CVP analysis is relatively straight forward when applied to a single product or service. Using the tool when there are multiple products or services, requires the assumption that the sales mix remains constant. Now remember, the sales mix is the relative proportion of sales units or dollars that comes from each product or service. If we assume that the sales mix remains constant, then we can use the average contribution margin across all units, rather than the contribution margin of a single product in our analysis. Let's look at an example, let's return to our t-shirt maker. Suppose the t-shirt maker has expanded its product line, and now makes not only the basic t-shirt it was making, but a deluxe version of that t-shirt. Here we have the price, the variable cost per unit, and the contribution margin per unit for both versions. We see that total fixed cost remain at $40,000. And the company sells one deluxe t-shirts for every seven basic t-shirts it sells. The question for us is how many of each type of t-shirt must the company sell to break even? Again, recall that one of the assumptions in CVP analysis is that if the company sells more than one product or service the sales mix remains constant. Here the sales mix is one deluxe t-shirt for each seven basic t-shirts. To use CVP analysis we must assume that mix remains the same. So first we calculate the average contribution margin per unit, assuming that seven to one sales mix. That average contribution margin per unit is $6.25. The company sells seven basic t-shirts at a contribution margin of $6, and one deluxe t-shirt at a contribution margin of $8. So the total contribution margin of one bundle of seven basic and one deluxe t-shirts is $50. And we divide that by a total of 8 t-shirts in the bundle to get the average of 6.25 per t-shirt. We approach the problem just like we did when we were looking for breakeven sales volume when the company made only the basic t-shirt. We divide the fixed cost of $40,000 by the average contribution margin of $6.25. And see that the company must sell 6,400 t-shirts to break even. We know though that 7/8 of those t-shirts must be basic t-shirt's and 1/8 must be the deluxe t-shirt's. So the t-shirt maker must sell 5,600 of the basic t-shirt and 800 of the deluxe t-shirts to break even. Let's check to make sure we do indeed break even at these sales volumes. We have 5,600 basic t-shirts with a contribution margin per unit of $6. And we 800 deluxe t-shirts at the contribution margin per unit of $8. And of course we have the $40,000 in fixed costs. The total contribution from the basic t-shirts then is $33,600 and the total contribution from the deluxe t-shirts is $6,400. So the total contribution margin of $40,000 is exactly equal to the fixed cost. So our profit equals zero. Let's think back to our analysis, when the t-shirt maker made only basic t-shirts. We determined then that break-even quantity was 6,667 t-shirts. But if the company sells one deluxe t-shirt for every seven basic t-shirts, it's breakeven quantity is lower. Why? Because each deluxe t-shirt has a contribution margin of $8 Compared to $6 contribution margin for a basic t-shirt. So the company can break even by selling slightly fewer t-shirts in total, because the deluxe type has a higher contribution point. And similarly, note that if the company sees a shift in sales mix towards the basic t-shirts, then it will fall short of break even if it only sells 6,400 units. Again, because the contribution margin per unit for the basic t-shirt is less than the contribution margin per unit for the deluxe t-shirts. On the other hand, if the sales make shifts towards the deluxe t-shirts, the company will more than break even if it sells 6,400 t-shirts. Because it will be selling relatively more of the higher contribution t-shirts, the deluxe ones and relatively less of the lower margin t-shirts, the basic ones.
