Effects of Sales Mix on Income

Learning Objective 7 Apply CVP analysis to a company producing multiple products

assume sales mix of products remains constant as total units sold changes

Companies sell multiple products, each of which are drivers of revenues and costs. Sales mix is the quantities (or proportion) of various products (or services) that constitute a company’s total unit sales. Suppose Emma is now budgeting for another college fair in New York. She plans to sell two different test-prep packages—GMAT Success and GRE Guarantee—and budgets the following:

A table shows the budgets for two different test-prep packages, GMAT Success and GRE Guarantee.

The table depicts the expected sales, revenues at 200 dollars and 100 dollars per unit, variable costs at 120 dollars and 70 dollars per unit, and contribution margin at 80 dollars and 30 dollars per unit for GMAT Success and GRE Guarantee, plus the total expected sales, revenues, variable costs, contribution margin, fixed costs, and operating income. The details of the table are as follows:

Expected sales
- GMAT Success: 60
- GRE Guarantee: 40
- Total: 100
Revenues, 200 dollars and 100 dollars per unit
- GMAT Success: 12,000 dollars
- GRE Guarantee: 4,000 dollars
- Total: 16,000 dollars
Variable costs, 120 dollars and 70 dollars per unit
- GMAT Success: 7,200 dollars
- GRE Guarantee: 2,800 dollars
- Total: 10,000 dollars
Contribution margin at 80 dollars and 30 dollars per unit
- GMAT Success: 4,800 dollars
- GRE Guarantee: 1,200 dollars
- Total: 6,000 dollars
Fixed costs, Total: 4,500 dollars
Operating income, Total: 1,500 dollars

What is the breakeven point for Emma’s business now? The total number of units that must be sold to break even in a multiproduct company depends on the sales mix. For Emma, this is the combination of the number of units of GMAT Success sold and the number of units of GRE Guarantee sold. We assume that the budgeted sales mix (60 units of GMAT Success sold for every 40 units of GRE Guarantee sold, that is, a ratio of 3:2) will not change at different levels of total unit sales. That is, we think of Emma selling a bundle of 3 units of GMAT Success and 2 units of GRE Guarantee. (Note that this does not mean that Emma physically bundles the two products together into one big package.)

Each bundle yields a contribution margin of $300, calculated as follows:

A table shows how the contribution margin of 300 dollars is calculated.

The table depicts the number of units of GMAT Success and GRE Guarantee in each bundle, contribution margin per unit for GMAT Success and GRE Guarantee, and contribution margin of the bundle. The details of the table are as follows:

GMAT Success
- Number of units in bundle: 3
- Contribution margin per unit: 80 dollars
- Contribution margin of the bundle: 240 dollars
GRE Guarantee
- Number of units in bundle: 2
- Contribution margin per unit: 30 dollars
- Contribution margin of the bundle: 60 dollars
Total contribution margin of the bundle: 300 dollars

To compute the breakeven point, we calculate the number of bundles Emma needs to sell.

$\begin{matrix} Breakeven \\ point in \\ bundles \end{matrix} = \frac{Fixed costs}{Contribution margin per bundle} = \frac{$ 4,500}{$ 300 per bundle} = 15 bundles$

The breakeven point in units of GMAT Success and GRE Guarantee is as follows:

GMAT Success: 15 bundles times 3 units per bundle: 45 units

GRE Guarantee: 15 bundles times 2 units per bundle: 30 units

Total number of units to break even: 75 units

The breakeven point in dollars for GMAT Success and GRE Guarantee is as follows:

The breakeven point in dollars of GMAT Success and GRE Guarantee

GMAT Success: 45 units times 200 dollars per unit: 9,000 dollars

GRE Guarantee: 30 units times 100 dollars per unit: 3,000 dollars

Breakeven revenues: 12,000 dollars

When there are multiple products, it is often convenient to use the contribution margin percentage. Under this approach, Emma also calculates the revenues from selling a bundle of 3 units of GMAT Success and 2 units of GRE Guarantee:

A table shows how the 800 dollars revenue of the bundle is calculated.

The table depicts the number of units of GMAT Success and GRE Guarantee in each bundle, selling price for GMAT Success and GRE Guarantee, and revenue of the bundle. The details of the table are as follows:

GMAT Success
- Number of units in bundle: 3
- Selling price: 200 dollars
- Revenue of the bundle: 600 dollars
GRE Guarantee
- Number of units in bundle: 2
- Selling price: 100 dollars
- Revenue of the bundle: 200 dollars
Total revenue of the bundle: 800 dollars

$\begin{array}{rrl} \begin{array}{r} Contribution \\ margin \\ percentage for \\ the bundle \end{array} & = & \frac{Contribution margin of the bundle}{Revenue of the bundle} = \frac{$ 300}{$ 800} = 0.375, or 37.5 % \\ \begin{array}{r} Breakeven \\ revenues \end{array} & = & \frac{Fixed costs}{Contribution margin % for the bundle} = \frac{$ 4,500}{0.375} = $ 12,000 \\ \begin{array}{r} Number of bundles \\ required to be sold \\ to break even \end{array} & = & \frac{Breakeven revenues}{Revenue per bundle} = \frac{$ 12,000}{$ 800 per bundle} = 15 bundles \end{array}$

The breakeven point in units and dollars for GMAT Success and GRE Guarantee are as follows:

$\begin{array}{rr} GMAT Success : & 15 bundles \times 3 units per bundle = 45 units \times $ 200 per unit = $ 9,000 \\ GRE Guarantee : & 15 bundles \times 3 units per bundle = 30 units \times $ 100 per unit = $ 3,000 \end{array}$

Recall that the breakeven point calculations assume the same budgeted sales mix (3 units of GMAT Success for every 2 units of GRE Guarantee) at different levels of total unit sales.

Of course, there are many different sales mixes (in units) that can result in a contribution margin of $4,500 that leads to Emma breaking even, as the following table shows:

A table shows different sales mixes that can result in a contribution margin of 4,500 dollars for breaking even.

The table depicts the sales mix (with units of GMAT Success and units of GRE Guarantee), contribution margin (from GMAT Success units times 80 dollars and GRE Guarantee units times 30 dollars), and total contribution margin (GMAT Success contribution margin plus GRE Guarantee contribution margin). The details of the table are as follows:

Sales Mix: 48 units GMAT Success and 22 units GRE guarantee
- Contribution margin from GMAT Success: 3,840 dollars
- Contribution margin from GRE Guarantee: 660 dollars
- Total contribution margin: 4,500 dollars
Sales Mix: 36 units GMAT Success and 54 units GRE guarantee
- Contribution margin from GMAT Success: 2,880 dollars
- Contribution margin from GRE Guarantee: 1,620 dollars
- Total contribution margin: 4,500 dollars
Sales Mix: 30 units GMAT Success and 70 units GRE guarantee
- Contribution margin from GMAT Success: 2,400 dollars
- Contribution margin from GRE Guarantee: 2,100 dollars
- Total contribution margin: 4,500 dollars

If, for example, the sales mix changes to 3 units of GMAT Success for every 7 units of GRE Guarantee, the breakeven point increases from 75 units to 100 units, composed of 30 units of GMAT Success and 70 units of GRE Guarantee. The breakeven quantity increases because the sales mix has shifted toward the lower-contribution-margin product, GRE Guarantee ($30 per unit compared to GMAT Success’s $80 per unit). In general, for any given total quantity of units sold, a shift in sales mix towards units with lower contribution margins, decreases operating income.

Try It! 3-6

Best Windows plans to sell two different brands of windows—Chad and Musk—and budgets the following:

The table depicts the expected sales, revenues (at 700 dollars and 300 dollars per unit), variable costs (at 600 dollars and 250 dollars per unit), and contribution margin (100 dollars and 50 dollars per unit) for Chad Windows and Musk Windows as well as the total expected sales, revenues, variable costs, contribution margin, fixed costs, and operating income. The details of the table are as follows:

Expected sales
- Chad Windows: 3,000 dollars
- Musk Windows: 1,500 dollars
- Total: 4,500 dollars
Revenues (at 700 dollars and 300 dollars per unit)
- Chad Windows: 2,100,000 dollars
- Musk Windows: 450,000 dollars
- Total: 2,550,000 dollars
Variable costs (at 600 dollars and 250 dollars per unit)
- Chad Windows: 1,800,000 dollars
- Musk Windows: 375,000 dollars
- Total: 2,175,000 dollars
Contribution margin (at 100 dollars and 50 dollars per unit)
- Chad Windows: 300,000 dollars
- Musk Windows: 75,000 dollars
- Total: 375,000 dollars
Fixed costs, total: 160,000 dollars
Operating income, total: 215,000 dollars

Calculate the breakeven point for Best Windows in terms of (a) the number of units sold and (b) revenues.

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How do companies choose their sales mix? They adjust their mix to respond to demand changes. For example, when gasoline prices increased and customers wanted smaller cars, auto companies, such as Ford, Nissan, and Toyota, shifted their production mix to produce smaller cars. This shift to smaller cars increased the breakeven point because the sales mix had shifted toward lower-contribution-margin products. Despite this increase in the breakeven point, shifting the sales mix to smaller cars was the correct decision because the demand for larger cars had fallen. At no point should a manager focus on changing the sales mix to lower the breakeven point without taking into account customer preferences and demand.