A small insurance company estimates that next year it will receive $5 million in premiums that will flow in a steady rate throughout the year. This income will be invested at 20 per cent per annum, but the cost to the company of making an investment is $200 for each investment made and, in addition 2 per cent of the sum invested.

REQUIRED

(a) Show that this situation is an inventory problem in structure, and that the EOQ model may be used to determine the optimum investment policy, i.e. the timing of making the company's investments

(b) Determine how many investments should be made during the year, and the total cost of the policy as given by the EOQ model

(c) A reorganisation of the company's investment department would cause investment costs to change to $450 for each investment made plus 1 1/2 of the sum invested. How would this affect the company's optimum investment policy according to the EOQ model?

(d) Instead of reorganising the investment department, the company decides to hold, as buffer stock, cash to the value of 2 per cent of the yearly premiums; what will be the maximum holding of cash at any one time?

(e) Comment on the practical inadequacies of the EOQ model in this situation.

ACCA, PE (adapted). Section 2, Paper 12, Management Mathematics, December 1981.