AW sensitivity to investment and net annual cash flow

Net annual cash flow = 75,000 − 10,000 = 65,000. AW = −I(A/P,10%,10) + S(A/F,10%,10) + net annual cash flow, with (A/P,10%,10) = 0.16275 and (A/F,10%,10) = 0.06275.

Base case

AW₀ = −5,00,000(0.16275) + 50,000(0.06275) + 65,000
    = −81,373 + 3,137 + 65,000 = -13,235

AW for ±30% change

Sensitivity diagram (AW in Rs '000)

    11.2 |   I
         |
     5.1 |                                             N
         |          I
    -1.0 |--------------------------------------N----------
         |                 I
    -7.1 |                               N
         |
   -13.2 |                        *
         |
   -19.3 |                 N
         |                               I
   -25.4 |          N
         |                                      I
   -31.5 |   N
         |
   -37.6 |                                             I
         +-------------------------------------------------
            -30    -20    -10     0     10     20     30   
          % change   (y: AW in Rs '000; I = Initial investment, N = Net annual cash flow)

Interpretation

• Initial investment: AW changes from -37,647 to 11,176 over the range (swing 48,824). AW becomes zero at about -16.3% change (inside the range tested).

• Net annual cash flow: AW changes from -32,735 to 6,265 over the range (swing 39,000). AW becomes zero at about +20.4% change (inside the range tested).

• Each 10% change in investment moves AW by Rs 8,137; each 10% change in net annual cash flow moves AW by Rs 6,500.

• The base AW is negative (Rs -13,235), so at the stated values the project does not earn the 10% MARR. It becomes acceptable (AW > 0) if the investment falls by more than about 16% or the net annual cash flow rises by more than about 20%.

Answer: At the base values AW = Rs -13,235 per year < 0, so the project is not acceptable. AW is slightly more sensitive to the initial investment (swing Rs 48,824 over ±30%) than to the net annual cash flow (swing Rs 39,000). Only within the favourable ranges above does the project pass.