SENSITIVITY ANALYSIS

Sensitivity Analysis is a way of analysing change in the project's NPV for a given change in one of the variables affecting the NPV. It indicates how sensitive the NPV is to changes in particular variables. The more sensitive the NPV, the more critical the variable.

Steps followed in use of Sensitivity Analysis

1. Identification of all those variables which have an influence on the projects NPV.

2. Definition of the underlying (mathematical) relationship between variables.

3. Analysis of the impact of the change in each of the variables on the projects NPV.

Sensitivity Analysis allows the decision maker to ask "what if" questions.

To illustrate let us consider an example. A project has annual cashflows of Sh 30,000 and an initial cost of Sh 150,000. The useful life of the project is 10 years. The cashflows can further be broken as follows:

Sh

Revenue 375,000

Variable costs 300,000

Fixed costs 30,000

Depreciation 15,000345,000

Before tax profit 30,000

Tax (50%) 15,000

After tax profits 15,000

Add back depreciation 15,000

Net annual cashflows 30,000

The cost of capital is 10% and depreciation method is straight line.

The NPV of the project is:

NPV = 30,000 x PVIFA 10%, 10 yrs - 150,000

= 30,000 x 6.145 - 150,000

= Sh 34,350

The NPV is positive and therefore the project is acceptable. However, the investor should consider how confident he is about the forecast and what would happen if the forecast goes wrong. A sensitivity can be conducted with regard to volume, price, cost etc. In order to do so we must obtain pessimistic and optimistic estimates of the underlying variables.

Assume that in the above example, the variables used in the forecasts are:

(a) Volume of sale ( = market size x market share)

(b) Unit price

(c) Unit variable costs

(d) Fixed costs

Assume further that the pessimistic, expected and optimistic estimates are:

Variable Pessimistic Expected Optimistic

Market Size 9,000 10,000 11,000

Market Share 0.004 0.01 0.016

Unit price (Sh) 3,500 3,750 3,800

Unit variable costs (Sh) 3,600 3,000 2,750

Fixed costs (Sh) 40,000 30,000 20,000

The resulting NPVs would be:

NPV in shillings

Pessimistic Expected Optimistic

Market size 11,306.25 34,350 57,393.75

Market share -103,912.5 34,350 172,612.5

Unit price -42,462.5 34,350 49,712.5

Unit variable cost -150,000 34,350 11,162.5

Fixed costs 3,625 34,350 65,075

Note that NPV under this category is: Sh

Revenue = 3,750(9,000 x 0.01) = 90 x 3,750 337,500

Variables cost = 3,000 (9,000 x 0.01) = 90 x 3,000 270,000

Contribution margin 67,500

Less Fixed costs + Depreciation 45,000

22,500

11,250

Less tax 11,250

Add back depreciation 15,000

Net cashflows 26,250

NPV = 26,250 X 6.145 - 150,000

= Sh 11,306.25

It is important to note that only one variable is allowed to vary at a time and all the others are held constant (at their expected values).

It has been assumed that a negative pre-tax profit will be reduced by tax credit from the government.

From the project the most dangerous variables appear to be market share and unit variable cost. If the market share is 0.004 (and all other variables are as expected), then the project's NPV is -Sh 103,912.5. If unit variable cost is Sh 3,600 (and all other variables are as expected), then the project has an NPV of -150,000. Therefore the most sensitive factor is the unit variable cost, followed by market share and unit price follows. Market size and fixed costs are not very sensitive.