QUESTION 1 Decision Analysis
Guide to marks: 20 marks- 6 for a, 2 each for b1 & b2, 3 each for b3 & b4, 4 for b5
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 the differences among decision making under certainty, under risk and under complete uncertainty.
(b) Bikram Shrestha is considering investing some money that he inherited. The following payoff matrix gives the profits that would be realised during the next year for each of the investments that Bikram is considering.
Answer the following questions. Each answer must be supported with appropriate calculations and/or a table of figures, and you must state for questions 1 to 4 which alternative would be selected.
1 Which alternative would an optimist choose?
2 Which alternative would a pessimist choose?
3 Which alternative is indicated by the criterion of regret?
4 Assuming probability of a good economy = 0.3 using expected monetary values what is the optimum action?
5 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.
DO NOT ROUND probability calculations with Round Function. You may display them to 2 decimal places if you like but do not round in memory.
Jerry is thinking about opening a bicycle shop. He can open a large shop (a1) or a small shop (a2). He believes that a large shop would earn a profit of $80,000 if the market is good (s1) but would lose $40,000 if the market is poor (s2). A small shop would return $30,000 profit in a good market and a loss of $10,000 in a poor market. Jerry believes that there is a 50-50 chance that the market will be good.
(a) What should Jerry do? Show calculations.
A friend would charge him $3,000 for some market research providing.one of two signals, that the market is favourable or unfavourable. His past record is such that 80% of the time he would correctly provide a favourable market prediction when the market is good and 60% of the time he would correctly provide an unfavourable market prediction when the market is poor.
(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.
• The average selling price per tyre follows a discrete uniform distribution ranging from $60 to $80 each. This means that it can take on equally likely integer values between $60 and $80 – 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 $1500.
(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
• 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(60,80) in this case. But of course you will not enter (60,80) 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 Tully Tyres over the 12-month period..
(c) You present your findings to the manager of Tully Tyres. He thinks that with market forces he can increase the average selling price by $20 (ie range from $80 to $100) without losing sales. However he does suggest that the profit margin would then increase to range 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)
QUESTION 4 Regression Analysis
Guide to marks: 20 marks – 5 for a, 10 for b, 3 for c, 2 for d
Belinda, the accountant at Murray Manufacturing Company wants to identify cost drivers for support overhead costs. She has the impression that the staff spend a large part of their time ensuring that the equipment is correctly set up and checking the first units of production in each batch. Deborah has collected the following data for the past 12 months:
(a) Using the high-low method to estimate support overhead costs based on machine hours, what would be the estimated support overhead costs (to the nearest $) for a month in which 3,000 machine hours were used?
(b) Using Excel, perform three regression analyses to regress Overhead Cost against Machine Hours, then against Batches, then against both of them simultaneously. Paste your results into Word. State the cost equation from each. Analyse and comment on the results of each regression as you perform it and determine the best one to use as a basis for future use.
(c) If you had to settle for the results of a simple regression, which one would you use and why?
(d) Using the best regression result determine the projected Overhead Cost in a month in which there were 2000 machine hours worked and 150 batches produced.
QUESTION 5 CVP Analysis
Guide to marks: 20 marks – 4 for a, 4 for b, 4 for c, 8 for d
Show all calculations to support your answers.
A manufacturer can make two products, A and B. The following data are available:B
This assessment task covers topics 3,4,5,6 and 8: Decision analysis and value of information, simulation, correlation and regression analysis and CVP analysis. Specifically, it seeks to assess your ability to complete the following subject learning outcomes:
• apply decision theory to business situations
• use simulation in complex decisions
• demonstrate understanding of the application of statistical hypothesis testing in regression analysis
• apply CVP analysis to product mix decisions involving single and multiple products