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MATH 1053 — Quantitative Methods for Business

Case Study Part A (SP2 2025)
DUE by 11:00pm, Friday 4 April

Submission instructions:

· This case study relates to the material in Weeks 0 to 3 and is worth 15% of your final grade. It is due no later than 11pm on Friday the 4^th of April in Week 5.

· You will need to submit your assignment via learnonline. Feedback on your submission, will be provided to you via learnonline as well.

· This assignment must be completed using this template. You may change the visual style including fonts and colours, add a company logo, add extra figures, tables, etc. as you see fit, however basic structure must remain unchanged. Working out must be shown in the Appendix and interpretation must be provided in the Report Body; refer to the instructions contained in this template.

· Analysis methods and interpretation of results must be consistent with course materials, which are more than sufficient to successfully complete this assessment task. Should you use any other sources (not required or expected), a reference must be provided.

· The file you submit needs to be in a pdf format, prepared using this template. 

· Assignments submitted late, without an extension being granted, will attract a penalty of 10% of the maximum marks (that is, 10 marks) for each working day or any part thereof beyond the due date and time. Please refer to the Course Outline for the course policy regarding extensions.

· Failure to follow the template, not deleting text/pages as requested, photos of hand-written answers, poor communication or a messy layout will attract a penalty of up to 10 marks (10% of maximum marks available).

· Major components of the assignment are as follows:

Assignment component	Mark
Business report	30
Appendices	60
Presentation	10
TOTAL	100

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Academic Integrity 

Plagiarism is a specific form of academic misconduct.  We encourage and support working in groups and seeking help, however your final submission must always represent your individual work, opinions and recommendations.

If plagiarism is found, all parties involved will be penalised. You need to retain all your assignment computer files (Excel, Word etc.), which must remain unchanged after submission, for the purposes of checking, if required.

Plagiarism covers, but is not limited to, the following actions:

· Direct copying of the work of other persons, from one or more source, without clearly indicating the origin;

· Sending your files to another student for any reason whatsoever, even for the purposes of checking or comparing work;

· Submitting another student’s work in whole or in part;

· Copying computer files without clearly indicating their origin;

· Submitting work that has been derived, in whole or in part, from another student by a process of mechanical transformation (e.g. changing variable names in computer files, paraphrasing);

· Submitting work that has been written by someone else on the student’s behalf, which includes contract cheating sites and artificial intelligence;

· Working together is encouraged, however each written assignment submitted by each student must be written in its entirety by the individual student, including running analyses, producing Excel spread sheets other than the templates provided on the course learnonline and report writing. Working together where one individual types up the collective thoughts of a group/produces analyses and/or spread sheets and then shares these files will be investigated for plagiarism.

All parties found to be involved in academic misconduct will incur, if appropriate, a penalty and a record in the University's Academic Integrity Database as per the University policy.

If you are unsure about what constitutes Academic Integrity, you are always welcome to ask us for more information before submitting.

          

The J Spot

Baked with Love, Brewed to Perfection

For over 40 years, Dave’s Bakery has been a beloved family business, known for its wide selection of pies, pasties, pastries, cakes, and buns. Now, as owner Dave Gilmour steps into retirement at 66, he is passing the reins to his daughter, Jessie Gilmour, who has ambitious plans for the future.

Jessie aims to modernise and expand the business, starting with a rebrand—transforming Dave’s Bakery into a café called The J Spot. Her first step is to introduce freshly brewed espresso coffee, catering to the evolving tastes of the community. She also plans to extend operating hours to align with peak demand across six days a week.

With the neighbourhood changing and an influx of young professionals and families, Jessie sees an opportunity to blend heritage baking with modern café culture, ensuring The J Spot becomes a favourite destination for both longtime patrons and new visitors.

Anticipating this transition, Jessie encouraged her father to commission a market research study to assess local demand for coffee, including cappuccinos, lattes, and short blacks. Now, with valuable insights in hand, she is ready to make key financial decisions to drive the café’s success. While Dave is enthusiastic about Jessie’s vision, he also wants to be assured that she is making sound, strategic decisions to secure the future of the family business.

Perform the necessary quantitative analyses and prepare a business report for Dave, where you describe your findings and make appropriate recommendations. Specifically, perform the tasks outlined in this document and include FULL details of your working out in the Appendices. You will need to do the analysis and calculations that go in the appendices BEFORE you write your report. Read and understand this whole template before you begin.

Suggested assignment work timeline:

If you are not sure how to start the assignment, a suggested work breakdown schedule is below.  Feel free to use it (or ignore it) as you like J  

Some people like to complete each appendix and then write it up in the report, others prefer to complete all appendices first and then write up the report in one go.  Do whichever suits you!

A suggested schedule to work through this assignment is as follows:

Week	Suggested tasks to be completed
2	· Download and read through the assignment instructions. · Take the time to understand the structure of the submission template. · Complete Appendix 1a and b.
3	· Continue working on Appendix 1.
4	· Finish Appendix 1 and complete Appendix 2. · Start working on Appendix 3.
5	· Finish Appendix 3. · Write the report and double-check that you have addressed all the requested points. · Check the entire submission for completeness and adherence to the template, and submit J

Introduction

(2 marks)

Include:

· Purpose

· Qualitative description of report contents/problems addressed

Write this after you have a clear understanding of the content of your report.
There is no word limit, just ensure you have explained what the report will contain.  As a guideline, one or two paragraphs will be sufficient.

[Click here and insert your text for the Introduction]

1. Purchasing coffee making equipment for The J Spot

Write a report-style discussion of the main results of your analysis in Appendix 1. You may use subsections, tables etc. as you see fit.

Quote your results but do not include numerical calculations. These should be placed in Appendix 1.

 

(8 marks)

Summarise the aim of the section and include clear answers to the questions addressed in Appendix 1.

Do not confuse the different issues. For example, Dave does want to know what monthly repayment amount would pay off the loan in 12 months, but he also wants to know the outcome of paying $350 per month.

Comment on the outcome of the Net Present Value calculation. Does the coffee making equipment seem to be a good investment?

2. Funding for Jessie’s expansion plans

Write a report-style discussion of the main results of your analysis in Appendix 2. You may use subsections, tables etc. as you see fit.

Include your results but do not include numerical calculations. These should be placed in Appendix 2.

(6 marks)

Use your results from Appendix 2 to the three main questions addressed in Appendix 2: the resulting shortfall from $3,000 payments, the required payment amount, and the alternative interest rate required for $3,000 payments to be adequate. 

3.  Breaking even without breaking the crockery

Write a report-style discussion of the main results of your analysis in Appendix 3. You may use subsections, tables etc. as you see fit.

Quote your results but do not include numerical calculations. These should be placed in Appendix 3.

(10 marks)

Summarise the aim of the section, and include clear answers to the questions addressed in Appendix 3.

Present results of your break-even analysis. Include a copy and comment on your break-even graph. Discuss the implications of combining takeaways with serving coffee in-house and in reusable cups. Also discuss whether offering customers branded KeepCups is a good idea.

Describe each scenario briefly and carefully describe its impact on the café’s financial position. 

Conclusions and Recommendations

(4 marks)

Conclusions:

· Summarise the main findings of your report. Base this on your discussion.

· Do not introduce new information in the conclusions.

· Indicate whether the report fulfilled the purpose as stated in the introduction.

Recommendations:

· Base these on your conclusions.

· Do not introduce new information in the recommendations.

· Present options for resolving the issue (purpose) presented in the introduction.

· Be brief — use dot points.

There is no word limit. As a guideline, one to three paragraphs will be sufficient. 

Appendix 1 (22 marks) – Purchasing coffee making equipment for The J Spot

Jessie would eventually like to purchase a large commercial coffee machine and employ a skilled barista. Initially though, she will be making the coffee herself and so has chosen a La Marzocco Linea Mini espresso machine, a Mazzer Super Jolly grinder plus coffee art equipment with a total retail price of $6,650, including GST. The J Spot can claim a rebate from the Australian Taxation Office of all GST paid, so Jessie needs to fund only the GST exclusive price of the coffee making equipment.  By haggling with the retailer, Jessie negotiates a cash price of $5,500, excluding GST. The bank is offering a business infrastructure loan with interest at 6.95% per annum compounded monthly. Jessie thinks that profits from coffee sales will support repayments of $350 per month and would like to repay the loan within a year.

(a) (2 marks) The rate of GST (Goods and Services Tax) in Australia is 10%.  How much GST is included in a quoted retail GST inclusive price of $6,650? What is the corresponding GST exclusive price?

(b) (2 marks) In negotiating a GST exclusive price of $5,500, what percentage discount from the retail price has Jessie achieved?

(c) (2 marks) Use EXCEL to calculate the monthly repayment that Jessie would have to make on the business loan.

EXCEL Instructions: Refer to Topic 4 in the EXCEL booklet for instructions on how to use financial functions to make annuity calculations.

(d) (10 marks) Use EXCEL to set up an Amortisation Schedule for the loan. Include your EXCEL amortisation schedule in this Appendix.

EXCEL Instructions: Be sure to add your initials to all column names. You can build your amortisation schedule from scratch or modify an existing spreadsheet. You can use the car loan amortisation example from Week 2 or Jeannie’s loan example from Week 3 tutorial.

(e) (2 marks) Use your amortisation schedule from part (d) to analyse the outcome of this loan with repayments of $350 per month. How many months will it take to pay off the loan?  How much is still outstanding at the end of 12 months? Provide a screenshot of your modified amortisation schedule in this Appendix.

(f) (4 marks) Assuming that money is valued at 6.95% per annum compounded monthly, calculate the Net Present Value of the coffee machine purchase proposal. Its initial cost is $5,500, and maintenance costs are $1,500 every 6 months. Would maintenance be paid for at the end of 2 years, when the machine is to be discarded? Expected profits from coffee sales are $550 per month. You can use EXCEL or calculate the NPV by hand. In either case, show your working out in Appendix 1.

Appendix 2 (16 marks) – Funding for Jessie’s expansion plans

Jessie expects that in 3 years’ time she will be ready to expand The J Spot by buying the shop next door. She has an option to buy the shop for $520,000, and she estimates that the fit out and refurbishments will cost $150,000.  She can borrow only 80% of these costs from the bank and will need to have saved the other 20% as a deposit.  Jessie therefore decides to set up a bank account as a sinking fund. She will make payments of $3,000 per month into the account, which offers interest of 6.2% per annum, compounded monthly.

(a) (6 marks) Use EXCEL to calculate the balance in Jessie’s sinking fund at the given interest rate of 6.2% per annum after 3 years if the monthly deposits are $3,000. By how much will Jessie fall short of her target amount?

Excel Instructions: Prepare an EXCEL spreadsheet like the one shown below (values shown are arbitrary – you will have to insert correct ones). Cell B6 in the figure below is reserved for the formula for S, the accumulated value. Make sure the row names include your initials. Refer to Topic 4 in the EXCEL booklet for instructions on how to use financial functions to make annuity calculations.

 

(b) (4 marks) Use EXCEL to compute the size of the monthly deposits that Jessie should make into her account, in order to have the required amount in 3 years.

Excel Instructions:  In the same EXCEL spreadsheet you constructed for part (a), include calculations as shown below (you will have to insert correct values). Cell B14 contains the formula for R, the regular monthly deposit. Make sure the row names include your initials. Refer to Topic 4 in the EXCEL booklet for instructions on how to use financial functions to make annuity calculations.

 

(c) (6 marks) Jessie would prefer to use the original deposit amount of $3,000 and decides to shop around at other financial institutions for an interest rate that would enable her goal deposit to be achieved with that monthly deposit amount.

Use the EXCEL tool GoalSeek to determine the appropriate APR with monthly compounding.

Excel Instructions: Copy the part of your Excel spreadsheet that you used for part (a) to a new section of the spreadsheet and label it (c). Use GoalSeek to find the required monthly interest rate and then convert it to an APR by multiplying by 12.

Make sure that your labels include your initials. Include a screenshot of your spreadsheet before and after using GoalSeek.

 

Appendix 3 (22 marks) – Breaking even without breaking crockery

Initially, The J Stop would only sell takeaway coffee. Suppose also that instead of serving coffee herself, Jessie hires a barista at a cost of $5,000 per month. Other fixed costs would be maintenance of $500 per month, marketing of $1,000 per month and inventory (milk and coffee beans) of $2,500 per month.  Variable costs per cup are expected to be $1.80 for beans and milk, $0.50 for takeaway cup and lid and $0.20 for other ingredients (e.g., sugar). The market research indicates that a price of $5.00 per cup would be highly competitive.

(a) (6 marks) What is the break-even number of coffees per month? What is it per day? Remember that The J Spot is open 6 days a week and note that there are typically 4 Sundays in a month. Find the break-even point algebraically and illustrate it using an EXCEL graph (in cups of coffee per month). Include a copy of your EXCEL graph in this Appendix. On your graph, identify the region corresponding to profits and the region corresponding to losses. 

EXCEL Instructions: Create a column called Number of units and in that column enter values from 0 to 6,000 in increments of 500. Then create two more columns, one for Total Cost and another for Total Revenue. Enter appropriate formulae in EXCEL to obtain the total cost and total revenue corresponding to each value in the Number of units column. Highlight the resulting three sets of numbers and go to Insert à Charts à Scatter to obtain a graph. Make sure that your graph has been labelled appropriately (i.e. title, axis labels, legend) and that your chart title includes your network ID (this is the first part of your uni email address, e.g. bloggsj002).

Refer to Topic 3 in the EXCEL Booklet for further instructions on entering formulae in EXCEL, and break-even examples from Week 3.

(b) (8 marks) Jessie wants to introduce a sustainable theme to the café. She will do this by encouraging takeaway customers to use thermo mugs, and by introducing crockery cups and saucers for the use of customers who consume their coffee at The J Stop. Jessie will initially rent these crockery items, and she will also rent a commercial dishwasher to wash them. She is planning to offer a small discount to the users of thermo mugs. The resulting prices and variable costs will be as follows:

Customer type	Price per cup	Variable cost per cup	Contribution margin
Takeaway	$5.00	$2.50	$2.50
Thermo mug	$4.50	$2.20	$2.30
In-house	$5.00	$2.00	$3.00

The market research indicates that 40% of customers will choose takeaway coffee, 30% will bring reusable cups and 30% will drink coffee in house at The J Stop. If the estimated additional fixed costs per month are $2,000 (40 sets of crockery, dishwasher and detergent, additional labour), calculate the new number of coffees that need to be sold per day to break even. In Appendix 3, present appropriate calculations to justify your answer. Type them up in Word or use EXCEL.

(c) (8 marks) Suppose that Jessie decides to sell customised KeepCups with the café logo at $30 per cup. She can get KeepCups from a supplier at $12 per cup and estimates she will be able to sell 150 per month. The assumed customer breakdown in this scenario is as follows:

30% of customers will choose takeaway coffee

30% will bring reusable cups

30% will drink coffee in house at The J Stop

10% will buy and use The J Stop branded KeepCup

With these additional assumptions, calculate the new break-even number of coffees per day. In Appendix 3, present appropriate calculations to justify your answer. Type them up in Word or use EXCEL.