CHAPTER 9

CHAPTER 9

Replacement Analysis

ObjectivesObjectives

• To discuss the considerations To discuss the considerations involved in replacement analysisinvolved in replacement analysis

• To address the key question of To address the key question of whether an asset should be kept one whether an asset should be kept one or more years or immediately or more years or immediately replaced it with the best available replaced it with the best available alternativealternative

Reasons for replacement analysisReasons for replacement analysis

• Physical Impairment (Deterioration)Physical Impairment (Deterioration)• Altered RequirementsAltered Requirements• TechnologyTechnology• FinancingFinancing

Physical Impairment Physical Impairment (Deterioration)(Deterioration)

• Efficiency loss resulting from continued useEfficiency loss resulting from continued use– agingaging

• Increased routine and corrective maintenance Increased routine and corrective maintenance costscosts

• Greater energy requirementsGreater energy requirements

Altered RequirementsAltered Requirements

• Significant change in demand for related Significant change in demand for related products or servicesproducts or services

• Significant change in the composition or Significant change in the composition or design of associated products or servicesdesign of associated products or services

Technology and FinancingTechnology and Financing• TECHNOLOGY TECHNOLOGY

– Technological changes typically reduce cost Technological changes typically reduce cost per unit and improve quality of outputper unit and improve quality of output

– Results in earlier replacement of existing Results in earlier replacement of existing assets with improved assetsassets with improved assets

• FINANCINGFINANCING– May involve income tax considerations May involve income tax considerations

(depreciation and after-tax analysis) EG: (depreciation and after-tax analysis) EG: rental of assets may become more attractive rental of assets may become more attractive than ownershipthan ownership

Terminology• Defender Asset

– Currently installed asset

• Challenger Asset– The potential replacement or “challenging” asset– Under consideration to replace the defender asset

• Together Constitute mutually exclusive alternatives– Select one and reject the other., the Defender and

Challenger

Investment Concerns Defender• While it may seem strange to charge an investment cost

for keeping one’s own asset (the defender), this is what must occur

• Keeping the defender is not free! Why?• Because the firm is giving up the opportunity to receive

a possible cash flow from selling the current defender!• The appropriate investment cost to assign to the

defender asset is:– The current fair market value of the defender at the time the

replacement decision is being examined

The Sunk Cost Trap

• The past investment in the defender is “sunk” and not totally relevant to the analysis.

• A “sunk” cost is any cost that has occurred in the past and cannot be changed or altered by a current decision

• Only present and future cash flows should be considered in replacement studies

• Sunk costs are irrelevant to replacement decisions, except to extent they affect income taxes

• When tax considerations are involved, sunk costs must be included in study

Outsider ViewpointThe total investment in the defender is The total investment in the defender is the the opportunity cost of not selling the opportunity cost of not selling the existing asset for its current MVexisting asset for its current MV, , plus plus the cost of upgradingthe cost of upgrading to be competitive to be competitive with best available challengerwith best available challenger

Investment Concerns-Challenger• The total investment (Pchallenger) required in a new

(challenger) asset that will possibly replace the current defender

• Known with a fair amount of certainty• Often a trade-in value is offered by a vendor to

take in the defender with a credit on the purchase towards the challenger

Economic Service Life Economic life of an asset minimizes equivalent uniform

annual cost of owning and operating an asset• Economic life is often shorter than useful or physical life• Number of years for an alternative for which the AW or

EUAC is Minimum;– AW or EUAC is an analysis approach for replacement– Implies that a period-by-period analysis is performed;– Computing the AW for 1 year; then 2 years; …until a minimum

cost time period is found;– Performed manually or by spreadsheet.– Termed “The minimum cost life”

• Estimate the ESL for the challenger and defender.

ESL – General Format• Compute:

– AW(i%)t =

– Capital Recovery– AW of operating costs– Salvage values may be incorporated into the capital

recovery term.– Do this for n = 1, then n = 2, then n = … and observe

the min. cost “n” value.• The minimum cost life is that value of “n” that yields the

lowest annual cost over the range of “n” values applied.

Typical ESL Plot

Min. Total AW of costs life

Example• Defender Asset: 3 years old now, Market value now

$13,000, 5-year study period assumed, Requires estimates of the future salvage values and annual operating costs for the 5-year period.

• Estimated Future Market Values and AOC’s: (Assume the interest rate is 10% per year)MktVt AOCt

– t = 1: $9,000 $-2,500– t = 2: $8,000 -2,700– t = 3: $6,000 -3,000– t = 4: $2,000 -3,500– t = 5: $0 -4,500

Example: Find the ESL• Period-by-period analysis

– AW(10%)1 = (-$13,000)(A/P,10%,1) + $9,000(A/F,10%,1) –2,500= -$7,800

– AW(10%)2 = (-13,000)(A/P,10%,2) + 8,000(A/F,10%,2) -[2,500(P/F,10%,1) + 2,700(P/F,10%,2)](A/P,10%,2) = -$6,276/yr

– AW(10%)3 = (-13,000)(A/P,10%,3) +6,000(A/F,10%,3) -[2500(P/F,10%,1) + 2,700(P/F,10%,2) + 3,000(P/F,10%,3](A/P,10%,3) = -$6,132/yr

– AW(10%)4 = -$6,556/yr

– AW(10%)5= -$6,579/yr

Marginal Cost Approach• Marginal Costs are year-by-year estimates of the costs

to own the asset, and operate the asset for the current year in question

• Three Components of Marginal Costs:1. Cost of ownership (loss in Mkt. Value/yr);2. Foregone interest of Mkt. Value at beginning of the year;3. AOC for each year

Marginal Cost Analysis• Compute the marginal costs per year• Find their equivalent annual worth• AW of marginal costs = total AW of costs• Can perform either a ESL analysis or a Marginal Cost

analysis when yearly Mkt. Values are estimated• Same result!• The “n” value and the associated AWn are then used in

the replacement analysis

Marginal Cost Format: Example

Loss in MV Lost Interest Est. Year MV for Year on MV for Year AOC/Year

1 $9,000 -$4,000.00 -$1,300.00 -$2,500.002 $8,000 -$1,000.00 -$900.00 -$2,700.003 $6,000 -$2,000.00 -$800.00 -$3,000.004 $2,000 -$4,000.00 -$600.00 -$3,500.005 $0 -$2,000.00 -$200.00 -$4,500.00

Marginal Cost AW of time For the Year Marginal Costs

1 -$7,800.00 -$7,8002 -$4,600.00 -$6,2763 -$5,800.00 -$6,1324 -$8,100.00 -$6,5565 -$6,700.00 -$6,580

Min. Cost Life

Setting Up for a Replacement Analysis• Conduct the ESL for the defender and the challenger(s);• Form the following alternatives:

– Challenger Alternative (C): AWC for nC yrs;

– Defender Alternative: (D): AWD for nD yrs.

• “n” Not Known– For “n” of a defender or challenger that is not known or

assumed:– Compute the ESL for a range of “n” values where n = {1, then

2, …, then K};– From this period-by-period analysis, determine the min. cost

life and the associated AW for that life

Replacement: After-Tax• To properly evaluate a replacement- type problem, one

should always use an after-tax approach.• Elements that can alter the ATCF vs. a BTCF analysis

for replacement– Depreciation and the tax savings– Disposal implications of the defender

• Recaptured Depreciation, or• Loss on Disposal• Half-year convention for disposal during the life of the defender if it is

not fully recovered

Example• Existing pump A (defender)

– Capital investment when purchased 5 years ago -$17,000– Class life (SL half-year convention rule) 9 years– Annual expenses : O&M and Taxes and insurance -$5,340– Present market value $ 750– Estimated market value at the end of 9 additional years $ 200

• Replacement pump B (challenger)– Capital investment -$16,000– Class life 9 years– MACRS (GDS) property class 5 years– Estimated market value at the end of 9 years $3,200– Annual expenses: O&M and Taxes and insurance $3,320

• Effective income tax rate = 40%, MARR (before taxes) = 10%, MARR (after taxes)= 6%

• Use (a) a before-tax analysis, and then (b) an after-tax replacement analysis

Solution• Before-tax analysis

– AWA (10%) = -$5,340 – 750 (A/P, 10%, 9) + 200 (A/F, 10%, 9) = -$5,455

– AWB (10%)= -$3,320 – 16,000 (A/P, 10%, 9) + 3200 (A/F, 10%, 9) = -$5,862

• Decision: the defender should be kept at least one more year

Solution• After-tax Analysis for defenderEOY BTCF Dep. TI Taxes ATCF0 -750 1889 7,750* -3100 -38501 -5340 1889 -7229 +2892 -24482 -5340 1889 -7229 +2892 -24483 -5340 1889 -7229 +2892 -24484 -5340 1889 -7229 +2892 -24485 -5340 945 -6285 +2514 -28266 -5340 0 -5340 +2136 -32047 -5340 0 -5340 +2136 -32048 -5340 0 -5340 +2136 -32049 -5340 0 -5340 +2136 -32049 200 200 -80 120• *Gain or Loss on disposal (if sold now) =MV now – BV now (if sold now)

• BV now (if sold now) = 17,000 – [945+4(1889)]=8500• Loss on disposal (if sold now) = +750-8500 =-7,750• Since we are keeping the defender, we have the reverse effect on taxable income, an

increase of 7750 due to opportunity foregone

After-tax Analysis for ChallengerEOY BTCF Dep. TI Taxes ATCF0 -16,000 none -$16,0001 -3,320 3200 -6520 2608 - 7122 -3320 5120 -8440 3376 + 563 -3320 3072 -6392 2557 - 7634 -3320 1843 -5163 2065 - 12555 -3320 1843 -5163 2065 - 12556 -3320 922 -4242 1697 - 16237 -3320 0 -3320 1328 - 19928 -3320 0 -3320 1328 - 19929 -3320 0 -3320 1328 - 19929 3200 - 3200 -1280 + 1920• AW (6%) of pump A = -3,332 • AW (6%) of pump B = -3,375• Pump... is economically preferable

Another Example• Defender:

– Purchased 3 years ago for $600,000– Now outdated due to advancing technology– Assume classical straight line has been applied. (In reality, MACRS

would be applied.) with a 8-year recovery life– AOC: $100,000/year and worth $400,000 now!

• Challenger:– First Cost: $1,000,000– Assume straight-line depreciation with a 5- year life – Annual Operating costs: $15,000/year– Assume a “0” salvage value at the end of 5 years

• Other Parameters:– BT discount rate: 10%, AT discount rate: 7%, and effective tax rate:

34%

Economic Service Life Analysis• Assume further that a ESL analysis has been conducted

and the following information is available:– For the Defender: ESL from now is 5 more years.– For the Challenger: ESL is 5 years.– Assume a “0” salvage value for both alternatives applies

Example Summary• If the defender is retained:

• BTCF annual cost: $205,520/year

• ATCF annual cost: $138,056/year

• If the challenger is purchased:• BTCF annual cost: $278,800/year

• ATCF annual cost: $187,864/year

• Typically, MACRS would be used;– For the defender, only a ½ year of recovery would be permitted

– Thus, all ATCF values would be different than what has been shown