# 11.12 Break-Even Pricing

## Break-Even Pricing

In running a business, you must never forget the “bottom line.” In other words, if you fully understand how your products are priced, you will know when you are making or losing money. Remember, if you keep losing money you will not stay in business for long! 15% of new businesses will not make it past their first year, and 49% fail in their first five years. This number becomes even more staggering with an 80% failure rate within the first decade.^{[1]} Do not be one of these statistics! With your understanding of markup, you now know what it takes to break even in your business.** Break-even** means that you are earning no profit, but you are not losing money either. Your profit is zero.

If the regular unit selling price must cover three elements—cost, expenses, and profit—then the regular unit selling price must exactly cover your costs and expenses when the profit is zero. In other words, if Formula 1.5 is modified to calculate the selling price at the break-even point () with =0, then:

This is not a new formula. It just summarizes that at break-even there is no profit or loss, so the profit () is eliminated from the formula.

### How It Works

The steps you need to calculate the break-even point are no different from those you used to calculate the regular selling price. The only difference is that the profit is always set to zero.

Recall Example 1.2D that the cost of the MP3 player is $26.15 and expenses are $7.84.

The break-even price () is

This means that if the MP3 player is sold for anything more than $33.99, it is profitable; if it is sold for less, then the business does not cover its costs and expenses and takes a loss on the sale.

### Example 1.2H – Knowing Your Break-Even Price

John is trying to run an eBay business. His strategy has been to shop at local garage sales and find items of interest at a great price. He then resells these items on eBay. On John’s last garage sale shopping spree, he only found one item—a Nintendo Wii that was sold to him for $100. John’s vehicle expenses (for gas, oil, wear/tear, and time) amounted to $40. eBay charges a $2.00 insertion fee, a flat fee of $2.19, and a commission of 3.5% based on the selling price less $25. What is John’s minimum list price for his Nintendo Wii to ensure that he at least covers his expenses?

**Plan:**

You are trying to find John’s break-even selling price ().

**Understand:**

**Step 1:** John’s cost for the Nintendo Wii and all of his associated expenses are as follows:

= $100.00

(vehicle) = $40.00

(insertion) = $2.00

(flat) = $2.19

(commission) = 3.5%(S_{BE} − $25.00)

You have four expenses to add together that make up the in the formula.

**Step 2:** Formula 1.5 states . Since you are looking for the break-even point, then is set to zero and .

**Perform:
**

**Step 1:**

**Step 2:**

**Present:**

At a price of $148.51 John would cover all of his costs and expenses but realize no profit or loss. Therefore, $148.51 is his minimum price.

## Give It Some Thought Answers

- Cost, expenses, and profit. They are expressed either per unit or as a total.
- A specific dollar amount, a percentage of cost, or a percentage of the selling price.
- The net price paid for a product is the same as the cost of the product.
- False. The markup amount is a portion of the selling price and therefore is less than 100%.
- False. The markup amount plus the cost equals the selling price. It must be less than the selling price.
- True. A cost can be doubled or tripled (or increased even more) to reach the price.
- True. The base for markup on cost percentage is smaller, which produces a larger percentage.
- True. You could combine Formulas 1.7 and 1.8 to arrive at the selling price.
- True. You could convert the to a and solve as in the previous question.

### Exercises

Round all money to two decimals and percentages to four decimals for each of the following exercises.

## Mechanics

For questions 1–8, solve for the unknown variables (identified with a ?) based on the information provided.

Regular Unit Selling Price | Cost | Expenses | Profit | Markup Amount | Break-Even Price | Markup on Cost | Markup on Selling Price | |

1. | ? | $188.42 | $48.53 | $85.00 | ? | ? | ? | ? |

2. | $999.99 | ? | 30% of | 23% of | ? | ? | ? | ? |

3. | ? | ? | ? | 10% of | $183.28 | ? | 155% | ? |

4. | $274.99 | ? | 20% of | ? | ? | ? | ? | 35% |

5. | ? | ? | 45% of | ? | $540.00 | $1,080.00 | ? | ? |

6. | ? | $200 less 40% | ? | 15% of | ? | ? | 68% | ? |

7. | ? | ? | $100.00 | ? | $275.00 | ? | ? | 19% |

8. | ? | ? | 15% of | 12% of | ? | $253.00 | ? | ? |

## Applications

9. If a pair of sunglasses sells at a regular unit selling price of $249.99 and the markup is always 55% of the regular unit selling price, what is the cost of the sunglasses?

10. A transit company wants to establish an easy way to calculate its transit fares. It has determined that the cost of a transit ride is $1.00, with expenses of 50% of cost. It requires $0.75 profit per ride. What is its markup on cost percentage?

11. Daisy is trying to figure out how much negotiating room she has in purchasing a new car. The car has an MSRP of $34,995.99. She has learned from an industry insider that most car dealerships have a 20% markup on selling price. What does she estimate the dealership paid for the car?

12. The markup amount on an eMachines desktop computer is $131.64. If the machine regularly retails for $497.25 and expenses average 15% of the selling price, what profit will be earned?

13. Manitoba Telecom Services (MTS) purchases an iPhone for $749.99 less discounts of 25% and 15%. MTS’s expenses are known to average 30% of the regular unit selling price.

a. What is the regular unit selling price if a profit of $35 per iPhone is required?

b. What are the expenses?

c. What is the markup on cost percentage?

d. What is the break-even selling price?

14. A snowboard has a cost of $79.10, expenses of $22.85, and profit of $18.00.

a. What is the regular unit selling price?

b. What is the markup amount?

c. What is the markup on cost percentage?

d. What is the markup on selling price percentage?

e. What is the break-even selling price? What is the markup on cost percentage at this break-even price?

## Challenge, Critical Thinking, & Other Applications

15. A waterpark wants to understand its pricing better. If the regular price of admission is $49.95, expenses are 20% of cost, and the profit is 30% of the regular unit selling price, what is the markup amount?

16. Sally works for a skateboard shop. The company just purchased a skateboard for $89.00 less discounts of 22%, 15%, and 5%. The company has standard expenses of 37% of cost and desires a profit of 25% of the regular unit selling price. What regular unit selling price should Sally set for the skateboard?

17. If an item has a 75% markup on cost, what is its markup on selling price percentage?

18. A product received discounts of 33%, 25%, and 5%. A markup on cost of 50% was then applied to arrive at the regular unit selling price of $349.50. What was the original list price for the product?

19. Mountain Equipment Co-op (MEC) wants to price a new backpack. The backpack can be purchased for a list price of $59.95 less a trade discount of 25% and a quantity discount of 10%. MEC estimates expenses to be 18% of cost and it must maintain a markup on selling price of 35%.

a. What is the cost of backpack?

b. What is the markup amount?

c. What is the regular unit selling price for the backpack?

d. What profit will Mountain Equipment Co-op realize?

e. What happens to the profits if it sells the backpack at the MSRP instead?

20. Costco can purchase a bag of Starbucks coffee for $20.00 less discounts of 20%, 15%, and 7%. It then adds a 40% markup on cost. Expenses are known to be 25% of the regular unit selling price.

a. What is the cost of the coffee?

b. What is the regular unit selling price?

c. How much profit will Costco make on a bag of Starbucks coffee?

d. What markup on selling price percentage does this represent?

e. Repeat questions (a) through (d) if the list price changes to $24.00.

The section is reproduced from Chapter 4.2 in *Fundamentals of Business Mathematics* by OER Lab licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License

- Statistics Canada. (2000, February 16).
*Failure Rates for New Firms. The Daily.*www.statcan.gc.ca/daily-quotidien/000216/dq000216b-eng.htm. ↵