Uncertainty and risk in decision making Management Level
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Uncertainty and risk in decision making Management Level – Paper P 2 Advanced Management Accounting Lecture 27 Vidya Rajawasam ACMA CGMA MBA
Uncertainty and risk in decision making In the previous lectures we have discussed § Risk and Uncertainty § Research techniques use to reduce uncertainty § Quantitative methods of incorporating risk and uncertainty
Uncertainty and risk in decision making In this lecture we will discuss § Quantitative methods of incorporating risk and uncertainty
Uncertainty and risk in decision making Expected Values (EV) Expected values are widely used in decision making under uncertainty. Definition An expected value is a weighted average of all possible outcomes. It calculates the average return that will be made if a decision is repeated again and again.
Uncertainty and risk in decision making Expected Values (EV) In other words EV is obtained by multiplying the value of each possible outcome (x) by the probability of that outcome (p), and summing the results. The formula for the expected value is EV = Σpx
Uncertainty and risk in decision making Expected Values (EV) Example, Returns from a new restaurant venture depend on whether a competitor decides to open up in the same area. The following estimates are made : Competitor Probability (p) Project NPV (x) $ px ($) Yes 0. 30 (10, 000) (3, 000) No 0. 70 20, 000 14, 000 EV 11, 000
Uncertainty and risk in decision making Expected Values (EV) Since the expected value shows the long run average outcome of a decision which is repeated time and time again, it is a useful decision rule for a risk neutral decision maker. This is because a risk neutral investor neither seeks risk or avoids it; he is happy to accept an average outcome.
Uncertainty and risk in decision making Expected Values (EV) Since the expected value shows the long run average outcome of a decision which is repeated time and time again, it is a useful decision rule for a risk neutral decision maker. This is because a risk neutral investor neither seeks risk or avoids it; he is happy to accept an average outcome.
Uncertainty and risk in decision making Advantages and disadvantages of EVs Disadvantages § The probabilities used are usually very subjective. § The EV is merely a weighted average and therefore has little meaning for a one off project.
Uncertainty and risk in decision making Advantages and disadvantages of EVs Advantages § Takes uncertainty into account by considering the probability of each possible outcome and using this information to calculate an expected value. § The information is reduced to a single number resulting in easier decisions. § Calculations are relatively simple.
Uncertainty and risk in decision making Advantages and disadvantages of EVs Disadvantages § The EV gives no indication of the dispersion of possible outcomes about the EV, i. e. the risk. § The EV may not correspond to any of the actual possible outcomes.
Uncertainty and risk in decision making Payoff tables A profit table (pay off table) can be a useful way to represent and analyze a scenario where there is a range of possible outcomes and a variety of possible responses. A pay off table simply illustrates all possible profits/losses and as such is often used in decision making under uncertainty.
Uncertainty and risk in decision making Payoff tables Example, Geoffrey Ramsbottom runs a kitchen that provides food for various canteens throughout a large organisation. A particular salad is sold to the canteen for $10 and costs $8 to prepare. Therefore, the contribution per salad is $2.
Uncertainty and risk in decision making Payoff tables § § Example, Based upon past demands, it is expected that, during the 250 day working year, the canteens will require the following daily quantities: On 25 days of the year, 40 salads. On 50 days of the year, 50 salads. On 100 days of the year, 60 salads. On 75 days 70 salads.
Uncertainty and risk in decision making Payoff tables Example, The kitchen must prepare the salads in batches of 10 meals in advance. The manager has asked you to help decide how many salads the kitchen should supply for each day of the forthcoming year.
Uncertainty and risk in decision making Payoff tables Solution, Constructing a pay off table: If 40 salads will be required on 25 days of a 250 day year, then the probability that demand = 40 salads is P(Demand of 40) = 25 days ÷ 250 days = 0. 1 Likewise, P(Demand of 50) = 0. 20; P(Demand of 60) = 0. 4 and P(Demand of 70) = 0. 30
Uncertainty and risk in decision making Payoff tables Solution, Now let's look at the different values of profit or losses depending on how many salads are supplied and sold. For example, if we supply 40 salads and all are sold, our profits amount to 40 x $2 = 80. If however we supply 50 salads but only 40 are sold, our profits will amount to 40 × $2 (10 unsold salads × $8 unit cost) = 80 = 0.
Uncertainty and risk in decision making Payoff tables Solution, Similarly, we can now construct a pay off table as follows:
Uncertainty and risk in decision making Review MCQs The advantages of Excepted Value calculations ? a. The information is reduced to a single number resulting in easier decisions. b. Calculations are relatively simple c. Deals Only with financial risks. d. Non of the above
Uncertainty and risk in decision making Review MCQs The advantages of Excepted Value calculations ? a. The information is reduced to a single number resulting in easier decisions. b. Calculations are relatively simple c. Deals Only with financial risks. d. Non of the above
Uncertainty and risk in decision making Review MCQs What is the true statement related to the pay off tables? a. Provides additional information related to project costs. b. How responsive the project’s NPV is to changes in the variables used c. A pay off table simply illustrates all possible profits/losses. d. Non of the above.
Uncertainty and risk in decision making Review MCQs What is the true statement related to the pay off tables? a. Provides additional information related to project costs. b. How responsive the project’s NPV is to changes in the variables used c. A pay off table simply illustrates all possible profits/losses. d. Non of the above.
Uncertainty and risk in decision making Maximax, maximin and minimax regret Maximin, maximax and minimax regret are three approaches to decision making under uncertainty.
Uncertainty and risk in decision making Maximax, maximin and minimax regret Maximax The maximax rule involves selecting the alternative that maximises the maximum payoff available. This approach would be suitable for an optimist, or 'risk seeking' investor, who seeks to achieve the best results if the best happens. The manager who employs the maximax criterion is assuming that whatever action is taken, the best will happen; he/she is a risk taker. So, how many salads will Geoffrey decide to supply?
Uncertainty and risk in decision making Maximax, maximin and minimax regret Maximax Looking at the payoff table, the highest maximum possible pay off is $140. This happens if we make 70 salads and demand is also 70. Geoffrey should therefore decide to supply 70 salads every day.
Uncertainty and risk in decision making Maximax, maximin and minimax regret Maximin The maximin rule involves selecting the alternative that maximises the minimum pay off achievable. The investor would look at the worst possible outcome at each supply level, then selects the highest one of these. The decision maker therefore chooses the outcome which is guaranteed to minimize his losses. In the process, he loses out on the opportunity of making big profits.
Uncertainty and risk in decision making Maximin This approach would be appropriate for a pessimist who seeks to achieve the best results if the worst happens. How many salads will Geoffrey decide to supply? Looking at the payoff table, § If we decide to supply 40 salads, the minimum pay off is $80. § If we decide to supply 50 salads, the minimum pay off is $0.
Uncertainty and risk in decision making Maximin Looking at the payoff table, § If we decide to supply 60 salads, the minimum pay off is ($80). § If we decide to supply 70 salads, the minimum pay off is ($160). The highest minimum payoff arises from supplying 40 salads. This ensures that the worst possible scenario still results in a gain of at least $80.
Uncertainty and risk in decision making Minimax regret The minimax regret strategy is the one that minimizes the maximum regret. It is useful for a risk neutral decision maker. Essentially, this is the technique for a 'sore loser' who does not wish to make the wrong decision. 'Regret' in this context is defined as the opportunity loss through having made the wrong decision.
Uncertainty and risk in decision making Minimax regret To solve this a table showing the size of the regret needs to be constructed. This means we need to find the biggest pay off for each demand row, then subtract all other numbers in this row from the largest number. For example, if the demand is 40 salads, we will make a maximum profit of $80 if they all sell. If we had decided to supply 50 salads, we would achieve a nil profit. The difference or 'regret' between that nil profit and the maximum of $80 achievable for that row is $80.
Uncertainty and risk in decision making Minimax regret Regrets can be tabulated as follows :
Uncertainty and risk in decision making • • Minimax regret Regrets can be tabulated as follows : The maximum regrets for each choice are thus as follows (reading down the columns): If we decide to supply 40 salads, the maximum regret is $60. If we decide to supply 50 salads, the maximum regret is $80. If we decide to supply 60 salads, the maximum regret is $160. If we decide to supply 70 salads, the maximum regret is $240. A manager employing the minimax regret criterion would want to minimize that maximum regret, and therefore supply 40 salads only.
Uncertainty and risk in decision making Decision Trees Decision trees are used in the context of decision making under uncertainty and are a useful tool for seeing the various possible outcomes of different decisions
Uncertainty and risk in decision making Decision Trees A decision tree is a diagrammatic representation of a multi decision problem, where all possible courses of action are represented, and every possible outcome of each course of action is shown. • Decision trees should be used where a problem involves a series of decisions being made and several outcomes arise during the decision making process.
Uncertainty and risk in decision making Decision Trees Decision trees force the decision maker to consider the logical sequence of events. A complex problem is broken down into smaller, easier to handle sections. The financial outcomes and probabilities are shown separately, and the decision tree is 'rolled back' by calculating expected values and making decisions.
Uncertainty and risk in decision making Decision Trees Method Step 1: Draw the tree from left to right, showing appropriate decisions and events / outcomes. Some common symbols can be used: § a square is used to represent a decision point (i. e. where a choice between different courses of action must be taken. § A circle is used to represent a chance point. § The branches coming away from a circle with have probabilities attached to them. All probabilities should add up to '1'.
Uncertainty and risk in decision making Decision Trees Method Some common symbols can be used: § The branches coming away from a circle with have probabilities attached to them. All probabilities should add up to '1'. Label the tree and relevant cash inflows/outflows and probabilities associated with outcomes.
Uncertainty and risk in decision making Decision Trees Method Step 2: Evaluate the tree from right to left carrying out these two actions: (a) Calculate an expected value (EV) at each outcome point. (b) Choose the best option at each decision point. Step 3: Recommend a course of action to management.
Uncertainty and risk in decision making Review MCQs The Maximax approach focuses on? a. Changes in each key variable are isolated in order to focus on combined results. b. Selecting the alternative that maximises the maximum payoff available. c. There is a lot of confusion with regard to its application. d. Non of the above.
Uncertainty and risk in decision making Review MCQs The Maximax approach focuses on? a. Changes in each key variable are isolated in order to focus on combined results. b. Selecting the alternative that maximises the maximum payoff available. c. There is a lot of confusion with regard to its application. d. Non of the above.
Uncertainty and risk in decision making Review MCQs What is true related to decision tree applications ? a. Useful tool for seeing the various possible outcomes of different decisions b. Very difficult to obtain data/information related to industry activities. c. There is a lot of confusion with regard to its application. d. Non of the above.
Uncertainty and risk in decision making Review MCQs What is true related to decision tree applications ? a. Useful tool for seeing the various possible outcomes of different decisions b. Very difficult to obtain data/information related to industry activities. c. There is a lot of confusion with regard to its application. d. Non of the above.
Uncertainty and risk in decision making Lecture Summary We have discussed the § Quantitative methods of incorporating risk and uncertainty
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