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- Advanced Financial Management - AFM
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COST VOLUME PROFIT ANALYSIS The break-even point (the point of zero profit) and then see how each can be expanded to determine the number of units that must be sold to earn a targeted profit. The firm’s initial decision in implementing a units-sold approach to CVP analysis is the determination of just what a unit is. A second decision centers on the separation of costs into fixed and variable components. CVP analysis focuses on the factors that effect a change in the components of profit. Because we are looking at CVP analysis in terms of units sold, we need to determine the fixed and variable components of cost and revenue with respect to units. Thus, when we say variable costs, we mean all costs that increase as more units are sold, including direct materials, direct labor, variable overhead, and variable selling and administrative costs. Similarly, fixed costs include fixed overhead and fixed selling and administrative expenses. Operating Income Approach The operating income approach focuses on the income statement as a useful tool in organizing the firm’s costs into fixed and variable categories. The income statement can be expressed as a narrative equation: Operating income =Sales revenues - Variable expenses -Fixed expenses Note that we are using the term operating income to denote income or profit before income taxes. Operating income includes only revenues and expenses from the firm’s normal operations. We will use the term net income to mean operating income minus income taxes. Once we have a measure of units sold, we can expand the operating income equation by expressing sales revenue and variable expenses in terms of unit dollar amounts and number of units. Specifically, sales revenue is expressed as the unit selling price times the number of units sold, and total variable costs are the unit variable cost times the number of units sold. With these expressions, the operating income statement becomes: Operating income = (Price x Number of units)-(Variable cost per unit x Number of units) - Total fixed costs Suppose you were asked how many units must be sold in order to break even, or earn a zero profit. You could answer that question by setting operating income equal to zero and then solving the operating income equation for the number of units. For the coming year, the controller has prepared the following projected income statement: Sales (72,500 units @ $40) $2,900,000 Less: Variable expenses 1,740,000 Contribution margin $1,160,000 Less: Fixed expenses 800,000 Operating income $ 360,000 The price is $40 per unit, and the variable cost is $24 ($1,740,000/72,500 units). Fixed costs are $800,000. At the break-even point, then, the operating income equation would take the following form: 0 = ($40 x Units) - ($24 x Units)-$800,000

0= ($16 x Units) - $800,000 $16 x Units = $800,000 Units = 50,000 Therefore, More-Power must sell 50,000 sanders just to cover all fixed and variable expenses. A good way to check this answer is to formulate an income statement based on 50,000 units sold. Sales (50,000 units @ $40) $2,000,000 Less: Variable expenses 1,200,000 Contribution margin $ 800,000 Less: Fixed expenses 800,000 Operating income $0 Indeed, selling 50,000 units does yield a zero profit. An important advantage of the operating income approach is that all further CVP equations are derived from the variable-costing income statement. As a result, you can solve any CVP problem by using this approach. Contribution Margin Approach A refinement of the operating income approach is the contribution margin approach. In effect, we are simply recognizing that at break-even, the total contribution margin equals the fixed expenses. The contribution margin is sales revenue minus total variable costs. If we substitute the unit contribution margin for price minus unit variable cost in the operating income equation and solve for the number of units, we obtain the following break-even expression: Number of units = Fixed costs/Unit contribution margin Using More-Power Company as an example, we can see that the contribution margin per unit can be computed in one of two ways. One way is to divide the total contribution margin by the units sold for a result of $16 per unit ($1,160,000/72,500). A second way is to compute price minus variable cost per unit. Doing so yields the same result, $16 per unit ($40 - $24). Now, we can use the contribution margin approach to calculate the break-even number of units. Number of units = $800,000/ ($40 - $24) = $800,000/$16 per unit =50,000 units Of course, the answer is identical to that computed using the operating income approach. Profit Targets While the break-even point is useful information, most firms would like to earn operating income greater than zero. CVP analysis gives us a way to determine how many units must be sold to earn a particular targeted income. Targeted operating income can be expressed as a dollar amount (e.g., $20,000) or as a percentage of sales revenue (e.g., 15 percent of revenue). Both the operating income approach and the contribution margin approach can be easily adjusted to allow for targeted income. Targeted Income as a Dollar Amount Assume that More-Power Company wants to earn operating income of $424,000. How many sanders must be sold to achieve this result? Using the operating income approach, we form the following equation: $424,000 = ($40 x Units) - ($24 x Units) - $800,000 $1,224,000 - $16 x Units Units = 76,500 Using the contribution margin approach, we simply add targeted profit of $424,000 to the fixed costs and solve for the number of units.

Units = ($800,000 - $424,000)/ ($40 - $24) = $1,224,000/$16 = 76,500 More-Power must sell 76,500 sanders to earn a before-tax profit of $424,000. The following income statement verifies this outcome: Sales (76,500 units @ $40) $3,060,000 Less: Variable expenses 1,836,000 Contribution margin $1,224,000 Less: Fixed expenses 800,000 Income before income taxes $ 424,000 Another way to check this number of units is to use the break-even point. As was just shown, More-Power must sell 76,500 sanders, or 26,500 more than the break-even volume of 50,000 units, to earn a profit of $424,000. The contribution margin per sander is $16. Multiplying $16 by the 26,500 sanders above break-even produces the profit of $424,000 ($16 _ 26,500). This outcome demonstrates that contribution margin per unit for each unit above breakeven is equivalent to profit per unit. Since the break-even point had already been computed, the number of sanders to be sold to yield a $424,000 operating income could have been calculated by dividing the unit contribution margin into the target profit and adding the resulting amount to the breakeven volume. In general, assuming that fixed costs remain the same, the impact on a firm’s profits resulting from a change in the number of units sold can be assessed by multiplying the unit contribution margin by the change in units sold. For example, if 80,000 sanders instead of 76,500 are sold, how much more profit will be earned? The change in units sold is an increase of 3,500 sanders, and the unit contribution margin is $16. Thus, profits will increase by $56,000 ($16 x 3,500). Targeted Income as a Percent of Sales Revenue Assume that More-Power Company wants to know the number of sanders that must be sold in order to earn a profit equal to 15 percent of sales revenue. Sales revenue is selling price multiplied by the quantity sold. Thus, the targeted operating income is 15 percent of selling price times quantity. Using the operating income approach (which is simpler in this case), we obtain the following: 0.15($40) (Units) = ($40 x Units) - ($24 x Units) - $800,000 $6 x Units = ($40 x Units) - ($24 x Units) - $800,000 $6 x Units = ($16 x Units) - $800,000 $10 x Units =$800,000 Units = 80,000 Does a volume of 80,000 sanders achieve a profit equal to 15 percent of sales revenue? For 80,000 sanders, the total revenue is $3.2 million ($40 x 80,000). The profit can be computed without preparing a formal income statement. Remember that above break-even, the contribution margin per unit is the profit per unit. The break-even volume is 50,000 sanders. If 80,000 sanders are sold, then 30,000 (80,000 - 50,000) sanders above the break-even point are sold. The before-tax profit, therefore, is $480,000 ($16 x 30,000), which is 15 percent of sales ($480,000/$3,200,000). After-Tax Profit Targets When calculating the break-even point, income taxes play no role. This is because the taxes paid on zero income are zero. However, when the company needs to know how many units to sell to earn a particular net income, some additional consideration is needed. Recall that net income is operating income after income taxes and that our targeted income figure was expressed in before-tax terms. As a result, when the income target is expressed as net income, we must add back the income taxes to get operating income. Therefore, to use either approach, the aftertax profit target must first be converted to a before-tax profit target. In general, taxes are computed as a percentage of income. The after-tax profit is computed by subtracting the tax from the operating income (or before-tax profit).

Net income = Operating income - Income taxes =Operating income - (Tax rate x operating income) =Operating income (1 x Tax rate) or Operating income = Net income/ (1 x Tax rate) Thus, to convert the after-tax profit to before-tax profit, simply divide the after-tax profit by the quantity (1 x Tax rate). Suppose that More-Power Company wants to achieve net income of $487,500 and its income tax rate is 35 percent. To convert the after-tax profit target into a before tax profit target, complete the following steps: $487,500 = Operating income - 0.35(Operating income) $487,500 = 0.65(Operating income) $750,000 = Operating income 740 In other words, with an income tax rate of 35 percent, More-Power Company must earn $750,000 before income taxes to have $487,500 after income taxes. With this conversion, we can now calculate the number of units that must be sold. Units = ($800,000 - $750,000)/$16 =$1,550,000/$16 = 96,875 Let’s check this answer by preparing an income statement based on sales of 96,875 sanders. Sales (96,875 @ $40) $3,875,000 Less: Variable expenses 2,325,000 Contribution margin $1,550,000 Less: Fixed expenses 800,000 Income before income taxes $ 750,000 Less: Income taxes (35% tax rate) 262,500 Net income $ 487,500 Notice that sales revenue, variable costs, and contribution margin have been expressed in the form of percent of sales. The variable cost ratio is 0.60 ($1,740,000/$2,900,000); the contribution margin ratio is 0.40 (computed either as 1 _ 0.60 or as $1,160,000/$2,900,000). Fixed costs are $800,000. Given the information in this income statement, how much sales revenue must More-Power earn to break even? Operating income = Sales - Variable costs - Fixed costs 0 = Sales - (Variable cost ratio - Sales) - Fixed costs 0 = Sales (1 -Variable cost ratio) - Fixed costs 0 = Sales (1- 0.60) - $800,000 Sales (0.40) = $800,000 Sales = $2,000,000

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