1. Part Three: Information for decision-making Chapter Twelve: Decision-making under conditions of risk and uncertainty Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury

2. 12.1 1.Probabilities are used to measure the likelihood that an event or state of nature will occur 2. 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 0.9 0.6 Do not pass 0.1 0.4 1.0 1.0 3. Probability distributions provide more meaningful information than stating the most likely outcome (i.e. both students will pass). Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury

3. 12.2a 1.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 the decision were to be repeated many times. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury

4. 12.2b Example Product A probability distribution (1) (2) (3) Estimated Weighted amount Outcome probability (col.1× col.2) £ Profits of £600 000 0.10 60 000 Profits of £700 000 0.20 140 000 Profits of £800 000 0.40 320 000 Profits of £900 000 0.20 180 000 Profits of £1 000 000 0.10 100 0000 1.00 800 000 Expected value Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury

5. 12.3 Product B probability distribution (1) (2) (3) Estimated Weighted amount Outcome probability (col. X col.2) £ Profits of £400 000 0.05 20 000 Profits of £600 000 0.10 60 000 Profits of £800 000 0.40 320 000 Profits of £1 000 000 0.25 250 000 Profits of £1 200 000 0.20 240 000 1.00 890 000 Expected value Which product should the company make? Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury

6. 12.4a 1.Product C probability distribution Estimated Expected Outcome probability value (EV) £ Loss of £400 000 0.5 (200 000) Profit of £2 200 000 0.5 1 100 000 900 000 2.Product C has a higher EV than either products B or C, but it is subject to greater uncertainty. 3.The standard deviation is often used to measure the dispersion of the possible outcomes: SD of A = £109 540 SD of B = £214 240 SD of C = £1 300 000 Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury

7. 12.4b 4. The standard deviation measures dispersion around the expected value, but does not measure downside risk. 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 2 000 has the same relative variation as a SD of 2 000 with an EV of 20 000. 6. Where possible, it is preferable to focus on probability distributions rather than summary measures of EV and SD. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury

8. 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 90 0 Normal 100 100 Boom 110 200 Expected value 100 100 The probability of each outcome is 1/3. 2.The two alternatives have the same EV but different levels of risk. 3. - A risk-seeker will prefer B. - A risk-averter will prefer A. - A risk-neutral individual will be indifferent between A and B. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury

9. 12.6a Decision trees Decision trees are useful for clarifying alternative courses of action and their potential outcomes. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury

10. 12.6b Example A company is considering whether to develop and market a new product. Development costs are estimated to be £180 000, 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 £540 000. (ii) If the product is moderately successful, profits will be £100 000. (iii) If the product is a failure, there will be a loss of £400 000. Each of the above profit and loss calculations is after taking into account the development costs of £180 000. The estimated probabilities of each of the above events are as follows: (i)Very successful 0.4 (ii)Moderately successful 0.3 (iii)Failure0.3 Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury

11. 12.7 Decision tree for example on slide 6 Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury

12. 12.8a Maximin, maximax and regret criteria 1.Can be applied where it is not possible to assign meaningful probabilities to alternative courses of action. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury

13. 12.8b Example Low High demand Machine A £100 000 £160 000 Machine B £10 000 £200 000 2. With the maximin technique the largest payoff is selected based on the assumption that the worst possible outcome will occur. Machine A = £100 000 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 = £160 000 Machine B = £200 000 Decision = Choose product B 4. The aim of the regret criterion is to minimize the maximum possible regret. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury

14. 12.8c Regret table Low High demand occurs occurs Choose machine A 0 £40 000 Choose machine B £90 000 0 The maximum regret is £40 000 for A and £90 000 for B. Therefore,choose A. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury

15. 12.9 Risk reduction and diversification 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 UmbrellaIce-cream Combined manufacturing manufacturing activities £ £ £ Sunshine –40 000 +60 000 +20 000 Rain +60 000 –40 000 +20 000 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. Use with Management and Cost Accounting 8e by Colin Drury ISBN 9781408041802 © 2012 Colin Drury