The following scenario relates to questions 16–20.
Mylo runs a cafeteria situated on the ground floor of a large corporate office block. Each of the five floors of the building are occupied and there are in total 1,240 employees.
Mylo sells lunches and snacks in the cafeteria. The lunch menu is freshly prepared each morning and Mylo has to decide how many meals to make each day. As the office block is located in the city centre, there are several other places situated around the building where staff can buy their lunch, so the level of demand for lunches in the cafeteria is uncertain.
Mylo has analysed daily sales over the previous six months and established four possible demand levels and their associated probabilities. He has produced the following payoff table to show the daily profits which could be earned from the lunch sales in the cafeteria:
If Mylo adopts a maximin approach to decision-making, which daily supply level will he choose?
The maximin rule selects the maximum of the minimum outcomes for each supply level.
For Mylo the minimum outcomes are:
450 lunches – $1,170
620 lunches – $980
775 lunches – $810
960 lunches – $740
The maximum of these is at a supply level of 450 lunches.
If Mylo adopts a minimax regret approach to decision-making, which daily supply level will he choose?
The minimax regret rule selects the minimum of the maximum regrets.
Which of the following statements is/are true if Mylo chooses to use expected values to assist in his decision-making regarding the number of lunches to be provided?
(1) Mylo would be considered to be taking a defensive and conservative approach to his decision
(2) Expected values will ignore any variability which could occur across the range of possible outcomes
(3) Expected values will not take into account the likelihood of the different outcomes occurring
(4) Expected values can be applied by Mylo as he is evaluating a decision which occurs many times over
Expected values do not take into account the variability which could occur across a range of outcomes; a standard deviation would need to be calculated to assess that, so Statement 2 is correct.
Expected values are particularly useful for repeated decisions where the expected value will be the long-run average, so Statement 4 is correct.
Expected values are associated with risk-neutral decision-makers. A defensive or conservative decision-maker is risk averse, so Statement 1 is incorrect.
Expected values will take into account the likelihood of different outcomes occurring as this is part of the calculation, so Statement 3 is incorrect.
The human resources department has offered to undertake some research to help Mylo to predict the number of employees who will require lunch in the cafeteria each day. This information will allow Mylo to prepare an accurate number of lunches each day
What is the maximum amount which Mylo would be willing to pay for this information (to the nearest whole $)?
This requires the calculation of the value of perfect information (VOPI).
Expected value with perfect information = (0·15 x $1,170) + (0·30 x $1,612) + (0·40 x $2,015) + (0·15 x $2,496) = $1,839·50
Expected value without perfect information would be the highest of the expected values for the supply levels = $1,648·25 (at a supply level of 775 lunches).
The value of perfect information is the difference between the expected value with perfect information and the expected value without perfect information = $1,839·50 – $1,648·25 = $191·25, therefore $191 to nearest whole $.
Mylo is now considering investing in a speciality coffee machine. He has estimated the following daily results for the new machine:
The investment’s sensitivity to fixed costs is 550% ((385/70) x 100), so Statement 3 is correct.
The margin of safety is 84·6%. Budgeted sales are 650 units and BEP sales are 100 units (70/0·7), therefore the margin of safety is 550 units which equates to 84·6% of the budgeted sales, so Statement 4 is therefore correct.
The investment is more sensitive to a change in sales price of 29·6%, so Statement 1 is incorrect.
If variable costs increased by 44%, it would still make a very small profit, so Statement 2 is incorrect.