- 2065 Kartik · 8 marks
Find required annual receipts A
Short answer
Required A ≈ Rs 209,316/year at MARR 10% by setting present worth to zero. Benefits are uniform A plus gradient (base Rs 70,000, G=Rs 10,000), O&M Rs 50,000/year, salvage Rs 1,00,000 at year 5.
Find the required annual receipts 'A' for the following investment proposal: Initial investment = Rs. 10,00,000 Salvage value = Rs. 1,00,000 O & M expenses/year = Rs. 50,000
| End of year | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Benefits | A+70,000 | A+80,000 | A+90,000 | A+100,000 | A+110,000 |
The MARR is not given; assumption: MARR = 10% per year. "Required A" means the smallest A that makes the project just earn the MARR, i.e. PW = 0.
yr 0: -10,00,000
yr 1..5: benefit A + 70,000, A + 80,000, A + 90,000, A + 1,00,000, A + 1,10,000
O&M -50,000 every year
yr 5: salvage +1,00,000
The benefits are a uniform A plus a gradient series with base 70,000 and G = 10,000.
Factors at 10%, 5 years: (P/A) = 3.7908, (P/G) = 6.8618, (P/F) = 0.6209
Equation
PW = 0:
−10,00,000 + A (P/A) + 70,000 (P/A) + 10,000 (P/G) − 50,000 (P/A) + 1,00,000 (P/F) = 0
- A × 3.7908 = 10,00,000 − 70,000 × 3.7908 − 10,000 × 6.8618 + 50,000 × 3.7908 − 1,00,000 × 0.6209
- A × 3.7908 = 10,00,000 − 265,355 − 68,618 + 189,539 − 62,092
- A × 3.7908 = 793,474
- A = 793,474 / 3.7908
Answer: A ≈ Rs 209,316 per year at MARR = 10%. Each year's benefit is then A + 70,000, A + 80,000 and so on.
Sensitivity: the required A changes with the MARR as follows.
| MARR | 8% | 10% | 12% | 15% |
|---|---|---|---|---|
| Required A (Rs) | 194,946 | 209,316 | 223,923 | 246,256 |
✓ Answer checked by Claude Opus 5.5 (high effort)
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