Advanced: Impact of aggregating budget estimates and budget bias Devonshire Dairies pic sells a range of dairy

Question:

Advanced: Impact of aggregating budget estimates and budget bias Devonshire Dairies pic sells a range of dairy products on a national basis through a direct sales force organized into four geographical regions. In December the sales director had received sales budgets for the next year from his four regional managers, and was concerned that they appeared to represent very different standards of attainment. He also thought it unlikely that the national budget (i.e. the sum of the four regional budgets) could be achieved, and so had made his own estimates of the sales revenue he expected each division to obtain, as shown below:image text in transcribed

The sales director recognized that his estimates were subject to some uncertainty due to random events, and believed this could be adequately modelled by assuming that they represented the means of normal distributions having a standard deviation of £1 million for each region and that actual sales in each region were statistically inde¬ pendent of each other. However, he was reluctant to amend the budgets submitted to him as he could see the motivational advantages in letting each regional sales manager aim for a target which he had set for himself, and to which he was committed.
Requirements

(a) Calculate the probability of each sales region achieving at least the budget submitted by its regional manager, on the assumption that the sales director’s model is correct. Also calcu¬ late the probability that the total of the budget submissions will be at least achieved, and comment on your results.

(b) Discuss the reasons why managers may submit budgets that differ from their super¬ iors’ estimates of outcomes. What action would you recommend the sales director to take in this case? (8 marks)

(c) The company is considering implementing a system of performance-related pay whereby managers who achieve their annual sales budgets are rewarded by the payment of an annual bonus equivalent to one month’s salary. Discuss the impact such a system could have on the operation of the budgeting system, and suggest ways in which the proposed bonus system could be amended to minimize any adverse effects.

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