LO new venture or product line is being planned, the likelihood of the project’s suc- Define breakeven point,

4 LO new venture or product line is being planned, the likelihood of the project’s suc- Define breakeven point,

cess can be quickly measured by finding its breakeven point. If, for instance, the and use contribution margin breakeven point is 24,000 units and the total market is only 25,000 units, the to determine a company’s margin of safety would be very low, and the idea should be considered carefully. breakeven point for multiple The margin of safety is the number of sales units or amount of sales dollars by products. which actual sales can fall below planned sales without resulting in a loss—in this

example, 1,000 units.

Sales (S), variable costs (VC), and fixed costs (FC) are used to compute the breakeven point, which can be stated in terms of sales units or sales dollars. The general equation for finding the breakeven point is as follows:

S ⫺ VC ⫺ FC ⫽ $0 or as SP(X) ⫺ VR(X) ⫺ FC ⫽ $0

Suppose, for example, that one of the services My Media Place sells is website setups. Variable costs are $50 per unit, and fixed costs average $20,000 per year.

A unit is a basic website setup which sells for $90. 씰 Breakeven in sales units: Given this information, we can compute the

breakeven point for website setup services in sales units (X equals sales units):

S – VC – FC ⫽ $0 $90X ⫺ $50X ⫺ $20,000 ⫽ $0

$40X ⫽ $20,000

X ⫽ 500 Units

Breakeven Analysis

FIGURE 20-7

Graphic Breakeven Analysis for My Media Place

Total Revenue

Point in

Profit Area

Sales Dollars

$45 Total

Cost Line

Variable Costs

Dollars (in thousands)

Loss Area

Point in

Units of Output

씰 Breakeven by scatter diagram: In addition, we can make a rough estimate of the breakeven point using a scatter diagram. This method is less exact, but it does yield meaningful data. Figure 20-7 shows a breakeven graph for My Media Place. As you can see there, the graph has five parts:

1. A horizontal axis for units of output

2. A vertical axis for dollars

3. A line running horizontally from the vertical axis at the level of fixed costs

4. A total cost line that begins at the point where the fixed cost line crosses the vertical axis and slopes upward to the right (The slope of the line depends on the variable cost per unit.)

5. A total revenue line that begins at the origin of the vertical and horizontal axes and slopes upward to the right (The slope depends on the selling price per unit.)

At the point at which the total revenue line crosses the total cost line, revenues equal total costs. The breakeven point, stated in either sales units or dollars of sales, is found by extending broken lines from this point to the axes. As Figure 20-7 shows, My Media Place will break even when it has sold 500 website setups for $45,000.

Study Note

Contribution margin equals sales

Using an Equation to Determine the Breakeven Point

CHAPTER 20 Cost Behavior Analysis

A product line’s contribution margin represents its net contribution to pay-

ing off fixed costs and earning a profit. Profit (P) is what remains after fixed costs The maximum contribution a unit

Study Note

are paid and subtracted from the contribution margin:

of product or service can make is its selling price. After paying for

CM ⫺ FC ⫽ P

itself (variable costs), a product The example that follows uses the contribution margin income statement or service provides a contribution

margin to help pay total fixed approach to organize the facts and to determine the profitability of one of My

Media Place’s products.

costs and then earn a profit.

Units Produced and Sold

Symbols 250 500 750

Sales revenue ($90 per unit)

VC Less variable costs ($50 per unit)

CM Contribution margin ($40 per unit) $10,000 $20,000 $30,000 FC Less fixed costs

Profit (loss)

The breakeven point (BE) can be expressed as the point at which contribution margin minus total fixed costs equals zero (or the point at which contribution margin equals total fixed costs).

씰 Breakeven in sales units: In terms of units of product, the equation for the

breakeven point looks like this: (CM per Unit ⫻ BE Units) ⫺ FC ⫽ $0 It can also be expressed like this: BE Units ⫽ ___________ FC

CM per unit To show how the formula works, we use the data for My Media Place:

___________ __________ $20,000 BE Units ⫽ $20,000 FC ⫽ ⫽ ________ ⫽ 500 Units

CM per unit $90 – $50

씰 Breakeven in sales dollars: The breakeven point in total sales dollars may be determined by multiplying the breakeven point in units by the selling price (SP) per unit:

BE Dollars ⫽ SP ⫻ BE Units ⫽ $90 ⫻ 500 Units ⫽ $45,000 씰 An alternative way of determining the breakeven point in total sales dollars

is to divide the fixed costs by the contribution margin ratio. The contribu- tion margin ratio is the contribution margin divided by the selling price:

CM Ratio ⫽ CM ____ ⫽ ____ $40 ⫽ 0.444*, or 4/9

SP

BE Dollars ⫽ _________ $20,000 FC ⫽ ________ ⫽ $45,045*

CM Ratio

Breakeven Analysis

FIGURE 20-8

Express Websites Sales Mix for My Media Place

Standard Websites

100% of Sales

s selling prices. To calculate the breakeven point for each product, its unit contri-

Study Note

bution margin must be weighted by the sales mix. The sales mix is the propor- b

A company’s sales mix can tion of each product’s unit sales relative to the company’s total unit sales. t

be very dynamic. If the mix Let’s assume that My Media Place sells two types of websites: standard and is constantly changing, an

express. If the company sells 500 units, of which 300 units are standard and 200 e assumption of stability may

are express, the sales mix would be 3:2. For every three standard websites sold, a undermine the C-V-P analysis.

t two express websites are sold. The sales mix can also be stated in percentages. Of the 500 units sold, 60 percent (300 ÷ 500) are standard sales, and 40 percent t (200 ÷ 500) are express sales (see Figure 20-8). (

The breakeven point for multiple products can be computed in three steps:

1. Compute the weighted-average contribution margin.

2. Calculate the weighted-average breakeven point.

3. Calculate the breakeven point for each product. To illustrate, we will use My Media Place’s sales mix of 60 percent standard web-

sites to 40 percent express websites and total fixed costs of $32,000; the selling price, variable cost, and contribution margin per unit for each product line are shown in Step 1 below.

Step 1. Compute the weighted-average contribution margin. To do so, multiply the contribution margin for each product by its percentage of the sales mix, as follows:

Weighted- Selling Variable Contribution Percentage of Average

CM Standard $90 ⫺ $50 ⫽ $40 ⫻ 60% ⫽ $24

Price

Costs

Margin (CM)

Sales Mix

Express $40 ⫺ $20 ⫽ $20 ⫻ 40% ⫽ 8 Weighted-average contribution margin

$32 Step 2. Calculate the weighted-average breakeven point. Divide total fixed costs

CHAPTER 20 Cost Behavior Analysis Step 3. Calculate the breakeven point for each product. Multiply the weighted-

average breakeven point by each product’s percentage of the sales mix:

Weighted-Average Sales Breakeven Breakeven Point Mix Point

Standard 1,000 units ⫻ 60% ⫽ 600 units Express 1,000 units ⫻ 40% ⫽ 400 units

To verify, determine the contribution margin of each product and subtract the total fixed costs:

Contribution Margin

Standard 600 ⫻ $40 ⫽ $24,000 Express 400 ⫻ $20 ⫽ 8,000 Total contribution margin

Less fixed costs

Profit