copyright oxford university press 2009 chapter 13 replacement analysis

Copyright Oxford University Press 2009

Chapter 13Replacement Analysis


• 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


• 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


• 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


• 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


• 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


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


• 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


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


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


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


• 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


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%)


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%)


• 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


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


• 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


• 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



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


1j j


Example 13-6Finding Minimum Cost Life

YearMarket Value


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



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


1j j


• 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


• 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


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)


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


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


• Ordinary taxes• Gains and losses due to asset disposal

After-Tax Replacement Analysis


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


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


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


Example 13-10After-Tax Minimum Cost Life

Yr.

After-tax Market Value


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


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


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

copyright oxford university press 2009 chapter 13 replacement analysis

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