A machine costs $6800 to buy, $700 to install, and has no salvage value. Maintenance costs are expected to be $0 the first year, but will increase by $900 every year after that. Operating costs are expected to be $1200 every year. If the machine will last 10 years and the interest rate is 8%,

Question

A machine costs $6800 to buy, $700 to install, and has no salvage value. Maintenance costs are expected to be $0 the first year, but will increase by $900 every year after that. Operating costs are expected to be $1200 every year. If the machine will last 10 years and the interest rate is 8%, compute the machine’s economic life that minimizes the EUAC.

Accepted Answer

In earlier chapters, when we were given a life of 10 years we would have calculated the EUAC of ownership over 10 years.

[latex]EUAC_{10}=7500(A/P,8\%,10)+900(A/G,8\%,10)+1200=[/latex]

[latex]=7500(0.1490)+900(3.871)+1200=\$5801[/latex]

Now, this calculation is needed for every year.

If Retired at the End of Year n

Year, t EUAC of Capital EUAC of Maintenance EUAC of

Operating Costs: EUAC		and Repair Costs:	Recovery Costs:
Total	$1200	$900(A/G, 8%, t)	$7500(A/P, 8%, t)
$9300	$1200	$ 0	$8100	1
5838	1200	433	4206	2
4964	1200	854	2910	3
4728←	1200	1264	2264	4
4739	1200	1661	1878	5
4870	1200	2048	1622	6
5065	1200	2425	1440	7
5294	1200	2789	1305	8
5542	1200	3142	1200	9
5801	1200	3484	1117	10

The total EUAC data are plotted in Figure 13–1. From either the table or the figure, we see that the machinery’s minimum cost life is at 4 years, with a minimum EUAC of $4728 for each of those 4 years.

Looking at Figure 13–1 more closely, we see the effects of each of the individual cost components on total EUAC (capital recovery, maintenance/repair, and operating expense EUACs) and how they behave over time. The total EUAC curve of most assets tends to follow this concave “bathtub” shape—high for short lives due to capital recovery costs and high for long lives due to increased maintenance/repair and operating expenses. The minimum EUAC occurs somewhere between these high points.

Question 13.1: A machine costs $6800 to buy, $700 to install, and has no sa...

Related Answered Questions

The machine in Example 13–6 is the existing asset, and the machine in Examples 13–4 and 13–5 is a new alternative. When should the existing asset be replaced. ...

Verified Answer:

Verified Answer:

Verified Answer:

Verified Answer:

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 ...

Verified Answer:

Taking the machinery in Example 13–4 as a new asset, calculate the EUACt for each year from the marginal costs. ...

Verified Answer:

Verified Answer:

A machine costs $18,000 to buy and install. Its operating and maintenance (O&M) costs start at $900 per year and then climb $500 per year. Its selling price if sold used is $5000 at the end of year 1 and then it declines 10% per year. If the machine is to be used more than 5 years, an overhaul ...

Verified Answer:

Use the data from Example 13–1 and spreadsheets to model and solve for the minimum EUAC. ...

Verified Answer: