Q1 . Decision analysis: complete uncertainty
(a) A decision maker has formulated the following payoff (profits) matrix:
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s1
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s2
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s3
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s4
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a1
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4
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7
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9
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7
|
|
a2
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6
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5
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2
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3
|
|
a3
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8
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9
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5
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1
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a4
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3
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4
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3
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8
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a5
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10
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0
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6
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4
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What action should (s)he select if (s)he followed the criterion of: (i) Maximin?
(ii) Maximax? (iii) Laplace?
(iv) Minimax Regret?
Q2 Bayesian revision of probabilities
Seepage from dams containing uranium tailings is known to cause radio-active pollution of surrounding ground water of an average of 1 dam in 2000. The presence of radio-active pollution can be tested using a geiger-counter. This instrument, however, provides imperfect signals. Background atmospheric radiation causes it to indicate the presence of radio-active seepage on 15% of the occasions when no radio-active seepage has occurred. However, when radio-active seepage has occurred, it fails to accurately signal the presence of radio-active pollution only 2% of the time.
If a geiger-counter measurement indicates the presence of radio-active pollution, what is the probability that radio-active seepage has occurred?
Q3 Bayesian revision of probabilities
The manager of ABC Co. is concerned that a competing firm might be planning to introduce a new product that could seriously affect his sales. He feels that the chances are only one in five that the competitor is actually planning to introduce a new product.
He then discovers that the competitor is building a new plant. After careful consideration he decides that if a new product is to be introduced the odds would be 3 to 2 in favour of the building of a new plant, but if a new product is not to be introduced, the odds would be 4 to 1 against the building of a new plant.
(a) What is the manager's prior probability that his competitor is planning to introduce a new product?
(b) What is his revised probability of a new product given that the competitor is building a new plant?
Q4 Value of perfect and sample information
A firm is considering the marketing of a new product which will either be a success or a failure. The prior probability of success is judged to be 0.3. If the product is marketed and is a success the firm expects to earn $500 000, while
a failure is expected to lead to a loss of $300 000.
(a) Should the product be marketed? Why?
(b) What is the expected value of perfect information about the success or failure of the product
The firm is considering a market survey whose results can be classified as favourable, neutral or unfavourable. Some of the conditional probabilities are:
p(favourable|success) = 0.6 p(neutral|success) = 0.3 p(neutral|failure) = 0.2, p(unfavourable|failure) = 0.7.
(c) What is the posterior probability of success given a favourable survey result?
(d) What is the maximum the firm should be willing to pay for the market survey?
Q5 Suppose a simulation model has two random variables (eg. 'arrival time' and
'service time' in a queuing problem). What is wrong, if anything, with drawing a single random number on each trial and using this single number to determine the value for both random variables?
Q6 Analysing a service contract using simulation
The IDG Medical Fund is being considered as a group insurer for the employees of a large public company. If IDG wins the contract and insures the group, the daily frequency of claims is estimated as follows:
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Number of Claims
0
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Relative Frequency
0.05
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1
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0.06
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2
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0.08
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3
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0.10
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4
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0.33
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5
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0.14
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6
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0.11
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7
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0.07
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8
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0.04
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9
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0.02
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1.00
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The probability distribution of the cost of each claim has been estimated using historical data and is as follows:
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Average Cost per Claim
$800
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Probability
0.30
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900
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0.24
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1000
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0.22
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1100
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0.18
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1200
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0.06
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1.00
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(a) What is the probability that there will be 4 claims or fewer per day?
(b) Using the following random numbers from left to right simulate a 5-day working week and calculate the expected weekly cash outflow in settlement of claims.
Random numbers: Random numbers: Number of Claims Cost per Claim
40, 71, 18, 77, 42 14, 56, 20, 76, 29
Q7 Breach of contract; alternative uses of a product made to customer specification
Grumbles Industries Ltd is a large company with widespread interests in transport. They have just completed manufacturing a motorised barge for South Coast Steel who had intended to use the barge for dumping steelmaking waste 1 kilometre out at sea. Unfortunately, South Coast Steel have just gone into liquidation, being unable to compete successfully against the other major steel manufacturer. Further, environmental legislation has just been enacted prohibiting the dumping of garbage and industrial waste in the ocean.
The costs incurred in the production of the barge were: Direct materials $100 000
Direct labour 80 000
Manufacturing overhead allocated: Variable 10 000
Fixed 20 000 30 000
Fixed administrative expenses 5 000
Total $215 000
South Coast Steel had paid a deposit of $35 000, which was non-refundable, on the overall purchase price of $350 000.
If Grumbles wished to petition as a creditor, they estimate that they would eventually receive 25c in the dollar on unrecouped production costs, after delivering the barge to the receiver.
Greg Grimshaw, an oyster farmer, has signalled an interest in buying the barge if it is modified for the oyster business. He has offered to buy the modified barge for $75 000 on delivery. Grumbles estimate that the direct cost of the modifications would be:
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Direct materials
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$15 000
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Direct labour
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10 000
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$25 000
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A third alternative is for Grumbles to convert the barge to a river ferry. River Cruises Pty Ltd have indicated an interest in acquiring another steel-hulled ferry. The additional direct costs to convert the barge to a ferry are:
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Direct materials
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$100 000
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Direct labour
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100 000
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$200 000
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Grumbles have quoted a price for the ferry of $280 000.
Variable and fixed manufacturing overhead costs are allocated at rates of
12.5% and 25% respectively of direct labour cost. Fixed administrative expenses are charged at a rate of 6.25% of direct labour cost.
Required:
(a) Calculate the contribution each of the three alternatives will make to
Grumbles Industries' pre-tax profits.
(b) If River Cruises Pty Ltd tries to negotiate a lower price than $280 000 for the ferry, what is the lowest price Grumbles Industries should accept?
(c) Discuss the relevance of the costs already incurred in manufacturing the barge to the evaluation of the three alternatives examined above.
Q8 Transfer pricing: internal transfer versus external sale
Household Appliances Ltd is a divisionalised company in which each of the two divisions operates as an independent investment centre. For the coming financial year the pre-tax target rate of return for the divisions and for the company as a whole is 15%.
Division A produces electric motors and plans to sell 60% of its output to Division B for use in the production of tumble clothes dryers, while the remainder are to be sold to an outside user who has contracted to buy 2000 motors. No further outside sales appear possible. Division A is planning to produce 5000 motors (normal capacity).
Variable cost per motor is $30 while fixed production costs of $50 000 are expected in Division A. Division A allocates fixed costs on the basis of normal capacity, regardless of actual production.
The sales price for external sales is $55 per motor. For the purposes of
internal pricing the manager of Division A sets a profit markup of 50% on full absorption cost in order to earn a satisfactory return on divisional assets employed, $500 000.
Division B has in the past purchased all its motors from Division A. Division
B's costs consist of the transfer-in cost, additional variable production costs of
$48 per dryer, and $60 000 fixed production costs which are allocated to dryers on an expected annual production basis. Division B plans to produce
3000 dryers in the coming year. Division B sells the finished dryers to retailers for $180 each. Assets employed in Division B total $1 140 000.
An external supplier has offered to provide two-thirds of Division B's electric motor requirements for the coming year at a price of $45.
Required:
(a) Calculate the expected profit and rate of return on investment for each division and for the company as a whole in the coming year, if Division B purchases its motors from Division A, and sells its entire output to retailers.
(b) Should Division B buy its motors from the external supplier? Why? (c) Prepare divisional and corporate profit and loss statements on an
absorption costing basis on the assumption that Division B accepts the offer from the external supplier and Division A adjusts its planned output accordingly. Calculate the company and divisional rates of return. On the basis of these calculations state whether it would be in the best interests of the company to accept or reject the offer.
(b) Assume the payoff matrix is a cost matrix. What strategy would a pessimist select?