## RISK AND UNCERTAINTY

An example of a **risky situation **is one in which we can say that there is a 70% probability that returns from a project will be in excess of RWF100 million but a 30% probability that returns will be less than RWF100 million. If we cannot predict an outcome or assign probabilities, we are faced with an **uncertain** situation.

**Risk** involves situations or events which may or may not occur, but whose probability of occurrence can be calculated statistically and the frequency of their occurrence predicted from past records. Thus insurance deals with risk.

**Uncertain events** are those whose outcome cannot be predicted with statistical confidence

In everyday usage the terms risk and uncertainty are not clearly distinguished. If you are asked for a definition, do not make the mistake of believing that the latter is a more extreme version of the former. It is not a question of degree, it is a question of whether or not sufficient information is available to allow the lack of certainty to be quantified. As a rule, however, the terms are used interchangeably.

### Risk preference

People may be **risk seekers**, **risk neutral **or **risk averse**.

A **risk seeker** is a decision maker who is interested in the best outcomes no matter how small the chance that they may occur.

A decision maker is **risk neutral** if s/he is concerned with what will be the most likely outcome.

A **risk averse** decision maker acts on the assumption that the worst outcome might occur.

This has clear implications for managers and organisations. A **risk seeking manager** working for an **organisation** that is characteristically **risk averse** is likely to make decisions that are **not congruent with the goals of the organisation**. There may be a role for the management accountant here, who could be instructed to present decision-making information in such a way as to ensure that the manager considers *all *the possibilities, including the worst.

## ALLOWING FOR UNCERTAINTY

Management accounting directs its attention towards the **future **and the future is **uncertain**. For this reason a number of methods of taking **uncertainty** into consideration have evolved.

### Research techniques to reduce uncertainty

**Market research** can be used to reduce uncertainty.

**Market research** is the systematic process of gathering, analysing and reporting data about markets to investigate, describe, measure, understand or explain a situation or problem facing a company or organisation.

Market research involves **tackling problems**. The assumption is that these problems can be solved, no matter how complex the issues are, if the researcher follows a line of enquiry in a **systematic** way, without losing sight of the main objectives. Gathering and analysing all the facts will ultimately lead to **better decision making. **

**The role of market research **

In the last 20 years or so market research has become a much more widespread activity. Organisations – in the private sector, the public sector and the not-for-profit sector – rely on research to inform and improve their **planning and decision making**.

Market research enables organisations to understand the needs and opinions of their customers and other stakeholders. Armed with this knowledge they are able to make better quality decisions and provide better products and better services.

Thus, research influences what is provided and the way it is provided. It **reduces uncertainty and monitors performance.** A management team which possesses accurate information relating to the marketplace will be in a strong position to make the best decisions in an increasingly competitive world.

Decision-makers need data to reduce **uncertainty **and **risk **when planning for the future and to monitor business performance. Market researchers provide the data that help them to do this.

**Types of data collected **

Data can be either **primary **(collected at first hand from a sample of respondents), or **secondary **(collected from previous surveys, other published facts and opinions, or from experts). Secondary research is also known as **desk research**, because it can be carried out from one’s desk.

More importantly for research practice and analysis, data can be either quantitative or qualitative.

**Quantitative **data usually deal with numbers and typically provide the decision maker with information about **how many **customers, competitors etc act in a certain way. Quantitative data can, for example, tell the researcher **what **people need or consume, or **where**, **when **and **how **people buy goods or consumer services.

**Qualitative **data tell us **why **consumers think/buy or act the way they do. Qualitative data are used in **consumer insight **(eg understanding what makes consumers prefer one brand to another), **media awareness **(eg how much of an advertisement is noticed by the public), **new product development **studies and for many other reasons.

**Qualitative research **has as its specific purpose the uncovering and understanding of thought and opinion. It is carried out on relatively small samples and unstructured or semi-structured techniques, such as individual in depth interviews and group discussions (also known as **focus groups**), are used.

### Conservatism

This approach simply involves estimating outcomes in a conservative manner in order to provide a built-in safety factor.

However, the method fails to consider explicitly a **range** of outcomes and, by concentrating only on conservative figures, may also fail to consider the **expected** or most likely outcomes.

Conservatism is associated with **risk aversion **and prudence (in the general sense of the word). In spite of its shortcomings it is probably the **most widely used **method in practice.

### Worst/most likely/best outcome estimates

A more scientific version of conservatism is to measure the most likely outcome from a decision, and the worst and best possible outcomes. This will show the **full range of possible outcomes **from a decision, and might help managers to reject certain alternatives because the worst possible outcome might involve an unacceptable amount of loss. This requires the preparation of **pay-off tables.**

**Pay-off tables **

Pay-off tables **identify and record all possible outcomes (or pay-offs) **in situations where the action taken affects the outcomes.

## PROBABILITIES AND EXPECTED VALUES

**Expected values **indicate what an outcome is likely to be in the long term with repetition. Fortunately, many business transactions do occur over and over again.

Although the outcome of a decision may not be certain, there is some likelihood that probabilities could be assigned to the various possible outcomes from an analysis of previous experience.

### Expected values

Where probabilities are assigned to different outcomes we can evaluate the worth of a decision as the **expected value***,* or weighted average, of these outcomes. The principle is that when there are a number of alternative decisions, each with a range of possible outcomes, the optimum decision will be the one which gives the highest expected value.

**Limitations of expected values **

The preference for B over A on the basis of expected value is marred by the fact that A’s **worst possible** outcome is a profit of RWF5,000, whereas B might incur a loss of RWF2,000 (although there is a 70% chance that profits would be RWF7,000 or more, which would be more than the best profits from option A).

Since the decision must be made **once only **between A and B, the expected value of profit (which is **merely a weighted average **of all possible outcomes) has severe limitations as a decision rule by which to judge preference. The expected value will almost **never actually occur**.

Expected values are used to support a **risk-neutral attitude**. A risk-neutral decision maker will ignore any variability in the range of possible outcomes and be concerned only with the expected value of outcomes.

Expected values are more valuable as a guide to decision making where they refer to outcomes which will occur **many times over***.* Examples would include the probability that so many customers per day will buy a can of baked beans, the probability that a customer services assistant will receive so many phone calls per hour, and so on.

## DECISION RULES

The ‘play it safe’ basis for decision making is referred to as the **maximin basis**. This is short for ‘**maximise the minimum achievable profit**‘.

A basis for making decisions by looking for the best outcome is known as the **maximax basis**, short for **‘maximise the maximum achievable profit’**.

The ‘opportunity loss’ basis for decision making is known as **minimax** **regret**.

### The maximin decision rule

The **maximin decision rule **suggests that a decision maker should select the alternative that offers the least unattractive of the worst outcomes. This would mean choosing the alternative that* maximises *the *minimum *profits.

Suppose a businessman is trying to decide which of three mutually exclusive projects to undertake. Each of the projects could lead to varying net profit under three possible scenarios.

**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.

### Maximax

The **maximax criterion **looks at the best possible results. Maximax means ‘maximise the maximum profit’.

Using the information above, the maximum profit for D is 100, for E is 120 and for F is 85.

Project E would be chosen if the maximax rule is followed.

**Criticisms of maximax **

- It ignores probabilities.
- It is
**over-optimistic**.

### Minimax regret rule

The **minimax regret rule **aims to minimise the regret from making the wrong decision. **Regret** is the opportunity lost through making the wrong decision.

We first consider the extreme to which we might come to regret an action we had chosen.

Regret for any = Profit for best action in – Profit for the action combination of action those circumstances actually chosen in and circumstances those

circumstances

The minimax regret decision rule is that the decision option selected should be the one which **minimises the maximum potential regret** for any of the possible outcomes.

Using the example above, a table of regrets can be compiled as follows.

The **lowest **of maximum regrets is 40 with project F so project F would be selected if the minimax regret rule is used.

### Contribution tables

Questions requiring application of the decision rules often incorporate a **number of variables, each with a range of possible values**. For example these variables might be:

- Unit price and associated level of demand
- Unit variable cost

Each variable might have, for example, three possible values.

Before being asked to use the decision rules, exam questions could ask you to **work out** **contribution** for each of the possible outcomes. (Alternatively profit figures could be required if you are given information about fixed costs.)

## DECISION TREES

**Decision trees** are diagrams which illustrate the choices and possible outcomes of a decision.

**Rollback analysis** evaluates the EV of each decision option. You have to work from right to left and calculate Evs at each outcome point.

A probability problem such as ‘what is the probability of throwing a six with one throw of a die? Is fairly straightforward and can be solved using the basic principles of probability.

More complex probability questions, although solvable using the basic principles, require a clear logical approach to ensure that all possible choices and outcomes of a decision are taken into consideration.

**Decision trees **are a useful means of interpreting such probability problems.

A **decision tree **is a pictorial method of showing a sequence of interrelated decisions and their expected outcomes. Decision trees can incorporate both the 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.

*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.

- It helps to identify the
**decision point**, and any subsequent decision points in the tree, with a symbol. Here, we shall use a**square shape**. - There should be a
**line**, or**branc**h, for each**option**or**alternative**

**It is conventional to draw decision trees from left to right ,**and so a decision tree will start as follows.

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 that alternative is complete. **

If the outcome of a particular choice is uncertain, the various possible outcomes must be shown.

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 form the outcome point. The probability of each outcome occurring should be written on the branch of the tree which represents that outcome.

To distinguish decision points from outcome points, **a circle will be used as the symbol for an outcome point. **

In the example above, there are two choices facing the decision-maker, A and B. The outcome if A is chosen is known with certainly, 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 is usually simpler to show two or more stage of outcome points on the decision tree. **

**Example: Several possible outcomes **

A company can choose to launch a new product XYZ or not. If the product is launched, expected sales and expected unit costs might be as follows.

Sales | Units costs | ||

Units | Probability | RWF | Probability |

10,000 | 0.8 | 6 | 0.7 |

15,000 | 0.2 | 8 | 0.3 |

The decision tree could be drawn as follows

The layout shown above will usually be easier to use than the alternative way of drawing the tree, which is as follows.

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 a **two –stage tree, **as follows.

In this tree, either a choice between A and B or else a choice between C and D will be made, depending on the outcome which occurs after choosing X.

The decision tree should be in **chronological order **from **left to right. **When there are twostage decision trees, the first decision in time should be drawn on the left.

### Evaluating the decision with a decision tree

**Rollback analysis **evaluates the V or 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 . 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

## 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.

*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. |

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. |

### Perfect information and decision trees

When the option exists to obtain information, the decision can be shown, like any other decision, in the form of a decision tree, as follows. We will suppose, for illustration, that the cost of obtaining perfect information is RWF400.

The decision would be to obtain perfect information, since the EV of profit is RWF4,050 – RWF400 = RWF3,650.

You should check carefully that you understand the logic of this decision and that you can identify how the EVs at outcome boxes 1, 2, 3 and 4 have been calculated.

### The value of imperfect information

There is one serious drawback to the technique we have just looked at: in practice, useful information is never perfect unless the person providing it is the sole source of the uncertainty. Market research findings or information from pilot tests and so on are likely to be reasonably accurate, but they can still be wrong: they provide imperfect information. It is possible, however, to arrive at an assessment of **how much it would be worth paying for such imperfect information, given that we have a rough indication of how right or wrong it is likely to be. **

If you check the information given in the problem, you will find that these probabilities are not given.

- We are told that the engineer has assessed that there is a 20% chance of oil and an 80% chance of no oil (ignoring information entirely). These are the
**prior probabilities**of future possible outcomes. - The
**probabilities that there will be oil or no oil once the information has been obtained are “posterior” probabilities.**

## SENSITIVITY ANALYSIS

**Sensitivity analysis **can be used in any situation so long as the relationships between the key variables can be established. Typically this involves changing the value of a variable and seeing how the results are affected.

### Approaches to 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.

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. - 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.

- From your studies of information technology you may recognise this as
**what if analysis**that can be carried out using a**spreadsheet**. - From your studies of
**linear programming**you may remember that sensitivity analysis can be carried out to determine over which ranges the various constraints have an impact on the optimum solution. **Flexible budgeting**can also be a form of sensitivity analysis.

## SIMULATION MODELS

**Simulation models **can be used to deal with decision problems involving a number of uncertain variables. **Random numbers** are used to assign values to the variables.

One of the chief problems encountered in decision making is the uncertainty of the future. Where only a few factors are involved, probability analysis and expected value calculations can be used to find the most likely outcome of a decision. Often, however, in real life, there are so **many uncertain variables** that this approach does not give a true impression of possible variations in outcome.

To get an idea of what will happen in real life one possibility is to use a **simulation model** in which the **values and the variables are selected at random**. Obviously this is a situation **ideally suited to a computer** (large volume of data, random number generation).

The term ‘simulation’ model is often used more specifically to refer to modelling which **makes use of random numbers**. This is the **‘Monte Carlo’** method of simulation. In the business environment it can, for example, be used to examine inventory, queuing, scheduling and forecasting problems.

### Uses of simulation

In the supermarket example above, the supermarket would use the information to minimise stock holding without risking running out of the product. This will reduce costs but avoid lost sales and profit.

A supermarket can also use this technique to estimate queues with predicted length of waiting time and so determine the number of staff required.

## CHAPTER ROUNDUP

- An example of a
**risky situation**is one in which we can say that there is a 70% probability that returns from a project will be in excess of RWF100m but a 30% probability that returns will be less than RWF100m. If we cannot predict an outcome or assign probabilities, we are faced with an**uncertain** - People may be
**risk seekers**,**risk neutral**or**risk averse**. - Management accounting directs its attention towards the
**future**and the future is**uncertain**. For this reason a number of methods of taking**uncertainty**into consideration have evolved. **Market research**can be used to reduce**Expected values**indicate what an outcome is likely to be in the long term with repetition. Fortunately, many business transactions do occur over and over again.- The ‘play it safe’ basis for decision making is referred to as the
**maximin basis**. This is short for ‘**maximise the minimum achievable profit**‘. - A basis for making decisions by looking for the best outcome is known as the
**maximax basis**, short for**‘maximise the maximum achievable profit’**. - The ‘opportunity loss’ basis for decision making is known as
**minimax****regret**. **Decision trees**are diagrams which illustrate the choices and possible outcomes of a decision.**Rollback analysis**evaluates the EV of each decision option. You have to work from right to left and calculate EVs at each outcome point.**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. **Sensitivity analysis**can be used in any situation so long as the relationships between the key variables can be established. Typically this involves changing the value of a variable and seeing how the results are affected.**Simulation models**can be used to deal with decision problems involving a number of uncertain variables.**Random numbers**are used to assign values to the variables.