7,250
9	$6,250	$5,000	$8,000
10	$6,000	$6,000	$8,750

Next, we determine the marginal cost for each year as:

Marginal cost = Total cost for the year

= Capital recovery cost + Operating cost

For year 1:

Capital recovery cost = Loss in market value + I nterest lost

[latex]=(30,000-24,000)+15\% of \$30,000[/latex]

[latex]=6,000+4,500[/latex]

[latex]=\$10,500[/latex]

Operating cost = Maintenance and utility costs

[latex]=\$1,000+\$2,000[/latex]

[latex]=\$3,000[/latex]

Marginal cost [latex]=\$10,500 + \$3,000[/latex]

[latex]=\$13,500[/latex]

For year 2:

Capital recovery cost = Loss in market value + Interest lost

[latex]=(24,000-19,000) + 15\% of \$24,000[/latex]

[latex]=5,000+3,600[/latex]

[latex]=\$8,600[/latex]

Operating cost = Maintenance and utility costs

[latex]=\$1,000+\$2,750[/latex]

[latex]=\$3,750[/latex]

Marginal cost[latex]=\$8,600+\$3,750[/latex]

[latex]=\$12,350[/latex]

For year 3:

Capital recovery cost = Loss in market value + Interest lost

[latex]=(19,000-15,000)+ 15\% of \$19,000[/latex]

[latex]=4,000+2,850[/latex]

[latex]=\$6,850[/latex]

Operating cost = Maintenance and utility costs

[latex]=\$1,000+\$3,500[/latex]

[latex]=\$4,500[/latex]

Marginal cost [latex]=\$6,850+\$4,500[/latex]

[latex]=\$11,350[/latex]

The marginal cost for the other years can be determined the same way, and the results summarized as follows.

Year	Loss in Market Value	Interest Foregone	Operating Cost	Marginal Cost
1	$6,000	$4,500	$1,000+$2,000	$13,500
2	$5,000	$3,600	$1,000+$2,750	$12,350
3	$4,000	$2,850	$1,000+$3,500	$11,350
4	$3,000	$2,250	$1,000+$4,250	$10,500
5	$2,000	$1,800	$1,000+$5,000	$9,800
6	$1,500	$1,500	$2,000+$5,750	$10,750
7	$1,000	$1,275	$3,000+$6,500	$11,775
8	$50	$1,125	$4,000+$7,250	$13,125
9	$500	$1,013	$5,000+$8,000	$14,513
10	$250	$938	$6,000+$8,750	$15,938

In this example, the marginal cost decreases initially, reaching a minimum of $9,800 at year 5, and then increases. Therefore, the EUAC-based approach of Section 12.4 is appropriate for replacement analysis of this vision-based robotic system.

However, if a defender’s marginal cost increases each year, with no minimum, then the rule of replacement decision is:[latex]Keep the defender if its marginal cost is lower than the challenger’s EUAC ; if not , replace it with the challenger[/latex] .

Question 12.7: A vision-based robotic system is being considered for acquis...

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