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MATH 1053 — Quantitative Methods for Business

Case Study Part A (SP2 2024)

DUE by 11:00pm, Thursday 28 March

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 Thursday the 28^th of March in Week 5.

• You will need to submit your assignment via learnonline. Marked assignments will be returned to you electronically.

• 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. In particular, your working out must be shown and questions must be answered in either the Report Body or Appendix, according 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 and 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, 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

Flaming Crust Co

Fuelling your passion for pizza, one slice at a time

Food trucks offer a convenient and diverse dining experience, catering to a wide range of tastes and preferences. With the rise of foodie culture and the popularity of street food festivals and events, food trucks have become an integral part of urban dining scenes worldwide. Additionally, the COVID-19 pandemic has further accelerated the trend, as outdoor dining options and mobile eateries provide a safer alternative to traditional indoor dining establishments. Australian food trucks offer a diverse range of cuisines, from traditional favorites like burgers to more exotic options. This variety reflects the multicultural nature of Australia and caters to the increasingly adventurous palates of consumers.

Jamie Quinn is a young chef with a passion for artisanal pizza and a commitment to using locally sourced ingredients. With a diverse culinary background and a flair for creativity, Jamie has decided to make her mark on the street food scene in Adelaide and start a food truck business with the help of a good friend Alex Reed. Armed with a degree in business and marketing, Alex brings the necessary knowledge and expertise to ensure Jamie’s food truck achieves maximum visibility through innovative marketing and compelling social media campaigns. Driven by a shared vision and an entrepreneurial spirit, Jamie and Alex make the perfect team to conquer the food truck scene and delight customers with unique flavour combinations on delicious, wood fired pizza by the slice.

Jamie and Alex have asked you, the most talented quantitative analyst they know, to perform an analysis of their plans and financing options they have identified to help them set up their business. You will need to communicate your analysis in a format and language that they will understand since they do not have strong quantitative backgrounds. Be clear and concise and focus on practical implications!

Perform the necessary quantitative analyses and prepare a business report for Jamie and Alex, 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   

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 1.
3	• Complete Appendices 2 & 3.
4	• Complete Appendix 4. • Start working on the report.
5	• Finish 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

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. How expensive is a bank loan?

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.

(6 marks)

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

For example, Jamie and Alex will want to know what their quarterly repayment is going to be, how much they will pay in total, and how much of that will be interest. They will also need some advice from you about the effect of paying a 10% deposit. Should they pay it? Why or why not? Explain briefly.

[Click here and insert your report-style discussion of the matters addressed in Appendix 1]

2. Is an online lender’s offer a good idea?

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.

(5 marks)

Use your results from Appendix 2 to describe the key features of the loan offered by instalment plan offered by Direct Loan. Is this a good alternative to borrowing the amount required for the woodfire oven from the local bank (see Appendix 1)? Explain briefly. 

[Click here and insert your report-style discussion of the matters addressed in Appendix 2]

3.  How much to fund a café?

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.

(5 marks)

Use your results from Appendix 3 to answer the two main questions from that appendix:

-The resulting shortfall for $1,000 deposits;

-The required deposit amount.

[Click here and insert your report-style discussion of the matters addressed in Appendix 3]

4.  Will Flaming Crust Co break even?

Write a report-style discussion of the main results of your analysis in Appendix 4. 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 4.

(8 marks)

Discuss the results of your break-even analysis from Appendix 4. Include a copy and comment on your break-even graph. Comment on your profit calculation. Discuss revenue and profit implications of introducing signature pizzas and differentiated pricing.

[Click here and insert your report-style discussion of the matters addressed in Appendix 4]

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.

[Click here and insert the text for the Conclusions and Recommendations]

Appendix 1 (22 marks) – How expensive is a bank loan?

Highlight and delete the problem text below before submission.

Include full details of your working out in this appendix.

Clearly indicate which part you are answering, e.g. (a), (b) etc.

Jamie and Alex found a vintage food truck that is large and sturdy enough to accommodate a wood fire oven, but it needs to be refurbished and customized to suit their needs. Jamie and Alex have some money set aside to invest in the food truck business, but they have worked out that they will need an additional $50,000 to pay for the refurbishment. A local bank offers them equipment financing at 7.5% per year compounded quarterly. The loan must be repaid in 5 years.

• (4 marks) Use EXCEL to calculate the quarterly repayment that Jamie and Alex would have to make on this loan.

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

• (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 amortization schedule from scratch or modify an existing spreadsheet. Refer to the amortisation example from Week 2.

• (2 marks) Use your amortisation schedule from part (b) to calculate the total interest and the total amount paid over the life of the loan.

• (6 marks) Use your amortisation schedule to determine how much total interest paid on the loan would Jamie and Alex save by making a 10% deposit. Note that the deposit will reduce the borrowed amount and the quarterly repayment. Include your new amortisation schedule in this Appendix.

Appendix 2 (8 marks) – Is an online lender’s offer a good idea?

Highlight and delete the problem text below before submission.

Include full details of your working out in this appendix.

Clearly indicate which part you are answering, e.g. (a), (b) etc.

There is no Flaming Crust Co without a woodfire oven and Jamie has her heart set on a red Maximus Prime which is a portable oven handmade in Portugal that can be modified for use in a food truck. The oven plus modifications and installation would cost $8,000. Direct Loan, an online lender, offers a 0% APR loan with 5% establishment fee. The loan requires monthly repayments and has a term of one year. The establishment fee amount is based on the borrowed amount, and it is payable immediately. The monthly repayment amount is the borrowed amount divided by the number of monthly repayments.

Use EXCEL to calculate the APR (interest rate per year compounded monthly) implied by the Direct Loan offer, by setting the present value of monthly repayments to $8,000.

EXCEL Instructions: Prepare an EXCEL spreadsheet like the one shown below (only some values are shown – you will have to get Excel to work out the rest). Refer to the Excel exercise in Week 2 tutorial and ‘How to’ videos for examples of using GoalSeek.

Make sure that row and column names include your initials:

Now use GoalSeek (Data  What-If Analysis) in EXCEL to find the APR implied in this loan:

Include a copy of your ‘before’ and ‘after’ spreadsheet in the Appendix.

Appendix 3 (10 marks)– How much to fund a café?

Highlight and delete the problem text below before submission.

Include full details of your working out in this appendix.

Clearly indicate which part you are answering, e.g. (a), (b) etc.

Jamie’s goal is to open her own café in five years. She intends to start saving now to minimize the amount she will have to borrow to finance her cafe. She has set up a bank account that earns interest at 4.5% per year compounded monthly as a sinking fund. Jamie plans to make deposits of $1,000 per month into that account and she expects to have at least $75,000 available at the end of five years.

• (6 marks) Use EXCEL to calculate the balance in Jamie’s sinking fund at the given interest rate of 4.5% per annum after five years if the monthly payments are $1,000. By how much will Jamie fall short of her target amount?

Excel Instructions: Prepare an Excel spreadsheet like the one shown below (not all values shown are correct – 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.

• (4 marks) Use EXCEL to compute the size of the monthly deposits that Jamie should make into her account, in order to have the required amount in five 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.

Appendix 4 (20 marks) – Will Flaming Crust Co break even?

Highlight and delete the problem text before submission.

Include full details of your working out in this appendix.

Clearly indicate which part you are answering, e.g. (a), (b) etc.

Jamie and Alex estimate the following fixed costs of running their food truck to be around $13,400 per month, including wages, insurance, point of sale software, utility bills e.g. water and electricity, maintenance costs, marketing and advertising. Variable costs, including ingredients and packaging, are expected to be $1.55 per slice. Alex’s market research indicates that a price of $6.50 per slice would be highly competitive.

• (8 marks) What is the break-even number of units per month? Assuming six slices to a medium-sized pizza, how many medium-sized pizzas is it per day? Assume 30 days per month. What is the monthly break-even revenue? Find the break-even point algebraically and illustrate it using an EXCEL graph (in pizza slices 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  Charts  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.

• (6 marks) What unit sales are required to obtain a profit of $10,000 per month? How many medium-sized pizzas is it per day? In Appendix 3, present calculations to justify your answer. Type them up in Word or use EXCEL.

• (6 marks) Jamie loves to experiment with flavours and has created three signature gourmet pizza slices for the first month: Margherita Madness (a playful twist on a classic Margherita pizza), Hawaiian Heatwave (a hot and spicy version of a classic Hawaiian pizza) and Fig & Prosciutto Bliss (fig jam, goat cheese, prosciutto, arugula and balsamic glaze). These signature pizzas will be sold at $8.50 per slice and are expected to account for approximately 20% of monthly sales. Variable and fixed costs are expected to be unchanged. How many slices in total ($8.50 signature slices plus $6.50 slices) would Flaming Crust Co have to sell per month to generate the break-even revenue from part (a)? How many medium-sized pizzas is it per day? Would Flaming Crust Co be still just breaking even, or would they have a small profit? A small loss? In Appendix 3, present appropriate calculations to justify your answer. Type them up in Word or use EXCEL.