- 2066 Magh · 8 marks
Sensitivity on initial cost and life; interpret
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.
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).
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
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
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.
✓ Answer checked by Claude Opus 5.5 (high effort)
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