BUSF_A01.qxd

Sensitivity analysis

Greene plc has the opportunity to invest in plant for the manufacture of a new product, the

demand for which is estimated to be 5,000 units a year for five years. The following data

relate to the decision:

l The machine is estimated to cost £50,000 (payable immediately) and to have no residual

value.

l The selling price per unit is planned to be £10.

l Labour and material costs are estimated to be £4 and £3 per unit respectively.

l Overhead costs are not expected to be affected by the decision.

l The cost of capital for such a project is estimated to be 10 per cent p.a.

l The project is not expected to require any additional working capital.

l In the interests of simplicity, taxation will be ignored.

l Assume, also in the interests of simplicity, that all cash flows occur at year ends.

(a)Assess the project (using NPV) on the basis of the above estimates.

(b)Carry out a sensitivity analysis of the above estimates.

Example 6.1

The annual cash flows will be 5,000 ×£[10 −(4 +3)] =£15,000 each year. Thus the pro-

ject’s cash flows are estimated to be:

Year £

0 (50,000)

1 15,000

2 15,000

3 15,000

4 15,000

5 15,000

The annuity factor for five years at 10 per cent is 3.791 (see Appendix 2). The NPV is

therefore:

−£50,000 +(£15,000 ×3.791) =+£6,865

Thus on the basis of the estimates the project is favourable (it has a positive NPV) and

should be undertaken.

The estimates are not certain, however, so we shall now go on to look at each of the input

factors, one by one, to see how sensitive the decision is to each of them, that is, to see by

how much each factor could vary from the original estimate before the project would

become unfavourable (negative NPV). While we consider each factor we shall assume that

the others will all be as originally estimated.

The project’s NPV is given by:

−£50,000 +{£5,000 ×[10 −(4 +3)] ×3.791} =+£6,865

To carry out the sensitivity analysis, just one of the factors on the left-hand side of this

equation needs to be altered to a value that will make the NPV equal to zero. After this has

been done with the first factor, the process goes on to the next one, restoring the first one

to its original value and so on.

Solution

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