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Define ESL; find ESL of 50,000 asset

Short answer

Economic service life is the ownership period minimizing equivalent annual cost (capital recovery plus equivalent annual operating cost). For the asset with Rs 50,000 investment, operating costs starting at Rs 10,000 increasing 15% yearly, salvage declining 20% yearly, and 15% MARR, the ESL is 5 years with minimum AEC of Rs 25,456.

Define economic service life of an asset. From the following information find the economic service life of an asset.

Initial investment (Rs.)50,000
Annual operating cost (Rs.)10,000 for the first year and increasing by 15% over the previous year
Salvage value (Rs.)Declining each year by 20% from the previous year's salvage value
Useful life (year)7
MARR15%

Economic service life

The economic service life (ESL) of an asset is the number of years of ownership that gives the lowest equivalent annual cost (AEC), where AEC = capital recovery cost (investment less salvage) + equivalent annual operating cost. It differs from physical life and is the right period to use when evaluating replacements.

Calculation

P = 50,000; O&M in year k = 10,000(1.15)^(k−1); MV_n = 50,000(0.8)^n; MARR = 15%. AEC(n) = [50,000 + Σ O&M_k (P/F,15%,k) − MV_n (P/F,15%,n)] (A/P,15%,n)

nMV_nO&M year nPW of costAEC(n)
140,00010,00023,91327,500
232,00011,50043,19526,570
325,60013,22559,25525,952
420,48015,20973,07325,595
516,38417,49085,33325,456
613,10720,11496,50725,501
710,48623,131106,92825,701

Example, n = 3: PW = 50,000 + 10,000(0.8696) + 11,500(0.7561) + 13,225(0.6575) − 25,600(0.6575) = 59,255; AEC = 59,255(0.43798) = 25,952.

AEC falls until n = 5 (Rs 25,456) and then rises.

Answer: Economic service life = 5 years, with minimum AEC ≈ Rs 25,456 per year.

✓ Answer checked by Claude Opus 5.5 (high effort)

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