Lesson

Please see Box for Unit 3 Lecture Material that needs to be moved herCost-Volume-Profit (CVP) Analysis considers the impact that changes in output have on revenue, costs, and net income. In applying CVP analysis, costs are separated into variable and fixed costs. This distinction is important because, as mentioned previously, variable costs change with changes in output, whereas fixed costs remain constant throughout what is referred to as a relevant range. CVP analysis is based on the following equation.

Profit = Total Revenues – Total variable costs – Total fixed costs

The Contribution Margin Income Statement format is very useful in CVP analysis. Recall that the contribution margin income statement format is as follows.

Total Revenue – all variable costs = Contribution margin – fixed costs = Operating income

The contribution margin ratio is an important ratio that is reviewed by management and is calculated as follows.

Contribution Margin Ratio = Contribution Margin per Unit / Unit Selling Price

The contribution margin ratio tells us the percentage of revenue that will be available to cover fixed costs. Note that the information needed to calculate this ratio is generally not available in published financial statements since costs are not classified by their behavior.

A word of caution: Be sure that you understand the difference between gross profit and contribution margin. Gross profit is Net Sales less Cost of Goods Sold. Contribution Margin is Total Revenues less Total Variable Costs.

In this unit, we will also be looking at the breakeven point. The breakeven point is where total revenues equal total costs (net operating income will be zero). You may already have learned this concept in an economics course. As with many concepts, an illustration can be very helpful. Spend a little time with the chart below, and review the assumptions listed following the chart.  

CVP Chart    

The chart is a Cost-Volume-Profit chart. The vertical axis is dollars, and the horizontal axis is volume (number of units sold). The graph shows Total Revenue (Total units sold X Selling Price per unit) starting at zero and increasing with volume of units sold. There are two other lines on the graph.
 
One is Total Fixed Cost which intercepts the vertical axis at the dollar amount of total fixed costs and is parallel to the horizontal axis (because fixed cost does not increase with volume).
 
Finally, the Total Cost line starts at zero volume but at the point on the vertical axis that represents Total Fixed Cost. The Total Cost line begins at the Total Fixed Cost point, and increases with volume based on Total Units times Variable Cost per unit.
 
The point where the Total Cost line crosses the Total Revenue Line is the break-even point (BE) where Total Revenues equals Total Costs. The area to the left of the BE point represents a loss, and the area to the right of the BE point represents profit.

Underlying Assumptions of CVP Analysis

CVP analysis is based on a model that is a simplification of reality; therefore, it is not a perfect model. The assumptions are as follows.

• Revenues and variable costs per unit do not change within the relevant range. This means that the contribution margin will also be the same per unit within the relevant range. (Remember, relevant range often refers to existing capacity. Once production requirements exceed current capacity, an entire additional factory may be needed.)
• Total fixed costs do not change within the relevant range.
• The variable and fixed cost components of mixed costs have been separated. Accuracy of this separation is particularly unrealistic, but reliable estimates can be developed.
• Sales and production are equal; thus, there is no material fluctuation in inventory levels. This assumption is necessary because of the allocation of fixed costs to inventory at potentially different rates each year. This assumption is more realistic as companies begin to use just-in-time inventory systems.
• There will be no capacity additions during the period under consideration. If such additions were made, fixed (and, probably, variable) costs would change.
• In companies with more than one product, we assume that the sales mix will remain the same. If this assumption was not made, no useful weighted average contribution margin could be computed for the company for purposes of CVP analysis.
• There is either no inflation, inflation affects all cost factors equally, or if factors are affected unequally, the appropriate effects are incorporated into the CVP figures.
• Efficiency and productivity remain unchanged as the volume of production changes. We assume that there will be no changes in technology that will affect productivity or labor costs. We also assume that there will be no changes in the market.

A common application of CVP analysis is determining the break-even point (BEP). The following steps illustrate the derivation of the break-even formula in terms of both quantity and total revenue dollars.

Break-Even Quantity

The break-even point occurs when

Revenues (Sales) = Total Cost, (i.e., Net Income = 0 since Total Cost = Variable Cost) + Fixed Cost Break-even occurs when Revenues (Sales) = Variable Cost + Fixed Cost

The above is a foundation formula! Since Revenues = Quantity (Q) x Sales Price per Unit (P) and Variable Cost = Quantity (Q) x Cost per Unit (C) Break-even in dollars occurs when (Q x P) = (Q x C) + Fixed Cost or, (Q x P) - (Q x C) = Fixed Cost Q(P - C) = Fixed Cost

Break-Even Quantity (Q) = Fixed Cost ÷ (P - C) where (P - C) is the contribution margin per unit.

Break-Even Revenue

The break-even point can also be calculated in terms of total revenue dollars, as follows.

Recall that Revenues (Sales) - Variable Cost = Contribution Margin so, break-even occurs when Contribution Margin = Fixed Cost.

Since Contribution Margin = Revenue Dollars x Contribution Margin Ratio, break-even occurs when Revenue x Contribution Margin Ratio = Fixed Cost.

or

Break-Even Revenue = Fixed Cost ÷ Contribution Margin Ratio, where Contribution Margin Ratio = [Price per Unit (P) - Variable Cost per Unit (C)] ÷ Price Per Unit

The Break-Even Revenue can also be calculated by multiplying the Break-Even Quantity (Q) by the Sales Price per Unit.

The break-even formula can be modified to determine: (1) a Targeted Sales Volume in Units (Quantity), or (2) a Targeted Sales Volume in Total Dollars needed to achieve a targeted income.

Target Sales Volume in Units = (Fixed Cost + Target Income) ÷ Contribution Margin per Unit

Target Sales Volume in Dollars = (Fixed Cost + Target Income) ÷ Contribution Margin Ratio

NOTE: These formulas are the same as the break-even quantity and break-even revenue formulas, with the addition of the target income in the numerator.

Another variation on the theme is Margin of Safety. This indicates the quantity that sales can decrease from the targeted level (or current level) before the company will incur losses. This criterion is often used to evaluate the adequacy of planned sales. The margin of safety is expressed in terms of dollars or in terms of a percent.

This section needs to be moved to unit 4 LessonAbsorption costing is a costing method that is used for financial and tax reporting purposes (there are some slight variations, though). For financial and tax reporting purposes, this method does a better job of matching revenues with costs (matching principle). Costs of products will include direct materials, direct labor, and manufacturing overhead costs (both fixed and variable costs). Manufacturing overhead costs once again include indirect labor, indirect materials, factory costs (e.g., factory rent, factory building and equipment depreciation, factory real estate taxes, factory utilities, and other costs of production), and others. Manufacturing overhead will include costs that are variable and fixed. We use the traditional income statement format when we use the absorption method.

Under the variable costing method, it is argued that fixed manufacturing overhead costs are capacity costs and will be incurred even if nothing is produced. Under the variable costing method, fixed manufacturing overhead costs are treated as period costs instead of product costs. For the variable costing method, we use the contribution format income statement.

The only difference between the absorption costing and variable costing methods is how the fixed manufacturing overhead expenses are treated. For absorption costing, they are treated as product costs; for variable costing, they are treated as period costs.

One of the negative features for the absorption costing method is that if inventory levels increase, net income will increase. The reason why this happens is because more fixed manufacturing overhead costs are deferred in inventory. This can be a problem if users of financial information don’t understand the impact of increased inventory levels. They actually see a phantom profit. In some cases, managers may increase inventory levels just to increase profits.

If units produced and sold stay the same, inventory levels will stay the same and the net operating income will be the same under both methods. If units produced are greater than units sold, inventory will increase and net operating income will be greater under the absorption method. If units produced are less than units sold, inventory will decrease and net operating income will be less under the absorption method.

Today, we find that companies are working very hard to keep their inventory levels as low as possible. Many companies use JIT (just in time inventory production), which means that they only begin production when they have orders for goods. Because of this factor, inventory levels are lower. This means that the difference in net operating income between these methods is smaller than it might have been in the past. It is, however, important for managers to understand the impact of changes in inventory levels on net operating income under the two methods.