1. ACCOUNTING FOR RISK AND UNCERTAINTY
UNIT 7
ACCOUNTING FOR RISK AND UNCERTAINTY

2. INTRODUCTION
Decision making involves making decisions now which will affect future outcomes and it is unlikely that future cash flows will be known with certainty.
Risk
Risk exists where a decision maker has knowledge that several possible future outcomes are possible, usually due to past experience.
This past experience enables a decision maker to estimate the probability of the likely occurrence of each potential future outcome.

3. INTRODUCTION Uncertainty
Uncertainty exists when the future is unknown and the decision maker has no past experience on which to base predictions.
Techniques can be adopted to reduce uncertainty.
These might include:
market research
focus groups

4. RISK PREFERENCE
Risk preference is the term used to describe an investor /decision maker ‘s attitude to risk.
There is a relationship between risk and required reward , though individuals have different risk/reward profiles.
Decision makers are often classified into three groups as follows:
Risk seeker
An optimist. A decision maker who is interested in the best outcomes no matter how small a chance that they may occur.
ect

5. RISK PREFERENCE
Risk neutral
– A decision maker who is concerned with the most likely outcome.
Risk averse
– A pessimist.
A decision maker who acts on the assumption that the worst outcome might occur.

6. EXAMPLE:RISK PREFERENCE
Investment A B
Expected NPV K10, K10,000
Highest possible K25, K11,000
Lowest possible K(10,000) K9,000
Required
Which investment would be chosen by a decision maker who is:
(a) Risk seeking?
(b) Risk neutral?
(c) Risk averse?

7. TECHNIQUES TO APPRAISE UNCERTAINTY
The most commonly used techniques to appraise uncertainty and provide information to the decision maker are:
The pay off matrix or table.
Decision trees.
The pay of table is often used for single decisions, whereas decision trees are used for more complex situations where there are a number of interconnected decisions required.

8. TECHNIQUES TO APPRAISE UNCERTAINTY
In business decision making situations where the manager is confronted with uncertainty outcomes include the following:
The best case, where all variables combine to produce the most favourable possible outcome.
The worst case, where all variables combine to produce the least favourable possible outcome.
The expected case, where all variables combine to produce an outcome based on the weighted average of their probabilities.

9. THE SINGLE DECISIONS AND THE PAY OFF MATRIX
The pay off matrix is a tabular layout specifying the result (pay off ) of each combination of decision and the state of the world over which the decision maker has no control.

10. EXAMPLE:THE PAY OFF MATRIX
A company has three new products A,B and C of which it can introduce only one.
The level of demand for each course of action might be low, medium or high.
If the company decides to introduce product A, the net income that would result from the levels of demand are estimated at K20,000 , K40,000 and K50,000 respectively.
Similarly, if product B is chosen ,net income is estimated at K80,000 , K70,000 and K(10,000) and for product C K10,000 , K100,000 and K40,000 respectively.
Construct a pay off matrix to present this information concisely.

11. DECISION METHODS
Possible criteria for making a choice in situations involving A ,B and C above are as follows:
Maximin rule.
Maximax rule.
Minimax regret rule
Maximisation of expected values.
It is important to appreciate that no one criteria can be right or wrong.
They are alternatives and the one that is adopted in any given situation depends on circumstances and the attitude to risk of the decision maker.

12. MAXIMIN DECISIONS Maximise the minimum return of each decision.
Risk averse decision-maker.
This approach seeks to achieve the best results if the worst happens.
The logic here follows the ‘sod law’ principle.
If a bad outcome can happen ,then (no matter how unlikely the combination of circumstances required to make it happen) it will happen.
Apply the maximin rule to the example in the A/B/C case above to select a course of action.

13. CRITICISMS OF MAXIMIN
It is defensive and conservative, being a safety first principle of avoiding the worst outcomes without taking into account opportunities for maximising profits.
It ignores the probability of each different outcome taking place.

14. MAXIMAX DECISIONS
The maximax criterion looks at the best possible results.
Maximax means 'maximise the maximum profit'.
Commonly used by Risk seeking decision maker.
Apply the maximax rule to the example in the A/B/C case above to select a course of action. .

15. CRITICISMS OF MAXIMAX
Introducing product C will ensure maximum pay off if the best result were to happen in each case.
This decision making criteria has the following short comings:
Ignores the probability of each outcome occurring
Is overly optimistic

16. MINIMAX REGRET DECISION RULE
Regret' means opportunity cost from making the wrong decision.
The decision rule chooses the option which minimises the maximum opportunity cost from making the wrong decision.
Regret is opportunity loss through having made the wrong decision.
Opportunity losses for a given market state are obtained by subtracting each value in the row from the highest value in that row.

17. EXPECTED VALUES
The fundamental weakness of above rules is that they take no account of the relative likelihood of each of the possible outcomes occurring.
Where there is uncertainty and a range of possible future outcomes has been quantified (for example, best, worst and most likely) probabilities can be assigned to these outcomes and a weighted average (expected value) of those outcomes calculated.
Expected values indicate what an outcome is likely to be in the long term with repetition

18. EXPECTED VALUES
The expected value of a particular action is defined as the sum of the values of the possible outcomes each multiplied by their respective probabilities.
EV = px
where p is the probability of the outcome occurring and x is the value of the outcome (profit or cost).
When faced with a number of alternative decisions, the one with the highest EV should be chosen.

19. EXAMPLE:EXPECTED VALUES
Using data earlier given for product A , B and C and the following probabilities:
Low demand
Medium demand
High demand
Total
Apply the maximisation of expected values to decide the best course of action for the company?

20. LIMITATIONS OF EXPECTED VALUES
EV is a long-term average, so that the EV will not be reached in the short term and is therefore not suitable for one-off decisions.
The results are dependent on the accuracy of the probability distribution.
In particular, it uses discrete variables rather than continuous variables (i.e. variables are point estimates rather than a continuous range).
This may not accurately model the real situation.
EV takes no account of the risk associated with a decision.
The EV itself may not represent a single possible outcome.

21. TWO WAY DATA TABLE Purpose:
If there are two variables about which a company is concerned when planning, a two way data table can be prepared (using a spreadsheet model) which will display all possible outcomes.
Analysis:
Analysis could take the form of expected values or the data table could be used only to give management an overview of the decision it is facing.

22. TWO WAY DATA TABLE
Browns Ltd manufactures and sells a single product in a competitive market. The unit cost is K19 but sales price and demand are both uncertain. Brown Ltd believes that the following circumstances could occur:
Price Prob Demand Prob
K Units , , ,
Brown Ltd has fixed costs of K320,000.

23. TWO WAY DATA TABLE Required
Construct a two-way data table for contribution generated.
Calculate the expected value of Brown Ltd's contribution and also calculate the expected profit.
What is the probability of Brown Ltd at least breaking even?

24. DECISION TREES
A decision tree is a pictorial method of showing a sequence of interrelated decisions and their expected outcomes.
Decision trees can incorporate both probabilities of and values of expected outcomes and are used in decision making.
Exactly how does the use of a decision tree permit a clear and logical approach?
All the possible choices that can be made are shown as branches on the tree.
All the possible outcomes of each choice are shown as subsidiary branches on the tree.

25. CONSTRUCTING A DECISION TREE
There are two stages in preparing a decision tree.
Drawing the tree itself to show all the choices and outcomes
Putting in the numbers (the probabilities, outcome values and EVs)
Every decision tree starts from a decision point with the decision options that are currently being considered.

26. CONSTRUCTING A DECISION TREE
It helps to identify the decision point, and any subsequent decision points in the tree with a symbol.
We normally use the square shape to indicate a decision point.
There is normally a line or branch for each option or alternative.
It is conventional to draw decision trees from left to right and so a decision start as follows;

27. CONSTRUCTING A DECISION TREEB C D

28. CONSTRUCTING A DECISION TREE
The square is the decision point and A,B,C and D represent four alternatives from which a choice must be made (such as buy a new machine with cash ,hire a machine ,continue to use existing machine, raise a loan to buy a machine).
If the outcome from any choice is certain the branch of the decision tree for the alternative is complete.
If the outcome of a particular choice is uncertain, the various possible outcomes must be shown.

29. CONSTRUCTING A DECISION TREE
We show the various possible outcomes on a decision tree by inserting an outcome point on the branch of the tree.
Each possible outcome is then shown as a subsidiary branch coming out from outcome point.
The probability of each outcome occurring should be written on to the branch of the tree which represents the outcome.
To distinguish decision points from outcome points, a circle is normally used as the symbol for an outcome point

30. CONSTRUCTING A DECISION TREE
0.6 High sales B
0.4 Low sales

31. CONSTRUCTING A DECISION TREE
In the above graph there are two choices facing the decision maker A and B.
The outcome if A is chosen is known with certainty, but if B is chosen there are two possible outcomes, high sales (0.6 probability) or low sales (0.4 probability).
When several outcomes are possible it usually simpler to show two or more stages of outcome points on the decision tree.
Sometimes a decision taken now will lead to other decisions to be taken in the future.
When this situation arises the decision tree can be drawn as follows:

32. CONSTRUCTING A DECISION TREE
Decision A
0.7
Decision B
Decision C
Decision X
0.3
Decision D
Decision Y

33. CONSTRUCTING A DECISION TREE
In this tree either a choice between A and B or else a choice between C and D will be made depending outcome which occurs after choosing X.
The decision tree should be in chronological order from left to right.
When there are two stage decision trees the first decision in time should be drawn on the left.

34. EXAMPLE:A DECISION TREE
Beethoven has a new wonder product, the vylin, of which it expects great things.
At the moment the company has two courses of action open to it, to test market the product or abandon it.
If the company test markets it, the cost will be K100, 000 and the market response could be positive or negative with probabilities of 0.60 and 0.40.

35. EXAMPLE:A DECISION TREE
If the response is positive the company could either abandon the product or market it full scale.
If it markets the vylin full scale, the outcome might be low, medium or high demand, and the respective net gains/(losses) would be (200), 200 or 1,000 in units of K1,000 (the result could range from a net loss of K200,000 to a gain of K1,000,000).
These outcomes have probabilities of 0.20, 0.50 and 0.30 respectively.

36. EXAMPLE:A DECISION TREE
If the result of the test marketing is negative and the company goes ahead and markets the product, estimated losses would be K600, 000.
If, at any point, the company abandons the product, there would be a net gain of K50, 000 from the sale of scrap.
All the financial values have been discounted to the present.
Required
Draw a decision tree.
Include figures for cost, loss or profit on the appropriate branches of the tree.

37. EVALUATING THE DECISION WITH A DECISION TREE
Rollback analysis evaluates the EV of each decision option.
You have to work from right to left and calculate EVs at each outcome point.
The EV of each decision option can be evaluated, using the decision tree to help with keeping the logic on track.
The basic rules are as follows.
We start on the right hand side of the tree and work back towards the left hand side and the current decision under consideration.

38. EVALUATING THE DECISION WITH A DECISION TREE
This is sometimes known as the 'rollback' technique or 'rollback analysis
Working from right to left, we calculate the EV of revenue, cost, contribution or profit at each outcome point on the tree.
In the above example, the right-hand-most outcome point is point E, and the EV at that point is as follows:

39. EVALUATING THE DECISION WITH A DECISION TREE
Profit Probability
x p px
K' K'000
High 1,
Medium
Low (200) (40) EV

40. EVALUATING THE DECISION WITH A DECISION TREE
This is the EV of the decision to market the product if the test shows positive response.
It may help you to write the EV on the decision tree itself, at the appropriate outcome point (point E).
At decision point C, the choice is as follows.
Market, EV = + 360,000 (the EV at point E)
Abandon, value = + 50,000
The choice would be to market the product, and so the EV at decision point C is +360,000.
At decision point D, the choice is as follows.
Market, value = – 600,000

41. EVALUATING THE DECISION WITH A DECISION TREE
Abandon, value = +50,000
The choice would be to abandon, and so the EV at decision point D is +50,000.
The second stage decisions have therefore been made.
If the original decision is to test market, the company will market the product if the test shows positive customer response, and will abandon the product if the test results are negative.
The evaluation of the decision tree is completed as follows

42. EVALUATING THE DECISION WITH A DECISION TREE
Calculate the EV at outcome point B.
0.6 × 360,000 (EV at C) × 50,000 (EV at D)
= 216, ,000 = 236,000.
Compare the options at point A, which are as follows.
Test: EV = EV at B minus test marketing cost = k236,000 – K100,000 = K136,000
Abandon: Value = K50,000
The choice would be to test market the product, because it has a higher EV of profit.

43. EVALUATING DECISIONS BY USING DECISION TREES HAS A NUMBER OF LIMITATIONS.
The time value of money may not be taken into account.
Decision trees are not very suitable for use in complex situations.
The outcome with the highest EV may have the greatest risks attached to it. Managers may be reluctant to take risks which may lead to losses.
The probabilities associated with different branches of the 'tree' are likely to be estimates, and possibly unreliable or inaccurate

44. THE VALUE OF INFORMATION
Perfect information is guaranteed to predict the future with 100% accuracy.
Imperfect information is better than no information at all but could be wrong in its prediction of the future.
The value of perfect information is the difference between the EV of profit with perfect information and the EV of profit without perfect information.
Perfect information removes all doubt and uncertainty from a decision, and enables managers to make decisions with complete confidence that they have selected the optimum course of action

45. THE VALUE OF PERFECT INFORMATION
STEP 1:
If we do not have perfect information and we must choose between two or more decision options, we would select the decision option which offers the highest EV of profit.
This option will not be the best decision under all circumstances.
There will be some probability that what was really the best option will not have been selected, given the way actual events turn out.

46. THE VALUE OF PERFECT INFORMATION
STEP 2:
With perfect information, the best decision option will always be selected.
The profits from the decision will depend on the future circumstances which are predicted by the information; nevertheless, the EV of profit with perfect information should be higher than the EV of profit without the information.
STEP 3: The value of perfect information is the difference between these two EVs.

47. EXAMPLE: THE VALUE OF PERFECT INFORMATION
The management of Ivor Ore must choose whether to go ahead with either of two mutually exclusive projects, A and B. The expected profits are as follows.
Profit if there is strong demand
Profit/ (loss) if there is weak demand
Option A
K4, 000
K (1,000)
Option B
K1, 500
K500
Probability of demand
0.3
0.7

48. EXAMPLE: THE VALUE OF PERFECT INFORMATION
Required
Ascertain what the decision would be, based on expected values, if no information about demand were available.
Calculate the value of perfect information about demand.

49. SENSITIVITY ANALYSIS
Sensitivity analysis is a term used to describe any technique whereby decision options are tested for their vulnerability to changes in any 'variable' such as expected sales volume, sales price per unit, material costs, or labour costs.
Typically this involves changing the value of a variable and seeing how the results are affected
Sensitivity analysis can be used in any situation so long as the relationships between the key variables can be established

50. SENSITIVITY ANALYSIS
Here are three useful approaches to sensitivity analysis.
To estimate by how much costs and revenues would need to differ from their estimated values before the decision would change.
To estimate whether a decision would change if estimated costs were x% higher than estimated, or estimated revenues y% lower than estimated.

51. SENSITIVITY ANALYSIS
To estimate by how much costs and/or revenues would need to differ from their estimated values before the decision maker would be indifferent between two options.
The essence of the approach, therefore, is to carry out the calculations with one set of values for the variables and then substitute other possible values for the variables to see how this affects the overall outcome.

52. EXAMPLE: SENSITIVITY ANALYSIS
Sensivite has estimated the following sales and profits for a new product which it may launch on to the market.
K K
Sales (2,000 units) 4,000
Variable costs: materials ,000
labour ,000
(3,000)
Contribution ,000
Less incremental fixed costs
Profit
Required :Analyse the sensitivity of the project.

53. THE END OF UNIT SEVEN