--- title: "Sensitivity graph, most sensitive element" subject: "Engineering Economics" chapter: 6 key: "semester_6/engineering_economics:sensitivity-graph-20000-7000" source: https://www.bctengineer.com/q/semester_6/engineering_economics/sensitivity-graph-20000-7000 site: BCT Engineering --- # Sensitivity graph, most sensitive element Engineering Economics · Chapter 6: Risk Analysis - Asked in: 2069 Bhadra, 8 marks - Video: [Sensitivity Analysis |Economics |Board Exam Solution in NEPALI](https://www.youtube.com/watch?v=Zo-O4TCa8TA) — 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-graph-20000-7000 - Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-6 ## Question A proposal is described by the following estimates: P = \$20000, S = 0, N = 5 and net annual receipts = \$7000. A rate of return of 20 percent is desired on such proposals. Construct a sensitivity graph for deviations over a range of ±20 percent in the life, annual receipts, and rate of return. To which element is the decision most sensitive? ## Short answer Base PW = $934. Most sensitive to annual receipts (PW zero at -4.5% change), then life (PW zero at -7.1%), then rate of return (PW zero at +10.5%). Proposal marginally acceptable; a 4.5% drop in receipts makes it unacceptable. ## Answer Data: P = \$20,000; S = 0; N = 5 years; A = \$7,000/year; desired rate of return i = 20%. Use PW = −20,000 + A(P/A,i,N), varying one element at a time over ±20%. #### Base case PW₀ = −20,000 + 7,000(P/A,20%,5) = −20,000 + 7,000(2.9906) = **\$934** #### Values used | Change | Life N | Receipts A | Rate i | |---|---|---|---| | −20% | 4 | 5,600 | 16% | | −10% | 4.5 | 6,300 | 18% | | 0 | 5 | 7,000 | 20% | | +10% | 5.5 | 7,700 | 22% | | +20% | 6 | 8,400 | 24% | Example: life −20% → N = 4: PW = −20,000 + 7,000(2.5887) = -1,879. Rate −20% → i = 16%: PW = −20,000 + 7,000(3.2743) = 2,920. #### Sensitivity results | Change | PW: Annual receipts | PW: Life | PW: Rate of return | |---|---|---|---| | -20% | -3,253 | -1,879 | 2,920 | | -10% | -1,159 | -408 | 1,890 | | +0% | 934 | 934 | 934 | | +10% | 3,028 | 2,160 | 45 | | +20% | 5,121 | 3,279 | -782 | #### Sensitivity graph ```text 5.1 | A | 4.1 | | 3.0 | R A L | 2.0 | R L | 0.9 | * | -0.1 |-------------------------------R------------- | L R -1.2 | A | L -2.2 | | -3.3 | A +--------------------------------------------- -20 -10 0 10 20 % change (y: PW in $ '000; A = Annual receipts, L = Life, R = Rate of return) ``` #### Interpretation - **Annual receipts:** PW changes from -3,253 to 5,121 over the range (swing 8,374). PW becomes zero at about -4.5% change (inside the range tested). - **Life:** PW changes from -1,879 to 3,279 over the range (swing 5,157). PW becomes zero at about -7.1% change (inside the range tested). - **Rate of return:** PW changes from -782 to 2,920 over the range (swing 3,702). PW becomes zero at about +10.5% change (inside the range tested). The receipts line is the steepest and crosses zero at about -4.5% (A = \$6,688 a year), the closest to the base point. A fall of more than about 4.5% in receipts alone makes the proposal unacceptable at 20%. **Answer: The decision is most sensitive to the annual receipts**, followed by life and then the rate of return. The proposal is only marginally acceptable (PW = \$934). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is PW at the base values (P = 20,000, A = 7,000, N = 5, i = 20%)? A. Rs -1,879 B. Rs 934 C. Rs 15,000 D. Rs 2,920 Answer: B. PW = -20,000 + 7,000(2.9906) = 934, so the proposal is only marginally acceptable. (Key point: Base case PW) 2. To which element is the decision most sensitive? A. Rate of return B. Life C. Salvage value D. Annual receipts Answer: D. Annual receipts have the steepest line and PW becomes zero at about -4.5%. (Key point: Most sensitive element) 3. What happens to PW when the required rate falls to 16%? A. PW rises to about 2,920 B. PW falls to negative C. PW stays 934 D. PW becomes zero Answer: A. A lower discount rate increases (P/A), so PW = -20,000 + 7,000(3.2743) = 2,920. 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