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Libby, Libby and ShortCHAPTER
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1. Determine the number of units that must be sold to break even or earn a target profit.
2. Calculate the amount of revenue required to break even or to earn a targeted profit.
3. Apply cost-volume-profit analysis in a multiple-product setting.
4. Prepare a profit-volume graph and a cost-volume-profit graph, and explain the meaning of each.
Objectives
Chapter 1 -
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5. Explain the impact of risk, uncertainty, and changing variables on cost-volume-profit analysis.
6. Discuss the impact of activity-based costing on cost-volume-profit analysis
Objectives
Narrative Equation
Sales revenue
– Variable expenses
– Fixed expenses
= Operating income
Chapter 1 -
Sales (1,000 units @ $400) $400,000
Less: Variable expenses 325,000
0 = ($400 x Units) – ($325 x Units) – $45,000
Break Even in Units
Break Even in Units
0 = ($75 x Units) – $45,000
$75 x Units = $45,000
$60,000 = ($400 x Units) – ($325 x Units) – $45,000
$105,000 = $75 x Units
$60 x Units = ($400 x Units) – $325 x Units) – $45,000
Units = 3,000
$60 x Units = ($75 x Units) – $45,000
$15 x Units = $45,000
= Operating income – (Tax rate x Operating income)
After-Tax Profit Targets
Or
$48,750 = 0.65 (Operating income)
$75,000 = Operating income
If the tax rate is 35 percent and a firm wants to achieve a profit of $48,750. How much is the necessary operating income?
Chapter 1 -
How many units would have to be sold to earn an operating income of $48,750?
Units = ($45,000 + $75,000)/$75
Net income $ 48,750
First, the contribution margin ratio must be calculated.
Sales $400,000 100.00%
Break-Even Point in Sales Dollars
Given a contribution margin ratio of 18.75%, how much sales revenue is required to break even?
Operating income = Sales – Variable costs – Fixed costs
$0 = Sales – (Variable costs ratio x Sales)
– $45,000
Sales (0.1875) = $45,000
Contribution Margin
Contribution Margin
Contribution Margin
Profit Targets and Sales Revenue
How much sales revenue must a firm generate to earn a before-tax profit of $60,000. Recall that fixed costs total $45,000 and the contribution margin ratio is .1875.
Sales = ($45,000 + $60,000)/0.1875
Contribution margin $ 90,000 $160,000 $ 250,000
Less: Direct fixed expenses 30,000 40,000 70,000
Product margin $ 60,000 $120,000 $ 180,000
Less: Common fixed expenses 26,250
Operating income $ 153,750
Contribution margin $ 34,650 $ 61,600 $ 96,250
Less: Direct fixed expenses 30,000 40,000 70,000
Segment margin $ 4,650 $ 23,600 $ 26,250
Less: Common fixed expenses 26,250
Operating income $ 0
The profit-volume graph portrays the relationship between profits and sales volume.
Chapter 1 -
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Example
The Tyson Company produces a single product with the following cost and price data:
Total fixed costs $100
Chapter 1 -
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The cost-volume-profit graph depicts the relationship among costs, volume, and profits.
Chapter 1 -
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Chapter 1 -
Assumptions of C-V-P Analysis
1. The analysis assumes a linear revenue function and a linear cost function.
2. The analysis assumes that price, total fixed costs, and unit variable costs can be accurately identified and remain constant over the relevant range.
3. The analysis assumes that what is produced is sold.
4. For multiple-product analysis, the sales mix is assumed to be known.
5. The selling price and costs are assumed to be known with certainty.
Chapter 1 -
Alternative 1: If advertising expenditures increase by $8,000, sales will increase from 1,600 units to 1,725 units.
BEFORE THE WITH THE
Total contribution margin $120,000 $129,375
Less: Fixed expenses 45,000 53,000
Profit $ 75,000 $ 76,375
DIFFERENCE IN PROFIT
Less: Change in fixed expenses 8,000
Increase in profits $1,375
Profit $ 75,000 $50,000
Alternative 2: A price decrease from $400 to $375 per lawn mower will increase sales from 1,600 units to 1,900 units.
Decrease in profits $ -25,000
Profit $ 75,000 $ 77,000
Less: Change in fixed expenses 8,000
Increase in profit $ 2,000
Assume that a company has the following projected income statement:
Sales $100,000
R = $30,000 ÷ .4 = $75,000
Chapter 1 -
DOL = $40,000/$10,000 = 4.0
Now suppose that sales are 25% higher than projected. What is the percentage change in profits?
Percentage change in profits = DOL x percentage change in sales
Percentage change in profits = 4.0 x 25% = 100%
Chapter 1 -
Proof:
Variable cost 5
Fixed costs (ABC) $100,000 with $80,000 subject to ABC analysis
Other Data:
Chapter 1 -
= 18,000 units
Chapter 1 -
= 16,900 units
3. What is the BEP if setup cost could be reduced to $450 and inspection cost reduced to $40?
CVP and ABC

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