Management Accounting
solomonongauh
L7_Risk_and_Uncertainty_2017-181.pptxRisk and Uncertainty
AC2125
Lecture 7
Reading:
Drury : Management & Cost Accounting 9th Edition Chapter 12.
Objectives:
By the end of the lecture you should be able to :
Calculate and explain the meaning of expected values;
Construct a decision tree;
Describe and calculate the value of perfect information;
Explain and apply the maximin, maximax and regret criteria
Why do we need to consider uncertainty?
We have worked on the assumption that we know what will happen up to now. Clearly, in reality we cannot be so certain of what will happen because we cannot possibly know what other things outside of our control might influence us.
If we were to consider two alternatives, we would normally go for the one that is going to give us the biggest return. If we weren’t completely confident about the projected returns, then we would be worried that we weren’t really taking the best option.
Decision-making process
Identify objectives
The decision maker’s objective/ target (e.g. maximisation of profit)
Search for possible courses of action
How can we achieve that objective?
Identify states of nature
Because we are making the decision in an uncertain environment, we have to consider the things that could affect us that are outside of our control. A good example when setting prices would be the chance of a competitor releasing a similar or better product at the same time.
These uncontrollable factors that may occur are called ‘states of nature’ or ‘events’.
List possible outcomes
This is all possible outcomes from the combination of actions and events.
Measure profits
Having identified all the possible outcomes, then the ‘payoff’ of each needs to be calculated. These are commonly expressed in monetary terms, but as management accountants, we are also interested in non-financial measures e.g. time saved, quality, market share etc.
Select course of action
We are now in a position to make a decision.
Risk and Uncertainty in calculating the payoff.
(that is in calculating the figures we need at step 5).
Risk - we have past information to base predictions on.
Uncertainty - little or no past information to base predictions on
Most business situations would be one of uncertainty. In practice the distinction is not really important and the terms are usually used interchangeably.
The likelihood that any event will happen is its probability.
Spinning a coin. If you spin a coin, it has to come down either heads or tails.
The probability of it coming up heads is half the time i.e. 50% of the time, so the probability is represented as 0.5. The probability of it coming up tails is half the time i.e. 50% of the time, so the probability is represented as 0.5.
The probabilities of all the alternatives have to end up to 1.0.
So if the probability of a competitor doing something is 60%, then the probability of them not doing it is 40%. That is doing it = 0.6, not doing it = 0.4.
This can be shown as the Probability Distribution
Outcome Probability
Does it 0.6
Doesn’t do it 0.4
Total 1.0 Must add up to 1
In certain circumstances there can be very many possible outcomes, but the probability of all of them happening still only adds up to 1.0.
It is common to give a probability distribution for a business decision that also includes the expected financial result for each outcome as this not only shows what could happen but also the likelihood of each.
Some probabilities can be known or calculated from past data e.g. tossing a coin. These are known as objective probabilities.
Many probabilities cannot be known with certainty or there is little or no data to base the calculations on, this is the situation in most business situations. These are known as subjective probabilities.
Horse Racing; Man U v Bolton not 50:50
Subjective probabilities are based on expert knowledge, past experience, observations of current conditions and estimates. They are unlikely to be estimated correctly, it is a question of degree of error. The better your expert, the less error there will be (hopefully!). It is normal to also say how confident you are in your estimate. The more confident you are the better.
We have two products we could launch, but we can do only one. Taking into account our expectations we have the following probability distributions.
Q1. What are the expected values of each launch?
Product A Probability Distribution
Outcome
Estimated
Probability
Weighted
Profit of
£5,000
0.1
500
Profit of
£6,000
0.2
1,200
Profit of
£7,000
0.3
2,100
Profit of
£8,000
0.4
3,200
1
Expected value
£7,000
But, what are the chances of us not achieving the expected value?
Probability of not achieving the expected value for A.
0.1+0.2
=
0.3
Product B Probability
Distribution
Outcome
Estimated
Probability
Weighted
Profit of
£6,000
0.2
1,200
Profit of
£7,000
0.3
2,100
Profit of
£8,000
0.2
1,600
Profit of
£9,000
0.2
1,800
Profit of
£10,000
0.1
1,000
1
Expected value
£7,700
We then compare the two expected values and will adopt the project with the highest expected value
But, what are the chances of us not achieving the expected value?
Probability
of not achieving the expected value for B.
0.2+0.3
= 0.5
Which one of the two projects would we feel safer adopting?
A
more likely to be achieved
Drawing a decision tree.
What we have just discussed could be drawn as a decision tree. It’s a graphical representation of the decision taking process that makes it easier for us to envisage all the options and see which is the best decision.
By convention, decision points are shown by squares and possible events are shown by circles.
Start at the middle left edge of the page.
Using Decision Trees
A decision tree is a diagram that we use as an analytical device. It shows the potential outcomes for each course of action.
Each alternative is shown as a different branch of the tree. At the end of the branches (the twigs?) we will have calculated the outcome. Boxes show decisions; the branches coming from them are the alternatives. The circles indicate the points where there are environmental changes / events that change the consequences of prior decisions.
Consider this situation
A company is trying to decide between two machines of identical cost – the Giant and the Minnow. The probability of high future demand is assessed as 0.4 and low demand 0.6. If the demand is high 5,000 units can be made and sold using the Giant but only 4,000 units for the Minnow. For low demand the respective figures are 1,000 units for the Giant but 3,000 units for the Minnow. The contribution per unit for the Giant’s product is £40 and the Minnow £35 per unit.
Draw a decision tree to show the options that can occur and calculate the expected value for each machine and hence recommend which one should be purchased.
Giant
Minnow
High
Low
High
Low
Probability
0.4
0.6
1.0
0.4
0.6
1.0
Units Demand
5,000
1,000
4,000
3,000
Contribution
per Unit
£40
£40
£35
£35
Expected
Value
£80,000
£24,000
£104,000
£56,000
£63,000
£119,000
Therefore we would chose the Minnow given the above data.
Look at the Drury Example 12.2 p. 279
Development costs £180,000, 0.75 probability that it will be successful. If successful, the product will be marketed it is estimated that profit after taking into account the development cost will be :
If very successful profits will be £540,000
If moderately successful profits will be £100,000
If not successful, there will be a loss of £400,000
Estimated probability of each of the three alternatives:
Very successful 0.4
Moderately successful 0.3
Not successful 0.3
Here we have the situation of combined probabilities – where one thing occurring is dependant on another happening.
So in this situation, we need to MULTIPLY the two probabilities together to discover the likelihood of it occurring
Remember, the probability of spinning a coin and getting two heads is:
0.5 x 0.5 = 0.25 (1 in 4)
Proof: - HH; HT; TT; TH
Very
Development
succeeds
Moderate
0.75
Low
Develop
Development
Fails
0.25
Don't
Develop
Probability
0.4
0.3
0.3
1.0
Profit
£540,000
£100,000
-
£400,000
-
£180,000
£0
Combined
Probability
0.300
0.225
0.225
0.750
0.250
1.000
1.000
Expected
Value
£162,000
£22,500
-
£90,000
-
£45,000
£49,500
£0
Page for workings for example 12.3. Start at the bottom left corner of the page.
Remember doing nothing is always a possible alternative
The sum of the probabilities calculated at step 6 must be 1.0.
Check this.
Possible profit
Probability
Expected value
Profit of £540,000
0.300
£162,000
Profit of £100,000
0.225
£ 22,500
Loss of £180,000
0.250
£(45,000)
Loss of £400,000
0.225
£(90,000)
1.0
£ 49,500
The
problem for us is that the Expected Value is not a guaranteed result, its only the average we
would get if we did the project a great number of times. Most probably though, we are only going
to do it once. So what will actually happen?
Will be either :
£540,000 profit
£100,000 profit
£180,000 loss or
£400,000
N.B . Only one actual outcome can occur
How do you feel about risk?
Individuals can seek to avoid risk or be prepared to take greater levels of risk in the hope of greater levels of reward.
You could try to avoid risk – risk averse
You could be indifferent to risk
You could seek out risk – risk seeker
Buying better information – Perfect Information
When we are faced with making a decision, we might want more information. More information usually costs more (time, data analysis, consultants) all of which in some way or another costs more money.
Rather than just ask for more information and incur additional costs, we should consider whether the extra costs would be money well spent.
We should compare the expected value of the decision if we get the extra information against the expected value if we don’t get the extra information.
The difference between the two is the most it is worth paying for the additional information.
Example Drury 12.3 p. 280
Low Demand High Demand Expected Value
Machine A £100,000 £160,000 £130,000
Machine B £ 10,000 £200,000 £105,000
Two machines, B is better in situations of high demand, A is better in situations of low demand.
Assume there is only either high or low demand and the probability is 0.5 for each.
Expected Value for Machine A = (100,000 x 0.5) + (160,000 x 0.5) = £130,000
Expected Value for Machine B = (10,000 x 0.5) + (200,000 x 0.5) = £105,000
If we employ consultants we will know if it is going to be high or low demand.
How much can we afford to pay for perfect information?
Which machine would we buy if we knew demand was going to be low? Which machine would we buy if we knew demand was going to be high?
Perfect Information
Perfect Estimate – Know when Low; Know when High but cannot change probability of it occurring so we will always make the best choice based on the market conditions.
If Low = Machine A = £100,000 x 0.5 = £ 50,000
If High = Machine B = £200,000 x 0.5 = £100,000 Total £150,000
This is £20,000 more than the next largest expected value (£150,000 -£130,000 choosing Machine A ) so we would be prepared to pay up to but not more than £20,000 to gain this advantage.
Maximin
,
maximax
and regret criteria.
You
can’t always come up with plausible probabilities, so you can
use
maxmin
,
maximax
or regret criteria to help you decide what to
do.
Maximin
:
Assume the worst possible outcome will always occur, therefore you
choose the largest payoff possible under the
worst
possible
outcome i.e. the Max you can get in the Min situation.
= Machine A
Maximax
:
Assume
the best possible outcome will always occur, therefore you
choose the largest payoff possible under the
best
possible outcome
i.e. the Max you can get in the Max situation.
= Machine B
Regret criterion:
When you choose one alternative that turns out not to be the best, you are
going to regret not choosing
the other
alternative
.
States of nature
Low Demand
High Demand
Low
High
Machine
A
£100,000
£
160,000
£
Nil
£40,000
Machine B
£ 10,000
£200,000
£
90,000
£Nil
Therefore would chose Machine A as the most you could regret would be
£40,000 smallest figure
(If you had chosen Machine B and it turned out to be Low demand your
regret would be much larger at £90,000).
Conclusion
Probability is another topic where as well as the calculations, you will be expected to discuss the risks of not achieving your expected returns and the concepts of Perfect Knowledge of Maximin, Maximax, etc.
Please remember 50% of the marks for this module relates to written discussion of the concepts
