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Sensitivity of PW, most sensitive parameter

Short answer

Base PW = Rs 63,192 (N=10, MARR=10%, salvage=Rs 10,000). Over ±15%, annual revenue is most sensitive (PW swing Rs 119,819), then initial investment (Rs 37,500), then useful life (Rs 32,078). PW stays positive; revenue would need ~16% fall to reach zero.

A project costs Rs 125,000 with annual revenue of Rs 65,000 and annual cost of Rs 35,000. Salvage value will be 8% of the initial investment. Perform sensitivity analysis using PW formulation over a range of ±15% in (i) initial investment (ii) annual revenue (iii) useful life. Draw the sensitivity diagram and indicate which parameter is most sensitive.

Assumptions (not given in the question): useful life N = 10 years, MARR = 10%, salvage value S = 8% × 125,000 = 10,000 (kept at this base value when the investment is varied). Net annual revenue = 65,000 − 35,000 = 30,000.

PW = −I + (R − C)(P/A,10%,N) + S(P/F,10%,N)

Base case

PW₀ = −125,000 + 30,000(P/A,10%,10) + 10,000(P/F,10%,10)
    = −125,000 + 30,000(6.1446) + 10,000(0.3855)
    = 63,192

One parameter is changed at a time; the others stay at base values. For useful life the factors are computed by formula for the (fractional) life, e.g. at +15%, N = 11.5.

Results of ±15% change

ChangePW: Initial investmentPW: Annual revenuePW: Useful life
-15%81,9423,28346,009
-10%75,69223,25352,012
-5%69,44243,22357,735
+0%63,19263,19263,192
+5%56,94283,16268,396
+10%50,692103,13273,357
+15%44,442123,10278,087

Sensitivity diagram

   123.1 |                                             A
         |
   107.7 |
         |                                      A
    92.3 |
         |   I                           A
    76.9 |          I                           U      U
         |                 I             U
    61.6 |                 U      *
         |          U                    I      I
    46.2 |   U             A                           I
         |
    30.8 |
         |          A
    15.4 |
         |
     0.0 |---A---------------------------------------------
         +-------------------------------------------------
            -15    -10    -5      0      5     10     15   
          % change   (y: PW in Rs '000; I = Initial investment, A = Annual revenue, U = Useful life)

Interpretation

  • Annual revenue: PW changes from 3,283 to 123,102 over the range (swing 119,819). PW becomes zero at about -15.8% change (beyond the range tested).
  • Initial investment: PW changes from 44,442 to 81,942 over the range (swing 37,500). PW becomes zero at about +50.6% change (beyond the range tested).
  • Useful life: PW changes from 46,009 to 78,087 over the range (swing 32,078). PW becomes zero at about -47.0% change (beyond the range tested).

Steepest line (largest swing): Annual revenue. A 15% fall in annual revenue (= Rs 9,750 a year) cuts PW by about Rs 59,910, about 3.2 times the effect of a 15% rise in investment (Rs 18,750).

Answer: The most sensitive parameter is annual revenue, then initial investment, then useful life. The project remains acceptable (PW > 0) in all cases; only a fall of about 16% in revenue would make PW zero.

✓ Answer checked by Claude Opus 5.5 (high effort)

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