QUESTION 1 Decision Analysis

Guide to marks: 20 marks- 6 for a, 6 for b1, 1 each for b2 & b3, 2 each for b4 & b5 & b6

Show all calculations to support your answers.

You may follow the methods shown in the mp4 on Decision Analysis for a way to do part (b) of this question if you wish.

(a) Discuss how a utility function can be assessed. What is a standard gamble and how is it used in determining utility values?

(b) Alan Barnes invests primarily in the share market. Recently he has become concerned about the share market as a good investment. During the next year he must decide whether to invest $10,000 in the share market or in a government bond at an interest rate of 9%.

Alan expects the share market to be good, fair or bad, giving a return of 14%, 8% or 0% respectively on his money.

1.Develop a decision matrix showing the two possible strategies, the three states of the share market and the monetary gains or losses under the six possible action-state scenarios.

Answer the following questions. Each answer must be supported with appropriate calculations and/or a table of figures, and you must state for questions 2 to 5 which alternative would be selected.

2. Which alternative would an optimist choose?

3. Which alternative would a pessimist choose?

4. Which alternative is indicated by the criterion of regret?

5. Assuming probability of a good market = 0.4, a fair market = 0.4 and a bad market = 0.2, using expected monetary values what is the optimum action?

6. What is the expected value of perfect information?

QUESTION 2 Value of information

Guide to marks: 20 marks – 4 for a, 8 for b, 2 for c, 6 for d

Show all calculations to support your answers. You may follow the methods shown in the mp4 on Value of info for a way to answer this question if you wish, but however you do the calculations you must specifically provide answers to the 4 questions.

ROUND probability calculations with Round Function to 2 decimal places.

Jim is thinking about producing a new type of electric razor for men. If the market were favourable he would get a return of $100,000, but if the market were unfavourable he would lose $60,000. Jim estimates the probability of a favourable market is 0.5.

(a) What should Jerry do? Show calculations.

A friend would charge him $5,000 for some market research providing one of two signals, that the market is favourable or unfavourable. His friend’s past record is such that 70% of the time he would correctly provide a favourable market prediction and 20% of the time he would incorrectly provide a favourable market prediction.

(b)Revise the prior probabilities in light of his friend’s track record.

(c)What is the posterior probability of a good market given that his friend has provided an unfavourable market prediction?

(d)What is the expected net gain or loss from engaging his friend to conduct the market research? Should his friend be engaged? Why?

QUESTION 3 Monte Carlo Simulation

This is a work integrated assessment item. The tasks are similar to what would be carried out in the workplace.

Guide to marks: 20 marks – 12 for a, 2 for b, 6 for c

Tully Tyres sells cheap imported tyres. The manager believes its profits are in decline. You have just been hired as an analyst by the manager of Tully Tyres to investigate the expected profit over the next 12 months based on current data.

•Monthly demand varies from 100 to 200 tyres – probabilities shown in the partial section of the spreadsheet below, but you have to insert formulas to ge the cumulative probability distribution which can be used in Excel with the VLOOKUP command.

•The average selling price per tyre follows a discrete uniform distribution ranging from $160 to $180 each. This means that it can take on equally likely integer values between $160 and $180 – more on this below.

•The average profit margin per tyre after covering variable costs follows a continuous uniform distribution between 20% and 30% of the selling price.

•Fixed costs per month are $2000.

(a)Using Excel set up a model to simulate the next 12 months to determine the expected average monthly profit for the year. You need to have loaded the Analysis Toolpak Add-In to your version of Excel. You must keep the data separate from the model. The model should show only formulas, no numbers whatsoever except for the month number.

You can use this partial template to guide you:

Ajax Tyres

DATA

Prob Cum prob Demand Selling Price $160 $180

0.05 100 Monthly Fixed cost $2,000

0.10 120 Profit Margin 20% 30%

0.20 140

0.30 160

0.25 180

0.10 200

1.00

MODEL

Selling Profit Fixed

Month RN1 Demand Price RN2 Margin Costs Profit

1 0.23297 #N/A $180 0.227625 0.2

The first random number (RN 1) is to simulate monthly demands for tyres.

•The average selling price follows a discrete uniform distribution and can be determined by the function =RANDBETWEEN(160,180) in this case. But of course you will not enter (160,180) but the data cell references where they are recorded.

•The second random number (RN 2) is used to help simulate the profit margin.

•The average profit margin follows a continuous uniform distribution ranging between 20% and 30% and can be determined by the formula =0.2+(0.3-0.2)*the second random number (RN 2). Again you do not enter 0.2 and 0.3 but the data cell references where they are located. Note that if the random number is high, say 1, then 0.3-0.2 becomes 1 and when added to 0.2 it becomes 0.3. If the random number is low, say 0, then 0.3-0.2 becomes zero and the profit margin becomes 0.2.

•Add the 12 monthly profit figures and then find the average monthly profit.

Show the data and the model in two printouts: (1) the results, and (2) the formulas. Both printouts must show the grid (ie., row and column numbers) and be copied from Excel and pasted into Word. See Spreadsheet Advice in Interact Resources for guidance.

(b)Provide the average monthly profit to Ajax Tyres over the 12-month period.

(c)You present your findings to the manager of Ajax Tyres. He thinks that with market forces he can increase the average selling price by $40 (ie from $200 to $220) without losing sales. However he does suggest that the profit margin would then increase from 22% to 32%.

He has suggested that you examine the effect of these changes and report the results to him. Change the data accordingly in your model to make the changes and paste the output in your Word answer then write a report to the manager explaining your conclusions with respect to his suggestions. Also mention any reservations you might have about the change in selling prices.

The report must be dated, addressed to the Manager and signed off by you.

(Word limit: No more than 150 words)

Guide to marks: 20 marks- 6 for a, 6 for b1, 1 each for b2 & b3, 2 each for b4 & b5 & b6

Show all calculations to support your answers.

You may follow the methods shown in the mp4 on Decision Analysis for a way to do part (b) of this question if you wish.

(a) Discuss how a utility function can be assessed. What is a standard gamble and how is it used in determining utility values?

(b) Alan Barnes invests primarily in the share market. Recently he has become concerned about the share market as a good investment. During the next year he must decide whether to invest $10,000 in the share market or in a government bond at an interest rate of 9%.

Alan expects the share market to be good, fair or bad, giving a return of 14%, 8% or 0% respectively on his money.

1.Develop a decision matrix showing the two possible strategies, the three states of the share market and the monetary gains or losses under the six possible action-state scenarios.

Answer the following questions. Each answer must be supported with appropriate calculations and/or a table of figures, and you must state for questions 2 to 5 which alternative would be selected.

2. Which alternative would an optimist choose?

3. Which alternative would a pessimist choose?

4. Which alternative is indicated by the criterion of regret?

5. Assuming probability of a good market = 0.4, a fair market = 0.4 and a bad market = 0.2, using expected monetary values what is the optimum action?

6. What is the expected value of perfect information?

QUESTION 2 Value of information

Guide to marks: 20 marks – 4 for a, 8 for b, 2 for c, 6 for d

Show all calculations to support your answers. You may follow the methods shown in the mp4 on Value of info for a way to answer this question if you wish, but however you do the calculations you must specifically provide answers to the 4 questions.

ROUND probability calculations with Round Function to 2 decimal places.

Jim is thinking about producing a new type of electric razor for men. If the market were favourable he would get a return of $100,000, but if the market were unfavourable he would lose $60,000. Jim estimates the probability of a favourable market is 0.5.

(a) What should Jerry do? Show calculations.

A friend would charge him $5,000 for some market research providing one of two signals, that the market is favourable or unfavourable. His friend’s past record is such that 70% of the time he would correctly provide a favourable market prediction and 20% of the time he would incorrectly provide a favourable market prediction.

(b)Revise the prior probabilities in light of his friend’s track record.

(c)What is the posterior probability of a good market given that his friend has provided an unfavourable market prediction?

(d)What is the expected net gain or loss from engaging his friend to conduct the market research? Should his friend be engaged? Why?

QUESTION 3 Monte Carlo Simulation

This is a work integrated assessment item. The tasks are similar to what would be carried out in the workplace.

Guide to marks: 20 marks – 12 for a, 2 for b, 6 for c

Tully Tyres sells cheap imported tyres. The manager believes its profits are in decline. You have just been hired as an analyst by the manager of Tully Tyres to investigate the expected profit over the next 12 months based on current data.

•Monthly demand varies from 100 to 200 tyres – probabilities shown in the partial section of the spreadsheet below, but you have to insert formulas to ge the cumulative probability distribution which can be used in Excel with the VLOOKUP command.

•The average selling price per tyre follows a discrete uniform distribution ranging from $160 to $180 each. This means that it can take on equally likely integer values between $160 and $180 – more on this below.

•The average profit margin per tyre after covering variable costs follows a continuous uniform distribution between 20% and 30% of the selling price.

•Fixed costs per month are $2000.

(a)Using Excel set up a model to simulate the next 12 months to determine the expected average monthly profit for the year. You need to have loaded the Analysis Toolpak Add-In to your version of Excel. You must keep the data separate from the model. The model should show only formulas, no numbers whatsoever except for the month number.

You can use this partial template to guide you:

Ajax Tyres

DATA

Prob Cum prob Demand Selling Price $160 $180

0.05 100 Monthly Fixed cost $2,000

0.10 120 Profit Margin 20% 30%

0.20 140

0.30 160

0.25 180

0.10 200

1.00

MODEL

Selling Profit Fixed

Month RN1 Demand Price RN2 Margin Costs Profit

1 0.23297 #N/A $180 0.227625 0.2

The first random number (RN 1) is to simulate monthly demands for tyres.

•The average selling price follows a discrete uniform distribution and can be determined by the function =RANDBETWEEN(160,180) in this case. But of course you will not enter (160,180) but the data cell references where they are recorded.

•The second random number (RN 2) is used to help simulate the profit margin.

•The average profit margin follows a continuous uniform distribution ranging between 20% and 30% and can be determined by the formula =0.2+(0.3-0.2)*the second random number (RN 2). Again you do not enter 0.2 and 0.3 but the data cell references where they are located. Note that if the random number is high, say 1, then 0.3-0.2 becomes 1 and when added to 0.2 it becomes 0.3. If the random number is low, say 0, then 0.3-0.2 becomes zero and the profit margin becomes 0.2.

•Add the 12 monthly profit figures and then find the average monthly profit.

Show the data and the model in two printouts: (1) the results, and (2) the formulas. Both printouts must show the grid (ie., row and column numbers) and be copied from Excel and pasted into Word. See Spreadsheet Advice in Interact Resources for guidance.

(b)Provide the average monthly profit to Ajax Tyres over the 12-month period.

(c)You present your findings to the manager of Ajax Tyres. He thinks that with market forces he can increase the average selling price by $40 (ie from $200 to $220) without losing sales. However he does suggest that the profit margin would then increase from 22% to 32%.

He has suggested that you examine the effect of these changes and report the results to him. Change the data accordingly in your model to make the changes and paste the output in your Word answer then write a report to the manager explaining your conclusions with respect to his suggestions. Also mention any reservations you might have about the change in selling prices.

The report must be dated, addressed to the Manager and signed off by you.

(Word limit: No more than 150 words)

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