Question 5.A.17: Calculate the standard deviation for the Satellite project. ...
Calculate the standard deviation for the Satellite project. Which project has the higher level of risk?
To answer this activity, the steps outlined above must be followed. Thus:
Step 1. Calculate the ENPV:
| (a) NPV £m |
(b) Probability of occurrence |
(a × b) ENPV £m |
| 15 | 0.6 | 9.0 |
| 20 | 0.2 | 4.0 |
| 40 | 0.2 | 8.0 |
| 21.0 |
Step 2. Calculate the deviations around the ENPV:
| (a) Possible NPV £m |
(b) ENPV £m |
(a – b) Deviation £m |
| 15 | 21 | -6 |
| 20 | 21 | -1 |
| 40 | 21 | 19 |
Step 3. Calculate the variance (that is, sum the squared deviations):
| Deviations £m |
Squared deviations £m |
| -6 | 36 |
| -1 | 1 |
| 19 | 361 |
| Variance 398 | |
Step 4. Find the square root of the variance (that is, the standard deviation):*
Standard deviation = \sqrt{398(£m)^{2}}
= £19.95m
The Satellite project has the higher standard deviation and therefore the greater variability of possible outcomes. Hence, it has the higher level of risk.
* Computer software or calculators with statistical functions can be used to calculate the standard deviation and so this manual approach need not be used in practice. It is shown here for illustrative purposes.