--- title: "Sensitivity on initial cost and life; interpret" subject: "Engineering Economics" chapter: 6 key: "semester_6/engineering_economics:sensitivity-30-initial-cost-life-25" source: https://www.bctengineer.com/q/semester_6/engineering_economics/sensitivity-30-initial-cost-life-25 site: BCT Engineering --- # Sensitivity on initial cost and life; interpret Engineering Economics · Chapter 6: Risk Analysis - Asked in: 2066 Magh, 8 marks - Video: [Sensitivity Analysis | Economic Numerical | most asked problem | PW Method | 2022 PU | TU.PU.KU.POU](https://www.youtube.com/watch?v=RxPZy1gCC8s) — Sudip Dhakal - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/engineering_economics/sensitivity-30-initial-cost-life-25 - Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-6 ## Question Perform sensitivity analysis over ±30% in initial cost and useful life. Draw sensitivity diagram and interpret the result. Data: initial cost = Rs. 25 lakh, salvage value = Rs. 5 lakh, useful life = 10 years, annual benefits = Rs. 10 lakh, annual O & M = Rs. 5 lakh, MARR = 8% (PW formulation). ## Short answer Base PW is Rs 1,086,637, so the project is acceptable. Over ±30% variation, PW ranges from 336,637 to 1,836,637 for initial cost and 394,930 to 1,635,737 for useful life. PW is more sensitive to initial cost, but the project remains acceptable within the entire tested range. ## Answer Net annual benefit = 10 − 5 = 5 lakh = 5,00,000. PW = −I + 5,00,000(P/A,8%,N) + 5,00,000(P/F,8%,N), MARR = 8%. #### Base case ```text PW₀ = −25,00,000 + 5,00,000(P/A,8%,10) + 5,00,000(P/F,8%,10) = −25,00,000 + 5,00,000(6.7101) + 5,00,000(0.4632) = −25,00,000 + 3,355,041 + 231,597 = 1,086,637 ``` #### PW for ±30% change | Change | PW: Initial cost | PW: Useful life | |---|---|---| | -30% | 1,836,637 | 394,930 | | -20% | 1,586,637 | 643,454 | | -10% | 1,336,637 | 873,568 | | +0% | 1,086,637 | 1,086,637 | | +10% | 836,637 | 1,283,924 | | +20% | 586,637 | 1,466,596 | | +30% | 336,637 | 1,635,737 | #### Sensitivity diagram ```text 1836.6 | I | 1607.1 | I U | U 1377.5 | I | U 1147.9 | | * 918.3 | U | I 688.7 | U | I 459.2 | | U I 229.6 | | 0.0 |------------------------------------------------- +------------------------------------------------- -30 -20 -10 0 10 20 30 % change (y: PW in Rs '000; I = Initial cost, U = Useful life) ``` #### Interpretation - **Initial cost:** PW changes from 336,637 to 1,836,637 over the range (swing 1,500,000). PW becomes zero at about +43.5% change (beyond the range tested). - **Useful life:** PW changes from 394,930 to 1,635,737 over the range (swing 1,240,807). PW becomes zero at about -44.5% change (beyond the range tested). - Base PW = Rs 1,086,637 (about Rs 10.9 lakh), so the project is acceptable. - Initial cost: each +10% (Rs 2.5 lakh) reduces PW by Rs 2.5 lakh. PW is zero when cost rises by about 43%, so even a +30% rise leaves PW positive (Rs 336,637). - Useful life: PW falls to Rs 394,930 at −30% (7 years) and is still positive. PW would be zero at a life 44% shorter (about 5.6 years). **Answer:** The project stays acceptable over the whole ±30% range for both factors. PW is **more sensitive to initial cost** than to useful life. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which expression gives the PW used in the sensitivity analysis? A. PW = -I + 5,00,000(P/A,8%,N) + 5,00,000(P/F,8%,N) B. PW = -I + 10,00,000(P/A,8%,N) + 5,00,000(P/F,8%,N) C. PW = -I + 5,00,000(A/P,8%,N) + 5,00,000(F/P,8%,N) D. PW = -I + 5,00,000(P/A,8%,N) Answer: A. Net annual benefit is 10 - 5 = 5 lakh, and the salvage value of 5 lakh is brought back with (P/F). (Key point: PW formulation) 2. What is the base-case PW and what does it imply? A. Rs 1,086,637, but the project is rejected because it is below the cost B. Rs 1,086,637, positive, so the project is acceptable C. Rs -1,086,637, so the project is rejected D. Rs 336,637, so the project is acceptable Answer: B. PW0 = -25 lakh + 3,355,041 + 231,597 = 1,086,637 > 0 at MARR 8%. (Key point: Base case result) 3. When initial cost rises by 10% (Rs 2.5 lakh), what happens to PW? A. It rises by Rs 2.5 lakh B. It falls by about Rs 2.14 lakh because of discounting C. It falls by Rs 2.5 lakh, since initial cost enters PW directly D. It stays the same as the benefits are unchanged Answer: C. Initial cost occurs at time 0, so PW changes one-for-one with it. (Key point: Effect of initial cost) 4. What conclusion does the answer draw over the +/-30% range? A. The project becomes unacceptable at +30% initial cost B. PW is more sensitive to useful life than to initial cost C. The project is unacceptable at -30% useful life D. The project stays acceptable for both factors, and PW is more sensitive to initial cost Answer: D. The lowest PW values are 336,637 (cost +30%) and 394,930 (life -30%), both positive; the swing for cost (1,500,000) exceeds that for life (1,240,807). 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