A new piece of production machinery has the following costs.

Investment cost =$25, 000

Annual operating and maintenance cost =$2000 in Year 1 and then increasing by

$500 per year

Annual cost for risk of breakdown =$5000 per year for 3 years, then increasing by $1500 per year

Useful life =7 years

MARR =15%

Calculate the marginal cost of keeping this asset over its useful life.

Question

A new piece of production machinery has the following costs.

Investment cost =$25, 000

Annual operating and maintenance cost =$2000 in Year 1 and then increasing by

$500 per year

Annual cost for risk of breakdown =$5000 per year for 3 years, then increasing by $1500 per year

Useful life =7 years

MARR =15%

Calculate the marginal cost of keeping this asset over its useful life.

Accepted Answer

From the problem data we can easily find the marginal costs for O&M and risk of breakdowns. However, to calculate the marginal capital recovery cost, we need estimates of each year’s market value.

Year	Market Value
1	$18,000
2	13,000
3	9,000
4	6,000
5	4,000
6	3,000
7	2,500

We can now calculate the machinery’s marginal cost (year-to-year cost of ownership) over its 7-year useful life.

Year, n	Loss in Market Value in Year n	Interest in Year n	O&M Cost in Year n	Cost of Breakdown Risk in Year n	Total Marginal Cost in Year n
1	$25,000 − 18,000 = $7000	$25,000(0.15) = $3750	$2,000	$5,000	$17,750
2	18,000 − 13,000 = 5000	18,000(0.15) = 2700	2500	5,000	15,200
3	13,000 − 9,000 = 4000	13,000(0.15) = 1950	3000	5,000	13,950
4	9,000 − 6,000 = 3000	9,000(0.15) = 1350	3500	6,500	14,350
5	6,000 − 4,000 = 2000	6,000(0.15) = 900	4000	8,000	14,900
6	4,000 − 3,000 = 1000	4,000(0.15) = 600	4500	9,500	15,600
7	3,000 − 2,500 = 500	3,000(0.15) = 450	5000	11,000	16,950

Notice that each year’s total marginal cost includes loss in market value, interest, O&M cost, and cost for risk of breakdowns. For example, the Year-5 marginal cost of $14,900 is calculated as 2000 + 900 + 4000 + 8000.

Question 13.2: A new piece of production machinery has the following costs....

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