Unit 3 – Business Mathematics

BUSN125 U3 IP template.docx Unit 3 – Business mathematics

This assignment requires you to develop a comprehensive business plan including an introduction of your business, financial projections such as revenue, expenses, and profits, product pricing and costs, investment requirements with loan repayment schedules, a balance sheet with vertical analysis, and a concluding summary. You must include detailed financial calculations, conduct a vertical analysis of assets and liabilities, and provide a proper APA-formatted references section with scholarly sources. The goal is to demonstrate understanding of mathematics in business decision-making through creating realistic financial and operational plans for a startup business.

Paper For Above instruction

Starting a new business involves careful planning and financial analysis to ensure sustainability and profitability. The first step is to define the business concept: what it will sell, why it is interesting, and who the target customers are. For instance, I plan to open a specialty coffee shop that offers unique brewing methods and organic products. This business interests me because of my passion for coffee and the growing consumer preference for organic and specialty beverages. It also provides an opportunity to serve a community need for quality coffee experiences while creating a cozy environment that encourages customer loyalty.

In understanding the role of mathematics in business, I have projected year one sales by estimating the number of units sold and the unit price. Suppose I anticipate selling 10,000 cups of coffee at an average price of $4 each, resulting in projected sales of $40,000 for the first year. Expenses will include rent, equipment, supplies, wages, and marketing. For example, rent could be $1,500 per month ($18,000 annually), equipment costs around $10,000, and wages approximately $8,000 per month ($96,000 annually). Adding these expenses, total projected costs may reach approximately $124,000 in year one.

Calculating the proportion of revenue consumed by expenses involves dividing total expenses by sales revenue, yielding the expense ratio. If expenses are $124,000 and sales are $40,000, expenses exceed revenue, indicating a need for strategic adjustments. Typically, in the initial phase, expenses might overshadow profits, but with increased sales volume or price adjustments, profitability can improve. The specific ratios, expressed as fractions and percentages, reveal the operational scale and financial health of the startup.

Regarding profitability, the portion of sales revenue that remains as profit depends on controlling costs and increasing sales. For example, if the business manages to increase unit sales or optimize costs, profit margins can be improved, enabling sustainable growth. These calculations are crucial for making informed business decisions about pricing, cost management, and investment.

Next, I will define the pricing strategy and costs for each product or service. For instance, my coffee will be priced at $4 per cup, with ingredient and operational costs amounting to $1.50 per cup, resulting in a markup of $2.50 or 166.7%. In dollar terms, markup per unit is calculated as selling price minus cost ($4 - $1.50 = $2.50). This markup ensures cover for fixed costs and profit generation. Adjustments to pricing may occur based on competition, customer willingness to pay, and cost fluctuations.

In terms of investment, I plan to open business accounts—checking and savings—to manage cash flows. The initial capital requirement includes covering startup costs, which I estimate to be about $50,000. If I need to finance part of this through a loan, I would seek a bank loan matching my projected expenses. Assuming a loan amount of $124,000, I will compare repayment schedules for 10 years under different interest regimes: 6% compound interest and 8% simple interest.

The loan with compound interest at 6% can be calculated using the amortization formula, resulting in annual payments that gradually reduce the principal while covering interest. Over ten years, the schedule would include fixed annual payments based on the amortization of the principal plus accumulated interest. Conversely, the simple interest loan calculates interest as a percentage of the original principal, with equal annual payments including interest, simplifying the calculation but possibly increasing total interest paid over the term.

A balance sheet for year one will organize assets such as cash, inventories, equipment, and receivables, alongside liabilities like loans and accounts payable. Equity includes owner investments and retained earnings. Vertical analysis will highlight the largest asset—likely to be equipment—and the most significant liability—probably the loan principal. This analysis illuminates the business’s financial structure and liquidity position.

Finally, the conclusion will synthesize the business goals, potential challenges like cash flow management, and expectations of profitability and growth. It emphasizes how mathematical and financial planning underpin successful entrepreneurship, providing confidence that the business can reach its strategic objectives through informed financial decisions and diligent management.

References

• American Psychological Association [APA]. (2010). Publication manual of the American Psychological Association (6th ed.). Washington, DC: Author.
• Brigham, E. F., & Ehrhardt, M. C. (2016). Financial Management: Theory & Practice. Cengage Learning.
• Garrison, R. H., Noreen, E. W., & Brewer, P. C. (2018). Managerial Accounting. McGraw-Hill Education.
• Ross, S. A., Westerfield, R., & Jaffe, J. F. (2013). Corporate Finance. McGraw-Hill Education.
• Shim, J. K., & Siegel, J. G. (2012). Financial Management Basics. Barron’s Educational Series.
• Horngren, C. T., Sundem, G. L., & Elliott, J. A. (2013). Introduction to Financial Accounting. Pearson.
• Clare, A. (2011). Business Math Using Excel. Human Resource Management.
• Kanaran, B. (2017). Financial Ratios and Business Analysis. Journal of Business Strategies.
• Investopedia. (2020). Loan Amortization Formula. Retrieved from https://www.investopedia.com/terms/a/amortization.asp
• U.S. Small Business Administration. (2021). Business Planning and Financial Management. SBA.gov.