1. MANAGEMENT AND COST ACCOUNTING
SIXTH EDITION
COLIN DRURY

2. Part Three: Information for decision-making
Chapter Twelve: Decision-making under conditions of risk & uncertainty
© 2000 Colin Drury

3. 12.1a
RISK AND UNCERTAINTY
1.The decision-making model involves the following stages:
(i) Identify objectives.
(ii) Search for possible courses of action.
(iii) Identify potential events or states of nature.
(iv) List possible outcomes for each state of nature applying to each
alternative course of action.
(v) Measure the pay-off for each alternative course of action.
(vi) Select course of action.
2. Probabilities are used to measure the likelihood that an
event or state of nature will occur.
© 2000 Colin Drury

4. 12.1b
3. A probability distribution lists all possible outcomes for an event and the probability that each will occur:
Student A Student B
probability probability
Outcome:
Pass examination
Do not pass
4. Probability distributions provide more meaningful information than stating the most likely outcome (i.e.both students will pass).
© 2000 Colin Drury

5. 12.2a
Instead of presenting probability distributions for each alternative, two summary measures are often used:
(i) expected value.
(ii) standard deviation.
2. The expected value is the weighted average of the possible outcomes. It represents the long-run average outcome if thedecision were to be repeated many times.
© 2000 Colin Drury

6. 12.2b Example Product A probability distribution (1) (2) (3)
(1) (2) (3)
Estimated Weighted amount
Outcome probability (col.1× col.2)
Profits of £
Profits of £
Profits of £
Profits of £
Profits of £
Expected value
© 2000 Colin Drury

7. Which product should the company make?
12.3
Product B probability distribution
(1) (2) (3)
Estimated Weighted amount
Outcome probability (col. X col.2) £
Profits of £
Profits of £
Profits of £
Profits of £
Profits of £
Expected value
Which product should the company make?
© 2000 Colin Drury

8. 12.4a Product C probability distribution Estimated Expected
Outcome probability value (EV) £
Loss of £ (2 000)
Profit of £
9 000
Product C has a higher EV than either products B or C, but it is subject to greater uncertainty.
The standard deviation is often used to measure the dispersion of the possible outcomes:
SD of A = £1 096
SD of B = £2 142
SD of C = £13 000
© 2000 Colin Drury

9. 12.4b 4. The standard deviation measures dispersion around the
expected value, but does not measure downside risk. The
SD would increase if product C was replaced with £
instead of £22 000, but does this make the product more
risky?
5. The coefficient of variation V is a relative measure of risk:
V = Standard deviation
Expected value
For example, a SD of 200 with an EV of has the same
relative variation as a SD of with an EV of
6. Where possible, it is preferable to focus on probability
distributions rather than summary measures of EV and SD.
© 2000 Colin Drury

10. Attitudes towards risk
12.5
Attitudes towards risk
1. The selection of an alternative is influenced by an individual ’s attitude towards risk.
Example
Possible outcomes A B
Recession
Normal
Boom
Expected value
The probability of each outcome is 1/3.
2. The two alternatives have the same EV but different levels of risk.
A risk-seeker will prefer B.
- A risk-averter will prefer A.
- A risk-neutral individual will be indifferent between A and B.
© 2000 Colin Drury

11. 12.6a
Decision trees
Decision trees are useful for clarifying alternative courses of action and their potential outcomes.
© 2000 Colin Drury

12. 12.6b
Example
A company is considering whether to develop and market a new product. Development costs are estimated to be £ , and there is a 0.75 probability that the development effort will be successful and a 0.25 probability that the development effort will be unsuccessful. If the development is successful, the
product will be marketed, and it is estimated that:
(i) If the product is very successful,profits will be £
(ii) If the product is moderately successful,profits will be £
(iii) If the product is a failure,there will be a loss of £
Each of the above profit and loss calculations is after taking into account the development costs of £ The estimated probabilities of each of the above events are as follows:
(i) Very successful 0.4
(ii) Moderately successful 0.3
(iii) Failure 0.3
© 2000 Colin Drury

13. Decision tree for example on slide 12.6
12.7
Decision tree for example on slide 12.6
© 2000 Colin Drury

14. Maximin, maximax and regret criteria
Can be applied where it is not possible to assign meaningful probabilities to alternative courses of action.
© 2000 Colin Drury

15. 12.8b Example Low High demand demand Machine A £100 000 £160 000
Machine B £ £
2. With the maximin technique the largest payoff is selected based on the
assumption that the worst possible outcome will occur.
Machine A = £
Machine B = £10 000
Decision = Choose product A
3. With the maximax technique the largest payoff is selected assuming the
best possible outcome will occur.
Machine A = £
Machine B = £
Decision = Choose product B
4. The aim of the regret criterion is to minimize the maximum possible regret.
© 2000 Colin Drury

16. 12.8c Regret table Low High demand demand occurs occurs
Choose machine A £40 000
Choose machine B £
The maximum regret is £ for A and £ for B.
Therefore,choose A.
© 2000 Colin Drury

17. 12.9
Portfolio approach
1. Alternatives should not be considered in isolation. Account should be taken of how they interact with existing activities and other alternatives.
Example
States of nature Umbrella Ice-cream Combined
manufacturing manufacturing activities
£ £ £
Sunshine –
Rain –
Assume there are only two possible states of nature.
2. Each activity is risky on its own, but when the activities are combined risk is eliminated.
© 2000 Colin Drury