### Cost Volume Profit (CVP) Analysis

**Cost-Volume-Profit Analysis**

- · Cost-Volume-Profit (CVP) is a managerial decision-making tool that focuses on the relationships among product prices, the volume and mix of units sold, variable and fixed costs, and profit. This approach allows managers to see how a change in one or more of these variables will impact profitability while holding everything else constant.

- o Assumptions of Cost-Volume-Profit Analysis – CVP analysis is based on the following assumptions:
- § A straight line can be used to describe how total cost and total revenue change across the relevant range of activity – The first assumption continues the linear approach we learned in the cost behavior section. Although total cost and activity are not always perfectly linear, a straight line should provide a reasonable approximation, at least within a limited range of activity (relevant range).
- § All costs can be accurately described as either fixed or variable – all costs can be classified as variable or fixed. For mixed costs or those that have both a fixed and variable component, we can use the high-low method or least squares regression to separate the two effects.
- § Changes in total cost are due strictly to changes in the volume of units produced or customers served – The third assumption is that total costs change only as a result of a change in the number of units produced or customers served. We ignore other factors that can affect total cost such as employee learning curves, productivity gains, and quantity discounts for buying in bulk.
- § Production and sales are equal – Production equals sales, keeps inventory levels constant and avoids any difference in profit that can occur due to the accounting method used to value inventory.
- § Companies that sell more than one product or service maintain a constant product or sales mix – this assumption is needed to perform multi-product CVP analysis.

- o Cost-Volume-Profit (CVP) Graph – A CVP graph is useful for visualizing the relationship between total revenue, total costs, the volume of units sold, and profit. Although the CVP graph is useful for conceptualizing cost and revenue relationships, we must use equations or formulas to compute the exact numbers.

- o Break-Even Analysis – determines the level of sales (unit or total sales dollars) needed to break even, or earn zero profit. Several methods used to find the break even point are:

- § Profit Equation Method – uses an equation in which profit is defined as the difference between total sales revenue and total fixed and variable costs. The equation is as follows:
- · Total Sales – Total Var. Costs – Total Fixed Costs = Profit

(Unit Price x Q) – (Unit VC x Q) – Total FC = Profit. To find the break even point we set the equation equal to zero and solve for Q, which is the quantity of units which need to be sold in order to break even.

- § Unit Contribution Margin Method – the unit contribution margin tells us how much contribution margin is generated by each additional unit sold. The contribution margin is used to cover fixed costs, and what ever is left is profit. At break even, the total contribution margin equals total fixed costs so that profit is zero. The equation is: BE units = Total Fixed Costs/Unit Contribution Margin.

- § Contribution Margin Ratio Method – the third way to calculate the breakeven point is based on the contribution margin (CM) ratio. Recall that the contribution margin ratio is calculated by dividing the contribution margin by the sales revenue. The contribution margin ratio tells us how much contribution margin is generated by each dollar of sales revenue. At break even the total contribution margin must equal total fixed costs, with no profit leftover. The equation is: BE sales = Total Fixed Costs/Contribution Margin Ratio (%)

- o Target Profit Analysis – Although break-even is a common starting point for performing CVP, most managers want to do more than just break even. They want to earn a profit. Target profit analysis is extension of break-even analysis that allows managers to determine the number of units or total sales revenue needed to earn a target profit. To earn a target profit, the total contribution margin must be enough to cover the fixed costs plus the target profit. The following equations show the target profit in units or sales dollars:

Target Units = Total FC + Target profit/Unit Contribution Margin

Target Sales – Total FC + Target Profit/Contribution Margin Ratio (%)