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 incraesing 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 incraesing 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 or salvage value.

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

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

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

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.

In each year the marginal cost is the cost to keep the asset for one more year. The pattern in Example 13–4 is typical. In early years the marginal costs are decreasing because the capital costs are being spread over more years. In later years the marginal costs are increasing because yearly costs are increasing. As the asset ages it will be replaced when its marginal cost exceeds the EUAC of the best new alternative.

Example 13–5 shows how EUAC’s can be calculated from the marginal cost data in Example 13–4.

Question 13.4: A new piece of production machinery has the following costs....

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