What effect does the sales mix have?
Break-even and cost-volume-profit analysis requires some additional computations and assumptions when a company produces and sells more than one product. In multi-product firms, sales mix is an important factor in calculating an overall company break-even point.

Different selling prices and different variable costs result indifferent unit CM and CM ratios. As a result, the break-even points and cost-volume-profit relationships vary with the relative proportions of the products sold, called the sales mix.

In break-even and CVP analysis, it is necessary to predetermine the sales mix and then
compute a weighted average unit CM. It is also necessary to assume that the sales mix does not change for a specified period. The break-even formula for the company as a whole is:

Break-even sales in units (or in dollars) = (Fixed Cost/Weight Average Unit CM(or CM Ratio))
Assume that Knibex, Inc. produces cutlery sets out of high-quality wood and steel. The company makes a deluxe cutlery set and a standard set that have the following unit CM data:

Deluxe Standard
Selling price $15 $10
Variable cost per unit 12 5
Unit CM $3 $5
Sales mix 60% 40%
(based on sales volume)
Fixed costs $76,000

The weighted average unit CM = ($3)(0.6) + ($5)(0.4) = $3.80. Therefore, the company`s break-even point in units is:

$76,000/$3.80 = 20,000 units

which is divided as follows:

Deluxe: 20,000 units x 60% = 12,000 units
Standard: 20,000 units x 40% = 8,000
20,000 units

Note: An alternative is to build a package containing 3 deluxe models and 2 standard models (3:2 ratio). By defining the product as a package, the multiple-product problem is converted into a single-product one. Then use the following three steps as follows:

Step 1: Computer the package CM as follows:

Deluxe Standard
Selling price $15 $10
Variable cost per unit 12 5
Unit CM $3 $5
Sales mix 3 2
Package CM $9 $10
$19 package total

Step 2: Determine the number of packages that need to be sold to break even, as follows:

$76,000/$19 per package = 4,000 packages

Step 3: Multiply this number by their respective mix units:

Deluxe: 4,000 packages x 3 units = 12,000 units
Standard: 4,000 packages x 2 units = 8,000 units 20,000 units

Assume that Dante, Inc. is a producer of recreational equipment. It expects to produce and sell three types of sleeping bags--the Economy, the Regular, and the Backpacker. Information on the bags is given below:

The CM ratio for Dante, Inc. is $31,000/$100,000 = 31 percent.

Therefore the break-even point in dollars is

$18,600/0.31 = $60,000

which will be split in the mix ratio of 3:6:1 to give us the following break-even points for the individual products:

Economy: $60,000 x 30% = $18,000
Regular: $60,000 x 60% = 36,000
Backpacker $60,000 x 10% = 6,000


One of the most important assumptions underlying CVP analysis in a multi-product firm is that the sales mix will not change during the planning period. But if the sales mix changes, the break-even point will also change.

Assume that total sales from Example 15 was achieved at $100,000 but that an actual mix came out differently from the budgeted mix (i.e., for Economy, 30% to 55%, for Regular, 60% to 40%, and for Backpacker, 10% to 5%).

* $26,667 = $40,000 x (100% - 33 1/3%) = $40,000 x 66 2/3%
* $2,500 = $5,000 x (100% - 50%) = $5,000 x 50%

Note: The shift in sales mix toward the less profitable line ,Economy, has caused the CM ratio for the company as a whole to drop from 31 percent to 26.83 percent.

The new break-even point will be $18,600/0.2683 = $69,325

The break-even dollar volume has increased from $60,000 to $69,325.

The deterioration (improvement) in the mix caused net income to go down (up). It is important to note that generally, the shift of emphasis from low-margin products to high-margin ones will increase the overall profits of the company.

What are the limitations of break-even analysis?
In its simplest form, break-even analysis makes a num­ber of assumptions about which you must be very clear. One such assumption treats the unit selling price as a constant. This, in turn, rests on two further assumptions: (I) the elas­ticity of demand must be very high for the unit selling price to remain constant as sales volume expands and (2) the sell­ing price must remain relatively stable over the income peri­od. In truth, neither is likely to hold in actual practice, and this makes forecasting the unit selling price much more difficult.
The second major assumption holds that unit variable costs are also constant and that fixed and variable costs have been properly separated, identified, and quantified. However, separating out variable from fixed costs is an ongoing problem.
Once you have determined the unit variable cost, make certain it remains constant over the income period. If it does not, then you must compute a series of breakdown calcula­tions incorporating the most probable unit variable costs.
Likewise, examine the likelihood that total fixed costs will remain constant. Do this at every level of your analysis. If you find factors that will cause fixed costs to vary, then you must compute a series of break-even analyses using the most probable values of total fixed costs.
A RULE FOR MANAGEMENT EXECIJTIVES: One of your major objectives should be to keep a tight grip on your company`s break-even volume. This means constant efforts to keep break-even from increasing as a result of adverse conditions that lower unit selling price and raise unit vari­able costs and total fixed costs.

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