BUSF_A01.qxd

Use of probabilities

Solution

Figure 6.1

Possible

outcomes of

Greene plc’s

investment

opportunity

This shows the nine possible outcomes (A to I) that could result from this project. Each

one’s likelihood of occurrence is found by multiplying the probability of the relevant

outcome for sales volume with its counterpart for labour cost.

This situation is rather more complicated in that there are now nine possible outcomes. Each

of the three possible sales volume outcomes could occur in conjunction with each of the

three possible labour costs.

The outcomes might usefully be represented in a diagram (see Figure 6.1). For ease of ref-

erence the nine possible outcomes are labelled A to I inclusive. Outcome F, say, will occur

if 4,500 units p.a. are sold and the labour cost is £5/unit. As the probability of the first is 0.5

and of the second 0.2 then the joint probability is the product of these, which is 0.10 (that is,

0.5 ×0.2).

Note that the sum of the probabilities of all the nine possibilities is 1.00, that is, one of

them is certain to occur, though we do not know which one.

‘

The NPVs of each possibility are:

A: NPV =−50,000 +{4,000 ×[10 −(3 +3)] ×3.791} =+£10,656

B: NPV =−50,000 +{4,000 ×[10 −(4 +3)] ×3.791} =−£4,508

C: NPV =−50,000 +{4,000 ×[10 −(5 +3)] ×3.791} =−£19,672

D: NPV =−50,000 +{4,500 ×[10 −(3 +3)] ×3.791} =+£18,238

E: NPV =−50,000 +{4,500 ×[10 −(4 +3)] ×3.791} =+£1,179