Now that you have learned about cost behavior, let’s see how managers use this informa- tion to make business decisions. Cost-volume-profit (CVP) analysis is a planning tool that looks at the relationships among costs and volume and how they affect profits (or losses). CVP is also sometimes referred to as cost-volume-price analysis because changes in sales prices also affect profits (or losses). Smart Touch Learning uses CVP analysis to estimate how changes in sales prices, variable costs, fixed costs, and volume will affect profits.
Assumptions
CVP analysis assumes the following for the relevant range:
• The price per unit does not change as volume changes. For example, Smart Touch Learn- ing assumes that all tablets will sell for $500 each.
• Managers can classify each cost as variable, fixed, or mixed.
• The only factor that affects total costs is a change in volume, which increases or decreases total variable and mixed costs. Smart Touch Learning assumes the variable cost per tablet is $275.
• Total fixed costs do not change. Smart Touch Learning assumes fixed costs are $13,500 per month.
• There are no changes in inventory levels. Smart Touch Learning assumes the number of tablets produced equals the number of tablets sold.
Most business conditions do not perfectly meet these general assumptions, so manag- ers regard CVP analysis as a good approximation even though it is not exact.
Breakeven Point—Three Approaches
CVP analysis can be used to estimate the amount of sales needed to achieve the breakeven point. The breakeven point is the sales level at which the company does not earn a profit or a loss but has an operating income of zero. Required sales can be expressed as either a
Learning Objective 3 Use cost-volume-profit (CVP) analysis for profit planning
Cost-Volume-Profit (CVP) Analysis
A planning tool that expresses the relationships among costs, volume, and prices and their effects on profits and losses.
Breakeven Point
The sales level at which operating
Try It!
A furniture manufacturer specializes in wood tables. The tables sell for $100 per unit and incur $40 per unit in variable costs. The company has $6,000 in fixed costs per month.
6. Prepare a contribution margin income statement for one month if the company sells 200 tables.
7. What is the total contribution margin for the month when the company sells 200 tables?
8. What is the unit contribution margin?
9. What is the contribution margin ratio?
Check your answers online in MyAccountingLab or at http://www.pearsonhighered.com/Horngren.
For more practice, see Short Exercises S20-4 and S20-5. MyAccountingLab
The Equation Approach
Let’s start by expressing income in equation form and then breaking it down into its components:
Net sales revenue - Total costs = Operating income Net sales revenue - Variable costs - Fixed costs = Operating income
Net sales revenue equals the unit sales price ($500 per tablet in this case) multiplied by the number of units (tablets) sold. Variable costs equal variable cost per unit ($275 in this case) times the number of units (tablets) sold. Smart Touch Learning’s fixed costs total $13,500 per month. If the company desires to break even, then the target profit is $0. How many tablets must Smart Touch Learning sell to break even?
Net sales revenue− Variable costs − Fixed costs = Target profit (+500 per unit * Units sold) - (+275 per unit * Units sold) - +13,500 = +0
[(+500 per unit - +275 per unit) * Units sold] - +13,500 = +0
+225 per unit * Units sold = +0+ +13,500 +225 per unit * Units sold = +13,500
Units sold = +13,500 / +225 per unit Units sold = 60 units
Be sure to check your calculations. We can prove the required sales by substituting the number of units into the operating income equation and then checking to ensure that this level of sales results in $0 in profit.
Net sales revenue− Variable costs − Fixed costs = Operating income (+500 per unit * 60 units) - (+275 per unit * 60 units) - +13,500 = Operating income
+30,000 - +16,500 - +13,500 = +0
Based on these calculations, then, Smart Touch Learning must sell 60 tablets per month to achieve the breakeven point. Expressed in dollars, the company must have total sales of $30,000 per month (60 tablets * $500 per tablet).
The Contribution Margin Approach
The contribution margin approach is a shortcut method of computing the required sales in units. Notice in the previous example that the fixed costs were divided by the contribution margin per unit ($225 per unit). We can rewrite the equation approach to derive the follow- ing equation:
Required sales in units = Fixed costs + Target profit Contribution margin per unit
Using this formula, we can enter the given amounts to calculate the required sales in units. Notice that the formula is dividing dollars by dollars per unit. When the dollars cancel out during the division process, the result is expressed in units.
Required sales in units = Fixed costs + Target profit Contribution margin per unit
= (+13,500 + +0) +225 per unit
= 60 units
6
Previously, we proved our answer using the equation approach. We can also prove our answer using the contribution margin income statement format:
Net sales revenue ($500 per unit × 60 units) $ 30,000 Variable costs ($275 per unit × 60 units)
($225 per unit × 60 units)
16,500
Contribution margin 13,500
Fixed costs Operating income
13,500
$ 0
−
−
Contribution Margin Ratio Approach
Companies can use the contribution margin ratio approach to compute required sales in terms of sales dollars rather than in units. The formula is the same as using the contribution margin approach, except that the denominator is the contribution margin ratio rather than contribution margin per unit.
We previously computed the contribution margin ratio for Smart Touch Learning as 45%:
Contribution margin ratio = Contribution margin / Net sales revenue
= +225 per tablet / +500 per tablet
= 45%
Notice that when we use the ratio as the denominator in the formula, we are dividing dollars by a percentage. Therefore, the result will be expressed in dollars.
Required sales in dollars = Fixed costs + Target profit Contribution margin ratio
= (+13,500 + +0) 45%
= +30,000
Target Profit
A variation of the breakeven point calculation is the target profit calculation. Target profit is the operating income that results when net sales revenue minus variable and fixed costs equals management’s profit goal. The same three approaches can be used. The only difference is that a company uses a target profit instead of the breakeven point of $0.
Exhibit 20-7 (on the next page) shows the calculation of the target profit calculations for Smart Touch Learning using the three approaches when management’s profit goal is
$4,500 per month.
Target Profit
The operating income that results when net sales revenue minus variable and fixed costs equals management’s profit goal.
Exhibit20-7 | Target Profit Calculations for Smart Touch Learning
Equation Approach
Net sales revenue Variable costs Fixed costs = Target profit ($500 per unit * Units sold) - ($275 per unit * Units sold) - $13,500 = $4,500
[($500 per unit - $275 per unit) * Units sold] - $13,500 = $4,500 $225 per unit * Units sold = $18,000
Units sold = $18,000 / $225 per unit Units sold = 80 units
Contribution Margin Approach
Fixed costs + Target profit Contribution margin per unit Required sales in units =
$13,500 + $4,500
$225 per unit
=
= 80 units
Contribution Margin Ratio Approach
Fixed costs + Target profit Contribution margin ratio Required sales in dollars =
$13,500 + $4,500
= 45%
= $40,000
Solution
Omitting fixed costs from the target profit calculations will understate the amount of sales required to reach the target profit. If required sales are understated, then managers might make decisions that could be detrimental to the company.
Donna should convince her supervisor to admit her mistake and provide corrected estimates to managers. If Donna is unable to convince Nicole to admit her mistake, she should discuss the error and the possible consequences with Nicole’s supervisor. Failure to report the error is a violation of IMA’s credibility standard of ethical practice.
Did you check the formula?
Donna Dickerson is the assistant controller for a large manufac- turing company and works directly under the supervision of the controller, Nicole Randall. While reviewing some documents Nicole prepared, Donna notices a mistake in the target profit calculations. The Excel spreadsheet used to summarize fixed costs has an error in the formula, and some of the individual costs listed are not included in the total. Donna is aware that the target profit calculations are used for planning purposes, so she brings the error to the controller’s attention. Nicole doesn’t seem concerned. “It doesn’t really matter,” says Nicole. “Those figures never show up on the financial statements, so a little mistake won’t matter.” Is Nicole correct? What should Donna do? What would you do?
ETHICS
CVP Graph—A Graphic Portrayal
A CVP graph provides a picture that shows how changes in the levels of sales will affect profits. As in the variable, fixed, and mixed cost graphs of Exhibits 20-1, 20-2, and 20-4, the volume of units is on the horizontal axis and dollars are on the vertical axis. The five steps to graph the CVP relationships for Smart Touch Learning are illustrated in Exhibit 20-8.
Exhibit20-8 | Cost-Volume-Profit Graph for Smart Touch Learning
Step 1 Sales Revenue
Step 3 Total Costs
Step 2 Fixed Costs Step 4
Breakeven Point
Operating Loss
Operating Income
$80,000
$70,000
$60,000
$50,000
$40,000
$30,000
$0
0 50 100 150
$20,000
$10,000
Number of Tablets
Dollars
Tablets 100
Sales Revenue
$50,000
Fixed Costs
$13,500
Total Costs
$41,000 Sales Revenue Fixed Costs Total Costs
Step 1: Choose a sales volume, such as 100 tablets. Plot the point for total sales revenue at that volume: 100 tablets * $500 per tablet = $50,000. Draw the sales revenue line from the origin ($0) through the $50,000 point. Why start at the origin? If Smart Touch Learning sells no tab- lets, there is no revenue.
Step 2: Draw the fixed cost line, a horizontal line that intersects the dollars axis at $13,500.
The fixed cost line is flat because fixed costs are the same, $13,500, no matter how many tablets are sold.
Step 3: Draw the total cost line. Total costs are the sum of variable costs plus fixed costs.
Thus, total costs are mixed. The total cost line follows the form of the mixed cost line in Exhibit 20-4. Begin by computing total variable costs at the chosen sales volume:
100 tablets * $275 per tablet = $27,500. Add total variable costs to fixed costs:
$27,500 + $13,500 = $41,000. Plot the total cost point of $41,000 for 100 tablets. Then draw a line through this point from the $13,500 fixed cost intercept on the dollars vertical axis. This is the total cost line. The total cost line starts at the fixed cost line because even if Smart Touch Learning sells no tablets, the company still incurs the $13,500 of fixed costs.
Step 4: Identify the breakeven point. The breakeven point is where the sales revenue line
Graphs like Exhibit 20-8 are helpful to managers because the managers can use the graphs to prepare a quick estimate of the profit or loss earned at different levels of sales.
The three target profit formulas are also useful, but they only indicate income or loss for a single sales amount.
Try It!
A furniture manufacturer specializes in wood tables. The tables sell for $100 per unit and incur $40 per unit in variable costs. The company has $6,000 in fixed costs per month. The company desires to earn an operating profit of $12,000 per month.
10. Calculate the required sales in units to earn the target profit using the equation method.
11. Calculate the required sales in units to earn the target profit using the contribution margin method.
12. Calculate the required sales in dollars to earn the target profit using the contribution margin ratio method.
13. Calculate the required sales in units to break even using the contribution margin method.
Check your answers online in MyAccountingLab or at http://www.pearsonhighered.com/Horngren.
For more practice, see Short Exercises S20-6 through S20-11. MyAccountingLab