Sunk cost, ESL, replacement strategy from AEC table

Sunk cost

A sunk cost is a cost that has already been incurred and cannot be recovered whatever is decided now, for example the book value of an old machine above its present market value. It must be ignored in replacement analysis; only the present market value of the defender and future cash flows matter. Treating the sunk cost as part of the defender's investment would wrongly favour keeping the old asset.

Economic life

Economic life (economic service life) is the period of service that minimises the asset's equivalent annual cost (AEC). Before it, capital recovery cost is falling faster than operating cost rises; after it, rising operating and maintenance cost dominates.

Reasons for replacement

• Physical impairment: wear and tear raises maintenance cost and reduces output or quality.
• Obsolescence: a new machine gives the same service at lower cost or better quality.
• Inadequacy: capacity is no longer enough for the demand.
• Requirement changes: changes in product, law or safety standards.
• Financial reasons: lease or buy decisions, tax effects, or the risk of high repair bills.

Strategy from the AEC table (MARR = 10%, 8-year horizon)

From the table: defender minimum AEC = 5,200 at n = 2 (ESL = 2 years); challenger minimum AEC = 5,600 at n = 4 (ESL = 4 years). Because the defender's minimum is lower than the challenger's, keep it at least until year 2. Since the horizon is 8 years and tables stop at 6, each plan is the defender for n years followed by challengers covering the remaining years. PW of a plan = AEC_D(n)(P/A,10%,n) + AEC_C(m)(P/A,10%,m)(P/F,10%,n) (+ the same for a second challenger, if used).

Worked example, defender 2 years then challenger 3 + 3 years:

PW = 5,200(P/A,10%,2) + [5,700(P/A,10%,3)](P/F,10%,2) + [5,700(P/A,10%,3)](P/F,10%,5)
   = 5,200(1.7355) + 5,700(2.4869)(0.8264) + 5,700(2.4869)(0.6209)
   = 9,025 + 11,714 + 8,802 = 29,541

The lowest PW is Rs 29,541 (equivalent to Rs 5,537 per year).

Answer: Keep the defender for 2 years (its economic life), then replace it by the challenger and use challengers (each replaced after 3 years) for the remaining 6 years. The three plans "defender 1 yr, then challengers 4 + 3", "defender 3 yr, then challenger 5" and "challenger replaced after 4 yr each" are within about 1% of this, so the choice is not very sensitive.