Financial Mathematics and Business Statistics: Resit Individual Coursework

Instructions

This coursework tests your basic financial mathematics and statistical modelling skills, using spreadsheet software (Excel – formulae, financial maths, graphical features, Data Analysis and Solver tools) as well as your awareness of the reality of how financial products work. Your answers are to be presented in an essay/report format, for which you will use a word processor. In writing your report, please:

x state and explain all assumptions, on which your answers are based; x clearly indicate your answer/recommendations;

x no evidence of use of excel will result in a fail mark for this element of the coursework component of your mark;

x support any answers with the appropriate calculations to arrive at the answer; x include selected screens of formulae underlying computed values. Failure to demonstrate you have created appropriate formulations on excel will be severely penalised. Despite the fact that you will be submitting the Excel file as well, your report is a stand-alone document, meaning a reader should not be required to look at the Excel file to understand your analysis, findings and recommendations;

x please note that adequate usage of the excel calculations in the report is important. This means that the key data/findings needs to be included in the report and appropriate referencing needs to be done, i.e. the relevant cell/table/range in the relevant tab of the excel file mentioned at the point of the report when it should be consulted.

The report will have a maximum of 10 pages (including any Appendixes; penalties will be applied for longer submissions – you are required to develop your judgement on what is and isn’t important). Ten percent of the total mark is allowed for quality of the presentation and these marks are distributed among the questions.

Deadline: The coursework is to be submitted on Moodle no later than 8.00pm on 14th August 2015. You will need to submit a Word document with the report (see instructions above) and an Excel file with the calculations. If in doubt on how to submit both files on Moodle, please contact Dilip Parmar in the course office allowing sufficient time for him to clarify any doubts you have in advance of the submission deadline.

Also, please note that late submissions will be penalised, no matter how small and irrespective of computer or internet crashes or any other last minute unexpected problem, so make sure you plan your submission allowing enough time to overcome any last minute problems. This includes keeping up-to-date back-ups of your work!

Notes:

This coursework is your own (individual) work. Any student found guilty of plagiarism will be penalised. Standard penalties for late submissions are applicable.

Question 1: (20%)

On the 5th of March 2009, the Bank of England (BoE) lowered its main interest rate to 0.5%, the lowest on record since the Bank has published rates in 1970, which still remains unchanged. As a consequence of this low level of rates, HSBC’s Lifetime Tracker Special mortgage rate stands at 3.99%. John McEnroe is about to buy a house in the countryside which costs £500,000 and is taking out a 25-year repayment mortgage for 75% of the acquisition value of the house. John has asked you to assess his ability to pay, in case the BoE increases its interest rate, as her maximum monthly payment can not exceed £2,200. You are required to:

1. Calculate the monthly payment John will need to meet under current conditions.

2. Assess the effect on John’s monthly payments for each quarter percentage point increase in the BoE rate, up to 4% and identify at which rate John would no longer be able to make the monthly payment.

3. Determine the shortest length (to the nearest month) of mortgage John could take out if he wanted his monthly payment to be exactly the maximum he could afford (based on current mortgage assumptions).

Question 2: (25%)

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:

ProcessMachine Basic Medium Luxury Cost per hour Max. Available

Forming 1.5 hours 3 hours 7 hours £5.50 6,500 hours

Machining 5 hours 8 hours 14 hours £7.50 18,000 hours

Assembly 2.5 hours 4.5 hours 8 hours £9.50 8,500 hours

Testing 2 hours 2 hours 2 ½ hours £12.00 5,200 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:

a. Maximum demand for Medium model was 1,000; OR

b. Maximum available Assembly hours were 9,500.

3. Write a report with a recommended production and marketing plan for the company.

Question 3: (10%)

A retailer knows the annual demand for one of its product is 100,000 units, the ordering costs are £25 per order and the average carrying cost per unit is 35 pence. You are required to:

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 4: (10%)

Rondo plc, a sports apparel manufacturer with a cost of capital of 13.75%, is looking to expand its activity and is considering two possible countries to open a sales subsidiary. Rondo only has the ability to raise £1,300,000, which is the amount required to open each of the subsidiaries, so it needs to choose between the two investments, which are expected to generate the following cash flows:

Year Country Far Away

(in £’000) Country Nearby

(in £’000)

1 600 200

2 600 300

3 600 1,000

4 750 1,500

Make a recommendation to Rondo, plc as to which project it should implement, including an indication of whether that decision should be different in case the cost of capital changes in the near future.

Question 5: (25%)

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. 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 written. The data randomly generated is given in the table below:

Acting. Acting.

QM Study QM Exam Study Exam

Student Hours Grade Hours Grade

1 25 80.0 45 96.0

2 5 8.0 3 29.0

3 18 16.0 14 46.0 4 29 87.0 49 32.5

5 17 95.0 11 61.0

6 39 14.0 19 61.0

7 49 9.5 43 12.0

8 25 10.0 44 46.5

9 6 35.0 0 95.0

10 22 58.0 38 66.0

11 37 8.0 38 24.0

12 31 89.0 50 62.0 13 18 57.0 17 60.5

14 45 22.0 33 10.0 15 5 39.5 33 61.0

16 4 90.0 42 36.0

17 17 23.0 45 39.0

18 29 55.0 34 86.0 19 16 74.0 15 87.0

20 22 29.0 29 100.0

21 28 69.5 49 76.0

22 6 27.0 39 50.5

23 21 12.0 31 55.0

24 4 82.0 14 67.5

25 24 26.0 10 94.0

26 12 13.0 17 33.0

27 4 23.0 34 85.0

28 38 24.5 45 33.0

29 31 77.0 3 19.0

30 5 71.0 44 38.0

Required:

1. Summarise the distribution of expected grades for both exams, according to the data given.

2. Construct a 95% confidence interval for the exam marks for each of the subjects.

Is there a significant difference between them?

3. By constructing a regression model for each of the subjects, indicate for which does study hours have a higher impact on exam grades. Do you think this result is significant?

4. For the best regression model in the previous question, identify whether a better model can be developed by splitting the data into students who study more than 20 hours versus students that study less than 20 hours.

5. Without further calculations, discuss whether you believe these results will be replicated when data is collected for students that actually sat the exam.

Instructions

This coursework tests your basic financial mathematics and statistical modelling skills, using spreadsheet software (Excel – formulae, financial maths, graphical features, Data Analysis and Solver tools) as well as your awareness of the reality of how financial products work. Your answers are to be presented in an essay/report format, for which you will use a word processor. In writing your report, please:

x state and explain all assumptions, on which your answers are based; x clearly indicate your answer/recommendations;

x no evidence of use of excel will result in a fail mark for this element of the coursework component of your mark;

x support any answers with the appropriate calculations to arrive at the answer; x include selected screens of formulae underlying computed values. Failure to demonstrate you have created appropriate formulations on excel will be severely penalised. Despite the fact that you will be submitting the Excel file as well, your report is a stand-alone document, meaning a reader should not be required to look at the Excel file to understand your analysis, findings and recommendations;

x please note that adequate usage of the excel calculations in the report is important. This means that the key data/findings needs to be included in the report and appropriate referencing needs to be done, i.e. the relevant cell/table/range in the relevant tab of the excel file mentioned at the point of the report when it should be consulted.

The report will have a maximum of 10 pages (including any Appendixes; penalties will be applied for longer submissions – you are required to develop your judgement on what is and isn’t important). Ten percent of the total mark is allowed for quality of the presentation and these marks are distributed among the questions.

Deadline: The coursework is to be submitted on Moodle no later than 8.00pm on 14th August 2015. You will need to submit a Word document with the report (see instructions above) and an Excel file with the calculations. If in doubt on how to submit both files on Moodle, please contact Dilip Parmar in the course office allowing sufficient time for him to clarify any doubts you have in advance of the submission deadline.

Also, please note that late submissions will be penalised, no matter how small and irrespective of computer or internet crashes or any other last minute unexpected problem, so make sure you plan your submission allowing enough time to overcome any last minute problems. This includes keeping up-to-date back-ups of your work!

Notes:

This coursework is your own (individual) work. Any student found guilty of plagiarism will be penalised. Standard penalties for late submissions are applicable.

Question 1: (20%)

On the 5th of March 2009, the Bank of England (BoE) lowered its main interest rate to 0.5%, the lowest on record since the Bank has published rates in 1970, which still remains unchanged. As a consequence of this low level of rates, HSBC’s Lifetime Tracker Special mortgage rate stands at 3.99%. John McEnroe is about to buy a house in the countryside which costs £500,000 and is taking out a 25-year repayment mortgage for 75% of the acquisition value of the house. John has asked you to assess his ability to pay, in case the BoE increases its interest rate, as her maximum monthly payment can not exceed £2,200. You are required to:

1. Calculate the monthly payment John will need to meet under current conditions.

2. Assess the effect on John’s monthly payments for each quarter percentage point increase in the BoE rate, up to 4% and identify at which rate John would no longer be able to make the monthly payment.

3. Determine the shortest length (to the nearest month) of mortgage John could take out if he wanted his monthly payment to be exactly the maximum he could afford (based on current mortgage assumptions).

Question 2: (25%)

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:

ProcessMachine Basic Medium Luxury Cost per hour Max. Available

Forming 1.5 hours 3 hours 7 hours £5.50 6,500 hours

Machining 5 hours 8 hours 14 hours £7.50 18,000 hours

Assembly 2.5 hours 4.5 hours 8 hours £9.50 8,500 hours

Testing 2 hours 2 hours 2 ½ hours £12.00 5,200 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:

a. Maximum demand for Medium model was 1,000; OR

b. Maximum available Assembly hours were 9,500.

3. Write a report with a recommended production and marketing plan for the company.

Question 3: (10%)

A retailer knows the annual demand for one of its product is 100,000 units, the ordering costs are £25 per order and the average carrying cost per unit is 35 pence. You are required to:

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 4: (10%)

Rondo plc, a sports apparel manufacturer with a cost of capital of 13.75%, is looking to expand its activity and is considering two possible countries to open a sales subsidiary. Rondo only has the ability to raise £1,300,000, which is the amount required to open each of the subsidiaries, so it needs to choose between the two investments, which are expected to generate the following cash flows:

Year Country Far Away

(in £’000) Country Nearby

(in £’000)

1 600 200

2 600 300

3 600 1,000

4 750 1,500

Make a recommendation to Rondo, plc as to which project it should implement, including an indication of whether that decision should be different in case the cost of capital changes in the near future.

Question 5: (25%)

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. 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 written. The data randomly generated is given in the table below:

Acting. Acting.

QM Study QM Exam Study Exam

Student Hours Grade Hours Grade

1 25 80.0 45 96.0

2 5 8.0 3 29.0

3 18 16.0 14 46.0 4 29 87.0 49 32.5

5 17 95.0 11 61.0

6 39 14.0 19 61.0

7 49 9.5 43 12.0

8 25 10.0 44 46.5

9 6 35.0 0 95.0

10 22 58.0 38 66.0

11 37 8.0 38 24.0

12 31 89.0 50 62.0 13 18 57.0 17 60.5

14 45 22.0 33 10.0 15 5 39.5 33 61.0

16 4 90.0 42 36.0

17 17 23.0 45 39.0

18 29 55.0 34 86.0 19 16 74.0 15 87.0

20 22 29.0 29 100.0

21 28 69.5 49 76.0

22 6 27.0 39 50.5

23 21 12.0 31 55.0

24 4 82.0 14 67.5

25 24 26.0 10 94.0

26 12 13.0 17 33.0

27 4 23.0 34 85.0

28 38 24.5 45 33.0

29 31 77.0 3 19.0

30 5 71.0 44 38.0

Required:

1. Summarise the distribution of expected grades for both exams, according to the data given.

2. Construct a 95% confidence interval for the exam marks for each of the subjects.

Is there a significant difference between them?

3. By constructing a regression model for each of the subjects, indicate for which does study hours have a higher impact on exam grades. Do you think this result is significant?

4. For the best regression model in the previous question, identify whether a better model can be developed by splitting the data into students who study more than 20 hours versus students that study less than 20 hours.

5. Without further calculations, discuss whether you believe these results will be replicated when data is collected for students that actually sat the exam.

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