[ Music ] >> In this lesson we'll pursue the following objectives. Specifically we'll understand how to apply CVP analysis in more complex scenarios, specifically when there are multiple products being produced by the organization. And then we'll talk about how to customize this analysis to correspond with assumptions, uncertainty, and managers' needs. Next we're going to talk about a third example, one in which involves multiple products. In this example we have HOSA Company, they manufacture two products, generically referred to as Product X and Product Y. We're provided information about each of these products. Specifically we're told the selling price, variable costs and fixed costs for each product. Product X has a $10 selling price and $6 worth of variable costs on a per unit basis. The fixed costs for Product X are $10,000. For Product Y the selling price is $15, variable costs per unit are $12, and the fixed costs for Product Y are reported as $12,000. So the first question that we would say that HOSA would be interested in is to compute the break-even point for the firm as a whole. Well, on the surface what HOSA would likely do is treat each product separately. They would calculate a break-even point for Product X and a separate break-even point for Product Y. Recalling our equation, our break-even quantity is equal to the total fixed costs divided by the contribution margin per unit. For Product X, that's going to be the $10,000 in fixed costs for Product X divided by the contribution margin per unit for Product X, which as reported was $10 in selling price, $6 in variable costs. That is going to yield $10,000 divided by $4 contribution margin, 2,500 units of X. The same calculation can be done for Product Y. For Y the fixed costs are reported to be $12,000. The selling price for Y is $15 and the variable costs for Y are 12. $12,000 divided by the contribution margin for Y, which is 3, is equal to 4000 units of Y. So when HOSA's managers ask, "What's the break-even point for our products," they would be reported as 2500 units of Product X and 4000 units of Product Y. Now this is a way that we can think about our business. If we produce and sell 2500 units of X and 4000 units of Y we'll have a break-even point, we'll earn no profit. However, you can start to replace Product X for Product Y. If you sell more of X beyond the 2500 point, because you sold less of Y than the 4000 point for Y, then the products of contribution margins can offset each other. So this is not the only point at which things break even, but given the allocation of fixed costs between products X and Y, you can think about these break-even points separately, one for X and one for Y. Now turning back to the problem, you might wonder, does this allocation of fixed costs actually make sense. It does in certain situations. Let's suppose that Product X is manufactured in the -- in a factory on the East Coast and Product Y is manufactured in a factory on the West Coast. In this case, we know the fixed costs of each of those individual factories, and a good estimate of the fixed cost for Product X, $10,000, would be reliable because they're particular to the factory where Product X is manufactured. The same for Product Y, if that was manufactured in its own factory, the $12,000 would be a good estimate of Y's share of the fixed costs. But how about situations when X and Y are produced in the same factory? Oftentimes firms produce multiple versions of the same product. Perhaps Product X is a basic version of the product and Product Y is more of a deluxe or advanced version of the product. In that case, it's often -- it's often the situation that firms will use the same product line in the same factory to produce each of the products. In this case, both products share a total fixed cost for that factory or that capacity. In such cases, it might not make sense to allocate fixed costs to Product X and Product Y, because those would just be arbitrary allocations that accountants perform. Sometimes that's based on the square footage of the factory that's allocable to each of the products. Sometimes it's based on the time spent producing. But those aren't perfect estimators of each shares -- each products share of fixed costs. So let's turn to a different piece of information so that we can adopt a different methodology in this multi-product scenario. Let's suppose that we know HOSA's sales mix is 60% Product X and 40% Product Y. What that means is that for every 100 units sold, 60 of them are X and 40 are Y. We can rely on this information in situations where the allocation of fixed costs is questionable, therefore potentially making the analysis more reliable. So to do this we have to think about a composite version of each product's contribution margin. We call this the weighted average contribution margin. It relies on the production and sales mix to create or compute a composite contribution margin number, and what that allows is a single break-even calculation in multi-product scenarios. In this situation we don't have to worry about the allocation of fixed costs between products because we're relying on that single calculation. So in this situation we would take the information for Product X and the information for Product Y and compute a weighted average contribution margin. We would use the percentage of sales for each product as those weights. So for Product X we would have a 60% weight on top of the contribution margin that we compute for Product X, and a 40% weight for the contribution margin on Product Y. So for Product X we had a $10 selling price, a $6 variable cost, otherwise a $4 contribution margin, and for Product Y, to which we're assigning a 40% weight, we have a $15 selling price, and a $12 variable cost, yielding a $3 contribution margin. Calculating this out yields a weighted average contribution margin of $3.60 per unit. Now let's stop a moment and think about what this actually means. This means that if there was a big bucket of Product X and Product Y and we reached in, then on average the unit that we pulled out would yield a contribution margin of $3.60. Now it's never officially that number, because it's either Product X yielding a $4 contribution margin, or Product Y, yielding a $3 contribution margin, but on average we earn $3.60 in contribution for each unit produced and sold. We can use this number than to calculate the break-even point for the firm as a whole. That break-even point is going to be the total fixed costs for the firm, which were originally reported to us as $10,000 originally allocated to X and $12,000 originally allocated to Y. And the denominator, we use the same old contribution margin. However, is the weighted average contribution margin per unit, a composite measure of both of our products together. When we calculate this n umber we get 6111 units. And it's important to identify what these units are, generically we refer to them as composite units. Now, if a manager wants more information, we can break this down into the relative proportions of Product X and Product Y. What proportions? The ones we relied on initially, 60% of this number, with some rounding, is 3667 units. Again, 60% of that total composite units. And 40% of this number is 2444. Each of these numbers corresponds to the units of Product X in the form of 3667, and the number of units of Product Y in the form of 2444. This is the breakdown of the 6111 composite units between each of the two products. Now, using this methodology of course opens us up to being susceptible to the assumption that the product mix is constant going forward. To the extent that our product mix changes from 60/40 to some other combination, then our analysis becomes less reliable. Take for instance if we were to decrease the relative proportion on Product X and increase the proportion on Product Y, in that case, less of our units would be the $4 contribution and more of our units would be a lesser contribution in the form of $3. In this case, our break-even point would go up because it would take more total units to reach the same level of fixed costs. If the opposite were to occur, more mix goes towards Product X and less toward Product Y, then our break-even point would decrease. Reason being, more of our overall sales is compromised of a higher contribution margin item. So obviously between these two methods you're going to be susceptible to some assumption. In the first method, when we broke apart the two -- the fixed costs across the units, we were really reliant on that appropriate allocation, and in some situations that's appropriate, because we know what the fixed costs are for each of the products, like in cases where there are separate factories. But in situations where that's not the case, and we can reasonably estimate the percentage of sales of each type of product, then the second methodology may be the more reliable one. Again, we're susceptible to something in the sense that if the product mix changes we might lose the reliability of the output of this particular analysis. As an ending thought to this example, you can see how susceptible you are to the assumptions that underlie the analysis. Depending on the circumstance, we can use different methods and draw different conclusions from CVP analysis. This is just one of many examples where the nature of the assumption that you're making determines the reliability of the analysis.