[ Music ] >> Welcome to Module Four. In Module Four, we pick up where we left off way back in Module One, talking about cost behavior and how it applies at the heart of Cost-Volume-Profit-Analysis. In this first lesson, we pursue two objectives. First, you will understand the fundamental components or concepts of Cost-Volume-Profit-Analysis, otherwise known as CVP Analysis. And second, we'll learn how to apply CVP analysis recognizing the influence of setting characteristics on the different methods we can use and the conclusions we can draw. So, what is Cost-Volume-Profit-Analysis? Well, actually, it's quite complex and in the coming slides, we'll see a variety of calculations and ways in which this analysis is used. But for now, just to gain an understanding of it, we can think of Cost-Volume-Profit-Analysis as an analytic tool that's useful for asking questions, what-if type questions. So, in terms of projecting what future profits will be, CVP analysis is useful for saying, "What if variable costs increase? What if fixed costs decrease? What if costs that were once variable become fixed? What if production and our sales volume changes? What happens to profits in those situations?" We can ask these questions to try to hedge risk or leverage opportunities that we might have in the future. Basically, CVP analysis uses the relationships among fundamental components of the basic accounting quest -- equation, the equation that's used to calculate income. Let's delve into that equation a little bit more. Turning back to Module One, we talked about a financial accounting oriented perspective of the financial statements and in the income statement, you're likely to start off with revenue. Subtracting from revenue, direct materials, direct labor, and overhead collectively referred to as "Cost of goods sold," yields gross margin or gross profit. What's left after that is "Other Expenses," operating expenses not related to the production of the good. Subtracting those from grow margin yields profit. Alternatively we can look at the income statement from a more managerial or decision-oriented perspective. When doing that, we start with the same revenue and end with the same profit. We're not changing the nature of the information in any way, just the organization of it. So, starting with revenue, subtracting first, all costs that are variable in nature. Those would be direct materials and direct labor for the most part, but then also overhead that tends to be variable and other expenses and operating expenses that are variable. Revenue minus all of our variable costs yields what's referred to as contribution margin. What's left to subtract from there is everything we have included thus far which would be all fixed expenses. Subtracting those from the contribution margin yields profit. So, again, these two perspectives are quite different, not in their starting and end points but the organization of the information in between. In financial, we think about cost of goods sold and operating and other expenses. In managerial, we organize the information according to cost behavior. As we will see, this organization will be very useful in decision-making and Cost-Volume-Profit-Analysis. So, let's delve into this fundamental equation of accounting and have it create an equation for us that we'll find is the heart of CVP analysis. The equation in particular is operating profit is equal to revenues minus total variable costs minus total fixed costs. We can use this equation to ask a very basic question, "How many units do we have to sell for the firm to break even?" So, starting with that equation, we can use the magic of Algebra to convert what we have into something that's more useful. Step one is to consider that break-even point. Set the operating profit to zero dollars. Very simply, just rewrite the equation so we have a zero in the place of the operating profit. The rest of the equation is the same, revenues minus total variable cost, minus total fixed costs, is equal to zero. And what this means is that revenues are exactly equal to the sum of the total variable costs and the total fixed costs. Now, step two is to break apart some of the components of this equation where applicable. So, let's simplify some of these terms. The first one we can do is revenues; we can break that into the two components that comprise revenues, the selling price per unit and the quantity sold. So, selling price times Q replaces the revenues in the equation. The same can be applied for total variable cost. We can replace that with variable cost per unit times Q or the quantity produced. Total fixed cost is a little more tricky. We prefer to keep that in total because breaking that into a per Q amount can be quite confusing. Onto Step three. We have zero is equal to selling price times quantity, minus variable cost times quantity, minus total fixed cost. Step three is to move some terms around, so first off, let's isolate total fixed cost from the remainder of the equation and the second step will be to factor out Q of the terms in which it is. So, adding total fixed costs to both sides turns that first zero into total fixed costs, removes it from the right side of the equation and what's left is selling price times quantity minus variable cost times quantity. Well, here's where the Algebra kicks in. We can factor out the Q from both of those terms and ultimately what we're left with is Q multiplied by the difference between selling price and variable cost. The equation hasn't changed, it's just that we've rearranged the terms around a little bit. The final step is to ultimately isolate Q. We can divide both sides of this equation by the difference between selling price and variable cost and that ultimately yields quantity is equal to total cost, divided by selling price minus variable cost. Now, if you recall our equation from before, revenues or selling price minus all the variable cost is equal to the contribution margin. In this place, we can reduce the term in the denominator with the contribution margin per unit. So, ultimately Q is equal to the total fixed cost divided by the contribution margin per unit. As we'll see in the coming slides, this is a fundamental equation that's very useful in CVP Analysis.
