Discussing How a Utility Function Can Be Assessed
(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:
- Identifying the worst and best attribute levels
- Assigning utility of zero to worst outcome and 1 to best outcome
- Naming the desirable outcome at 50:50
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.
- 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.
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 |
- Which alternative would an optimist choose? The share market
3. Which alternative would a pessimist choose? The bonds market
4. Which alternative is indicated by the criterion of regret? There is no alternative indicated under 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?
|
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
- What should Jerry do?
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 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.
Table 1: Results
b)Provide the average monthly profit to Ajax Tyres over the 12-month 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: 19th 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.
Case Study on Investment Decisions
Thank you for your time,
John Connor,
Snr. Sales Officer.
QUESTION 4 Regression Analysis
(a)Using the high-low 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/ (12.75-8.5) = 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/ (12.75-8.5) = 2858 units
Units for A = 2,858*3/4 = 2,143
Units for B = 2,858*1/4 = 715
