## Financial maths and business statistics

Question 1: (10%)With the reduction in sales driven(,gamyro) by the financial crisis which have not fully recovered yet, Office Trade, a wholesaler of office equipment has been conducting a review of its stock ordering system. The management of the company has asked each of the analysts in its finance department, to look at each of its products, and you were asked to look at book shelving units. Having made your research, you have determined that it is uncertain when the recovery will start, so you have established the following demand scenarios for the next 12 months:

Scenario Crisis Continues Slow Recovery Medium Recovery Fast Recovery Probability 20% 40% 35% 5% Demand 25,000 35,000 50,000 75,000

Considering the cost per order is £30 and the average carrying cost per unit is £2:

a) Determine the Economic Order Quantity (is the number of units that a company should add to inventory with each order to minimize the total costs of inventory—such as holding costs, order costs, and shortage costs.) given the data above.

b) Produce sensitivity analysis assuming a change of up to 10% up or down on each of the factors individually and on all factors simultaneously. c) Make a final recommendation to the board of the company, as to the number of units it should include in each order.

Question 2: (15%)

A car manufacturer is looking to reorganise and increase the efficiency of its manufacturing operations, and is currently looking at an engine assembly line, which makes three different engines (1.8, 2.0 and 2.5Iitre). The prices charged for the engines are £2,500, £2,850 and £3,750 respectively, while the inputs required to make each of the engines are listed in the table below:

Product Basic Medium High Max. Available Aluminium 10 units 11 units 12 units 52,000 Other Metals 5 units 7 units 6 units 30,000 Other Materials 6 units 4 units 9 units 28,000 Labour 2 hours 2 1/4 hours 2 1/2 hours 10,000

The costs for the inputs are £25 per hour for Labour and £100, £120 and £35 per unit for Aluminium, Other Metals and Other Materials, respectively. There is also a maximum daily demand for the engines, which is 4,000 1.8Iitre, 3,500 2.01itre and 2,000 2.5Iitre.

Formulate this problem as a linear program and use Excel’s Solver to arrive at a solution. Write a short report describing your procedure, justify your formulation and give a recommendation to the firm on the best daily production mix.

Question 3: (30%) 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 and are looking to take on a 25-year mortgage. 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 plans to 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: • 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 at the end of January, he has identified the following as the best available mortgage rates: Repayment fixed rate for 2-years of 1.89%. After that period, the rate reverts to the bank’s standard variable rate, which currently is 3.69%; repayment fixed rate for 5-years of 2.34%. After that period, the rate reverts to the bank’s standard variable rate, which currently is 3.69%; 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

If

If

If

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. Assess: a) What is the maximum John and Julia can borrow while taking advantage of the bank’s best mortgage rate: b) The amount you advise them to borrow, given their financial and professional situation: c) Which is the best mortgage that John and Julia to take out (assume they take out the amount you recommended in by d) Whether that advice would change if interest rates went up or down by up to three percentage points.

If

Question 4:

(20%)

Garnett plc has seen sales in one of its product lines decline over the last two years. The production is currently subcontracted and any changes require a six month notice, so Garnett has to decide now what to do for their most important advertising period, which is in September every year. The options it has identified are: Option A – Invest £1 million to make small changes to the product design and manufacturing process, which will generate increased cash flows in the short term: Option B — completely redesign the product and production process, which will have a longer lasting effect on cash flows, but will require an investment of £7million.

If

If

Garnett’s required rate of return on investments is 12.5% and the estimated cash flows for the two options are as follows (in ‘000s):

Year Option A Option B

1 1,000 300 2 1,500 1,500 3 1,750 3,000 4 500 3,000 5 3,000 6 3,000 7 2,700 8 2,000 9 1,500 10 1,000

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 £250,000 in the first year, £750,000 in the second and £1,250,000 in the subsequent four years, would your answer to part c) change? How? (Note: production can’t be further increased in the future if option B is chosen now)

Question 5: (15%)

The table below represents data for the profits, sales, average shop size and number of product lines sold by the 20 branches of a retailing company. You have been asked to analyse the data, using the Data Analysis tool in Excel, and make recommendations, including the following:

a) Summarise the distribution of profits of the twenty branches and comment on the results, including identification of any particularly good or poorly performing branches. b) Identify whether there is evidence that the average number of lines stocked per branch is significantly different from 150. c) Identify whether there is a significant difference between the profits of two groups of branches, split by the level of sales, with the threshold being £600,000. d) Based on this sample, provide a 98% confidence interval for the profits of the twenty branches and comment on the outcome.

Profit (£000s) Sales (£000s) Size (000s sq. ft.) Lines

77.5 613.9 3.2 80 91 217.4 4.3 200 20.7 900.9 3.1 164 40.8 673.4 1.5 150 45.8 424.7 3.2 69 41.1 542.2 1.8 128 47.5 564.6 2.5 75 80.4 662.1 3.1 182 16.5 583.6 4.2 126 22.3 720.2 0.6 164 40.8 881.5 1.8 145 68.1 227.7 0.8 130 17.7 807.4 3.8 154 66.2 656.4 0.3 124 31.3 632.8 2.3 142 15 548.5 5 178 67.8 533.6 1.5 173 55 147.5 1.7 199 8.6 311.4 3.8 98 16.5 450.1 4.6 148