--- title: "Sensitivity of PW to investment and MARR" subject: "Engineering Economics" chapter: 6 key: "semester_6/engineering_economics:sensitivity-investment-marr-10-50" source: https://www.bctengineer.com/q/semester_6/engineering_economics/sensitivity-investment-marr-10-50 site: BCT Engineering --- # Sensitivity of PW to investment and MARR Engineering Economics · Chapter 6: Risk Analysis - Asked in: 2076 Shrawan, 6 marks; 2071 Bhadra, 6 marks (asked 2 times) - Video: [Sensitivity Analysis using PW method ||Sensitivity Graph |Board Exam Solution in NEPALI Economics](https://www.youtube.com/watch?v=K1f9_a5tE7E) — OPengineer - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/engineering_economics/sensitivity-investment-marr-10-50 - Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-6 ## Question Perform sensitivity analysis of the following project over a range of 10 to 50 percent in (i) initial investment and (ii) MARR using PW formulation. Assume Sv = 0. Draw sensitivity diagram also. | Initial Investment | Rs 100000 | |---|---| | Annual Income | Rs 40000 | | Useful Life | 6 Years | | MARR | 10% | ## Short answer Base PW = Rs 74,210. Over ±50% range, PW remains positive for both parameters. A 10% change in initial investment shifts PW by Rs 10,000, while a 10% MARR change shifts it by ~Rs 5,000. The project is more sensitive to initial investment than to MARR. ## Answer Base case: I = 1,00,000; A = 40,000 per year; N = 6; S = 0; MARR = 10%. PW = −I + A(P/A, i, 6). Base: (P/A,10%,6) = 4.3553, so PW₀ = −100,000 + 40,000(4.3553) = **Rs 74,210**. Vary one parameter at a time, with the other held at its base value. #### (i) Initial investment: PW = −I(1 + x) + 40,000(4.3553) #### (ii) MARR: PW = −100,000 + 40,000(P/A, 10%(1 + x), 6) (e.g. +50% gives i = 15%: (P/A,15%,6) = 3.7845, PW = −100,000 + 40,000(3.7845) = 51,379) | Change | Investment | PW (i) | MARR | PW (ii) | |---|---|---|---|---| | -50% | 50,000 | 124,210 | 5.0% | 103,028 | | -40% | 60,000 | 114,210 | 6.0% | 96,693 | | -30% | 70,000 | 104,210 | 7.0% | 90,662 | | -20% | 80,000 | 94,210 | 8.0% | 84,915 | | -10% | 90,000 | 84,210 | 9.0% | 79,437 | | +0% | 100,000 | 74,210 | 10.0% | 74,210 | | +10% | 110,000 | 64,210 | 11.0% | 69,222 | | +20% | 120,000 | 54,210 | 12.0% | 64,456 | | +30% | 130,000 | 44,210 | 13.0% | 59,902 | | +40% | 140,000 | 34,210 | 14.0% | 55,547 | | +50% | 150,000 | 24,210 | 15.0% | 51,379 | #### Sensitivity diagram (PW against % change) ```text 124.2 | I | 108.7 | | M I 93.2 | M | I 77.6 | M * | M 62.1 | I M | M 46.6 | I | 31.1 | | I 15.5 | | 0.0 |------------------------------------------------- +------------------------------------------------- -50 -30 -10 0 10 30 50 % change (y: PW in Rs '000; I = investment, M = MARR) ``` #### Interpretation - The investment line is steeper: every 10% change in investment moves PW by Rs 10,000, whereas each 10% step in MARR moves it by only about Rs 4,200–6,300 (about Rs 5,000 near the base value). - PW stays positive over the whole range for both. The investment would have to rise by 74.2% (to Rs 1,74,210) before PW becomes zero. MARR can rise to the IRR of 32.7% (a 227% increase) before the project is rejected. **Answer:** The project stays acceptable throughout the ±50% range, and PW is **more sensitive to the initial investment than to MARR**. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How is the sensitivity analysis carried out? A. All parameters are changed together B. One parameter is varied at a time while the other is held at its base value C. Only the life is varied D. Only the salvage value is varied Answer: B. Each parameter is changed individually over the range and PW recalculated. (Key point: Method of sensitivity analysis) 2. What is the base PW with I = 1,00,000, A = 40,000, N = 6, i = 10%, S = 0? A. Rs 40,000 B. Rs 140,000 C. Rs 74,210 D. Rs 24,210 Answer: C. PW = -100,000 + 40,000(4.3553) = 74,210. (Key point: Base case PW) 3. Which conclusion is correct for this project? A. PW is more sensitive to MARR than to investment B. Both lines have the same slope C. The project becomes unacceptable at +50% MARR D. PW is more sensitive to the initial investment; a 10% rise lowers PW by Rs 10,000 against about Rs 5,000 for MARR Answer: D. The investment line is steeper, so it is the more sensitive factor, and PW stays positive across the range. 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