We have looked at the breakeven calculations for a single-product firm. However, most firms make more than one product - or service. Conceptually, multiple-product breakeven is the same as single product breakeven. However, when there are multiple products, there will be variable and fixed costs associated with individual products. There will also be fixed cost that is common to all products. This makes things a little trickier. Let's look at two possibilities: calculating the breakeven point in sales for the firm as a whole, and calculating the breakeven points for each individual product.

Overall Breakeven Sales for the Multi-Product Firm. The firm must determine its total variable costs and total fixed costs. Then the contribution margin ratio can be computed by dividing total contribution margin by sales.

Example: Jem Company makes a number of different small household appliances. The company presented the following income statement (for all products) for last year.

Sales	$294,000		100.00%
Total variable cost	170,000		57.82%
Contribution margin	$124,000		42.18%
Total fixed cost	86,000
Operating income	$38,000

Notice that the contribution margin ratio is 42.18% (rounded to four significant digits). It is a simple matter to calculate the overall breakeven sales dollars for Jem Company:

Breakeven sales = $86,000/0.4218 = $203,888

Breakeven Units for each Product. Suppose that Jem Company wanted to know the breakeven point for each product? In that case, it would need more information for each product. Specifically, it would need the price and unit variable cost for each product, the overall fixed cost, and the sales mix. Then, the company could form a composite unit - or package - to calculate breakeven units.

The sales mix is the number of units of each product that are typically sold. So, if a company typically sells twice as much of product A as of product B, the sales mix is 2:1 (note that the first mentioned product comes first in the sales mix). If the company sold three times as much of product A as of product B, the sales mix is 3:1, and so on. While any sales mix that preserves the ratio of one product to another is correct, we typically reduce the sales mix to the lowest whole numbers. So, a sales mix of 3:5 can also be described as 6:10 or 30:50, and so on. These are all correct.

Example: Jem Company sold 10,000 units of Product 1 and 6,000 units of Product 2 last year. From the following list, select "Yes or No" for the correct sales mix of Product 1 to Product 2:

10:6
10:1
6:10
5:3
3:5
10,000:6,000
20,000:12,000
Cannot tell from this information

Once we have the sales mix, we can form a package or composite unit. It will consist of the number of units of each product times the unit contribution margin. This total contribution margin can be divided into total fixed costs to get the number of breakeven packages. Finally, the breakeven packages can be multiplied by the number of units of each product to get the breakeven units of each product.

Example: Jem Company two different small household appliances. Total fixed cost is $86,000. Unit information for each product is as follows:

	Product 1		Product 2
Price	$15		$24
Unit variable cost	$8		$15
Units sold last year	10,000		6,000

The sales mix for Jem Company last year was 10:6 or 5:3, and Jem assumes this mix will hold constant in the coming year. The package or composite unit is formed as follows:

Product	Price		Unit Variable Cost		Unit Contribution Margin		Sales Mix		Total Contribution Margin
Product 1	$15		$8		$7		5		$35
Product 2	24		15		9		3		27
Total									$62

Round the breakeven packages to four significant digits and breakeven units of each product to the nearest unit.

Breakeven packages = $86,000/$62 = 1,387.0968
Breakeven units Product 1 = 1,387.0968 × 5 = 6,935
Breakeven units Product 2 = 1,387.0968 × 3 = 4,161

Notice that we did not round the breakeven packages. This is because Jem Company is not selling packages, and the total number of packages will be multiplied by the number of units of each product in the package. However, we did round the breakeven units of each product to the nearest unit (you cannot sell a part of a unit).

Let's prepare an income statement to show that these breakeven units do result in zero profit.

Product	Product 1		Product 2		Total
Sales	$104,025		$99,864		$203,889
Total variable cost	55,480		62,415		117,895
Contribution margin	$48,545		$37,449		$85,994
Total fixed cost					86,000
Operating income					$(6)

The operating income is very close to zero due to rounding error in computing the breakeven packages and units. Notice that the total sales revenue at breakeven is virtually identical to that computed using the contribution margin ratio on the total fixed cost from the original example income statement.

Margin of Safety

CVP analysis assumes linear cost and revenue functions, no finished goods ending inventories, a constant sales mix, and that prices and costs are known with certainty. However, at least one assumption does not hold in practice. In particular, firms often do not know the prices, unit variable costs, and fixed costs that will occur in the future. This uncertainty regarding costs, prices, and sales mix affect the breakeven point.

Sensitivity analysis allows managers to vary costs, prices, and sales mix to show various possible break-even points. This type of analysis also allows managers to model the impact of nonlinear cost and revenue functions, as they can choose the budgeted units and use the unit cost or price that is associated with that level. Spreadsheets make this kind of analysis much easier.

Determination of the margin of safety allows managers to see how much the company's actual sales or units are above or below the break-even point.

Margin of safety in dollars = Actual sales - Break-even sales
Margin of safety in units = Actual units sold - Break-even units

Example: Lesher Company makes one product with the following price and cost structure:

Price	$12.00
Unit variable cost	$8.40
Total fixed cost	$50,400

Next year, Lesher Company expects to sell 18,000 units. What is the expected margin of safety in units and sales dollars?

Break-even units = $50,400/($12.00 - $8.40) = 14,000 units

Break-even sales = 14,000 × $12 = $168,000

Margin of safety in units = 18,000 - 14,000 = 4,000
Margin of safety in sales dollars = ($12 × 18,000) - $168,000 = $48,000

Suppose Lesher Company's price next year dropped to $11, the margin of safety would . Suppose instead that Lesher Company expected unit sales next year of 18,600, the margin of safety would . If the margin of safety equals zero, then the company is selling .

Select "Yes or No" from the following actions which can increase the margin of safety for a company.

Increasing fixed costs.
Increasing break-even units.
Increasing actual price.
Decreasing actual price.
Decreasing unit variable cost.

Operating Leverage

Operating leverage is the use of fixed costs to increase the percentage change in profits as sales activity changes. Typically a company has a choice of various ways to make a product or service. Costs could be relatively more variable (e.g., if the process used is labor intensive) or relatively more fixed (e.g., if the process is machine or capital intensive). If a company trades off variable costs for fixed costs, unit contribution margin increases. Then an increase in units sold adds more to profits than would be the case for a company with relatively higher variable costs. Of course as units sold decreases, the impact on profit is greater for a company with relatively lower variable costs. The degree of operating leverage is measured as follows:

Degree of operating leverage = Total contribution margin/Profit

Example: Sharda Company is considering two different processes to make its product—process 1 and process 2. Process 1 requires manufacturing subcomponents of the product in-house. As a result, materials are less expensive, but fixed overhead is higher. Process 2 involves purchasing all subcomponents from outside suppliers. The direct materials costs are higher, but fixed factory overhead is considerably lower. Relevant data for a sales level of 30,000 units follow:

	Process 1		Process 2
Sales	$6,000,000		$6,000,000
Total variable costs	2,700,000		4,200,000
Contribution margin	$3,300,000		$1,800,000
Total fixed expense	1,925,000		600,000
Operating income	$1,375,000		$1,200,000
Price	$200		$200
Unit variable cost	$90		$140
Unit contribution margin	$110		$60

Process 1 degree of operating leverage = $3,300,000/$1,375,000 = 2.4
Process 2 degree of operating leverage = $1,800,000/$1,200,000 = 1.5

If sales were 30% higher than budgeted, operating income will increase for each process as follows:
Process 1 increase in operating income = 2.4 × 30% = 72%
Process 2 increase in operating income = 1.5 × 30% = 45%

Process 1 increase in profit = 0.72 × $1,375,000 = $990,000
Process 2 increase in profit = 0.45 × $1,200,000 = $540,000

Process 1 new profit = $1,375,000 + $990,000 = $2,365,000
Process 2 new profit = $1,200,000 + $540,000 = $1,740,000

Suppose sales are 10 percent lower than budgeted. By what percentage will operating income decrease for Process 1? fill in the blank c5eda3045fd3020_1%. By what percentage will operating income decrease for Process 2? fill in the blank c5eda3045fd3020_2%. What will be the total operating income for Process 1? $fill in the blank c5eda3045fd3020_3. What will be the total operating income for process 2? $fill in the blank c5eda3045fd3020_4.