MANAGEMENT AND COST ACCOUNTING SIXTH EDITION COLIN DRURY

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

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

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 0.9 0.6 Do not pass 0.1 0.4 1.0 1.0 4. Probability distributions provide more meaningful information than stating the most likely outcome (i.e.both students will pass). © 2000 Colin Drury

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

12.2b Example Product A probability distribution (1) (2) (3) (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 © 2000 Colin Drury

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 £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? © 2000 Colin Drury

12.4a 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 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

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 £122 000 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 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. © 2000 Colin Drury

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 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. © 2000 Colin Drury

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

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) Failure 0.3 © 2000 Colin Drury

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

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

12.8b Example Low High demand 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. © 2000 Colin Drury

12.8c Regret table Low High demand 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. © 2000 Colin Drury

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 –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. © 2000 Colin Drury