--- title: "PW sensitivity to investment, income, life by ±25%" subject: "Engineering Economics" chapter: 6 key: "semester_6/engineering_economics:sensitivity-pw-400000-60000-25" source: https://www.bctengineer.com/q/semester_6/engineering_economics/sensitivity-pw-400000-60000-25 site: BCT Engineering --- # PW sensitivity to investment, income, life by ±25% Engineering Economics · Chapter 6: Risk Analysis - Asked in: 2067 Mangsir, 10 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-pw-400000-60000-25 - Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-6 ## Question What will be the impact of change in value of present worth of the following project if changes occurs in (i) initial investment (ii) net annual income and (iii) useful life by ±25%? Draw necessary graph also. | Initial Investment | Rs. 4,00,000 | |---|---| | Net Annual income | Rs. 60,000 | | Useful life | 12 years [?] | | MARR | 15% | ## Short answer Base PW = Rs -74,763 (not acceptable, IRR ~10.4%). Most sensitive to initial investment (PW zero at -18.7% change), then net annual income (PW zero at +23%), least to useful life (never reaches zero). A 25% rise in income or fall in investment makes it acceptable. ## Answer **Assumptions:** the life is printed as "12 years [?]"; take N = 12 years. No salvage value. MARR = 15%. PW = −I + A(P/A,15%,N). #### Base case PW₀ = −4,00,000 + 60,000(P/A,15%,12) = −4,00,000 + 60,000(5.4206) = **Rs -74,763** #### Impact of ±25% change (one parameter at a time) | Change | PW: Initial investment | PW: Net annual income | PW: Useful life | |---|---|---|---| | -25% | 25,237 | -156,072 | -113,705 | | -12.5% | -24,763 | -115,418 | -92,200 | | +0% | -74,763 | -74,763 | -74,763 | | +12.5% | -124,763 | -34,108 | -60,623 | | +25% | -174,763 | 6,546 | -49,158 | (Life uses fractional years in the formula, e.g. −25% gives N = 9, −12.5% gives 10.5.) #### Graph (PW against % change) ```text 25.2 | I | N 0.2 |---------------------------------------- | -24.8 | I | N -49.8 | U | U -74.8 | * | U -99.8 | | U N -124.8 | I | -149.8 | | N -174.8 | I +---------------------------------------- -25 -12.5 0 12.5 25 % change (y: PW in Rs '000; I = Initial investment, N = Net annual income, U = Useful life) ``` #### Impact and interpretation - **Initial investment:** PW changes from -174,763 to 25,237 over the range (swing 200,000). PW becomes zero at about -18.7% change (inside the range tested). - **Net annual income:** PW changes from -156,072 to 6,546 over the range (swing 162,619). PW becomes zero at about +23.0% change (inside the range tested). - **Useful life:** PW changes from -113,705 to -49,158 over the range (swing 64,547). PW does not reach zero within any realistic change. - A rise of 25% in investment (Rs 1,00,000 more) reduces PW by Rs 1,00,000; a fall of 25% in income (Rs 15,000/yr) reduces PW by Rs 81,309. The investment line is therefore the steepest. - Life matters least over this range because the later years are heavily discounted at 15%. - The base PW is negative (the project does not earn 15%); the IRR is about 10.4%. A 25% rise in income or a 25% fall in investment each makes it acceptable (PW > 0). **Answer:** At the stated values the project is **not acceptable** (PW = Rs -74,763). PW is **most sensitive to the initial investment**, then to the net annual income, with useful life least sensitive. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the base PW (I = 4,00,000, A = 60,000, N = 12, 15%)? A. Rs +74,763 B. Rs -74,763 C. Rs 0 D. Rs -400,000 Answer: B. -400,000 + 60,000(5.4206) = -74,763, so the project does not earn 15%. (Key point: Base case PW) 2. What happens to PW if net annual income rises 25% (to Rs 75,000)? A. PW stays negative at about -74,763 B. PW becomes about -156,072 C. PW becomes positive, about Rs 6,546, making the project acceptable D. PW becomes exactly zero Answer: C. PW = -400,000 + 75,000(5.4206) = about 6,546, so a 25% rise in income makes the project acceptable. (Key point: Effect of +25% income) 3. Why does useful life have the least effect? A. Later years are heavily discounted at 15% B. There is no salvage value C. Life cannot change D. The investment is paid late Answer: A. Extra years at 15% add little present worth, so PW changes little. 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