Sensitivity graph, most sensitive element

Data: P = $20,000; S = 0; N = 5 years; A = $7,000/year; desired rate of return i = 20%. Use PW = −20,000 + A(P/A,i,N), varying one element at a time over ±20%.

Base case

PW₀ = −20,000 + 7,000(P/A,20%,5) = −20,000 + 7,000(2.9906) = $934

Values used

Example: life −20% → N = 4: PW = −20,000 + 7,000(2.5887) = -1,879. Rate −20% → i = 16%: PW = −20,000 + 7,000(3.2743) = 2,920.

Sensitivity results

Sensitivity graph

     5.1 |                                        A
         |
     4.1 |
         |
     3.0 |    R                          A        L
         |
     2.0 |             R                 L
         |
     0.9 |                      *
         |
    -0.1 |-------------------------------R-------------
         |             L                          R
    -1.2 |             A
         |    L
    -2.2 |
         |
    -3.3 |    A
         +---------------------------------------------
             -20      -10       0       10       20    
          % change   (y: PW in $ '000; A = Annual receipts, L = Life, R = Rate of return)

Interpretation

• Annual receipts: PW changes from -3,253 to 5,121 over the range (swing 8,374). PW becomes zero at about -4.5% change (inside the range tested).
• Life: PW changes from -1,879 to 3,279 over the range (swing 5,157). PW becomes zero at about -7.1% change (inside the range tested).
• Rate of return: PW changes from -782 to 2,920 over the range (swing 3,702). PW becomes zero at about +10.5% change (inside the range tested).

The receipts line is the steepest and crosses zero at about -4.5% (A = $6,688 a year), the closest to the base point. A fall of more than about 4.5% in receipts alone makes the proposal unacceptable at 20%.

Answer: The decision is most sensitive to the annual receipts, followed by life and then the rate of return. The proposal is only marginally acceptable (PW = $934).