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Chapter 13Replacement Analysis
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• Replacement Problem• Replacement Analysis Decision Maps• Minimum-Cost Life• Marginal Cost of Keeping an Asset one more year• Replacement Analysis Techniques• Replacement Repeatability Assumptions• After-tax Replacement Analysis• Spreadsheet and Replacement Analysis
Chapter Outline
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• Recognize and develop replacement problems• Use the decision map to select the appropriate
replacement analysis technique to apply• Calculate the minimum cost life of an asset• Apply replacement analysis techniques correctly• Perform replacement problems on an after-tax
basis• Use spreadsheet in solving replacement
analysis problems
Learning Objectives
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• Should the existing equipment be retained or replaced?
• The “Defender” is the existing equipment.• The “Challenger” is the best available
replacement equipment.• If the defender proves more economical, it will
be retained. If the challenger proves more economical, it will be installed.
Replacement Analysis
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• Obsolescence occurs when an asset’s technology is surpassed by newer and/or different technologies (PC)
• Depletion is the gradual loss of market value of an asset as it is being consumed or exhausted (Oil well, Timber)
• Deterioration is the general loss in value of an asset due to aging process (Production machinery)
The Replacement Problem
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• Planned replacements can be scheduled to minimize the time and cost of disruptions.
• Variations of replacement problems, such as abandonment, retirement, improvements of defender or keeping defender as spare, can be considered as potential new challenger.
• Since replacement problems usually are considered with “fixed output”, only costs of defender and challengers are analyzed.
• Due to the lives of the defender and challengers are usually different, most calculations focus on annual marginal costs or on EUAC.
The Replacement Problem
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Replacement Analysis Decision Map
Identify Alternatives Best ChallengerDefender
Defender Marginal Cost Data?
Analysis Technique 3:Defender’s EUAC over its remaining life Challenger’s EUAC at its min. cost life
Analysis Technique 2:Defender’s lowest EUAC Challenger’s EUAC at its minimum cost life
Defender Marginal CostIncreasing?
Available
Find EUACover given life
Not Available
Find lowest EUACfor Defender
No
Analysis Technique 1:Defender’s next year marginal cost Challenger’s EUAC
Yes
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• The minimum cost life of any new asset is the number of years at which the EUAC of ownership is minimized.
• Because of increasing operating and maintenance costs, the minimum cost life is often shorter than the asset’s useful life.
• EUAC for each possible life, less than or equal to the useful life, is determined. The number of years at which the EUAC is minimum can then be identified.
Minimum Cost Life of a New Asset
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Example 13-1Minimum Cost Life of a New Asset
EUAC(O&M) CR EUAC(Total)$500 $8,100 $8,600 1,125 4,206 5,331 1,733 2,910 4,644 2,325 2,264 4,590* 2,900 1,878 4,779 3,459 1,622 5,082 4,002 1,441 5,442 4,528 1,305 5,833 5,038 1,201 6,239 5,533 1,118 6,650 6,011 1,051 7,062 6,474 995 7,470 6,922 949 7,871 7,355 910 8,265 7,773 876 8,649
Year Maint. Operating O&M1 $0 $500 $500 2 900 900 1,800 3 1,800 1,300 3,100 4 2,700 1,700 4,400 5 3,600 2,100 5,700 6 4,500 2,500 7,000 7 5,400 2,900 8,300 8 6,300 3,300 9,600 9 7,200 3,700 10,900
10 8,100 4,100 12,200 11 9,000 4,500 13,500 12 9,900 4,900 14,800 13 10,800 5,300 16,100 14 11,700 5,700 17,400 15 12,600 6,100 18,700
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Example 13-1Minimum Cost Life of a New Asset
0
2000
4000
6000
8000
10000
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Year
Co
st
Capital Recovery
O&M
Total EUAC
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Replacement Analysis Decision Map
Identify Alternatives Best ChallengerDefender
Defender Marginal Cost Data?
Analysis Technique 3:Defender’s EUAC over its remaining life Challenger’s EUAC at its min. cost life
Analysis Technique 2:Defender’s lowest EUAC Challenger’s EUAC at its minimum cost life
Defender Marginal CostIncreasing?
Available
Find EUACover given life
Not Available
Find lowest EUACfor Defender
No
Analysis Technique 1:Defender’s next year marginal cost Challenger’s EUAC
Yes
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• Are the defender marginal cost data available?• Are the defender marginal costs increasing?• The total marginal cost for any year can include:
• Capital recovery cost (loss in market value and loss interest for the year)
• Yearly operating and maintenance costs• Yearly taxes and insurance• Any other expenses that occurs during that year
• The marginal cost is calculated as an equivalent end-of-year cash flow
Defender’s Marginal Cost Data
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Example 13-2 Marginal Cost Calculation
YearMarket Value
Capital Recovery O&M
Cost of Breakdown
Risk
Total Marginal
Cost1 $18,000 $10,750 $2,000 $5,000 $17,750 2 13,000 7,700 2,500 5,000 15,2003 9,000 5,950 3,000 5,000 13,9504 6,000 4,350 3,500 6,500 14,3505 4,000 2,900 4,000 8,000 14,9006 3,000 1,600 4,500 9,500 15,6007 2,500 950 5,000 11,000 16,950
Capital Recovery Cost = MVN-1(A/P, 15%, 1) – MVN(A/F, 15, 1)= MVN-1(1+15%) – MVN(1)= (MVN-1 – MVN) + MVN-1(15%)
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Example 13-3 Marginal Cost Calculation
YearMarket Value
Capital Recovery
Operating Cost
Total Marginal
Cost0 $15,000 1 14,000 $3,250 $10,000 $13,250 2 13,000 3,100 11,500 14,6003 12,000 2,950 13,000 15,9504 11,000 2,800 14,500 17,3005 10,000 2,650 16,000 18,650
Capital Recovery Cost = MVN-1(A/P, 15%, 1) – MVN(A/F, 15, 1)= MVN-1(1+15%) – MVN(1)= (MVN-1 – MVN) + MVN-1(15%)
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• Maintain the Defender as long as the marginal cost of ownership for one more year is less than the Challenger’s minimum EUAC.
• When the Defender’s marginal cost becomes greater than the Challenger’s minimum EUAC, then replace the Defender with the Challenger.
Replacement Analysis Technique 1:Defender Marginal Cost Increasing
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Example 13-4 Replacement Analysis Technique 1
YearChallenger
Marginal CostChallenger
EUAC1 $17,750 $17,750.00 2 15,200 16,563.95 3 13,950 15,811.20 4 14,350 15,518.57 5 14,900 15,426.83* 6 15,600 15,446.61 7 16,950 15,582.46
YearDefender
Marginal Cost1 $13,250 2 14,6003 15,9504 17,3005 18,650
)N%,15,PA]()j%,15,FP)(Cost (Marginal[UACEN
1j j
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• Currently available best Challenger will continue to be available in subsequent years and will be unchanged in its economic costs. When the Defender is ultimately replaced, it will be replaced with this Challenger.
• The period of needed services of the asset is indefinitely long.
Replacement Repeatability Assumption
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• Calculate the Defender’s minimum EUAC.• If the Defender’s minimum EUAC exceeds the
Challenger’s minimum EUAC, then replace immediately.
• If the Defender’s minimum EUAC is lower than the Challenger’s minimum EUAC, then the Defender will be kept at least the minimum cost life.
• After the minimum cost life, then replace when the Defender’s increasing marginal cost exceeds the Challenger’s minimum EUAC.
Replacement Analysis Technique 2:Defender Marginal Cost Not Increasing
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Example 13-5 Replacement Analysis Technique 2
Year
Challenger Marginal
CostChallenger
EUAC1 $17,750 $17,750.00 2 15,200 16,563.95 3 13,950 15,811.20 4 14,350 15,518.57 5 14,900 15,426.83* 6 15,600 15,446.61 7 16,950 15,582.46
Year
Defender Marginal
CostDefender
EUAC1 $16,000 $16,000.00 2 14,000 $15,069.77 3 13,500 $14,617.71* 4 15,300 $14,754.35 5 17,500 $15,161.57
)N%,15,PA]()j%,15,FP)(Cost (Marginal[UACEN
1j j
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Example 13-6Finding Minimum Cost Life
YearMarket Value
Capital Recovery O&M
Marginal Cost EUAC
0 $5,0001 4,000 $1,500 $0 $1500 $1,500.00 2 3,500 900 100 1000 1,261.90 3 3,000 850 200 1050 1,197.89 4 2,500 800 300 1100 1,176.79 5 2,000 750 400 1150 1,172.41 6 2,000 200 500 700 1,111.18 7 2,000 200 600 800 1,078.38 8 2,000 200 700 900 1,062.78 9 2,000 200 800 1000 1,058.16*
10 2,000 200 900 1100 1,060.78 11 2,000 200 1,000 1200 1,068.29
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Example 13-7 Replacement Analysis Technique 2
YearChallenger
EUAC1 $8,600 2 5,331 3 4,644 4 4,590* 5 4,779
Year
Defender Overhaul
CostDefender
O&M
Defender Marginal
CostDefender
EUAC0 $4,0001 $1,800 $6,120 $6,120.00 2 1,800 1,800 4,043.08 3 2,800 2,800 3,660.17* 4 3,800 3,800 3,691.20 5 4,800 4,800 3,880.20
)N%,8,PA]()j%,8,FP)(Cost (Marginal[UACEN
1j j
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• Calculate the Defender’s EUAC over its stated useful life.
• If the Defender’s EUAC exceeds the Challenger’s minimum EUAC, then replace immediately.
• If the Defender’s EUAC is lower than the Challenger’s minimum EUAC, then the Defender will be kept.
Replacement Analysis Technique 3:Defender Marginal Cost Not Available
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• Present market value, not the trade-in value, should be assigned as the first cost of the Defender.
• The first cost of the Challenger should include the purchase price, sales tax, installation cost, and other items that occur initially on a one-time basis if the Challenger is selected.
• The Defender’s potential market (or salvage) value should not be subtracted from the Challenger’s first cost.
Defining First Costs of Defender and Challenger
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Defender: SK-30, purchased 2 years ago for $1600, was depreciated with SL using 4-year life and 0 salvage.
Challenger: EL-40, $1200 with a trade-in allowance of $350 for the SK-30; $1050 without a trade-in.
Current price for new SK-30 is $995.
Example 13-8 Defining Defender First Cost
Defender: SK-30, • Original cost: $1600 (Basis for SL depreciation)• Present cost: $995 (Irrelevant)• Book value: $800 (Useful in determining depreciation
recapture or loss)• Trade-in value: $350 (Irrelevant)• Market value: $200 (First cost assigned to Defender)
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Circumstances where Repeatability Assumption may not apply:
• When there is a specific study period instead of an indefinite need for the asset
• When future Challengers are not assumed to be identical to the current best Challenger
Repeatability Assumption Not Acceptable
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A Closer Look at Future Challengers
• It seems likely that future challengers will be better than the present Challenger
• The prospect of better future challengers may make it more desirable to retain the Defender and to reject the present Challenger
• Selecting the current best Challenger could be risky if 1) high cost and/or 2) long economic life 0 1 2 3 4
Year
EU
AC
at
Ec
on
om
ic L
ife
Present Challenger
Uniform Decline
Rapid ImprovementsIn Technology
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• Ordinary taxes• Gains and losses due to asset disposal
After-Tax Replacement Analysis
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Example 13-9Marginal Costs on After-Tax Basis
YearMarket Value
Book Value
Recaptured Depr. or
Loss Tax
After-Tax Market Value
0 $25,000 $25,000 $25,0001 18,000 20,000 -$2,000 -$800 18,8002 13,000 15,000 -2,000 -800 13,8003 9,000 10,000 -1,000 -400 9,4004 6,000 5,000 1,000 400 5,6005 4,000 4,000 1,600 2,4006 3,000 3,000 1,200 1,8007 2,500 2,500 1,000 1,500
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Example 13-9Marginal Costs on After-Tax Basis
Year
After-Tax
Market Value
Capital Recovery
O&M+Ins.
Taxable Income Tax
After-Tax Marginal
Cost0 $25,0001 18,800 $8,700 $7,000 -$12,000 -$4,800 $10,9002 13,800 6,880 7,500 -12,500 -5,000 9,3803 9,400 5,780 8,000 -13,000 -5,200 8,5804 5,600 4,740 10,000 -15,000 -6,000 8,7405 2,400 3,760 12,000 -17,000 -6,800 8,9606 1,800 840 14,000 -14,000 -5,600 9,2407 1,500 480 16,000 -16,000 -6,400 10,080
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Example 13-10After-Tax Minimum Cost Life
YearMarket Value
MACRS Depr.
Book Value
Recaptured Depr. or
Loss Tax
After-Tax Market Value
0 $100,000 $100,000 $100,0001 50,000 $14,290 85,710 -$35,710 -$14,284 64,2842 45,000 24,490 61,220 -16,220 -6,488 51,4883 40,000 17,490 43,730 -3,730 -1,492 41,4924 35,000 12,490 31,240 3,760 1,504 33,4965 30,000 8,930 22,310 7,690 3,076 26,9246 25,000 8,920 13,390 11,610 4,644 20,3567 20,000 8,930 4,460 15,540 6,216 13,7848 15,000 4,460 0 15,000 6,000 9,0009 10,000 0 10,000 4,000 6,000
10 5,000 0 5,000 2,000 3,000
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Example 13-10After-Tax Minimum Cost Life
Yr.
After-tax Market Value
Capital Recovery O&M
Taxable Income Tax
After-Tax Marginal
Cost EUAC
0$100,00
01 64,284 $41,716 $10,000 -$24,290 -$9,716 $42,000 $420002 51,488 16,653 14,000 -38,490 -15,396 15,257 290183 41,492 13,085 18,000 -35,490 -14,196 16,889 252084 33,496 10,486 22,000 -34,490 -13,796 18,690 237185 26,924 8,582 26,000 -34,930 -13,972 20,610 231676 20,356 8,183 30,000 -38,920 -15,568 22,615 23088*7 13,784 7,793 34,000 -42,930 -17,172 24,621 232708 9,000 5,611 38,000 -42,460 -16,984 26,627 236109 6,000 3,540 42,000 -42,000 -16,800 28,740 24056
10 3,000 3,360 46,000 -46,000 -18,400 30,960 24580
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Example 13-11Before-Tax Minimum Cost Life
Yr.Market Value
Capital Recovery O&M EUAC(O&M)
Total EUAC
0 $19,9991 13,999 $8,281.62 $50 $50.00 $8,331.62 2 11,199 6,174.98 50 50.00 6,224.98 3 8,960 5,232.66 50 50.00 5,282.66 4 7,168 4,623.71 450 138.77 4,762.48 5 6,092 4,113.17 850 260.00 4,373.17 6 5,179 3,740.77 1,250 394.95 4,135.72 7 4,402 3,452.78 1,650 535.61 3,988.39 8 3,742 3,221.47 2,050 677.99 3,899.45 9 3,180 3,030.81 2,450 819.89 3,850.69
10 2,703 2,870.70 2,850 960.03 3,830.73 11 2,298 2,734.39 3,250 1,097.60 3,831.99 12 1,953 2,617.10 3,650 1,232.10 3,849.20
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Example 13-11Before-Tax Minimum Cost Life
)N%,8,FA)(250MV()N%,8,PA)(400999,19(CR NN
)N%,8,PA]()j%,8,FP()M&O([)M&O(EUACN
1jjN
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