Sensitivity to investment, revenue and life

PW = −I + A(P/A,10%,N) + S(P/F,10%,N). One parameter is varied at a time, the others held at base values (fractional lives use the same formula).

Base case

PW₀ = −5,00,000 + 1,20,000(P/A,10%,6) + 80,000(P/F,10%,6)
    = −5,00,000 + 1,20,000(4.3553) + 80,000(0.5645)
    = −5,00,000 + 522,631 + 45,158 = 67,789

PW for ±30% change

Sensitivity diagram

   224.6 |   I                                         N
         |
   185.4 |
         |          I                           N      U
   146.2 |
         |                 I             N      U
   107.0 |                               U
         |
    67.8 |                        *
         |
    28.6 |                 U
     9.0 |-----------------N-------------I-----------------
   -10.6 |          U
         |          N                           I
   -49.8 |   U
         |
   -89.0 |   N                                         I
         +-------------------------------------------------
            -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 -89,000 to 224,579 over the range (swing 313,579). PW becomes zero at about -13.0% change (inside the range tested).
• Initial investment: PW changes from -82,211 to 217,789 over the range (swing 300,000). PW becomes zero at about +13.6% change (inside the range tested).
• Useful life: PW changes from -50,531 to 167,457 over the range (swing 217,988). PW becomes zero at about -17.8% change (inside the range tested).

Answer: The project is acceptable at the base values (PW = Rs 67,789) and over most of the range. It becomes unacceptable (PW < 0) if the investment rises by more than about 14% or the net annual revenue falls by more than about 13%. PW is most sensitive to net annual revenue and then to the initial investment; useful life is the least sensitive, but a life shorter by more than about 18% also gives PW < 0.