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Sensitivity chart of PW to interest and investment

Short answer

Base PW = Rs 8,594 (i=10%). Over ±30%, investment is more sensitive: 10% investment change alters PW by Rs 1,000 vs ~Rs 500 for interest. PW remains positive; zero at ~86% investment increase or 37.4% IRR.

Draw sensitivity chart using PW formulation of the following cash information. It is desired to evaluate the sensitivity of PW to ±30% changes on (i) interest (ii) investment. [Figure: cash flow diagram, outflow 10000 at year 0; inflows 4000, 4500, 5000, 5500, 6000 at the ends of years 1, 2, 3, 4, 5]

Assumption: the interest rate (MARR) is not printed; take i = 10%. Cash flows: −10,000 at year 0 and 4,000, 4,500, 5,000, 5,500, 6,000 at years 1 to 5. The receipts form an arithmetic gradient series, so PW can be found term by term (or as 4,000(P/A) + 500(P/G)).

PW = −I + 4,000/(1+i) + 4,500/(1+i)² + 5,000/(1+i)³ + 5,500/(1+i)⁴ + 6,000/(1+i)⁵

Base case (i = 10%, I = 10,000)

PW₀ = −10,000 + 4,000(0.9091) + 4,500(0.8264) + 5,000(0.7513) + 5,500(0.6830) + 6,000(0.6209)
    = −10,000 + 3,636 + 3,719 + 3,757 + 3,757 + 3,725 = 8,594

Results (one factor changed at a time)

ChangeInterest iPW (varying i)InvestmentPW (varying I)
-30%7.0%10,2247,00011,594
-20%8.0%9,6578,00010,594
-10%9.0%9,1149,0009,594
+0%10.0%8,59410,0008,594
+10%11.0%8,09611,0007,594
+20%12.0%7,61812,0006,594
+30%13.0%7,15913,0005,594

Sensitivity chart

    11.6 |   V
         |          V
    10.1 |   I
         |          I      *
     8.7 |                        *
         |                               I      I
     7.2 |                               V             I
         |                                      V
     5.8 |                                             V
         |
     4.3 |
         |
     2.9 |
         |
     1.4 |
         |
     0.0 |-------------------------------------------------
         +-------------------------------------------------
            -30    -20    -10     0     10     20     30   
          % change   (y: PW in Rs '000; I = interest, V = investment)

Interpretation

  • A 10% change in investment alters PW by exactly Rs 1,000 (slope 100 per 1%). A 10% change in interest (1 percentage point) alters PW by only about Rs 460 to 570.
  • PW is zero when investment rises by about 86% (to Rs 18,594) or when the interest rate reaches the project IRR of 37.4% (a rise of 274%).

Answer: The project is acceptable throughout ±30% (PW > 0 everywhere). PW is more sensitive to the investment than to the interest rate.

✓ Answer checked by Claude Opus 5.5 (high effort)

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