- 2072 Asoj · 4+4+4 marks
Replacement strategy for four-year need
Short answer
Existing machine AEC for 4 years is Rs 6,352 (ESL 1 year, AEC Rs 6,000). New machine AEC for 4 years is Rs 7,582 (ESL 4 years). Best strategy: keep the existing machine for the entire 4 years, since its AEC is lower than any plan involving the new machine.
An existing machine has market value of Rs. 10000 and decreases by Rs. 2000 per year. Its operating cost is Rs. 2500 in year 1 and increases by 20% each year for 4 years. New machine costs Rs. 20000 now and its market value will decrease by Rs. 20% per year for 4 years. Operating cost is Rs. 1500 in first year and increase by 30% each year. Calculate equivalent uniform annual cost of both existing and new machines. MARR = 15%. Formulate the best replacement strategy if we need the machine for four years only.
AEC(n) = [P + Σ O&M_k (P/F,15%,k) − MV_n (P/F,15%,n)] (A/P,15%,n), with P = 10,000 for the existing machine (its present market value) and 20,000 for the new machine.
Existing machine (MV_n = 10,000 − 2,000n; O&M = 2,500(1.2)^(k−1))
| n | MV_n | O&M in year n | PW of cost | AEC(n) |
|---|---|---|---|---|
| 1 | 8,000 | 2,500 | 5,217 | 6,000 |
| 2 | 6,000 | 3,000 | 9,905 | 6,093 |
| 3 | 4,000 | 3,600 | 14,179 | 6,210 |
| 4 | 2,000 | 4,320 | 18,136 | 6,352 |
New machine (MV_n = 20,000(0.8)^n; O&M = 1,500(1.3)^(k−1))
| n | MV_n | O&M in year n | PW of cost | AEC(n) |
|---|---|---|---|---|
| 1 | 16,000 | 1,500 | 7,391 | 8,500 |
| 2 | 12,800 | 1,950 | 13,100 | 8,058 |
| 3 | 10,240 | 2,535 | 17,713 | 7,758 |
| 4 | 8,192 | 3,296 | 21,646 | 7,582 |
Example (existing, n = 2): PW = 10,000 + 2,500(0.8696) + 3,000(0.7561) − 6,000(0.7561) = 9,905; AEC = 9,905(A/P,15%,2 = 0.61512) = 6,093.
- Existing machine: minimum AEC at n = 1, so ESL = 1 year (AEC = 6,000).
- New machine: AEC keeps falling to n = 4, so ESL = 4 years (AEC = 7,582).
Best replacement strategy for a 4-year need
The need is for exactly 4 years, so compare "keep the existing machine for n years, then use the new machine for the remaining 4 − n years". Each plan is costed as one PW at 15% and then converted to a 4-year AEC.
| Defender | Then | PW of cost |
|---|---|---|
| Keep defender 4 yr | - | 18,136 |
| Keep defender 3 yr | new for 1 yr | 19,039 |
| Keep defender 2 yr | new for 2 yr | 19,811 |
| Keep defender 1 yr | new for 3 yr | 20,620 |
| Replace now | new for 4 yr | 21,646 |
Check, plan "keep 4 years": PW = 18,136; AEC = 6,352.
Answer: Keep the existing machine for the full 4 years and do not buy the new one. Its AEC is Rs 6,352 per year for the 4 years, lower than every strategy that buys the new machine (the best of which costs Rs 6,669 per year and a new machine kept 4 years costs Rs 7,582 per year).
✓ Answer checked by Claude Opus 5.5 (high effort)
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