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Repeatability, two mutually exclusive options
Short answer
Using repeatability and AW at 12% MARR: Option I AW = Rs. 628/yr, Option II AW = Rs. 690/yr. Both positive; Option II has higher annual worth. Recommend Option II.
Consider the following two mutually exclusive alternatives, recommend the best alternative using repeatability assumptions. MARR = 12%
| Option-I (Rs.) | Option-II (Rs.) | |
|---|---|---|
| Initial Cost | 20,000 | 30,000 |
| Annual receipts | 10,000 | 14,000 |
| Annual cost | 5,000 | 8,000 |
| Salvage Value | 4000 | 0 |
| Useful Life | 6 years | 10 years |
Repeatability assumption: each option is repeated with identical cash flows, so the unequal lives (6 and 10 years) are compared by annual worth (AW) over one cycle of each. MARR = 12%.
Option I (N = 6)
(A/P, 12%, 6) = 0.2432, (A/F, 12%, 6) = 0.1232 AW = -20,000(0.2432) + (10,000 - 5,000) + 4,000(0.1232) = -4,865 + 5,000 + 493 = Rs. 628 per year
Option II (N = 10)
(A/P, 12%, 10) = 0.1770 AW = -30,000(0.1770) + (14,000 - 8,000) + 0 = -5,310 + 6,000 = Rs. 690 per year
| Option | Life | AW (Rs./yr) |
|---|---|---|
| I | 6 | 628 |
| II | 10 | 690 |
Both are positive (acceptable), and Option II has the larger AW.
Answer: Recommend Option II, which gives about Rs. 62 more annual worth than Option I.
✓ Answer checked by Claude Opus 5.5 (high effort)
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