# Expected Value; Meaning, Example And Solution. – Investment Appraisal.

There is no future without risk and uncertainty. An investment is made to guarantee future positive returns and protect such returns against a decline or a loss.

It is therefore important to carry out some form of appraisal of the risk and uncertainty associated with an investment or a project.
Relying on a single Net Present Value (NPV) can be very misleading because other key factors (sales price, labor cost, material cost, sales volume and others) are also subject to uncertainty. This calls for a more reliable approach.

One of the alternative approaches used to assess risk and uncertainty in a project/investment is expected value. Expected value is the average value of an event that has many possible outcomes. It simplifies the evaluation of the effects of uncertainty.

Expected value generates information that incorporates uncertainties by combining key factors (variables) and their probabilities (likelihoods). It is this combination that makes the expected value to be better than sensitivity analysis.

For some projects where several alternatives with several outcomes are considered, the rule is to choose the alternative with the highest expected value.

How is expected value or average calculated?
It is calculated by multiplying the value of each outcome by its probability. The probability or likelihood is based on the judgment.

An example;

Expected values in project appraisal.

1. the outcomes of Project X are; the probability of \$10,000 NPV is 30% and the probability of \$12,000 is 55% NPV,
2. the outcomes of Project Y are ; the probabilities of \$3,000, \$9,000 and \$10,000 NPVs are 30%, 50% and 55% respectively and,
3. the outcomes of Project Z are: the probabilities of \$2,000, \$3,500, \$4,500 and \$6,000 NPVs are 10%, 20%, 25% and 40% respectively.

The project with the highest expected value should be chosen.

Calculation of the expected NPV:

Project X:

(0.3 x 10,000) + (0.55 x 12,000) = \$9,600

```  Project Y:
(0.3 x 3,000) + (0.5 x 9,000) + (0.55 x 10,000)                      = \$10,900
```

Project Z
(0.1 X 2,000) + ( 0.2 X 3,500) + (0.25 X 4,500) + (0.4 X 6,000) = \$4,425

Project Y has the highest NPV.

Notes:

What is Net Present Value (NPV)?

1. Net Present Value (NPV) is the present day value of various cash inflows and outflows which are expected to occur at different periods in the future.

2. What is Sensitivity analysis?

Sensitivity analysis is used to show the effects of uncertainty by varying the values of variables one after the other and showing the effect of the variation on a project outcome. The aim is identify the variable that affects the outcome most.