Advanced: Expected values, maximin criterion and value of perfect informationRecyc pic is a company which reprocesses factory
Question:
Advanced: Expected values, maximin criterion and value of perfect informationRecyc pic is a company which reprocesses factory waste in order to extract good quality aluminium. Information concerning its operations is as follows:
(i) Recyc pic places an advance order each year for chemical X for use in the aluminium extraction process. It will enter into an advance contract for the coming year for chemical X at one of three levels - high, medium or low, which correspond to the requirements of a high, medium or low level of waste available for reprocessing.
(ii) The level of waste available will not be known when the advance order for chemical X is entered into. A set of probabilities have been estimated by management as to the likelihood of the quantity of waste being at a high, medium or low level.
(iii) Where the advance order entered into for chemical X is lower than that required for the level of waste for processing actually received, a discount from the original demand price is allowed by the supplier for the total quantity of chemical X actually required.
(iv) Where the advance order entered into for chemical X is in excess of that required to satisfy the actual level of waste for reproces¬ sing, a penalty payment in excess of the original demand price is payable for the total quantity of chemical X actually required.
A summary ofthe information relating to the above points is as follows:
Aluminium is sold at £0.65 per kg. Variable costs (excluding chemical X costs) are 70% of sales revenue.
Aluminium extracted from the waste is 15% of the waste input. Chemical X is added to the reprocessing at the rate of 1 kg per 100 kg of waste.
Required:
(a) Prepare a summary which shows the budgeted contribution earned by Recyc pic for the coming year for each of nine possible outcomes. (14 marks)
(b) On the basis of maximising expected value, advise Recyc pic whether the advance order for chemical X should be at low, medium or high level. (3 marks)
(c) State the contribution for the coming year which corresponds to the use of (i) maximax and (ii) maximin decision criteria, and comment on the risk preference of manage¬ ment which is indicated by each. (6 marks)
(d) Recyc pic are considering employing a consultant who will be able to say with certainty in advance of the placing of the order for chemical X, which level of waste will be available for reprocessing.
On the basis of expected value, determine the maximum sum which Recyc pic should be willing to pay the consultant for this informa¬ tion. (6 marks)
(e) Explain and comment on the steps involved in evaluating the purchase of imperfect informa¬ tion from the consultant in respect of the quantity of waste which will be available for reprocessing. (6 marks)
(Total 35 marks) ACCA Paper 9 Information for Control and Decision Making
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