HW 10: Replacement Problems

1.)(50 pts, total) A company is looking for the best option to replace an existing piece of equipment, and has identified four options (A – D) with the required 10 year physical life. The cash flow data for the options are listed in the table (below). For each option, the table shows the 1st cost, annual operating cost, and the estimated salvage value at the end of the first year. The amount that the annual operating cost will increase each following year and the amount that the salvage value will decrease each successive year are also listed.

Option: / A / Option: / B / Option: / C / Option: / D
Life: / 10 / years / Life: / 10 / years / Life: / 10 / years / Life: / 10 / years
1st Cost: / $ 10,000 / 1st Cost: / $ 12,000 / 1st Cost: / $ 15,000 / 1st Cost: / $ 18,000
Ann. Cost: / $ 48,000 / per year / Ann. Cost: / $ 48,000 / per year / Ann. Cost: / $ 47,000 / per year / Ann. Cost: / $ 47,000 / per year
Increase: / $ 1,000 / per year / Increase: / $ 950 / per year / Increase: / $ 650 / per year / Increase: / $ 650 / per year
Salvage: / $ 6,000 / Salvage: / $ 9,000 / Salvage: / $ 10,500 / Salvage: / $ 12,000
Decrease: / 10% / per year / Decrease: / 9% / per year / Decrease: / 8% / per year / Decrease: / 5% / per year
Ownership / Operating / Ownership / Operating / Ownership / Operating / Ownership / Operating
Cost / Cost / EAC / Cost / Cost / EAC / Cost / Cost / EAC / Cost / Cost / EAC
$ 5,200 / $ 48,000 / $ 53,200 / $ 4,440 / $ 48,000 / $ 6,300 / $ 47,000 / $ 53,300 / $ 8,160 / $ 47,000 / $ 55,160
$ 51,842 / $ 3,237 / $ 48,448 / $ 4,319 / $ 47,307 / $ 51,625 / $ 5,273 / $ 47,307 / $ 52,580
$ 51,648 / $ 2,788 / $ 48,878 / $ 3,612 / $ 47,601 / $ 51,213 / $ 4,285 / $ 47,601 / $ 51,886
$ 2,377 / $ 49,359 / $ 51,736 / $ 2,532 / $ 49,291 / $ 3,228 / $ 47,883 / $ 51,111 / $ 3,774 / $ 47,883 / $ 51,657
$ 2,154 / $ 49,775 / $ 51,929 / $ 2,357 / $ 49,686 / $ 2,977 / $ 48,153 / $ 51,131 / $ 3,455 / $ 48,153 / $ 51,608
$ 1,996 / $ 50,172 / $ 52,168 / $ 2,227 / $ 50,063 / $ 2,796 / $ 48,412 / $ 51,207 / $ 3,234 / $ 48,412 / $ 51,646
$ 1,875 / $ 50,551 / $ 52,427 / $ 2,123 / $ 50,424 / $ 2,656 / $ 48,658 / $ 51,314 / $ 3,070 / $ 48,658 / $ 51,728
$ 1,780 / $ 50,913 / $ 52,693 / $ 2,038 / $ 50,767 / $ 2,543 / $ 48,894 / $ 51,437 / $ 2,942 / $ 48,894 / $ 51,836
$ 1,702 / $ 51,257 / $ 52,959 / $ 1,966 / $ 51,095 / $ 2,450 / $ 49,117 / $ 51,568 / $ 2,839 / $ 49,117 / $ 51,957
$ 1,637 / $ 51,585 / $ 53,222 / $ 1,904 / $ 51,405 / $ 2,372 / $ 49,330 / $ 51,702 / $ 2,755 / $ 49,330 / $ 52,085
ESL: / years / ESL: / years / ESL: / years / ESL: / years

If the company uses a 12% per year cost of funds (compounded yearly), show your work and fill in the table to answer the following questions for a replacement analysis:

a)(20 pts) Compute the missing ownership and operating cost values for Option A

b)(10 pts) Compute the missing EAC values until you know the ESL for Option B

c)(12 pts) Find the economic service lives for Options A, B, C, and D

d)(5 pts) Determine which of these options is the best choice for a challenger today

e)(3 pts) When should we next plan to replace the best choice challenger?

2.)(50 pts, total) Two years ago, an automated testing machine was installed to monitor product quality. The equipment originally cost $25,000 and is capable of testing 400 units per day at a total operation and maintenance cost of $0.26 per unit. The O&M costs for this type of machine are predicted to increase by $1, 000 per year, starting today. Product sales have now increased to the point that it is necessary to increase production to 700 units per day and the company must choose between replacing the current equipment, or buying an additional machine of the same type. A new 400 unit per shift machine would cost $27,000 today, and have O&M costs identical to the existing machine. Anindependent, used equipment reseller has offered $10,000 for the existing equipment.

A larger machine with a capacity of 800 units per shift would cost $66,500 and have operating and maintenance costs of $0.22 per unit. These costs are assumed to increase by a total of $800 each succeeding year.

It is expected that all testing equipment will be required for five more years, the total salvage value of the two older machines would be about $30,000 at the end of the current year, and the salvage value of the high-capacity machine would be $40,000 at the end of the current year. All salvages values will decrease by 10% each year after that. Assuming the company continues on a single shift, 250 days-per year operation, determine which alternative should be selected using a MARR of 12% per year, compounded annually.

a.)(10 pts, 5 pts each) Draw the cash flow diagrams for both the Defender and the Challenger using the Opportunity Cost Approach

b.)(30 pts, 15 pts each) Identify the economic service life and equivalent annual cost for both options

c.)(5 pts) Identify which option should be chosen today, and

d.)(5 pts) Identify when the current best option should be replaced

Hints: The salvage value can be modeled as S1( 1– d%)N – 1 if the rate of annual decrease (d%) is a percentage/year and is expressed in decimal form (geometric decline).

The salvage value can be modeled as S1 – d$ (N – 1) if the rate of annual decrease (d$) is expressed as dollars/year (linear decline). These would be good formulas to put in an engineering notebook!