Ch13 Replacement Class

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Copyright Oxford University Press 2009

Chapter 13

Replacement 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 replacementanalysis problems

Learning Objectives


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Should the existing equipment be retained orreplaced?

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 moreeconomical, it will be installed.

Replacement Analysis


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Obsolescenceoccurs when an assets technologyis surpassed by newer and/or differenttechnologies (PC)

Depletionis the gradual loss of market value of anasset as it is being consumed or exhausted (Oilwell, Timber)

Deteriorationis the general loss in value of anasset due to aging process (Production machinery)

The Replacement Problem


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Planned replacements can be scheduled to minimizethe time and cost of disruptions.

Variations of replacement problems, such asabandonment, retirement, improvements of defender

or keeping defender as spare, can be considered aspotential new challenger.

Since replacement problems usually are consideredwith fixed output, only costs of defender and

challengers are analyzed. Due to the lives of the defender and challengers areusually different, most calculations focus on annualmarginal costs or on EUAC.

The Replacement Problem


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Replacement AnalysisDecision Map

Identify Alternatives Best ChallengerDefender

DefenderMarginal Cost Data?

Analysis Technique 3:Defenders EUACover its remaining lifeChallengers EUACat its min. cost life

Analysis Technique 2:Defenders lowestEUACChallengersEUAC at its minimumcost life

DefenderMarginal CostIncreasing?

Available

Find EUACover given life

Not Available

Find lowest EUACfor Defender

No

Analysis Technique 1:Defenders next yearmarginal costChallengers EUAC

Yes


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The minimum cost life of any new asset is the number ofyears at which the EUAC of ownership is minimized.

Because of increasing operating and maintenancecosts, the minimum cost life is often shorter than the

assets useful life. EUAC for each possible life, less than or equal to the

useful life, is determined. The number of years atwhich 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 $8,6001,125 4,206 5,3311,733 2,910 4,6442,325 2,264 4,590*

2,900 1,878 4,7793,459 1,622 5,0824,002 1,441 5,4424,528 1,305 5,8335,038 1,201 6,2395,533 1,118 6,650

6,011 1,051 7,0626,474 995 7,4706,922 949 7,8717,355 910 8,2657,773 876 8,649

Year Maint. Operating O&M1 $0 $500 $5002 900 900 1,8003 1,800 1,300 3,1004 2,700 1,700 4,400

5 3,600 2,100 5,7006 4,500 2,500 7,0007 5,400 2,900 8,3008 6,300 3,300 9,6009 7,200 3,700 10,900

10 8,100 4,100 12,200

11 9,000 4,500 13,50012 9,900 4,900 14,80013 10,800 5,300 16,10014 11,700 5,700 17,40015 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

Cost

Capital Recovery

O&M

Total EUAC


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Replacement AnalysisDecision Map

Identify Alternatives Best ChallengerDefender

DefenderMarginal Cost Data?

Analysis Technique 3:Defenders EUACover its remaining lifeChallengers EUACat its min. cost life

Analysis Technique 2:Defenders lowestEUACChallengersEUAC at its minimumcost life

DefenderMarginal CostIncreasing?

Available

Find EUACover given life

Not Available

Find lowest EUACfor Defender

No

Analysis Technique 1:Defenders next yearmarginal costChallengers 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 andloss 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 equivalentend-of-year cash flow

Defenders Marginal Cost Data


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Example 13-2Marginal Cost Calculation

YearMarketValue

CapitalRecovery O&M

Cost ofBreakdown

Risk

TotalMarginal

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 15,600

7 2,500 950 5,000 11,000 16,950Capital Recovery Cost = MVN-1(A/P, 15%, 1)MVN(A/F, 15, 1)

= MVN-1(1+15%)MVN(1)= (MVN-1MVN) + MVN-1(15%)


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Example 13-3Marginal Cost Calculation

YearMarketValue

CapitalRecovery

OperatingCost

TotalMarginal

Cost0 $15,000

1 14,000 $3,250 $10,000 $13,2502 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-1MVN) + MVN-1(15%)


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Maintain the Defender as long as themarginal cost of ownership for one moreyear is less than the Challengers minimum

EUAC. When the Defenders marginal cost

becomes greater than the Challengersminimum EUAC, then replace the Defender

with the Challenger.

Replacement Analysis Technique 1:Defender Marginal Cost Increasing


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Currently available best Challenger willcontinue to be available in subsequent yearsand will be unchanged in its economic costs.

When the Defender is ultimately replaced, itwill be replaced with this Challenger. The period of needed services of the asset

is indefinitely long.

Replacement RepeatabilityAssumption


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Calculate the Defenders minimum EUAC. If the Defenders minimum EUAC exceeds the

Challengers minimum EUAC, then replaceimmediately.

If the Defenders minimum EUAC is lower than theChallengers minimum EUAC, then the Defenderwill be kept at least the minimum cost life.

After the minimum cost life, then replace when theDefenders increasing marginal cost exceeds theChallengers minimum EUAC.

Replacement Analysis Technique 2:Defender Marginal Cost Not Increasing


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Example 13-5Replacement Analysis Technique 2

Year

ChallengerMarginal

CostChallenger

EUAC1 $17,750 $17,750.00

2 15,200 16,563.953 13,950 15,811.204 14,350 15,518.575 14,900 15,426.83*6 15,600 15,446.61

7 16,950 15,582.46

Year

DefenderMarginal

CostDefender

EUAC1 $16,000 $16,000.00

2 14,000 $15,069.773 13,500 $14,617.71*4 15,300 $14,754.355 17,500 $15,161.57

)N%,15,PA]()j%,15,FP)(Cost(Marginal[UACE N

1j j


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Example 13-6Finding Minimum Cost Life

YearMarketValue

CapitalRecovery O&M

MarginalCost EUAC

0 $5,000

1 4,000 $1,500 $0 $1500 $1,500.002 3,500 900 100 1000 1,261.903 3,000 850 200 1050 1,197.894 2,500 800 300 1100 1,176.795 2,000 750 400 1150 1,172.416 2,000 200 500 700 1,111.18

72,000

200 600 800 1,078.388 2,000 200 700 900 1,062.789 2,000 200 800 1000 1,058.16*10 2,000 200 900 1100 1,060.7811 2,000 200 1,000 1200 1,068.29


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Example 13-7Replacement Analysis Technique 2

YearChallenger

EUAC1 $8,6002 5,3313 4,6444 4,590*5 4,779

Year

DefenderOverhaul

CostDefender

O&M

DefenderMarginal

CostDefender

EUAC0 $4,0001 $1,800 $6,120 $6,120.00

2 1,800 1,800 4,043.083 2,800 2,800 3,660.17*4 3,800 3,800 3,691.205 4,800 4,800 3,880.20

)N%,8,PA]()j%,8,FP)(Cost(Marginal[UACE N

1j j


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Calculate the Defenders EUAC over its stateduseful life.

If the Defenders EUAC exceeds the Challengersminimum EUAC, then replace immediately.

If the Defenders EUAC is lower than theChallengers minimum EUAC, then the Defenderwill 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 theDefender.

The first cost of the Challenger should include thepurchase price, sales tax, installation cost, andother items that occur initially on a one-time basisif the Challenger is selected.

The Defenders potential market (or salvage) value

should not be subtracted from the Challengersfirst cost.

Defining First Costs ofDefender and Challenger


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Defender: SK-30, purchased 2 years ago for $1600, wasdepreciated with SL using 4-year life and 0 salvage.

Challenger: EL-40, $1200 with a trade-in allowance of $350for the SK-30; $1050 without a trade-in.

Current price for new SK-30 is $995.

Example 13-8Defining Defender First Cost

Defender: SK-30, Original cost: $1600 (Basis for SL depreciation) Present cost: $995 (Irrelevant)

Book value: $800 (Useful in determining depreciationrecapture or loss)

Trade-in value: $350 (Irrelevant) Market value: $200 (First cost assigned to Defender)


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Circumstances where Repeatability Assumption maynot apply:

When there is a specific study period instead of anindefinite need for the asset

When future Challengers are not assumed to beidentical to the current best Challenger

Repeatability AssumptionNot Acceptable


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A Closer Look at Future Challengers

It seems likely that futurechallengers will be betterthan the present Challenger

The prospect of better

future challengers maymake it more desirable toretain the Defender and toreject the presentChallenger

Selecting the current bestChallenger could be risky if1) high cost and/or 2) longeconomic life 0 1 2 3 4

Year

EUACatEcono

micLife

PresentChallenger

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

YearMarketValue

BookValue

RecapturedDepr. or

Loss Tax

After-TaxMarketValue

0 $25,000 $25,000 $25,000

118,000

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 2,400

6 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

MarketValue

CapitalRecovery

O&M+Ins.

TaxableIncome Tax

After-TaxMarginal

Cost

0 $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 8,740

5 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

YearMarketValue

MACRSDepr.

BookValue

RecapturedDepr. or

Loss Tax

After-TaxMarketValue

0 $100,000 $100,000 $100,0001 50,000 $14,290 85,710 -$35,710 -$14,284 64,284

2 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 20,356

7 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-taxMarketValue

CapitalRecovery O&M

TaxableIncome Tax

After-TaxMarginal

Cost EUAC0 $100,0001 64,284 $41,716 $10,000 -$24,290 -$9,716 $42,000 $42000

2 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

)N%,8,FA)(250MV()N%,8,PA)(400999,19(CR NN

)N%,8,PA]()j%,8,FP()M&O([)M&O(EUACN

1j

jN

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