had to face in the last few years, the management team at Dreamcatcher, a games’

Financial Mathematics and Business Statistics: Coursework Due to the weakness in the market, most companies had to face in the last few years, the management team at Dreamcatcher, a games’ retailer has been reviewing its stock ordering system and has managed to negotiate a reduction in ordering costs with their main supplier from £280 to £190. Despite selling different games, their similar size and packaging allows games to be managed as a single product. The expectations regarding next year’s state of the economy are as follows: Considering that the average carrying cost per unit is £1.45: a) Make a recommendation to the board of Dreamcatcher, as to how often it should order and what level or stock should be ordered each time; b) Assess the savings achieved by the recent renegotiation with the main supplier; and c) Assess the impact of this recommendation at the different levels of demand. A company that manufactures electrical appliances is looking at one of its lines (microwave ovens), where it offers three different levels of specification: Cheap which sells for £50, Average which sells for £100 and Premium which sells for £250. The production of each oven goes through four different stages and you have been provided with the following data table: The marketing department has also conducted market research and believes demand for each of the models is limited to 2,000 units of the basic model, 1,200 of the medium and 700 of the luxury. You are required to: a) Formulate this problem as a linear program and use Excel’s Solver to arrive at a solution, identifying what is the maximum profit the company can achieve in the microwave ovens product line, under current conditions. b) How would your answer change if the following happened: 1. Maximum demand for Premium model was 1,000; 2. Maximum available Machining hours were 20,000. c) Make a recommendation of the production mix and marketing plan for the company. The majority of banks, when making decisions on mortgage applications, will look at two indicators: salary and borrowing as a percentage of purchase price. On the first indicator, banks are normally willing to lend 2.5 times one’s salary or 3.25 times joint salary in a joint mortgage application, while currently most banks will lend up to 75% of the property price on their best rate with penalties for higher percentages. John and Julia are getting married and decided to buy a flat to move into once they do. You have been given the following data: John’s current salary is £39,000 p.a. and Julia’s is £37,500 p.a. plus a bonus likely to be around £5,000 (based on previous 3 years experience); Both have jobs where they partly telecommute, so on average each works from home 2 days a week; Their total savings at the moment are £25,000; John owns a flat which he would sell, and has been advised that he should be able to sell it for £150,000. The mortgage outstanding on this flat is £112,000; John and Julia are planning to apply for a 25 year mortgage; The average price of flats in the area they would like to move into is as follows: studios £150,000;  1-bedroom £220,000; 2-bedroom £325,000; 3-bedroom £450,000; 4-bedroom £600,000 Having contacted a financial adviser, he has identified the following as the best available mortgage rates: Repayment fixed rate for 2-years of 3.69%. After that period, the rate reverts to the bank’s standard variable rate, which currently is 5.7%; repayment fixed rate for 5-years of 4.29%. After that period, the rate reverts to the bank’s standard variable rate, which currently is 5.7%; interest only mortgage at 5% for the life of the loan. In this instance, you would be required to create an investment fund, which pays an interest rate of 3.9% to cover the repayment of the mortgage. All the rates above are for loans of up to 75% of the property value. There is an increase of 1.5%age points if borrowing is up to 90% of the property value. a) b) c) d) A statistician is trying to find whether there is a relationship between the number of hours of study and exam results, or whether exam results are random. Looking at two different subjects (quantitative methods and accounting), the first part of his study was to generate random numbers of study hours and exam grades, which will be compared to the actual results once the exams are taken and marked. The data randomly generated is given in the table below: Required: a) Summarise the distribution of expected grades for both exams, according to the data given. Discuss the key characteristics of the data. b) Construct a 95% confidence interval for the expected exam marks for each of the subjects. Is there a significant difference between them? c) Would you expect the actual exam results to show a pattern similar to the calculations above? Discuss why/why not and whether you believe the type of exam and questions (numerical, essay-type, multiple choice, etc.) will have an influence in the outcomes. Required: a) Discuss and compare the different types of investment appraisal methods Garnett can use, including a discussion of the advantages and disadvantages of each. b) If Garnett had a rule that all investment projects need to payback within 3 years, what project would be chosen? Comment. c) Make a recommendation as to which project should be undertaken. d) If Garnett believes there is an opportunity to start exporting its product line to another country once sales are finished in its home country (i.e. from year 5), and it thinks it will be able to generate cash flows of £660,000 in the first year, £1,540,000 in the second and £2,300,000 in the subsequent four years, would your answer to part c) change? How?