## Break-Even Point in units - Examples and Formulas

Break-even Example Using Questions & Answers

Ron Ross has been working for a major chair retailer for the past 15 years. The thought of opening his own chair retail outlet has crossed his mind many times over the last few years. Four months ago, Ron visited his bank and communicated his intentions of owning his own business to a loans manager. The loans manager told him to "prepare a business plan and be sure to include annual forecasted financial statements for a three year period". In addition, the banker wanted Ron to present the answers to the following nine questions at their next meeting.

1. What will your selling price per chair be for each of the three years?
2. What will your forecasted variable cost be for each of the three years?
3. What will your forecasted fixed costs be for each year of the three years?
4. How would you calculate the break-even point?
5. How many chairs would you have to sell in order to break-even?
6. How many chairs would you have to sell to achieve a Net Income before tax of \$0.00?
7. How many chairs will you have to sell to achieve each year's forecasted net income (B/T)?
8. How many chairs will you have to sell to achieve a 200X net income before tax of \$50,000
9. How would a business, selling multiple products, calculate its break-even point?

Ron completed his business plan including his forecasted financial statements (balance sheet, income statement, cash flow statement). The following is a condensed forecasted income statement for Ron Ross Chair Company for years ending March 31, 200X, 200Y, and 200Z. Following the forecasted financial statements is additional information needed to answer each of the banker's nine questions.

 Ron Ross Chair Company Condensed Forecasted Income Statement For Years Ending March 31, 200X, 200Y, 200Z 200X 200Y 200Z Total Chair Sales \$80,000 \$200,000 \$240,000 Cost of Goods Sold \$48,000 \$120,000 \$144,000 Gross Margin \$32,000 \$ 80,000 \$ 96,000 Operating Expenses \$20,000 \$ 50,000 \$ 70,000 Net Income Before Taxes \$12,000 \$ 30,000 \$ 26,000 Less; Taxes (@ 40%) \$ 4,800 \$ 12,000 \$ 10,400 Net Income After Taxes \$ 7,200 \$ 18,000 \$ 15,600

A.   Ron will buy preassembled chairs from a wholesaler at a cost of \$100 each. In addition, it costs Ron, on average, \$20 per chairs to have a shipping company delivery each one to his retail outlet. He sells the same chairs to his customers for \$200 each.

B.   Assume Ron's Selling Price & Variable Costs are constant each year.

C.   Assume Ron's cost of goods sold comprise the company's total variable costs (IE product cost).

D.   Assume Ron's operating expenses (marketing & administrative) represent his total fixed costs.

E.   Assume the forecasted income tax rate is constant for each year (40%).

Ron now has all the information he needs in order to answer all of the banker's questions. Let's begin with the first question.

1.   What is Ron's Selling Price per Chair each Year?

Ron's selling price per chair is provided in the additional information section (above). He plans to sells each chair for \$200 each year.

 200X 200Y 200Z Selling Price per Year \$200 \$200 \$200

2.   What is Ron's Variable Cost per Chair each Year?
The only variable costs Ron's company has are the direct material costs (the chair) and the shipping costs per chair. Moreover, when Ron sells a chair to a customer, it costs him the amount he paid for the chair (\$100) as well as the cost to ship the chair to his store (\$20). Therefore, Ron's total variable costs amount to \$120.00 per chair  which is expected to remain constant over the three year forecasted period.

 200X 200Y 200Z Variable Cost per Year \$120 \$120 \$120

3.   What are Ron's Fixed Costs for each year?
As indicated in the additional information section, all Ron's Forecasted Operating Expenses (marketing & administrative expenses) are considered to be fixed. This will be the case for most businesses. Therefore, as stated in Ron's Forecasted Income Statement, Fixed Costs are estimated to be as follows for each year;

 200X 200Y 200Z Total Fixed Costs per year \$20,000 \$ 50,000 \$ 70,000

Let's now organize the Forecasted Selling Price Per unit, the Variable Costs per Unit, and the Fixed costs into a chart for easily reading;

 200X 200Y 200Z Selling Price per Chair (per year) \$ 200 \$ 200 \$ 200 Variable Costs per Chair (per year) \$ 120 \$ 120 \$ 120 Fixed Costs Per Year (per year) \$20,000 \$50,000 \$70,000

4.   What is the Formula for determining a company's Break Even Point?

Break-even Point     =                  Fixed Costs
Selling Price - Variable Costs

Ron knows the importance of this formula, since it determines the number of chairs he must sell in order to break-even or achieve a net income before taxes of ZERO.

5.   What is Ron's Break Even Point(B/E) in units each year?

Break-even Point     =                  Fixed Costs
Selling Price - Variable Costs
 200X 200Y 200Z Break-even in units = \$20,000 \$ 50,000 \$70,000 \$200- \$120 \$200- \$120 \$200 - \$120 = 250 chairs 625 chairs 875 chairs

Therefore:

• In 200X, Ron will need to sell 250 chairs in order to break-even.
• In 200Y, Ron will need to sell 625 chairs in order to break-even.
• In 200Z, Ron will need to sell 875 chairs in order to break-even.

6.   How many chairs (each year) must Ron sell to achieve a Net Income Before Tax of ZERO (\$0.00)?

Ron was rather confused when he came to this question because he thought he had already answered it in question 5 above. Moreover, he thought that the break-even point formula did, in fact, determine the number of chairs he would have to sell in order to achieve a net income before taxes of ZERO. Somewhat baffled, Ron called the loans manager at the bank and asked for some clarification. The loans manager was quite impressed with Ron's findings and congratulated him on his knowledge of the break-even formula. "You see Ron, I like to try to trick people just to see if they understand financial terms and procedures", said the bank manager. Ron hung up the phone, proud of his accomplishment and proceeded to answer the question. He wrote;

"Mr. Bank manager, you can't fool me. I know that the break-even point, calculated in question number 5, determines the number of chairs I have to sell in order to achieve a net income before taxes of ZERO. Next time you should give me a more difficult challenge!!! At any rate, here's the answer to your question."

250 chairs must be sold in 200X in order to break-even or achieve a net income before taxes of zero. 625 chairs must be sold in 200Y in order to break-even or achieve a net income before taxes of zero. 875 chairs must be sold in 200Z in order to break-even or achieve a net income of zero.

7.   How many chairs would Ron have to sell in order to achieve his Forecasted Net Income Before Taxes for each year?

To answer this question, Ron must refer back to his forecasted income statement.

 Ron Ross Chair Company Condensed Forecasted Income Statement For Years Ending March 31... 200X 200Y 200Z Total Chair Sales \$80,000 \$200,000 \$240,000 Cost of Goods Sold \$48,000 \$120,000 \$144,000 Gross Margin \$32,000 \$ 80,000 \$ 96,000 Operating Expenses \$20,000 \$ 50,000 \$ 70,000 Net Income Before Taxes \$12,000 \$ 30,000 \$ 26,000 Less; Taxes (@ 40%) \$ 4,800 \$ 12,000 \$ 10,400 Net Income After Taxes \$ 7,200 \$ 18,000 \$ 15,600

As you can see, Ron's forecasted Net Income Before Taxes for 200X is \$12,000, for 200Y is \$30,000 and for 200Z is \$26,000. Therefore, the banker wants Ron to determine the number of chairs he must sell in order to achieve his forecasted Net Income Before Taxes of \$12,000 for 200X, \$30,000 for 200Y, and \$26,000 for 200Z.

To answer this question, Ron must add the forecasted net income before taxes to his forecasted fixed costs and divide by his contribution margin (selling price per unit minus (-) variable costs per unit). Here's the formula.

 Break-even at desired income level = Fixed Costs + Desired Income before tax Selling Price per unit - Variable Cost per unit 200X Break-even at desired income level = \$20,000 + \$12,000 \$200 - \$120 = 400 chairs 200Y Break-even at desired income level = \$50,000 + \$30,000 \$200- \$120 = 1,000 chairs 200Z Break-even at desired income level = \$70,000 + \$26,000 \$200- \$120 = 1,200 chairs

Therefore:

• Ron must sell 400 chairs in 200X in order to achieve a net income before taxes of \$12,000.
• Ron must sell 1,000 chairs in 200Y in order to achieve a net income before taxes of \$30,000.
• Ron must sell 1,200 chairs in 200Z in order to achieve a net income before taxes of \$26,000.

8.  How many chairs would Ron have to sell in order to achieve a Net Income Before tax of \$50,000 in 200X?

This question is similar to the above question. Moreover, to answer this, Ron will add the desired net income before taxes to his forecasted fixed costs and divide by his contribution margin (selling price per unit minus (-) variable costs per unit).

Break-even at desired income level =    Fixed Costs + Desired income before tax
Selling Price per unit - Variable Costs per unit

Break-even at a desire income level    =              \$20,000 + \$50,000
\$200 - \$120

=                    875 chairs

Therefore, Ron will need to sell 875 chairs in 200X to achieve net income before taxes of \$50,000.

9.   How would a business, selling multiple products, calculate its break-even point?

Ron's struggled with this question for quite some time. Finally after reading several accounting books, he discovered the answer. Ron writes;

"A business selling multiple products will use the same break-even formula used by businesses selling a single product. They must, however, calculate a weighted average selling price and a weighted average product cost. The weighted average selling price considers all the selling prices for each product and reduces them down into one single selling price. In addition, the weighted average variable cost considers all variable costs for each product and reduces them down into one single variable cost".

Ron met with the loan's manger the following day and presented him with the answers to the above questions. The loan's manager quickly read the answers and congratulated Ron on his work. Ron presented his business plan to the loans manager, requesting a \$25,000 term loan. The loan application was filled out and within one week, Ron received the loan.

Categories: Financial