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Sensitivity on investment, revenue and life; interpret

Short answer

Base PW = Rs 39,036. Most sensitive to net annual revenue (PW zero at -28.9% change), then initial investment (PW zero at +39%), least to useful life (PW zero at -41.3%). Project accepted except when revenue falls ~29% or more.

Perform sensitivity analysis over a range of ±30% in (i) initial investment (ii) annual net revenue (iii) useful life.

Initial investment = Rs 100,000Salvage value = Rs 10,000
Annual benefits = Rs 25,000Annual expenses = Rs 3,000
Useful life = 10 yearsMARR = 10%
Draw sensitivity diagram and interpret the result.

Net annual revenue = benefits − expenses = 25,000 − 3,000 = 22,000. PW = −I + R(P/A,10%,N) + S(P/F,10%,N), S = 10,000, MARR = 10%.

Base case

PW₀ = −1,00,000 + 22,000(P/A,10%,10) + 10,000(P/F,10%,10)
    = −1,00,000 + 22,000(6.1446) + 10,000(0.3855)
    = −1,00,000 + 135,180 + 3,855 = 39,036

PW for ±30% change (other factors at base values)

ChangePW: Initial investmentPW: Net annual revenuePW: Useful life
-30%69,036-1,51812,237
-20%59,03612,00022,033
-10%49,03625,51830,940
+0%39,03639,03639,036
+10%29,03652,55446,396
+20%19,03666,07253,088
+30%9,03679,59059,170

Sensitivity diagram

    79.6 |                                             N
         |
    69.5 |   I
         |                                      N
    59.3 |          I                                  U
         |                               N      U
    49.2 |                 I
         |                               U
    39.0 |                        *
         |
    28.9 |                 U             I
         |          U      N
    18.8 |                                      I
         |   U      N
     8.6 |                                             I
         |
    -1.5 |---N---------------------------------------------
         +-------------------------------------------------
            -30    -20    -10     0     10     20     30   
          % change   (y: PW in Rs '000; I = Initial investment, N = Net annual revenue, U = Useful life)

Interpretation

  • Net annual revenue: PW changes from -1,518 to 79,590 over the range (swing 81,108). PW becomes zero at about -28.9% change (inside the range tested).

  • Initial investment: PW changes from 9,036 to 69,036 over the range (swing 60,000). PW becomes zero at about +39.0% change (beyond the range tested).

  • Useful life: PW changes from 12,237 to 59,170 over the range (swing 46,934). PW becomes zero at about -41.3% change (beyond the range tested).

  • The project has a healthy margin: PW = Rs 39,036 at the base case.

  • Net annual revenue has the steepest line. PW falls to zero if revenue is 29% lower (about Rs 15,647 a year), so a fall of 30% in revenue alone would make the project unacceptable.

  • Investment must rise by about 39% before PW is zero, and life must fall by about 41% (to 5.9 years).

Answer: Base PW = Rs 39,036. The result is most sensitive to net annual revenue, then to initial investment, and least to useful life. The project is accepted in every case except when revenue falls by about 29% or more.

✓ Answer checked by Claude Opus 5.5 (high effort)

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