FINANCIAL MATHEMATICS AND STATISTICS MODELLING

Kyle Dier is looking to buy his first home and through savings and a gift from his parents he has managed to raise £80,000. Kyle has identified two possible properties, a one bedroom flat in the centre of town that costs £250,000 and a three-bedroom house outside of town that costs £400,000 and he’s decided to ask for your help identifying the best mortgage offers he can choose.

 

Required:

 

  1. Identify (and clearly indicate them in your submission) a minimum of three lenders Kyle could borrow the money from and discuss the mortgage alternatives available and the respective terms and applicable interest rates;
  2. For the most favourable rate for each type of mortgage, calculate the monthly payment Kyle would need to make for each of the properties he’s looking to possibly buy if he chooses to take out a 20-year mortgage;
  3. Kyle believes it is highly likely that we will receive £50,000 in two years’ time and if he does, he will use the money to make a partial payment of the mortgage. For both options in b) and considering the payments he will have done by then as well as the one-off partial payment, calculate the monthly payments for the remaining 18 years of the mortgage.
  4. Make a recommendation on the property Kyle should buy purely on financial terms and identify what other factors should be taken in consideration when making the final decision.

 

Question 2:                                                                                                                 (10%)

 

Due to the continued low level of sales Toys For You, a wholesaler of toys and games has experienced in the last three years, the management 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 one of its product lines, and you were asked to look at board games. 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:

 

ScenarioCrisis ContinuesSlow RecoveryMedium RecoveryFast Recovery
Probability10%30%40%20%
Demand50,00065,00085,000100,000

 

Considering the cost per order is £50 and the average carrying cost per unit is £1.50:

 

  1. Determine the Economic Order Quantity given the data above.
  2. Produce sensitivity analysis assuming a change of up to 10% up or down on each of the factors individually and on all factors simultaneously.
  3. Make a final recommendation to the board of the company, as to the number of units it should include in each order.

Question 3:                                                                                                                                                        (20%)

 

A company that manufactures electrical appliances is looking at one of its lines (washing machines), where it offers three different levels of specification: Basic which sells for £250, Medium which sells for £450 and Luxury which sells for £700. The production of each machine goes through four different stages and you have been provided with the following data table:

 

ProcessMachineBasicMediumLuxuryCost per hourMax. Available
Forming1.5 hours3 hours7 hours£5.506,500 hours
Machining5 hours8 hours14 hours£7.5018,000 hours
Assembly2.5 hours4.5 hours8 hours£9.508,500 hours
Testing2 hours2 hours2 ½ hours£12.005,200 hours

 

The marketing department has also done some market research and believes demand for each of the models is limited to 1,450 units of the basic model, 900 of the medium and 750 of the luxury. You are required to:

 

  1. 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 washing machine product line.
  2. How would your answer change if the following happened:
    1. Maximum demand for Medium model was 1,000; OR
    2. Maximum available Assembly hours were 9,500.
  3. Write a report with a recommended production and marketing plan for the company.

 

Question 4:                                                                                                                                                        (15%)

 

Given the data included in the excel file “Assignment FM&BS 1516 Data”:

 

  • Summarise the distribution of family income and house price and comment on the results?
  • Is there evidence that the average house price is £500,000? Justify
  • Based on this sample, provide a 90% and a 99% confidence interval for the Family income and explain and justify the difference between the two intervals.
  • Would you expect to find a relationship between the two variables under study? If so, what type of relationship would you expect?
  • Does this data provide evidence to support your answer to part d)?

 

Question 5:                                                                                                                                                        (20%)

 

The management of Make More plc, a manufacturer of low cost electronic products, has seen a significant increase in the company’s activity over the last two years.

 

The company now has to decide whether to undertake a potential investment to make three additional products using a new technology. In order to undertake this investment, Make More is looking to lease a new facility for the next six years, after which it is expected that the technology will be obsolete. The forecasted cash flows put together by the management of the business are as follows:

 

  • Sales of the three products in year one will be 50,000 units at an average price of £55;
  • Sales volume is expected to grow at 20% a year for the first three years, and decrease at 25% a year for the remainder of the project;
  • Cost of sales will be 65% of sales;
  • Selling and administrative expenses specific to this project will be £450,000;
  • The lease rent will be £150,000;
  • In order to manufacture the three products, Make More is going to buy equipment worth £1m. This equipment is expected to have a scrap value of £150,000 in six years time;
  • Equipment will be depreciated using straight line depreciation (Note: depreciation is not a cash flow, but since it is a cost, it affects the tax calculation and tax paid is a cash flow);
  • Corporate tax rate is 20%;
  • The current cost of capital of Make More is 15%, but this project is considered to be riskier and the cost of capital for companies with comparable levels of risk is 20% higher.

 

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