### Cost Volume Profit

#### Breakeven Point

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# Learning Objectives

###### How to Calculate Breakeven for Singular and Multiple Product Lines

###### What is the Breakeven Point?

The breakeven point refers to the point in production that does not make or lose money. In other words, it's the point where profit = 0. Increasing production beyond the breakeven point will generate a profit and producing less than the breakeven point will produce a loss. The formula for breakeven is as follows:

Breakeven Point in Units = Fixed Costs / Contribution Margin A business can use the breakeven point to determine how risky it can be to achieve a profit.

###### Worked Example: Breakeven Point in Units

John runs a shoe manufacturing business. He sells each shoe for $65 while his direct materials are $30 and direct labour is $20 for each shoe. His factory overheads are $120,000 for the year.

What is John's breakeven point in units and dollars?

**Solution: **

1. First step is to calculate the contribution margin per unit.

As stated in previous pages, the contribution margin formula is as follows: Contribution Margin Per Unit = Selling Price Per Unit - Variable Cost Per Unit Our selling price per unit is $65. Our variable costs per unit are comprised of direct materials and direct labour.

Therefore our Variable Cost Per Unit is $30 + $20 = $50.

Hence our contribution margin: Contribution Margin Per Unit = $65 - $50 Contribution Margin Per Unit = $15

2. After obtaining the contribution, we can now calculate the breakeven point in units. Remember, the formula for breakeven point in units is as follows: Breakeven Point in Units = Fixed Costs / Contribution Margin Our fixed costs is the factory overheads at $120,000. Therefore, our breakeven points in units is: Breakeven Point in Units = $120,000 / $15 Breakeven Point in Units = 8,000 units

3. Lastly, we now have to calculate our breakeven point in dollars. To do this, simply multiply the breakeven point in units by the selling price. Breakeven Points in Dollars = Breakeven Point in Units * Selling Price Breakeven Points in Dollars = 8,000 * $65 Breakeven Points in Dollars = $520,000 That's it! The breakeven point in units is $8,000 and the breakeven point in dollars is $520,000.

###### How do we calculate breakeven point for multiple product lines?

The breakeven point for multiple product lines is the same as the simple formula, except this time we are using the Weighted Average Contribution Margin.

Go to the Weighted Average Contribution Margin Section in CVP for more information on how to calculate it. The formula for breakeven is as follows: Breakeven Point in Units = Fixed Costs / Weighted Average Contribution Margin After we calculate the Breakeven Point overall, we simply calculate the Sales Mix of a Specific Product by the Breakeven Point to get the Breakeven Point in units of that specific product.

Breakeven Point in Units (Product A) = Sales Mix (Product A) * Breakeven Point in Units See below for the worked example.

###### Worked Example: Breakeven Point for Multiple Product Lines

Dumbler Muffin is a Paper Company that sells three products, Printers, Paper and Ink. The expected sales and costs of each product are outlined below.

Printer: Sold for $300 each, variable costs per unit is $250. Expected sales for the year are 5,000 units.

Paper: Sold for $10 each, variable costs per unit is $5. Expected sales for the year are 30,000 units.

Ink: Sold for $30 each, variable costs per unit is $20. Expected sales for the year are 15,000 units.

Fixed Costs: $320,000 for the year.

Calculate the breakeven point for each of the three products.

**Step 1: Calculate the Sales Mix of Each Product Line **

Sales Mix = Product Line Sales (Units) / Total Sales (Units)

Total Sales = 5,000 printer units + 30,000 paper units + 15,000 ink units = 50,000 units

Printer Sales Mix = 5,000/50,000 = 10%

Paper Sales Mix = 30,000/50,000 = 60%

Ink Sales Mix = 15,000/50,000 = 30%

**Step 2: Calculate the Contribution Margin of Each Product **

Contribution Margin = Sale Price Per Unit - Variable Cost Per Unit

Printer Contribution Margin = $300 (SP) - $250 (VC) = $50 per unit

Paper Contribution Margin = $10 (SP) - $5 (VC) = $5 per unit

Ink Contribution Margin = $30 (SP) - $20 (VC) = $10 per unit

**Step 3: Multiply the Sales Mix by the Respective Contribution Margin of Each Product to Get the Weighted Average Contribution Margin **

Printer Weighted Ave Contribution Margin: 10% * $50 = $5

Paper Weighted Ave Contribution Margin: 60% * $5 = $3

Ink Weighted Ave Contribution Margin: 30% * $10 = $3

Therefore, the total Weighted Average Contribution Margin Per Unit: = $5 (Printer) + $3 (Paper) + $3 (Ink) = $11

**Step 4: Calculate the Breakeven Point Using the Weighted Average Contribution Margin **

Breakeven Point in Units = Fixed Costs / Weighted Average Contribution Margin Breakeven Point in Units = $320,000 / $11 = 29,091 units

**Step 5: Calculate the Breakeven of Each Product **

Remember the breakeven of each product is:

Sales Mix (Product A) * Breakeven Point in Units

Printer Breakeven in Units = 10% * 29,091 units = 2,909 units

Paper Breakeven in Units = 60% * 29,091 units = 17,455 units

Ink Breakeven in Units = 30% * 29,091 units = 8,727 units

**Step 6: Calculate Breakeven in Dollars Multiply the Breakeven in Units by the Sales Price to get the Breakeven in Dollars **

Printer = 2,909 units * $300 = $872,700

Paper = 17,455 units * $10 = $170,455

Ink = 8,727 units * $30 = $261,810