- 2070 Magh · 8 marks
Break-even hours for two pumps
Short answer
Fixed costs: Khasa Rs 200,252, Sarvo Rs 351,704; energy cost/hour: Rs 1,492 and Rs 1,326.22. Equating: 200252+1492h = 351704+1326.22h gives break-even 914 hours/year. At 5h/day (1,825 h) Sarvo saves ~Rs 1.51 lakh/year and is recommended.
Calculate break-even hours of operation per year to become cost equal and recommend the economic pump if it is to be operated 5 hours daily at full load.
| KHASA Pump | SARVO Pump | |
|---|---|---|
| Capacity | 100 hp | 100 hp |
| Purchase cost (Rs.) | 5,00,000 | 10,00,000 |
| Tax per year (Rs.) | 10,000 | 15,000 |
| Maintenance cost per year (Rs.) | 36,500 | 29,200 |
| Efficiency | 80% | 90% |
| Life, year | 5 | 5 |
| Salvage value | 20% of purchase cost for both | |
| MARR | 20% per year | |
| Electricity cost | Rs. 16/kwh |
Approach
Compare the annual cost of each pump as a function of operating hours h per year: Annual cost = fixed annual cost + (energy cost per hour) × h. Set them equal to get the break-even hours.
Assumptions
1 hp = 0.746 kW; the motor draws power = rated output ÷ efficiency (full load); interest rate = MARR = 20%; capital cost is converted to an annual figure by capital recovery with salvage.
Capital recovery (CR) = (P − S)(A/P, 20%, 5) + S(0.20), where (A/P, 20%, 5) = 0.33438
Annual fixed cost
| Item | KHASA | SARVO |
|---|---|---|
| P (Rs) | 500,000 | 1,000,000 |
| S = 20% of P (Rs) | 100,000 | 200,000 |
| CR (Rs/yr) | 400,000×0.33438 + 100,000×0.2 = 153,752 | 800,000×0.33438 + 200,000×0.2 = 307,504 |
| Tax (Rs/yr) | 10,000 | 15,000 |
| Maintenance (Rs/yr) | 36,500 | 29,200 |
| Fixed cost (Rs/yr) | 200,252 | 351,704 |
Energy cost per hour
- KHASA: 100 × 0.746 / 0.80 = 93.25 kW; × Rs 16 = Rs 1,492 per hour
- SARVO: 100 × 0.746 / 0.90 = 82.89 kW; × Rs 16 = Rs 1,326.22 per hour
Break-even hours
200,252 + 1,492 h = 351,704 + 1,326.22 h 165.78 h = 151,452 h = 913.6 hours per year
Decision for 5 hours daily
Hours = 5 × 365 = 1,825 h per year (> 913.6 h).
- KHASA: 200,252 + 1,492 × 1,825 = Rs 2,923,152 per year
- SARVO: 351,704 + 1,326.22 × 1,825 = Rs 2,772,059 per year
Answer: Break-even = about 914 hours per year. At 1,825 hours the SARVO pump is cheaper (Rs 2.77 million vs 2.92 million per year, saving about Rs 151,000), so SARVO is recommended. SARVO is better whenever it runs more than about 914 hours per year.
✓ Answer checked by Claude Opus 5.5 (high effort)
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