Chapter 12 – Decision-making under conditions of risk and uncertainty
MULTIPLE CHOICE
1. Which of the following represent states of nature?
a.
a potential set of outcomes expressed in monetary terms
b.
the most likely result that is going to occur
c.
a list of potential courses of action that can be undertaken
d.
a list of different conditions that might be experienced relating to the economy such as
recession, boom etc.
2. Which of the following is NOT a feature of a probability distribution?
a.
a value of 0 for an event denotes a nil likelihood of occurrence
b.
a value of 1 for an event signifies absolute certainty
c.
the total of the probabilities for all possible events listed in the distribution can vary
d.
a probability distribution attempts to provide a list of all possible outcomes
3. Which of the following best describes objective probabilities?
a.
repeating an experiment that exactly simulates the decision and using the data to derive the
probability
b.
obtaining an estimate from an expert
c.
using a firm of management consultants to provide the value of the probability
d.
none of the above
4. The following represent a tutor’s estimate of the probability of students A, B, C and D failing an
examination. Which student does the tutor consider has the best chance of passing the examination?
a.
student A = 0
b.
student B = 0.5
c.
student C = 0.6
d.
student D = 0.2
5. Which of the following statements is untrue regarding a probability distribution?
a.
it will show all possible outcomes and their probabilities
b.
it can be used to provide an indication of the risk of undertaking a possible course of
action.
c.
it will show the average outcome that is expected to occur
d.
it will enable an estimate of the most likely outcome to be derived
6. The most likely outcome represents:
a.
the expected value.
b.
the actual outcome.
c.
the average outcome that is expected to occur.
d.
the outcome with the highest probability.
7. The expected value represents:
a.
the weighted average of the possible outcomes.
b.
the most likely outcome.
c.
the outcome with the highest probability.
d.
none of the above.
8. Which of the following assumptions apply when making decisions on the basis of expected values:
a.
the decision must be a ‘one–off’.
b.
there must be many possible outcomes.
c.
it is based on the assumption that the decision will be repeated many times.
d.
none of the above.
9. Which of the following are true with regard to expected values?
a. Expected values represent the single most likely estimate of the outcome.
b. Expected values take no account of decision-makers risk.
c. Expected values are reliant on the accuracy of the probability distribution.
a.
a, b and c
b.
a and b only
c.
a and c only
d.
b and c only
10. Which of the following is NOT a measure of uncertainty?
a.
the standard deviation of the probability distribution
b.
an examination of the probability distribution
c.
the expected value
d.
the coefficient of variation
11. The joint probability of two events occurring together is:
a.
the sum of the probabilities of the two events.
b.
the higher probability of the two events.
c.
the average of the probability for the two events.
d.
the probability of one event times the probability of the other event.
12. The following represent the expected values and standard deviations for alternatives a-d. Which
alternative has the highest absolute risk?
a.
Alternative A has an expected profit of £100,000 and a standard deviation of £18,000
b.
Alternative B has an expected profit of £300,000 and a standard deviation of £75,000
c.
Alternative C has an expected profit of £500,000 and a standard deviation of £70,000
d.
Alternative D has an expected profit of £700,000 and a standard deviation of £60,000
13. The following represent the expected values and standard deviations for alternatives W-Z:
a.
Alternative W has an expected profit of £100,000 and a standard deviation of £18,000
b.
Alternative X has an expected profit of £300,000 and a standard deviation of £54,000
c.
Alternative Y has an expected profit of £500,000 and a standard deviation of £90,000
d.
Alternative Z has an expected profit of £700,000 and a standard deviation of £126,000
Which of the following statements are true?
a.
Alternative Z has the highest amount of relative risk.
b.
Alternative W has the lowest amount of relative risk.
c.
All of the alternatives have an equal amount of relative risk.
d.
None of the above statements are true.
Figure 12-1
Joe Bloggs is considering the following three alternatives that are estimated to yield the following
potential monetary benefits:
Possible outcomes
Alternative A
Alternative C
1
£18,000
£0
2
20,000
20,000
3
22,000
40,000
It is estimated that all of the outcomes are equally likely.
14. Refer to Figure 12-1. Assuming that Joe is a risk averter which alternative is he likely to prefer?
a.
Alternative A
b.
Alternative B
c.
Alternative C
d.
He will be indifferent as to which alternative to choose.
15. Refer to Figure 12-1. Assume that Joe is a risk seeker. Which alternative is Joe likely to choose?
a.
Alternative A
b.
Alternative B
c.
Alternative C
d.
He will be indifferent between the three alternatives.
16. Refer to Figure 12-1. Assume that Joe is a risk neutral. Which alternative is Joe likely to choose?
a.
Alternative A
b.
Alternative B
c.
Alternative C
d.
He will be indifferent between the three alternatives.
Figure 12-2
ZX Company is faced with choosing from the following four mutually exclusive alternatives. Each
project has the same duration and the cash flows are expected to occur at the same point in time. Their
net cash inflows will be determined by the prevailing market conditions. The forecast net cash inflows
and their associated probabilities are shown below:
Market conditions
Poor
Excellent
Probability
0.20
0.30
Project A
£600,000
£660,000
Project B
500,000
684,000
Project C
440,000
570,000
Project D
432,000
504,000
17. Refer to Figure 12-2. Based on the expected value of net cash flows, which project should be
undertaken?
a.
Project A
b.
Project B
c.
Project C
d.
Project D
18. Refer to Figure 12-2. The expected value of Project D is:
a.
£472,000.
b.
£480,000.
c.
£477,600.
d.
None of the above.
19. In a decision tree the boxes refer to:
a.
The point at which decisions have to be taken.
b.
Possible alternative courses of action.
c.
The point at which environmental changes occur that affect the consequences of prior
decisions.
d.
The possible types of environment that may occur.
20. The maximum amount that is worth paying to obtain additional information consists of:
a.
the expected price of the information.
b.
the difference between the expected value if the information is acquired compared with the
expected value with the absence of the information.
c.
an amount equal to the most likely benefit that the information will provide.
d.
an amount equal to the highest benefit that the information will provide.
21. Sentosa Company is considering launching a new product which it believes has a 70% probability of
success. The company is, however, considering undertaking an advertising campaign costing £60,000,
which would increase the probability of success to 95%.
If successful the product would generate income of £240,000 otherwise £84,000 would be received.
What is the maximum amount that the company should be prepared to pay for advertising?
a.
£34,800
b.
£21,000
c.
£39,000
d.
£60, 000
22. The Tamesek Company is considering purchasing one of two mutually exclusive machines. Machine
A is most suited to low levels of demand whereas machine B is suited to high-level demand. There are
only two possible outcomes and each has the same level of probability. The estimated profits for each
demand level are as follows:
Low demand (£)
High demand (£)
Machine A
140,000
224,000
Machine B
14,000
280,000
There is a possibility of employing a firm of management consultants who would be able to provide a
perfect prediction of actual demand. What is the maximum amount that the company would be
prepared to pay for the additional information?
a.
£98,000
b.
£14,000
c.
£70,000
d.
None of the above
23. Jackson is considering launching a new product which it believes has an 80% probability of success.
The company, however, is considering undertaking an advertising campaign at a cost of £40,000
which would increase the probability of success to 90%.
If successful the product would generate income of £840,000 otherwise £294,000 would be received.
What will be the expected loss or gain from obtaining the additional information?
a.
a loss of £40,000
b.
a gain of £14,600
c.
a gain of £54,600
d.
None of the above
24. The decision rule under the maximin criterion is to:
a.
Select the alternative that has the best outcome should the worst event occur.
b.
Select the alternative that has the best average outcome.
c.
Select the alternative that has the best outcome should the best event occur.
d.
Select the alternative that has the best chance of maximising the return.
Figure 12-3
The Lee Company must choose between two mutually exclusive alternatives. With alternative 1 an
inferior product will be marketed that is best suited to low levels of demand whereas alternative 2 is a
superior product that is best suited to high levels of demand. There are only two possible levels of
demand – high and low and the probabilities of each event occurring is 0.5. The predicted profits for
each alterative are:
Low demand (£)
High demand (£)
Alternative 1
350,000
560,000
Alternative 2
35,000
700,000
25. Refer to Figure 12-3. Which alternative should the company choose using the maximax criterion?
a.
Neither alternative
b.
Alternative 1
c.
Alternative 2
d.
There is insufficient data to use the maximin criterion.
26. Refer to Figure 12-3. Using the data above relating to the Lee Company, which alternative should be
selected using the maximin criterion?
a.
Neither alternative
b.
Alternative 1
c.
Alternative 2
d.
It is not possible to use the maximin criterion for the data given.
27. Refer to Figure 12-3. Using the data above relating to the Lee Company, which alternative should be
selected using the regret criterion?
a.
Neither alternative
b.
Alternative 1
c.
Alternative 2
d.
It is not possible to use the regret criterion for the data given.
28. Refer to Figure 12-3. Using the data above relating to the Lee Company, what is the amount of regret
that is used to determine the choice of alternatives under consideration?
a.
£140,000
b.
£210,000
c.
£665,000
d.
£315,000
e.
It is not possible to apply the regret criterion to the data given.
29. Refer to Figure 12-3 and assume that the probabilities of 0.5 for high and 0.5 for low demand are
changed to 0.6 and 0.4 respectively. How would the change in probabilities change the values used to
apply the maximax, maximin and regret criteria?
a.
All of the values would increase.
b.
All of the values would decrease.
c.
Some values would increase and others would decrease.
d.
The values would remain unchanged.
e.
None of the above because it is not possible to apply any of the criteria from the data
given.
30. Under what circumstances can risk reduction NOT be achieved from combining investments?
a.
Where the projects are perfectly positively correlated
b.
Where the projects are perfectly negatively correlated
c.
Where the projects have low levels of positive correlation
d.
Where the projects have low levels of negative correlation