1. Cost and Management Accounting: An Introduction, 7 th edition Colin Drury ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA Cost and Management Accounting: An Introduction, 7 th edition Colin Drury ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA LEARNING NOTE 11.4 Incorporating uncertainty into the decision-making process LN11.4

2. Cost and Management Accounting: An Introduction, 7 th edition Colin Drury ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA Cost and Management Accounting: An Introduction, 7 th edition Colin Drury ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA RISK AND UNCERTAINTY 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). LN11.4 (1)

3. Cost and Management Accounting: An Introduction, 7 th edition Colin Drury ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA Cost and Management Accounting: An Introduction, 7 th edition Colin Drury ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA 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. LN11.4 (2a)

4. Cost and Management Accounting: An Introduction, 7 th edition Colin Drury ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA Cost and Management Accounting: An Introduction, 7 th edition Colin Drury ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA Example Product A probability distribution (1) (2) (3) Estimated Weighted amount Outcome probability (col.1× col. 2) £ Profits of £6 000 0.10 600 Profits of £7 000 0.20 1 400 Profits of £8 000 0.40 3 200 Profits of £9 000 0.20 1 800 Profits of £10 000 0.10 1 000 1.00 8 000 Expected value LN11.4 2b)

5. Cost and Management Accounting: An Introduction, 7 th edition Colin Drury ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA Cost and Management Accounting: An Introduction, 7 th edition Colin Drury ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA Product B probability distribution (1) (2) (3) Estimated Weighted amount Outcome probability (col. × col. 2) £ Profits of £4 000 0.05 200 Profits of £6 000 0.10 600 Profits of £8 000 0.40 3 200 Profits of £10 000 0.25 2 500 Profits of £12 000 0.20 2 400 1.00 8 900 Expected value Which product should the company make? LN11.4 (3)

6. Cost and Management Accounting: An Introduction, 7 th edition Colin Drury ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA Cost and Management Accounting: An Introduction, 7 th edition Colin Drury ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA 1.Product C probability distribution Estimated Expected Outcome probability value (EV) £ Loss of £4 000 0.5 (2 000) Profit of £22 000 0.5 11 000 9 000 2.Product C has a higher EV than either products B or C, but it is subject to greater uncertainty. LN11.4 (4a)

7. Cost and Management Accounting: An Introduction, 7 th edition Colin Drury ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA Cost and Management Accounting: An Introduction, 7 th edition Colin Drury ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA 3.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 4. The standard deviation measures dispersion around the expected value, but does not measure downside risk (i.e. measuring the possibility of deviations below the expected value). LN11.4 (4b)

8. Cost and Management Accounting: An Introduction, 7 th edition Colin Drury ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA Cost and Management Accounting: An Introduction, 7 th edition Colin Drury ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA 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. LN11.4 (4c)

9. Cost and Management Accounting: An Introduction, 7 th edition Colin Drury ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA Cost and Management Accounting: An Introduction, 7 th edition Colin Drury ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA Decision trees Decision trees are useful for clarifying alternative courses of action and their potential outcomes. LN11.4 (5a)

10. Cost and Management Accounting: An Introduction, 7 th edition Colin Drury ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA Cost and Management Accounting: An Introduction, 7 th edition Colin Drury ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA 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 LN11.4 (5b)

11. Cost and Management Accounting: An Introduction, 7 th edition Colin Drury ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA Cost and Management Accounting: An Introduction, 7 th edition Colin Drury ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA Decision tree for example on previous slide LN11.4 (6)