--- title: "AW sensitivity to investment and net annual cash flow" subject: "Engineering Economics" chapter: 6 key: "semester_6/engineering_economics:sensitivity-aw-500000-75000" source: https://www.bctengineer.com/q/semester_6/engineering_economics/sensitivity-aw-500000-75000 site: BCT Engineering --- # AW sensitivity to investment and net annual cash flow Engineering Economics · Chapter 6: Risk Analysis - Asked in: 2065 Chaitra, 6 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/engineering_economics/sensitivity-aw-500000-75000 - 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 ±30% in i) initial investment ii) net annual cash flow using annual worth formulation. | Initial Cost | Rs. 5,00,000 | |---|---| | Annual revenue | Rs. 75,000 | | Annual maintenance cost | Rs. 10,000 | | Useful life | 10 years | | Salvage value | Rs. 50,000 | | MARR | 10% | ## Short answer Base AW is Rs -13,235, so the project does not meet the 10% MARR. Over ±30%, AW ranges from -37,647 to 11,176 for initial investment and -32,735 to 6,265 for net annual cash flow. AW is slightly more sensitive to investment; acceptance requires cost reduction >16% or revenue increase >20%. ## Answer Net annual cash flow = 75,000 − 10,000 = 65,000. AW = −I(A/P,10%,10) + S(A/F,10%,10) + net annual cash flow, with (A/P,10%,10) = 0.16275 and (A/F,10%,10) = 0.06275. #### Base case ```text AW₀ = −5,00,000(0.16275) + 50,000(0.06275) + 65,000 = −81,373 + 3,137 + 65,000 = -13,235 ``` #### AW for ±30% change | Change | AW: Initial investment | AW: Net annual cash flow | |---|---|---| | -30% | 11,176 | -32,735 | | -20% | 3,039 | -26,235 | | -10% | -5,098 | -19,735 | | +0% | -13,235 | -13,235 | | +10% | -21,373 | -6,735 | | +20% | -29,510 | -235 | | +30% | -37,647 | 6,265 | #### Sensitivity diagram (AW in Rs '000) ```text 11.2 | I | 5.1 | N | I -1.0 |--------------------------------------N---------- | I -7.1 | N | -13.2 | * | -19.3 | N | I -25.4 | N | I -31.5 | N | -37.6 | I +------------------------------------------------- -30 -20 -10 0 10 20 30 % change (y: AW in Rs '000; I = Initial investment, N = Net annual cash flow) ``` #### Interpretation - **Initial investment:** AW changes from -37,647 to 11,176 over the range (swing 48,824). AW becomes zero at about -16.3% change (inside the range tested). - **Net annual cash flow:** AW changes from -32,735 to 6,265 over the range (swing 39,000). AW becomes zero at about +20.4% change (inside the range tested). - Each 10% change in investment moves AW by Rs 8,137; each 10% change in net annual cash flow moves AW by Rs 6,500. - The base AW is **negative** (Rs -13,235), so at the stated values the project does not earn the 10% MARR. It becomes acceptable (AW > 0) if the investment falls by more than about 16% or the net annual cash flow rises by more than about 20%. **Answer:** At the base values AW = Rs -13,235 per year < 0, so the project is **not acceptable**. AW is slightly **more sensitive to the initial investment** (swing Rs 48,824 over ±30%) than to the net annual cash flow (swing Rs 39,000). Only within the favourable ranges above does the project pass. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which expression gives the base AW? A. AW = -I(A/P,10%,10) + S(A/F,10%,10) + 65,000 B. AW = -I(A/F,10%,10) + S(A/P,10%,10) + 65,000 C. AW = -I(A/P,10%,10) - S(A/F,10%,10) + 75,000 D. AW = -I(P/A,10%,10) + S(P/F,10%,10) + 65,000 Answer: A. Investment is annualised with A/P, salvage with A/F, and net annual cash flow is 75,000 - 10,000 = 65,000. (Key point: AW formulation) 2. What is the base AW and the decision? A. AW = +13,235; acceptable B. AW = -13,235; not acceptable C. AW = -13,235; acceptable because revenue exceeds cost D. AW = 65,000; acceptable Answer: B. -81,373 + 3,137 + 65,000 = -13,235 < 0, so MARR 10% is not earned. (Key point: Base case result) 3. How much change makes the project acceptable? A. Investment rises by about 16% B. Net annual cash flow falls by about 20% C. Investment falls by more than about 16% or net annual cash flow rises by more than about 20% D. It becomes acceptable only beyond +/-30% Answer: C. AW crosses zero at about -16.3% for investment and +20.4% for net cash flow, both inside the range. (Key point: Zero-AW points) 4. Which factor is AW more sensitive to? A. Net annual cash flow (swing 48,824 vs 39,000) B. Both equally C. Neither, because AW is always negative D. Initial investment (swing 48,824 vs 39,000) Answer: D. Each 10% change moves AW by Rs 8,137 for investment but Rs 6,500 for net cash flow. 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