Sensitivity in 10% steps; interpret

Assumptions: MARR is not given; take 10%. No salvage value. Net annual revenue = 6,000 − 2,000 = 4,000. PW = −I + R(P/A,10%,N).

Base case

PW₀ = −20,000 + 4,000(P/A,10%,10) = −20,000 + 4,000(6.1446) = Rs 4,578

PW with changes in steps of 10%

Sensitivity diagram

    12.0 |                                             N
         |   I
    10.1 |
         |                                      N
     8.3 |          I                                  U
         |                               N      U
     6.4 |                 I             U
         |
     4.6 |                        *
         |
     2.7 |                 U             I
         |                 N
     0.9 |          U                           I
    -0.0 |----------N--------------------------------------
    -1.0 |   U
         |                                             I
    -2.8 |   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 -2,795 to 11,952 over the range (swing 14,747). PW becomes zero at about -18.6% change (inside the range tested).

• Initial investment: PW changes from -1,422 to 10,578 over the range (swing 12,000). PW becomes zero at about +22.9% change (inside the range tested).

• Useful life: PW changes from -526 to 8,413 over the range (swing 8,940). PW becomes zero at about -27.3% change (inside the range tested).

• Base PW = Rs 4,578, so the project is acceptable.

• A 10% fall in revenue costs about Rs 2,458 of PW; a 10% rise in investment costs exactly Rs 2,000; a 10% shorter life costs about Rs 1,542.

• PW becomes zero if revenue falls 19%, investment rises 23% or life falls to about 7.3 years (27% shorter).

Answer: The project is acceptable at the base values and PW is most sensitive to the net annual revenue, then the initial investment, then the useful life. It turns unacceptable if revenue falls by more than about 19%, investment rises by more than about 23%, or life falls by more than about 27%.