Chapter 6 • Risk in investment appraisal
Note that in this example, since there were constant annual cash flows (that is, an
annuity), apart from the cost of capital and the life of the project, all of the sensitivities
could be calculated directly. Where cash flows differ from one year to the next, deriv-
ing the sensitivities is a little more laborious.
The most practical approach, where the cash flows are not an annuity, is trial and
error, much the same approach as was used to derive IRR in Chapter 4. (Of course, the
15.24 per cent cost of capital figure is the IRR of this project.)
As an example of this trial and error approach, let us look at material cost per unit.
The original value was £3, and this, in combination with the other best estimates, leads
to a positive NPV. The value for this factor that leads to a zero NPV is obviously
higher than £3, so a higher value, say £4, could be tried. Depending on the result of
this trial, either other values could be tried (if the NPV using £4 is a long way from
zero) or the approach that was used with the cost of capital (and life of the project)
could be applied to calculate an approximate value. In practice, a computer spread-
sheet would normally be used in a sensitivity analysis.Practical use of sensitivity analysis
Sensitivity analysis is a type of break-even analysis in which, in respect of each factor,
we can assess the break-even point and the margin of safety.
Since it is most unlikely that all but one of the variables will turn out as estimated,
the rather static approach taken in our example gives a very limited perspective on the
project.
If the essentials of the project being assessed are put on to a computer spreadsheet,
the decision maker can, fairly effortlessly, take the analysis a lot further than we have
just done. A series of assumptions can be made about the variables, and the effect on
the project’s NPV of each combination of assumptions can be assessed. This approach
is known as scenario building.
Irrespective of the depth to which sensitivity analysis/scenario building is taken, it
enables the decision maker to ‘get inside’ a project, see which are the crucial estimates
and get a feel for its riskiness. It is clear that sensitivity analysis can be a very useful
approach to gaining an impression of a project.
Knowledge of the more sensitive factors might enable us to reassess those factors or
even take steps to reduce or eliminate their riskiness. In Example 6.1 we discovered
that the project’s success, in NPV terms, is very sensitive to the estimates both of sales
volume and of sales revenue per unit. We may feel that undertaking additional market
research would be a way either of reinforcing our confidence in the original estimates
or of changing our view of the project.
The results from a sensitivity analysis might cause us to take more positive steps to
deal with particularly sensitive factors. The analysis in the example shows the project’s
success to be fairly sensitive to material costs. It would be quite possible to place
orders at fixed prices for the raw material or to take out insurance cover against the
possibility of a material price increase. Alternatively, it might be possible to purchase
an option (that is, a right, but not an obligation) to buy the material at a set price on a
future date. This is an example of a derivative, which we discussed in Chapter 1. In its
2007 annual report, the airline business British Airways plcexplains how it uses
derivatives to set a maximum price on its future fuel requirements.‘