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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 actionstate 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.
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.
(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 AddIn 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+(0.30.2)*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 0.30.2 becomes 1 and when added to 0.2 it becomes 0.3. If the random number is low, say 0, then 0.30.2 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 12month 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)
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:
Month 
OH Cost 
MH 
Batches 
1 
$80,000 
2,200 
300 
2 
40,000 
2,400 
120 
3 
63,000 
2,100 
250 
4 
45,000 
2,700 
160 
5 
44,000 
2,300 
200 
6 
48,000 
3,800 
170 
7 
65,000 
3,600 
260 
8 
46,000 
1,800 
160 
9 
33,000 
3,200 
150 
10 
66,000 
2,800 
210 
Total 
530,000 
26,900 
1,980 
(a)Using the highlow method to estimate support overhead costs based on machine hours (MH), 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
Product 
A 
B 
Total 
Sales price per unit 
$12 
$15 

Variable cost per unit 
$8 
$10 

Total fixed costs/month 


$5000 




(a)Calculate the unit contribution margin for each product.
(b)This month the manufacturer will specialise in making only Product B. How many does he need to sell to break even?
(c)If they specialise in making only A what is the breakeven sales volume for the month in sales dollars?
(d)He now decides to manufacture both A and B this month in the ratio of 3 of A to 1 of B.
(i)How many of each product must be sold to earn a profit of $3,500 before tax for the month?
(ii)How many of each product must be sold to earn a profit of $8,400 after tax (of 30c in the dollar) for the month?
(a) Discuss how a utility function can be assessed. What is a standard gamble and how is it used in determining utility values?
Utility functions are assessed by:
The Standard Gamble (SG) measures the preference of an individual under uncertainty. It is used to express the outcome of different choices in utility values. Standard gamble determines the mean probability when a respondent is indifferent between accepting a gamble and continuing with the current situation.
(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.
Table 1: Data
Profit 
Shares 
Bonds 
Probability 
50% 
50% 
Good 
14% 
9% 
Fair 
8% 
9% 
Poor 
0% 
9% 
Table 2: Results
EMV 
Minimum 
Maximum 





0.115 
0.09 
0.14 

0.085 
0.08 
0.09 

0.045 
0 
0.09 

Maximum 
0.115 
0.09 
0.14 
Table 3: Criterion of regret
Regret 


Shares 
Bonds 

Expected 
Maximum 
Probability 
0.5 
0.5 



Good 
0% 
0 

0 
0 
Fair 
0.06 
0 

0.03 
0.06 
Poor 
0.14 
0 

0.07 
0.14 
Minimum 
0 
0 
Data 
Results 

Profit 
Shares 
Bonds 
EMV 
Minimum 
Maximum 

Probability 
50% 
50% 




Good 
40% 
9% 
0.245 
0.09 
0.4 

Fair 
40% 
9% 
0.245 
0.09 
0.4 

Poor 
20% 
9% 
0.145 
0.09 
0.2 

Maximum 
0.245 
0.09 
0.4 
The optimum action would be to invest wholly in the share market.
6. What is the expected value of perfect information?
Data 


Profit 
Shares 
Bonds 


Probability 
50% 
50% 


Good 
40% 
9% 


Fair 
40% 
9% 


Poor 
20% 
9% 




Expected Value of Perfect Information 

Column best 
40% 
9% 
Expected value with prefer information = (50%*40%) + (50%+9%) = 0.245
QUESTION 2 Value of information
Jerry should produce the new type of electric razor. The expected returns would be $20,000. The justification is as seen below:
(c)What is the posterior probability of a good market given that his friend has provided an unfavourable market prediction?
Posterior probability = 1  0.3*0.8 = 1  0.24 = 0.76
(d)What is the expected net gain or loss from engaging his friend to conduct the market research? Should his friend be engaged? Why?
The expected net gain from engaging his friends to conduct market research is $12,000. Since this is lower than if he had not consulted, then he should not consult his friend.
QUESTION 3 Monte Carlo Simulation
(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 AddIn 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.
Table 1: Results
b)Provide the average monthly profit to Ajax Tyres over the 12month period.
The average monthly profit as seen in table 1 is $5,511.60
(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%.
INTERNAL MEMO
To: Manager, Sales
From: John Doe, Snr. Sales Officer
Subject: Change in sales review
Date: 19^{th} September 2018
It is of my belief that the new prices suggested will bring a positive impact to the average monthly prices. The increase in selling price by $40 will see the company increase its profit margin from 22% to 32%.
Simulating the new selling price and the new profit margins, using the same model it will be seen that there was an increase in the average monthly profits from $5,511 to $8,217. Therefore, I wholly support the new move to increase the selling price from $160  $180 to $200  $220.
Thank you for your time,
John Connor,
Snr. Sales Officer.
QUESTION 4 Regression Analysis
(a)Using the highlow method to estimate support overhead costs based on machine hours (MH), what would be the estimated support overhead costs (to the nearest $) for a month in which 3,000 machine hours were used?
Variable Cost = (Total OH cost of high activity – total OH cost of low activity) / (highest activity unit – lowest activity unit)
Variable Cost = (48,000 – 46,000) / (3,800– 1,800) = $1
Total cost = (Variable cost per unit x MH) + Total fixed cost
48,000 = (1 * 3,800) + Total fixed cost
48,000 – 3,800 = Total fixed cost
Total fixed cost = $44,200
OH = 44,200 + 1*3,000 = $47,200
(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.
Regression 1: Overhead Cost against Machine Hours
OC = 9,205.66 – 0.93*MH + 233.83*Batches
(c)If you had to settle for the results of a simple regression, which one would you use and why?
The best result to settle is regression 2 (OC against batches) since the regression is statistically significant and has the highest adjusted r square of 0.81.
(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.
OC = 6,555.56 + 234.57*150 = 41741.1
QUESTION 5 CVP Analysis
(a)Calculate the unit contribution margin for each product.
Contribution margin = sales – variable cost
Thus, A contribution margin = $12 – 8 = $4
B contribution margin = $15  $10 = $5
(b)This month the manufacturer will specialise in making only Product B. How many does he need to sell to break even?
B Break Even Point = Total fixed costs/CM per unit
= 5,000/5
= $1,000
(c)If they specialise in making only A what is the breakeven sales volume for the month in sales dollars?
A Break Even Point = Total fixed costs/CM per unit
= 5,000/4
= $1,250
(d)He now decides to manufacture both A and B this month in the ratio of 3 of A to 1 of B.
(i)How many of each product must be sold to earn a profit of $3,500 before tax for the month?
Profitable sale point = (Profitable sale)/ (Weighted average selling price – weighted average variable expenses)
Weighted average selling price = (12*3/4) + (15*1/4) = $12.75
Weighted variable expenses = (8*3/4) + (10*1/4) = $8.5
Profitable sale = Fixed cost + profit = 5,000 +3,500 = 8,500
Total units = 8,500/ (12.758.5) = 2,000 units
Units for A = 2,000*3/4 = 1,500
Units for B = 2,000*1/4 = 500
(ii)How many of each product must be sold to earn a profit of $8,400 after tax (of 30c in the dollar) for the month?
30 cents per dollar
Thus, tax is 30%.
Sales – Fixed cost – tax = profit
S – 5,000 – 0.3*S = 3,500
0.7S = 8,500
S = $12,142.86
Units = 12,142.86/ (12.758.5) = 2858 units
Units for A = 2,858*3/4 = 2,143
Units for B = 2,858*1/4 = 715
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