[ Music ] >> Next we're going to move on to a second numerical example and this one will allow us to explore what happens when one of those assumptions that underlies CVP analysis is violated. In this example we have Taves Donuts. They sell donuts, coffee and other related food items. The following information is available for this company. The services they provide varies from a single cup of coffee to multiple dozens donuts. The average revenue earned for each customer, while it varies, is averaged out to be $8. The average cost of food and other variable costs for each customer is $3. Total fixed costs for the year is $450,000. We also know what the tax rate that Taves faces is and that's 30%. Finally, Taves cares about breaking even, but what they would really like to do is target a net income level of $105,000. So given our data, one of the first questions that we ask in CVP analysis is, "How many customers are needed to break even?" Followed by the next question, "How many customers are needed to reach the desired profit?" That $105,000 target. Let's start with the break-even point. Again, our equation to calculate the break even in units is total fixed costs divided by the contribution margin per unit. Given the information that we have about Taves, we know that the numerator, total fixed costs, is $450,000. The denominator, the contribution margin per unit, is comprised of the selling price minus the average variable cost. Eight minus 3 is $5, that is our contribution margin per unit. When we solve for the break-even point, $450,000 divided by 5, 90,000 customers. Throughout the year, if Taves brings in 90,000 customers, and on average buy things worth about $8 per customer, and the average variable cost of the goods that we sell them is $3, then 90,000 customers will yield a break even profit, zero profit. Now, Taves managers benefit from this information, but what they would really like to know is, how many customers do they need to reach the desired profit, $105,000. So what does this really mean? Well, they are asking about a quantity that not only just covers fixed costs, but also reaches a desired profit level. And just like fixed costs are something to cover with each individual unit produced and sold, so is the desired profit. So the formula can be adjusted to incorporate this desired profit. Fixed costs in the numerator, as always, and add to that the desired profit, dividing that by the contribution margin per unit will give us the quantity that is required to cover fixed costs as well as yield the desired profit. Now, in the Taves example, the desired profit was $105,000, and notably they used the term net income as the desired profit. Well let's think about where net income lies on the financial statements. Recall from our financial perspective that we start with revenues, subtract out cost of goods sold, to yield gross margin. After gross margin we subtract out other expenses and that will yield net income. But it's important to point out that this is net income before the usually reported last item on the income statement, before profit, and that is income taxes. So this is net income before tax. Subtracting from net income before tax -- [ Writing on Board ] -- yields net income. That is the level at which they desire $105,000. Now let's think about this income tax expense a little bit. What kind of cost is it? How does it behave? Is it fixed or variable? Well on the surface, the more the money -- the more money Taves makes, the higher income tax will be, means that -- or suggests that the income tax expense is variable. However, let's think about what it's a function of. Income tax expense is net income before tax multiplied by some tax rate, and so, therefore, it's a function of that net income before tax. Well what is net income before tax compromised of? Certainly revenues, which are variable in nature, and other variable costs as well, but we also incorporate above net income before tax, fixed costs. So net income before tax is a function of both variable costs and fixed costs. And since income tax expense itself is a function of net income before tax, itself is compromised of variable and fixed components. So income tax expense is one of those costs that violates the assumption that we can parse our costs between categories of variable of fixed. Income tax expense is both, and therefore it potentially violates our assumption underlying CVP analysis. So the answer here is to avoid the use of income taxes in our analysis. Try and back out the effect of those in order to avoid the violation of this assumption. And let's blow up this part of our equation and talk a little bit more about that. So net income before tax minus net income before tax times the tax rate is equal to net income. We know what our desired net income is and what we need to do is solve for the desired net income before taxes. So using Algebra, we can factor out the net income before tax from both of these terms. [ Writing on Board ] And then we can isolate net income before taxes on one side of the equation, since that is our unknown. [ Writing on Board ] This allows us to plug in what we know about net income, or the desired net income, the tax rate, and back into the desired net income before taxes. Using the information that's provided in the example, Taves managers desire a $105,000 net income number. And the tax rate that we're told is 30%. So $105,000 as being a target net income divided by 1 minus that 30%, which equals 70%, yield a net income before tax number of $150,000. This equivalent to achieving that desired net income number, it just avoids the effect of an expense or a cost that has both variable and fixed components, allowing us to get back in line with our assumptions that all costs that we incorporate as [inaudible] between variable and fixed categories. So turning back to Taves' original question, "How many units does it take to reach a desired net income of $105,000," we just converted this a little bit. And instead of relying on target net income, we're relying on target net income before tax. So the Q that we're looking for, which is the unknown, is equal to the $450,000 worth of fixed costs plus the $150,000 in target net income before tax that we just calculated. That amount is covered by each units' contribution margin, which we said was the difference between the selling price and the variable costs, or 8 minus 3. Ultimately, when we solve for the Q, we have 120,000 customers. [ Writing on Board ] If we reach that level in production and sales then we will not only cover all of our fixed costs, but yield $150,000 in net income before taxes. After income taxes are subtracted from that number, we're left with the desired net income number of 105,000. So as you can see, we've backed out the effect of taxes, which violates the assumption of all costs should be fixed or variable, and, therefore, are better able to compute the desired quantity to reach a target income. As you can see, these calculations can become quite complex, and the same backing out that we've just done with income taxes can be done with any cost that it's difficult to parse between fixed and variable components. This allows us to keep in check with our assumptions and therefore rely on the output of our analysis.