BUSF_A01.qxd

Chapter 6 • Risk in investment appraisal

As we have seen, a very modest attempt at reality causes complications. We can

well imagine the number of possible outcomes were we to explore a more realistic set

of possibilities for each of the input factors, even with our simple example.

How useful to us is the array of nine outcomes and probabilities shown above? The

NPV rule is to accept projects with positive NPVs and reject those with negative ones.

Here we know that four of the nine possible outcomes will yield a negative NPV, yet

the other five give positive ones. One of these nine possibilities will occur, but which

one? One way forward on the problem of the vast array of possible outcomes, and the

subsequent problem of making the decision once we have them, is through the notion

of expected value.

6.4 Expected value

As ever, when we are confronted by a mass of data, it can be useful if we can find some

way of summarising it so that we can more readily absorb and use it.

One way of summarising is to calculate a weighted average or expectedvalue. This

involves multiplying each possible outcome by its probability of occurrence. Taking

the array of outcomes from Example 6.3 gives us the following result:

F: NPV =−50,000 +{4,500 ×[10 −(5 +3)] ×3.791} =−£15,881

G: NPV =−50,000 +{5,000 ×[10 −(3 +3)] ×3.791} =+£25,820

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

I: NPV =−50,000 +{5,000 ×[10 −(5 +3)] ×3.791} =−£12,090

Listing these in order of size, we get:

Possible outcome NPV Probability

£

C −19,672 0.04

F −15,881 0.10

I −12,090 0.06

B −4,508 0.14

E +1,179 0.35

H +6,865 0.21

A +10,656 0.02

D +18,238 0.05

G +25,820 0.03

1.00

Note that, given the data, one of the above nine outcomes must occur, and only one can

occur.

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