1. Decision making under Risk and Uncertainty Chathuri Senarath Senior Lecturer- University of Kelaniya

2. Decision makers need to understand that they operate with uncertain futuristic information which in turn is likely to make their decision risky (due to inaccurate information taken in decision making). So for decision maker’s uncertainty & risk becomes important concepts to understand & mitigate eventually (if possible) in strengthening the decision making process of their respective organizations. RiskUncertainty Term used when there is a possibility of actual outcome varying from the expected outcome. Decision maker has prior experience with such events Decision maker has no prior experience with such events Allows the decision maker to assign a meaningful number (probability) to the possibility of occurrence. This allows the use mathematical modelling. Gives the decision maker no option of assigning statistical values for possible outcomes Therefore outcome cannot be mathematically modelled.

3. In tackling risk & uncertainty there are number of options available: Assigning Probabilities: Expected Values & Standard Deviations Assigning Probabilities: Decision Trees Data Tables Alternative Decision Making Criteria (Maximin, Maximax, Minimax regret) Sensitivity Analysis

4. Assigning Probabilities: Expected Values & Standard Deviations

5. This method involves identifying different outcomes possible and assigning values based on the possibility of their occurrence, the values assigned are normally known as probability. Probabilities are generally assigned from a scale of 0 to 1 or 0% to 100% (from no occurrence to full occurrence).If all the possible outcomes and their probabilities identified are shown together it’s normally known as a probability distribution. With probabilities assigned, decision making is normally based on the expected value calculation - which is similar to the average value calculation. Average value is calculated:

6. The problem with the above formula is that every outcome possible is given an equal weight (1/n). However in reality, the uncertainty and risk components of various outcomes tend to differ. So the equal weight (1/n) now needs to be replaced by different weightages (probabilities) giving a new formula:

7. With probabilities assigned, risk quantification is normally based on the definition of risk and uncertainty (possibility that actual outcomes might vary from that of expected.) So this deviation possible, which is normally measured through standard deviation (SD) identifies the level of risk under each product. Normal SD calculation uses the following formula. The problem with the above formula is that every deviation identified is given the same weight, where as in normal risk and uncertainty situations the probabilities from one outcome to another normally differ. So the formula now needs to be modified (as in AV to EV calculation) based on the different probabilities.

8. Question 01: A manager is considering whether to make product A or Product B, but only one can be produced. The estimated sales demand for each product is uncertain. A detailed investigation of the possible sales demand for each product gives the following probability distribution of the profits for each product. Product A Product B Outcome (in Profit) Estimated probability Outcome (in Profit) Estimated probability 60000.140000.05 70000.260000.1 80000.480000.4 90000.2100000.25 100000.1120000.20

9. Product A – Probability distribution table Product B – Probability distribution table Outcome (in Profit) Estimated probabilityWeighted Outcome (in Profit) Estimated probability Weighted 60000.160040000.05 70000.2140060000.1 80000.4320080000.4 90000.21800100000.25 100000.11000120000.20 Expected value8000 Expected value Using EV approach the company’s decision would be to produce ………….

10. Product A Profit deviation from EV Squared deviationProbability Weighted amount 6000 – 8000 = -20004,000,0000.1400,000 7000 – 8000 = -10001,000,0000.2200,000 8000 – 8000 = 000.40 9000 – 8000 = 10001,000,0000.2200,000 10000 – 8000 = 20004,000,0000.1400,000 Sum of weighted average1,200,000 Standard deviation1095.45

11. Product B Profit deviation from EV Squared deviationProbability Weighted amount Sum of weighted average Standard deviation Using SD approach the company’s decision would be to produce ………………..

12. Thus, after assigning probabilities we have looked at how to quantify return (EV) and risk (SD), but the exact decision making depends on the decision maker’s ‘risk return trade-off’ or in other words, decision maker’s ‘risk reward characteristics’. Risk/Return trade-off argument generally identifies three different types of decision makers: viz. Risk averse These are the decision makers who are reluctant to take excessive risks, but will generally take risks if the return is over and above the proportionate increase in risk. Risk lover/seekers These are decision makers who are willing to take more risks with the expectation of superior return. But it should be noted that many risk seekers take ‘calculated risks’ rather that ‘unplanned risk’. Risk neutral In this the decision maker is not sensitive to the risk, hence is likely to make the decision overwhelmingly on return.

13. Question 02: A company uses a third party delivery service to deliver goods to customers. The current average cost per delivery is Rs.12.50. The company is trying to decide whether to establish an in-house delivery service. A number of factors could affect the average total cost per delivery for the in-house delivery service. The table below shows the possible average total costs and the probability of each one occurring: The expected value of the average total cost, based on the probability distribution above, is Rs13. Required: Consider the decision that the company manager is likely to make, based on the probability distribution and the current delivery cost of Rs12.50 per delivery, if the manager is: Risk neutral Risk averse Risk seeking Average total costProbability Rs10.500.05 Rs10.700.10 Rs11.000.08 Rs12.100.12 Rs12.500.14 Rs12.600.16 Rs14.200.12 Rs15.600.18 Rs15.800.05

14. Assigning Probabilities: Decision Trees and Data tables

15. In ‘Question 01’ profit was identified as uncertain by citing demand as uncertain. But in reality demand might be uncertain because the selling price is uncertain, and selling price is uncertain because the cost/economy is uncertain. So in reality the end uncertainty is due to a chain reaction, therefore normal probability distribution will not work in such situations, a more useful technique is ‘decision trees’. When constructing decision trees there are two points to consider. Decision point: The decision is normally indicated through a ‘square’ Outcome point: Any outcome due of the decision is indicated through a ‘circle’

16. Steps: Step 1: Draw the tree from left to right showing appropriate decisions and events/outcomes. Step 2: Evaluate tree from right to left carrying out these two actions: Calculate an EV at each outcome point. Choose the best option at each decision point Step 3: Recommend a course of action to management

17. Question 03: 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 it is unsuccessful. If the development is successful, the product will be marketed, and it is estimated that: product is very successful profits will be 540,000 product is moderately successful profit will be 100,000 If the product is a failure, there will be a loss of 400.000 The above forecasts are after taking the development cost in to consideration. The estimated probabilities for each of the above events are as follows; - Very successful: 0.4 - Moderately successful: 0.3 - Failure: 0.3 Required: i) Draw a decision tree and identify the expected value of the decision. ii) Draw a probability table

19. ‘Decision Trees’ (& Decision making based on Expected Values) is generally criticized based on the following points: In decision making, with probabilities, the EV calculation used is with the assumption that numbers of outcomes are possible simultaneously, but in reality only one outcome would happen. EV heavily depends on probabilities assigned. Such assignment requires prior experience which is not possible or is difficult in the case of a new project. It is argued that although ‘decision trees’ identifies a chain reaction of uncertain events, there can be simultaneous uncertainties and decision trees cannot incorporate all such situations. Ex: success of a marketing plan depends on the success of the product development, competition levels, going market sentiments, support from authorities and etc. And if the project lasts for more than one year we need to incorporate time value for money.

20. Data (Payoff) Tables ‘Data/Payoff tables’ is an approach used to identify the various outcomes possible when multiple variables are changing. Question 04: A company is planning to launch a new product. The price at which it can sell the product will be determined by the number of other entrants into the market. The possible selling prices and variable costs and their respective associated probabilities are as follows: (i) Prepare a payoff table based on contribution. (ii) Construct probabilities to the payoff table, and calculate EV of the contribution per unit. (iii) Calculate the probability of the contribution being greater than Rs39 per unit Selling price per unitVariable cost per unit RsProbabilityRsProbability 800·25400·20 1000·30600·55 1200·45800·25

21. Payoff table based on contribution Payoff TableSelling price per unit Rs80Rs100Rs120 Variable cost per unit Probability0.250.300.45 Rs400·20 Rs600·55 Rs800·25

22. EV of contribution per unit: Expected value of selling price per unit …………………………………………………………………………….. Expected value of variable cost per unit ……………………………………………………………………………… Expected value of contribution per unit = ……………..

23. Probability of the contribution being greater than Rs39 per unit using the below table is: Payoff Table (with probabilities) Selling price per unit Rs80Rs100Rs120 Variable cost per unit Probability0.250.300.45 Rs400·20 Rs600·55 Rs800·25

24. Maximin, Maximax and Minimax regret

25. In tackling risk and uncertainty the above three methods had a heavy dependence on probabilities, but if assigning meaningful probabilities is a problem, three alternative criterion are available to make the decision: viz. Maximin The decision making is done with the assumption that ‘the worst possible outcome will happen and choose the best alternative under that’. Under profit situation: Take the maximum of the minimum (worst) achievable profit (Maximin) Under cost situation: Take the minimum of the maximum (worst) cost possible (Minimax) Maximax The decision making is done with the Assumption that the ‘best will happen and choose the best alternative out of it’ Under profit situations: Maximize the maximum (best) achievable profit (Maximax) Under cost situation: Minimize the minimum (best) cost (Minimin)

26. Minimax Regret In this technique, the decision maker looks to assign a value to the ‘state of mind’ post-decision making (after the decision is made), although currently, the decision maker is still in the pre-decision making stage. In other words; if an alternative is selected and it is not the right one there will be regret, and the decision making is now based on minimizing that maximum regret (least opportunity cost).

27. Question 05: Boston Company must choose between one of two machines-machine A has low fixed costs and high unit variable costs whereas machine B has high fixed costs and low unit variable costs. Consequently, machine A is most suited to low-level demand whereas machine B is suited to high level demand. It is expected that there will be two demand levels low and high with equal probability. The estimated profit for each demand level is as follows; Identify the best machine based on Maximin, Maximax, and Minimax regret criterions. Low demandHigh demand Machine A100,000160,000 Machine B10,000200,000

28. Value of information

29. The ‘alternative criteria decision making’ was required due to lack of certainty about future circumstances. But it is generally accepted that if a specialist external consultant was used the uncertainty can be eliminated (at least minimized). However since there is a cost involved in consulting an expert, organization need to identify the gain they stand to achieve in bringing a consultant onboard, and this gain would be the maximum the company should be willing to pay for better information (this is generally known as value of information).

30. Value of the information depends on the perfectness of information Perfect informationImperfect information Forecast of the future outcome is always correct. Forecast is usually correct but can be incorrect as well. If a firm can obtain 100% accurate prediction they can undertake the best course of action. Imperfect information needs to be further examined before using to take any decision. Highly valuable.Not as valuable as perfect information.

31. Question 06: A company has to decide which of three mutually exclusive projects to invest in during the next year. The directors believe that the success of the projects will vary depending on consumer demand. There is a 20% chance that consumer demand will be above average; a 45% chance that consumer demand will be average and a 35% chance that consumer demand will be below average. The net present value for each of the possible outcomes is as follows: A market research company believes it can provide perfect information on potential consumer demand in this market. Required: Calculate, on the basis of expected value, the maximum amount that should be paid for the information from the market research company. Consumer demand Project AProject BProject C Rs000s Above average 400300800 Average500400600 Below average 700600300

33. Sensitivity Analysis

34. Sensitivity analysis generally involves identifying how responsive is the each uncertain factor, when changes are made to the original items taken to calculate it. The motive behind this new sensitivity analysis is to identify the most critical element/elements of the decision made, by measuring the extent to which each individual element must change before it causes the decision maker to change their decision. StrengthsWeaknesses Not complicated to understand. Assumes changes to variables can be made independently. Facilitate the subjective judgment to decide different possible outcomes and their possibility. Only look at the extent to which the variable can be changed not the probability. Can identify different factors and aspects which are crucial to the success of the project. Even though information are provided it doesn’t point towards the correct decision.

35. Question 07: A company is planning to undertake an investment with 2m NPV, where investment is 2m and PV of future cash inflow is 6m and PV of future cash outflow is 2m. Required: Calculate sensitivity of the NPV if company now estimate the PV of cash inflow is likely to reduce by 1.5m. Calculate the sensitivity of the investment decision to a change in each of the original items taken to calculate NPV.