Replacement Analysis

Replacement Analysis

$Learning Objectives$

Distinguish defender and challenger alternatives in an asset replacement decision.
Use the defender's current market value as an opportunity cost rather than its historical purchase price.
Compare replacement alternatives using forward-looking equivalent annual costs or another common economic basis.
Define economic life as the service duration that minimizes equivalent annual cost or maximizes equivalent annual worth under stated forecasts.
Apply marginal keep-one-more-period logic without allowing sunk costs to influence the decision.

$Defender$

The defender is the currently owned or installed asset being considered for continued use. Its relevant time-zero economic value is generally the current opportunity cost of keeping it, commonly represented by its current market value.

$Challenger$

The challenger is a feasible replacement alternative available for acquisition now or at a modeled future date.

$Sunk Acquisition Cost$

The defender's original purchase cost is sunk when it cannot be changed by the current decision. It should not be charged again as the defender's present cost merely because it appears in historical records.

$Opportunity Cost of Retention$

The opportunity cost of retaining the defender is the value forgone by not taking the best feasible disposition action now, such as selling the asset at its current market value.

Equivalent Annual Cost of an Asset

Annualizes first/opportunity cost, salvage, and uniform operating cost over a stated life.

EAC=P(A/P,i,n)-S(A/F,i,n)+A_{\text{O\&M}}

Variables

Symbol	Description	Unit
$EAC$	Equivalent annual cost	-
$P$	First cost for challenger or current opportunity cost for defender	-
$S$	Expected market/salvage value at end of the modeled life	-
$A_{\text{O\&M}}$	Uniform annual operating and maintenance cost	-
$i$	MARR	-
$n$	Modeled service life	-

$Interactive Defender-Challenger and Economic-Life Laboratory$

Model current defender opportunity cost, first-year O&M, O&M escalation, expected market-value decline, and the maximum retention horizon. The laboratory recomputes EAC for every candidate horizon so the minimum-EAC year is visible instead of requiring a guessed life.

MARR10.00%

Defender — current asset

Current market value / opportunity costPHPO&M cost in first yearPHP/year

Annual O&M growth8.00%

Expected market value after year 1PHP

Annual market-value decline18.00%

Maximum evaluated retention life6 years

Challenger — proposed replacement

First costPHPO&M cost in first yearPHP/year

Annual O&M growth5.00%

Expected market value after year 1PHP

Annual market-value decline14.00%

Maximum evaluated retention life10 years

Defender economic life

5 years

₱892,814 minimum modeled EAC. The EAC rises again within the evaluated horizon, supporting an interior economic-life estimate.

Challenger minimum within horizon

10 years

₱759,710 minimum modeled EAC. The minimum occurs at the search boundary; extend the horizon before claiming the true economic life.

Forward-looking replacement decision

Replace with the challenger

Difference between current minimum modeled annual costs: ₱133,103. Because at least one minimum is a boundary result, extend that horizon before treating the comparison as a final economic-life conclusion.

Defender retention horizon

Keep	Year O&M	Terminal value	EAC
1 yr	₱520,000	₱1,050,000	₱1,010,000
2 yrs	₱561,600	₱861,000	₱936,476
3 yrs	₱606,528	₱706,020	₱909,628
4 yrs	₱655,050	₱578,936	₱897,369
5 yrs · minimum	₱707,454	₱474,728	₱892,814
6 yrs	₱764,051	₱389,277	₱893,353

Challenger ownership horizon

Keep	Year O&M	Terminal value	EAC
1 yr	₱230,000	₱2,450,000	₱1,300,000
2 yrs	₱241,500	₱2,107,000	₱1,075,952
3 yrs	₱253,575	₱1,812,020	₱980,273
4 yrs	₱266,254	₱1,558,337	₱920,128
5 yrs	₱279,566	₱1,340,170	₱876,466
6 yrs	₱293,545	₱1,152,546	₱842,602
7 yrs	₱308,222	₱991,190	₱815,432
8 yrs	₱323,633	₱852,423	₱793,229
9 yrs	₱339,815	₱733,084	₱774,905
10 yrs · minimum	₱356,805	₱630,452	₱759,710

The market-value and O&M trajectories are assumptions for scenario analysis, not forecasts guaranteed by the model. Historical acquisition cost is sunk; current market value is the relevant defender opportunity cost.

MARR9.00%

Alternative A

First costPHPAnnual net cash flowPHP/yearTerminal salvagePHP

Analysis life7 years

Alternative B

First costPHPAnnual net cash flowPHP/yearTerminal salvagePHP

Analysis life10 years

Alternative	Life	PW at time 0	FW at own terminal year	AW
A	7 years	₱1,248,471	₱2,282,254	₱248,059
B	10 years	₱2,854,873	₱6,758,524	₱444,847

Annual-worth preference

Alternative B

This unequal-life AW comparison assumes continuing service and a defensible replacement/repeatability basis for each alternative.

Equivalent-method cross-check

Raw own-life PW not ranked

Present worths shown over different terminal lives are descriptive values, not a valid mutually exclusive ranking unless a fixed common study period or explicit repeatability model is imposed.

A decision sign

Nonnegative AW

For an independent revenue project, nonnegative AW clears the economic screen at the stated MARR.

B decision sign

Nonnegative AW

Equivalent worth methods preserve accept/reject sign when the same cash flow, rate, and life are used.

Do not use a least-common-multiple life mechanically unless repeated replacement with comparable cost, performance, and salvage is a reasonable model. If repeatability is not defensible, define a fixed study period and model terminal values explicitly.

$Economic Life$

Economic life is the number of years an asset should be retained under the modeled forecasts to minimize its equivalent annual cost, or maximize annual worth, before replacement or disposal.

$Economic Life vs Physical Life$

Physical life is how long an asset can function. Economic life is how long it is economically attractive to retain under forecasts of market value, O&M, productivity, downtime, and capital cost. An asset may be physically usable beyond its economic life.

$Economic Life Is a Search Result, Not an Assumed Input$

When O&M and market value vary with age, calculate equivalent annual cost for each feasible retention horizon and identify the minimum. If the minimum occurs at the longest horizon evaluated, extend the search before claiming that the true economic life has been found; the apparent optimum may be only a boundary result.

$Marginal Cost of Retention$

The marginal cost of keeping an asset for one additional period includes the decline in its market value over that period plus the period's operating, maintenance, downtime, and other incremental costs, adjusted to the chosen time-value basis.

One-Year Marginal Ownership Cost at the Start of a Year

A common one-period expression comparing current market value MV_t with expected next-year market value MV_{t+1} and next-year O&M.

MC_{t\to t+1}=MV_t(1+i)-MV_{t+1}+C_{t+1}

Variables

Symbol	Description	Unit
$MC_{t\to t+1}$	End-of-next-year equivalent marginal cost of retaining for one more year	-
$MV_t$	Current market value at start of the year	-
$MV_{t+1}$	Expected market value one year later	-
$C_{t+1}$	Expected O&M and other incremental cost during the next year	-
$i$	MARR for the year	-

$Use Forward-Looking Values Only$

Replacement analysis starts now. Historical purchase price, accumulated depreciation, and past repair cost may explain records but do not become new future cash flows unless they affect current taxes, contract obligations, or another explicit future consequence.

$Book Value Is Not Defender Opportunity Cost$

Do not substitute book value for market value unless the problem explicitly makes them equal. Book value is accounting-derived; current market value represents the economic opportunity associated with disposition.

$Replacement Analysis Workflow$

STEP-BY-STEP

Define the required service and feasible defender/challenger options.
Estimate the defender's current market value and future O&M/market values.
Exclude sunk historical acquisition cost from the forward-looking comparison.
Estimate challenger first cost, O&M, salvage, and life.
Use a common MARR and an appropriate PW/AW/EAC study basis.
Calculate EAC over each feasible retention horizon when economic life is not already established.
Determine the economically preferred current action.
If timing of replacement is the question, compare economic-life and marginal keep/replace conditions over future years.
Perform sensitivity analysis on market value, downtime, maintenance escalation, and life assumptions.

Key Takeaways

The current asset is the defender; proposed replacements are challengers.
Defender current market value is usually an opportunity cost of retention; original purchase cost is sunk.
EAC provides a common annual basis for cost alternatives under stated life and replacement assumptions.
Economic life differs from physical life and should be found by evaluating feasible retention horizons under the forecasts.
A minimum at the end of the evaluated horizon is a boundary result that may require a wider search.
Marginal retention cost supports keep-one-more-year decisions.
Book value, market value, and historical cost must remain distinct in replacement analysis.