# Case Study – Chapter 8

Morden Shapiro

## Profit Analysis

Break-even point (BEP)

The breakeven point is the level of sales at which revenues equal all costs of production or of cost of goods sold.

Most businesses have two primary classifications of costs:

• Fixed costs which do not change over specified levels of operation (i.e. rent, insurance premiums, lease payments for equipment) and which are incurred (i.e. committed to by the business, such as salaries, loan payments etc.) and so must be paid regardless of sales or production.
• Variable costs which are incurred for each unit of sales or each unit of production.

### Background

Judy’s business is relatively simple. She operates a small retail establishment in which she sells Mogs. Her fixed costs are \$3,000.00 per month, including her leased storefront which is under a 4 years lease. Her variable costs are 25.00 per Mog. She sells each Mog for 42.00.

### Assignment 1

1. In mathematical terms express the calculation that Judy must make in order to determine how many Mogs she must sell each month in order to recover all of her monthly costs.
2. Develop the mathematical relationships that will allow Judy to determine her total monthly costs and total monthly sales given a specific number of Mogs produced and sold each month.
3. Use Demos graphing calculator (demos.com/calculator) to graph the relationships determined in B. Label the graph appropriately.
4. Describe how your calculation in A is reflected in the graph in C.
5. Determine the profit in terms of the number of Mogs produced and sold and graph it using Desmos. Explain the advantages of this mathematical analysis to Judy in terms of understanding her profit analysis.

### Assignment 2

Assume that Judy has the opportunity to lease the neighbouring storefront for a fixed additional amount per month for the balance of her current lease. The amount of monthly rent for the additional space will be the result of negotiations between Judy and her landlord.

Judy expects that she will be able to increase her monthly sales by 15% if she has the additional space.

1. Given her current monthly sales, express in mathematical terms the calculation that Judy must make in order to determine the amount by which she can afford to pay an increased rent so as to achieve her BEP.
2. Determine the functions that describes the additional rent Judy can afford to pay in terms of the current monthly sales.
3. Draw the graph of the relationship in B using Desmos. Interpret the meaning of the graph and its characteristics.

### Assignment 3

Reflect on the following questions Judy may consider and explain the context factors that are necessary for Judy to reasonably interpret and rely upon for decision making purposes. How will these context factors influence the output values in these relationships?

Suggested questions that Judy may consider:

– How certain am I that the variable costs will continue to be accurate across various level of scale?

– How tolerant will the market be of my sales pricing across various levels of scale?

– How certain am I of the impact that the additional space will have on my sales volume?

### Challenge

Construct additional questions that Judy ought to ask as part of her decision-making process.

Attribution: Case study by Morden Shapiro (Ontario Tech University), published under Creative Commons Attribution-NonCommercial-ShareAlike licence (CC-BY-NC-SA)

Any modifications to this case study may affect its solvability and caution is advised.