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One of the integral aspects of decision making in engineering is deciding when to replace an asset. Ordinarily, the decision to replace an asset aims at ensuring that the company gets maximum benefit from this decision. In this case, the company should replace the items when the decision will result in the company making gains from the replacement.
There are various reasons for replacements, which include:

  1. Obsolescence: It occurs when an asset is outdated due to changes in technology.
  2. Depletion: Refers to the gradual loss in market value due to exhaustion such as in mines or forests.
  3. Deterioration due to aging: Refers to wear and tear in machines (Sullivan 23-26).

Replacement Decision Map
The decision to replace an item is determined by the cost versus the benefit that a business will earn from the replacement. A replacement decision map is normally used to determine whether a business should replace its current assets. The decision map is as shown below.
 
The defender refers to the current asset in a company, while the challenger refers to alternative solutions that the company can implement.
Minimum Cost Life of a New Asset
The minimum cost life of a new asset is calculated by minimizing the number of years for an equivalent uniform annual cost (EUAC) of ownership. The EUAC is normally shorter than the useful life or physical life of an asset. When deciding whether to replace a defender by a challenger, the analysts considers the challenger that has the least minimum cost of all competing mutually exclusive challengers (Fuertes and Olmo 1-10). The minimum cost life of an asset is calculated by determining the EUAC for each possible life that is less than or equal to the useful life.
Defender Marginal Cost Data
Marginal costs refer to the annual cost of keeping an asset. EUAC can be applied in more than one year. Capital recovery, yearly taxes, annual operating and maintenance cost, the marginal cost of ownership, and insurance are included in the marginal cost of ownership.
Issues to Consider
Before deciding to replace an asset, an engineer must consider various factors that affect his/ her business environment. These are issues such as whether it is morally and ethically okay to replace an asset. Some replacements may lead to mass unemployment’s, which although they may result in more profits for the company due to reduced costs, they can negatively affect the society. There must also be the assessment of the reparability and service of damaged units. The engineer must assess on the cost-benefit analysis of buying new products. Moreover, he/ she must evaluate if there are enough experts to operate, repair, maintain, and service the machine.  The engineer should also evaluate the ability of the company to afford the asset in both short term and long term. In addition to the above, the engineer must consider the possible effects of technology on the product. He/ she must consider the technological changes and possible improvements. Ideally, he/ she must consider the compatibility of components, technological improvements, and overall cost associated with the new product. Finally, he/ she must consider the financial aspect of the replacement such as cost, tax consequences, and depreciation.
Replacement Analysis Technique 1
This method is used where the defender marginal costs can be computed and are increasing. A defender is maintained if the marginal cost of keeping it one more year is less than the challenger’s minimum EUAC, where it is increasing from year to year. This method assumes that the best challenger will be available at its initial minimum EUAC in future. It also assumes that the service is needed for an indefinite period. The repeatability assumption is used in this model in the annual cost method when comparing alternatives challengers that have different useful lives (Uzma 365-377). This method is called the replacement repeatability assumption and has the following model:

  1. The current best challenger will be available in the oncoming years and its economic position will not change
  2. The services offered by the challenger are needed indefinitely.

Assumption one is normally not held since new competitors usually develop more improved products. Under the repeatability assumption, if the defender’s marginal cost rises above challenger’s minimum EUAC, it will become greater Therefore, this method enables analysts to avoid the problem when the defender’s marginal cost are greater than challenger’s minimum EUAC.
Replacement Analysis Technique 2
This method assumes that the defender marginal costs can be computed and they are not increasing. In this method, the financial analysts are able to compare the defender and challenger even if the defender’s marginal costs are not increasing in a consistent manner. In this method, the defender’s minimum EUAC is used to evaluate if the replacement should occur immediately (Newnan 45-64). If the replacement cannot occur immediately, it happens after the defender’s minimum cost life when the marginal costs are increasing.
In brief, the following guidelines are used in the decision making between the defender and the challenger.

  1. The defender’s minimum EUAC is calculated where the defender’s marginal cost data is not increasing.
  2. The immediate replacement must occur where the challenger’s minimum EUAC is less than the defenders minimum EUAC.
  3. When the defender has an increasing marginal cost that exceeds that challenger’s minimum EUAC, it must be replaced immediately (French 287-296).

Replacement Analysis Technique 3
This method is used when the defender marginal cost data is not available. It is mainly used on systems that require overhauls such as pipeline replacements, construction, or factory overhauls. Replacement analysis technique 3 works by comparing the defender’s EUAC over its remaining useful life and comparing with the challenger’s EUAC at its minimum cost life. The lowest cost between the two is chosen.
Complications in Replacement Analysis
Identification of the defender and challenger first cost is the main challenge in replacement analysis. There is usually a problem of identifying the specific costs that should be allocated to the defender or the challenger. For instance, there is confusion when determining between trade in value, market value, book value, and salvage value (Sullivan 23-26). The market value is the most appropriate form since items should be valued based on their current market prices.
Repeatability Assumption
In some cases, the repeatability assumption may fail to work, such as when a person has taken an early retirement and he/ she is selling the business, or closing it down. Another scenario may be in the construction of temporary buildings such as tents. Since the replaceability assumption does not apply in these situations, the analyst must evaluate the challenger and the defender economic cost, benefits, and the salvage value at the end of specified periods. Similarly, replicability is not applicable when future challengers are not assumed the same (Brown and Byer 1-10).
Future challengers are expected to be better than the current ones due to technological innovations. In addition, due to their ease of production, they may be cheaper than the current ones. With these in mind, engineers are advised to have some cautious optimism when deciding whether to replace a defender with a challenger (Sullivan 23-26). In particular, this caution should be taken on expensive assets and those that have a long payback period.
After Tax Replacement Analysis
Tax effects can alter the costs of the defendants and challengers due to the tax shield. Marginal cost on after tax is the measure of the cost incurred in the ownership of a defender in each year. Consequently, a financial analyst should consider the effects of ordinary taxes as well as gains and losses that are due to asset disposal.
Minimum cost Life Problems
The after-tax minimum EUAC is affected by both the depreciation method used and the changes in the asset market value over time. Accelerated depreciated methods such as MACRS reduce the after-tax cost of an asset at an early stage of its formation (Sullivan 23-26). When the MACRS tax system is used, the after-tax cash flows are usually different in every year. Therefore, the net present value of the PMT function is needed to find the minimum EUAC after tax.
 
 
 
 
Questions
13-8
A machine that has been used for one year has a salvage value of $10,000 now, which will drop by $2,000 per year. The maintenance cost for the next 4 years are $1250, $1450, $1750, and $2250. Determine the marginal cost to extend service for each of the next 4 years if the MARR is 8%.
Solution
 
Challenger Min EUAC
Mytown street department repaves a street 8 years. Potholes cost $12,000 per mile beginning at the end of year 3 after construction or repaving. The cost to fix potholes generally increases by $12,000 each year. Repaving costs are $180,000 per mile. Mytown uses an interest rate of 6%. What is the EAC of Mytown policy? What is the EAC of the optimal policy?
Solution
The EAC for Mytown will be observed at the 6th year according to the town’s policy.
The optimal policy will be the one the results in the town having the least cost of road maintenance.
A/P = (i(1+i)n/ (1+i)n– 1
A/G= 1/i- (n/(1+i)n-1)
Where,
i= Interest rate
n= Time

Year, n EUAC of Capital Recovery Costs: $180,000(A/P, 6%,n) EUAC of Maintenance and Repair cost: $12,000(A/G, 6%, n) EUAC Total
1 190800 0 190800
2 117817.2 0 117817.2
3 67339.8 0 67339.8
4 51946.2 12000 63946.2
5 42732 34603.56 77335.56
6 36604.8 39964.8 76569.6

 
What is the EAC of Mytown’a policy?
EAC is $76569.6, found in year 6.
What is the optimal EAC policy?
EAC is $63946.2, found in year 4. It is the lowest cost.
What is the optimal policy?
The Town should repave at the end of the fourth year. It is the cheapest and most optimal level. Repaving in the 5th and 6th year is costly.
 
 
 
 
13-33
Bill’s father read that each year a car’s value declines by 25%. After a car is 3 years old, the rate of decline falls to 15%. Maintenance and operating costs increase as the car ages. Because of the manufacturer’s warranty, first-year maintenance is very low.
 

Age of Car (years) Maintenance Expense ($)
1 50
2 150
3 180
4 200
5 300
6 390
7 500

 
Bill’s dad wants to keep his annual cost of car ownership low. The car Bill’s dad prefers costs $11,200 new. Should he buy a newer used car and, if used, when would you suggest he buy it, and how long should it be kept? Give a practical, rather than a theoretical, solution.
Solution
The most optimal level is found at the point with the least marginal costs of owning a car.
 
 

Year. N Loss in Market Value (11,200 * (25% or 15%) Maintenance Cost Marginal Cost
1 2800 50 2850
2 2600 150 2750
3 1450 180 1630
4 652.5 200 852.5
5 554.625 300 854.625
6 471.43125 390 861.43125
7 400.71675 500 900.71675

 
Bill’s father should by his car at the end of year three and use it during year four, five and six. During this period, he will enjoy the least marginal cost of owning the car.
Through this method, he will enjoy the least costs since year 4, 5, and 6 have the least costs when compared to the other years.
13-8
A machine that has been used for one year has a salvage value of $10,000 now, which will drop by $2000 per year. The maintenance costs for the next 4 years are $1250, $1450, $1750, and $2250. Determine the marginal cost to extend service for each of the next 4 years if the MARR is 8%.
Solution
O& M is operation and maintenance.
St-1(1+i) is remaining salvage value and interest rate.
Interest rate is 8%
St is salvage value at end of year.

Year, n Loss in Market Value Year n Interest in Year n Operating Cost in Year n Marginal Cost in Year n
1 2000 0.08*10,000= 800 1250 4050
2 2000 0.08*8000= 640 1450 4050
3 2000 0.08*6000= 480 1750 4230
4 2000 0.08*4000= 320 2250 4570

 
 
 
13-51
Machine A has been completely overhauled for $9000 and is expected to last another 12 years. The $9000 was treated as an expense for tax purposes last year. Machine A can be sold now for $30,000 net after selling expenses, but will have no salvage value 12 years hence. It was bought new 9 years ago for $54,000 and has been depreciated since then by straight-line depreciation using a 12-year depreciable life.
Because less output is now required, Machine A can be replaced with a smaller machine: Machine B costs $42,000, has an anticipated life of 12 years, and would reduce operating costs $2500 per year. It would be depreciated by straight-line depreciation with a 12-year depreciable life and no salvage value. The income tax rate is 40%. Compare the after-tax annual costs and decide whether Machine A should be retained or replaced by Machine B. Use a 10% after-tax rate of return.
Solution
Old Machine
 

O&M Depreciation If disposed of Tax 10%
Year ATFC ATCF PW
-30000
1 2400 27600 -2727.27
2 3840 22260 -8396.83
3 2304 18456 -14438.46
4 782.4 15573.6 -18776.43
5 182.4 12691.2 -21844.8
6 -1108.8 10500 -24529.63
7 -2400 9000 -26,441.18
8 -3000 7500 -27708.33
9 -3600 6000 -28842.11
10 -4200 4500 -29862.5
11 -4800 3000 -30785.71
12 -5400 1500 -31625

 
 
New Machine

O&M Depreciation If disposed of Tax 10%
Year ATFC ATCF PW
-42000
1 4860 33840 -6818.18
2 6876 26364 -14300
3 4725.6 21038.4 -22181.54
4 3435.36 17003.04 -27401.14
5 3435.36 12967.68 -31064.6
6 2467.68 9900 -34270.2
7 1500 12600 -33,705.88
8 1500 10500 -35333.33
9 1500 8400 -36789.47
10 1500 6300 -38100
11 1500 4200 -39285.71
12 1500 2100 -40363.64

 
Machine A should be replaced by machine B. The replacement increases the true worth of the company.
13-4
Which one of the following is the proper dollar value of defender equipment to use in replacement analysis?

  1. Original cost
  2. Present market value
  3. Present trade-in value
  4. Present book value
  5. Present replacement cost, if different from original cost

Solution
The present market value is the most appropriate cost to use as the proper value of the defender in the replacement analysis. In most cases, the trade–in value is often inflated, a situation called overtrading. The original cost is wrong since it does not reflect the prevailing market changes. The book value may be faulty since companies may not want to absorb losses caused by the loss in value of products due to obsolescence. Therefore, since in most cases the defender always has a shorter remaining life than a new product, it is appropriate to assign its market value at time zero rather than subtracting this amount from the challenger’s first cost. The reason for this classification is because cash flow approach shows incorrect values when the challenger and defender have unequal lives.
 
 
 
 
 
 
 
 
Works Cited
Brown, B. and Steven B. Integrating Strategic Management and Financial Analysis: The Case of Discounted Cash Flow and Optionality. International Journal of Applied Finance for Non-Financial Managers, vol. 2, no. 2, 2005, pp. 1-10.
French, N. Discounted Cash Flow: Accounting for Uncertainty. Journal of Property Investment & Finance, vol. 23, no. 1, 1999, pp. 287-296.
Fuertes, A. and Jose, O. On Setting Day-Ahead Equity Trading Risk Limits: VaR Prediction at Market Close or Open? Journal of Risk Financial Management, vol. 9, no. 3, 2016, pp. 1-10.
Uzma, S. et al. Discounted Cash Flow and Its Implication on Intangible Valuation. Global Business Review, vol. 10, no. 3, 2010, pp. 365-377.
Newnan, D. et al. Engineering Economics Analysis 9th Ed. New York, NY: Oxford University Press. (2004). Print
Sullivan, W. et al. Engineering Economy (16th Ed.). Upper Saddle River, NJ: Person Publishers. (2014). Print.