CIMA BA2 Syllabus D. DECISION MAKING - Expected Values - Notes 2 / 7
What is an expected value?
Expected values are used in decision making when there are many possible outcomes and each outcome has a probability attached to it.
It is an expected value/outcome if the decision will be made.
E.V. = Σ (Each possible outcome x Probability)
Illustration
An ice cream salesman has varying levels of demand for his sales and probabilities for each level of demand occurring. (Table below)
What is the expected value of revenue for the ice cream salesman?
| Demand | Sales ($) | Probability |
|---|---|---|
| High | 500,000 | 0.2 |
| Medium | 300,000 | 0.5 |
| Low | 200,000 | 0.3 |
| 1 |
Solution
E.V. = Σ (Each possible outcome x Probability)
=(500,000 x 0.2) + (300,000 x 0.5) + (200,000 x 0.3)
= 310,000
Limitations of E.V.
The expected value assumes that the decision will be taken many times.
Therefore:
This is not good for one off decisions, because either the demand will be high, medium or low at any time and will have those corresponding sales - the expected value will show what you will get over the long term.
It ignores the investor's attitude to risk, as it is an average of all of the outcomes occurring based on their probability.
It ignores the range of all possible outcomes in between our high/medium and low demand
It is heavily dependent on the probability %.
Illustration - Joint Probabilities
| Overdraft Limit | 4,000 | ||||
|---|---|---|---|---|---|
| Overdraft at Start | 2,000 | ||||
| Forecast Cash Flows | Period 1 | Probability | Period 2 | Probability | |
| 10,000 | 20% | 8,000 | 40% | ||
| 6,000 | 40% | 5,000 | 50% | ||
| -5,000 | 40% | -2,000 | 10% | ||
| Closing balance at the end of P1 and P2 using EV | -2000 (at start) + (10,000 x 20%) + (6,000 x 40%) + (-5,000 x 40%) = 2,400 | -2,000 (at start) + (8,000 x 40%) + (5,000 x 50%) + (-2.000 x 10%) = 5,500 | |||
| Therefore my EV | -,2000 + 2,400 (P1) + 5,500 (P2) = 5,900 | ||||
| What is the chance of a negative cash balance at the end of P2? | |||||
| Option 1 | 10,000 (P1) | 8,000 (P2) | -2,000 (opening OD) | 16,000 | |
| Option 2 | 10,000 (P1) | 5,000 (P2) | -2,000 (opening OD) | 13,000 | |
| Option 3 | 10,000 (P1) | (2,000) (P2) | -2,000 (opening OD) | 6,000 | |
| Option 4 | 6,000 (P1) | 8,000 (P2) | -2,000 (opening OD) | 12,000 | |
| Option 5 | 6,000 (P1) | 5,000 (P2) | -2,000 (opening OD) | 9,000 | |
| Option 6 | 6,000 (P1) | (2,000) (P2) | -2,000 (opening OD) | 2,000 | |
| Option 7 | (5,000) (P1) | 8,000 (P2) | -2,000 (opening OD) | 11,000 | |
| Option 8 - NEGATIVE BALANCE | (5,000) (P1) (40%) | 5,000 (P2) (50%) | -2,000 (opening OD) | (2,000) | Chances of this are 40% x 50% = 20% |
| Option 9 - NEGATIVE BALANCE | (5,000) (P1) (40%) | (2,000) (P2) (10%) | -2,000 (opening OD) | (9,000) | Chances of this are 40% x 10% = 4% |
| 24% is the chance of having a negative cash balance at the end of P2 | |||||
| What is the probability of going over the OD at the end of P2? | Only in Option 9 - so 4% |