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Sensitivity of PW to investment and MARR

Short answer

Base PW = Rs 74,210. Over ±50% range, PW remains positive for both parameters. A 10% change in initial investment shifts PW by Rs 10,000, while a 10% MARR change shifts it by ~Rs 5,000. The project is more sensitive to initial investment than to MARR.

Perform sensitivity analysis of the following project over a range of 10 to 50 percent in (i) initial investment and (ii) MARR using PW formulation. Assume Sv = 0. Draw sensitivity diagram also.

Initial InvestmentRs 100000
Annual IncomeRs 40000
Useful Life6 Years
MARR10%

Base case: I = 1,00,000; A = 40,000 per year; N = 6; S = 0; MARR = 10%. PW = −I + A(P/A, i, 6). Base: (P/A,10%,6) = 4.3553, so PW₀ = −100,000 + 40,000(4.3553) = Rs 74,210. Vary one parameter at a time, with the other held at its base value.

(i) Initial investment: PW = −I(1 + x) + 40,000(4.3553)

(ii) MARR: PW = −100,000 + 40,000(P/A, 10%(1 + x), 6)

(e.g. +50% gives i = 15%: (P/A,15%,6) = 3.7845, PW = −100,000 + 40,000(3.7845) = 51,379)

ChangeInvestmentPW (i)MARRPW (ii)
-50%50,000124,2105.0%103,028
-40%60,000114,2106.0%96,693
-30%70,000104,2107.0%90,662
-20%80,00094,2108.0%84,915
-10%90,00084,2109.0%79,437
+0%100,00074,21010.0%74,210
+10%110,00064,21011.0%69,222
+20%120,00054,21012.0%64,456
+30%130,00044,21013.0%59,902
+40%140,00034,21014.0%55,547
+50%150,00024,21015.0%51,379

Sensitivity diagram (PW against % change)

   124.2 |   I
         |
   108.7 |
         |   M      I
    93.2 |          M
         |                 I
    77.6 |                 M      *
         |                               M
    62.1 |                               I      M
         |                                             M
    46.6 |                                      I
         |
    31.1 |
         |                                             I
    15.5 |
         |
     0.0 |-------------------------------------------------
         +-------------------------------------------------
            -50    -30    -10     0     10     30     50   
          % change   (y: PW in Rs '000; I = investment, M = MARR)

Interpretation

  • The investment line is steeper: every 10% change in investment moves PW by Rs 10,000, whereas each 10% step in MARR moves it by only about Rs 4,200–6,300 (about Rs 5,000 near the base value).
  • PW stays positive over the whole range for both. The investment would have to rise by 74.2% (to Rs 1,74,210) before PW becomes zero. MARR can rise to the IRR of 32.7% (a 227% increase) before the project is rejected.

Answer: The project stays acceptable throughout the ±50% range, and PW is more sensitive to the initial investment than to MARR.

✓ Answer checked by Claude Opus 5.5 (high effort)

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