1. The Van Shake ice cream company proposes to pay a university 1.2 million immediately in return for one year's exclusive rights to sell its ice cream products to students. This initial investment includes all the start-up costs. Consumer research estimates that each student consumes 0.5 litres of ice cream per month. The cost of manufacturing and delivering the ice cream is 40% of its retail price, which is 10 per litre. Sales receipts and manufacturing costs are processed by the company monthly in arrears. Due to a loophole in the university's regulations, mathematics students are entitled to free ice cream. There are approximately 40,000 students in the university, of whom 2,000 study mathematics. The effective annual interest rate is 2%. (a) Calculate the accumulated profit that the Van Shake company expects to make after one year, if its proposal is accepted. Give your answer to the nearest 1,000. (b) Find the yield of this proposal, giving your answer to three significant figures. The university suggests a counter-proposal in which the Van Shake company would instead pay 1.425 million immediately for the same access to students and exclusive rights to sell ice cream to staff too. Consumer research estimates that each staff member spends 2.50 per month on ice cream. There are approximately 13,000 staff in the university. (c) Calculate the accumulated profit and the yield of the counter-proposal, to the same accuracies. (d) On the same axes, sketch graphs of the net present values of the two proposals as functions of interest rate, and discuss briefly the merits of each proposal, from Van Shake's perspective. Provide sufficient detail of your calculations so that they can be checked. 1. The Van Shake ice cream company proposes to pay a university 1.2 million immediately in return for one year's exclusive rights to sell its ice cream products to students. This initial investment includes all the start-up costs. Consumer research estimates that each student consumes 0.5 litres of ice cream per month. The cost of manufacturing and delivering the ice cream is 40% of its retail price, which is 10 per litre. Sales receipts and manufacturing costs are processed by the company monthly in arrears. Due to a loophole in the university's regulations, mathematics students are entitled to free ice cream. There are approximately 40,000 students in the university, of whom 2,000 study mathematics. The effective annual interest rate is 2%. (a) Calculate the accumulated profit that the Van Shake company expects to make after one year, if its proposal is accepted. Give your answer to the nearest 1,000. (b) Find the yield of this proposal, giving your answer to three significant figures. The university suggests a counter-proposal in which the Van Shake company would instead pay 1.425 million immediately for the same access to students and exclusive rights to sell ice cream to staff too. Consumer research estimates that each staff member spends 2.50 per month on ice cream. There are approximately 13,000 staff in the university. (c) Calculate the accumulated profit and the yield of the counter-proposal, to the same accuracies. (d) On the same axes, sketch graphs of the net present values of the two proposals as functions of interest rate, and discuss briefly the merits of each proposal, from Van Shake's perspective. Provide sufficient detail of your calculations so that they can be checked
