cost-volume-profit relationships chapter 6. 6-2 learning objectives 1.explain how changes in...
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Cost-Volume-Profit Relationships
Chapter
6
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LEARNING OBJECTIVES
1. Explain how changes in activity affect contribution margin.
2. Compute the contribution margin ratio (CM) ratio and use it to compute changes in contribution margin and net income.
3. Show the effects on contribution margin of changes in variable costs, fixed costs, selling price and volume.
4. Compute the break-even point by both the equation method and the contribution margin method.
After studying this chapter, you should be able to:
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LEARNING OBJECTIVES
5. Prepare a cost-volume-profit (CVP) graph and explain the significance of each of its components.
6. Use the CVP formulas to determine the activity level needed to achieve a desired target profit.
7. Compute the margin of safety and explain its significance.
After studying this chapter, you should be able to:
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LEARNING OBJECTIVES
8. Compute the degree of operating leverage at a particular level of sales and explain how the degree of operating leverage can be used to predict changes to net income.
9. Compute the break-even point for a multiple product company and explain the effects of shifts in the sales mix on contribution margin and the break-even point.
10. (Appendix 6A) Understand cost-volume-profit with uncertainty.
After studying this chapter, you should be able to:
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Total Per UnitSales (500 bikes) 250,000$ 500$ Less: variable expenses 150,000 300 Contribution margin 100,000 200$
Less: fixed expenses 80,000 Net income 20,000$
WIND BICYCLE CO.Contribution Income Statement
For the Month of June
The Basics of Cost-Volume-Profit (CVP) Analysis
Contribution Margin (CM) is the amount remaining from sales revenue after variable expenses have been
deducted.
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Total Per UnitSales (500 bikes) 250,000$ 500$ Less: variable expenses 150,000 300 Contribution margin 100,000 200$
Less: fixed expenses 80,000 Net income 20,000$
WIND BICYCLE CO.Contribution Income Statement
For the Month of June
The Basics of Cost-Volume-Profit (CVP) Analysis
CM is used to cover fixed expenses.CM is used to cover fixed expenses.
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Total Per UnitSales (500 bikes) 250,000$ 500$ Less: variable expenses 150,000 300 Contribution margin 100,000 200$
Less: fixed expenses 80,000 Net income 20,000$
WIND BICYCLE CO.Contribution Income Statement
For the Month of June
The Basics of Cost-Volume-Profit (CVP) Analysis
After covering fixed costs, any remaining CM contributes to income.
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The Contribution Approach
For each additional unit Wind sells, $200 more in contribution margin will help to
cover fixed expenses and profit.
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The Contribution Approach
Each month Wind must generate at least $80,000 in total CM to break even.
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The Contribution Approach
If Wind sells 400 units in a month, it will be operating at the break-even point.
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Total Per UnitSales (401 bikes) 200,500$ 500$ Less: variable expenses 120,300 300 Contribution margin 80,200 200$
Less: fixed expenses 80,000 Net income 200$
WIND BICYCLE CO.Contribution Income Statement
For the Month of June
The Contribution Approach
If Wind sells one additional unit (401 bikes), net income will increase by $200.
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The Contribution Approach
The break-even point can be defined either as:The point where total sales revenue equals total
expenses (variable and fixed).The point where total contribution margin equals
total fixed expenses.
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Contribution Margin Ratio
The contribution margin ratio is:
For Wind Bicycle Co. the ratio is:
Contribution margin Sales
CM Ratio =
$200 $500
= 40%
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Contribution Margin Ratio
At Wind, each $1.00 increase in sales revenue results in a total contribution
margin increase of 40¢.
If sales increase by $50,000, what will be If sales increase by $50,000, what will be the increase in total contribution margin? the increase in total contribution margin?
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Contribution Margin Ratio
400 Bikes 500 BikesSales 200,000$ 250,000$ Less: variable expenses 120,000 150,000 Contribution margin 80,000 100,000 Less: fixed expenses 80,000 80,000 Net income -$ 20,000$
400 Bikes 500 BikesSales 200,000$ 250,000$ Less: variable expenses 120,000 150,000 Contribution margin 80,000 100,000 Less: fixed expenses 80,000 80,000 Net income -$ 20,000$
A $50,000 increase in sales revenue
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400 Bikes 500 BikesSales 200,000$ 250,000$ Less: variable expenses 120,000 150,000 Contribution margin 80,000 100,000 Less: fixed expenses 80,000 80,000 Net income -$ 20,000$
400 Bikes 500 BikesSales 200,000$ 250,000$ Less: variable expenses 120,000 150,000 Contribution margin 80,000 100,000 Less: fixed expenses 80,000 80,000 Net income -$ 20,000$
Contribution Margin Ratio
A $50,000 increase in sales revenue results in a $20,000 increase in CM
or ($50,000 × 40% = $20,000)
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Changes in Fixed Costs and Sales Volume
Wind is currently selling 500 bikes per month. The company’s sales manager believes that
an increase of $10,000 in the monthly advertising budget would increase bike sales
to 540 units.
Should we authorize the requested increase in the advertising budget?
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Current Sales (500 bikes)
Projected Sales (540 bikes)
Sales 250,000$ 270,000$ Less: variable expenses 150,000 162,000 Contribution margin 100,000 108,000 Less: fixed expenses 80,000 90,000 Net income 20,000$ 18,000$
Current Sales (500 bikes)
Projected Sales (540 bikes)
Sales 250,000$ 270,000$ Less: variable expenses 150,000 162,000 Contribution margin 100,000 108,000 Less: fixed expenses 80,000 90,000 Net income 20,000$ 18,000$
Changes in Fixed Costs and Sales Volume
Sales increased by $20,000, but net income decreased by $2,000..
Sales increased by $20,000, but net income decreased by $2,000..
$80,000 + $10,000 advertising = $90,000$80,000 + $10,000 advertising = $90,000
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Changes in Fixed Costs and Sales Volume
The Shortcut SolutionThe Shortcut Solution
Increase in CM (40 units X $200) 8,000$ Increase in advertising expenses 10,000 Decrease in net income (2,000)$
Increase in CM (40 units X $200) 8,000$ Increase in advertising expenses 10,000 Decrease in net income (2,000)$
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APPLICATIONS OF CVP
Consider the following basic data:
Per unit Percent
Sales Price $250 100
Less: Variable cost 150 60
Contribution margin 100 40
Fixed costs total $35,000
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APPLICATIONSCurrent sales are $100,000. Sales
manager feels $10,000 increase in sales budget will provide $30,000 increase in sales. Should the budget be changed?
Incremental CM approach:
$30,000 x 40% CM ratio 12,000
Additional advertising expense 10,000
Increase in net income 2,000
YES
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APPLICATIONSManagement is considering increasing
quality of speakers at an additional cost of $10 per speaker. Plan to sell 80 more units. Should management increase quality?
Expected total CM
= (480 speakers x$90) $43,200
Present total CM
= (400 speakers x$100) 40,000
Increase in total contribution margin 3,200 (and net income)
YES
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APPLICATIONSManagement advises that if selling price
dropped $20 per speaker and advertising increased by $15,000/month, sales would increase 50%. Good idea?
Expected total CM
= (400x150%x$80) $48,000
Present total CM (400x$100) 40,000
Incremental CM 8,000
Additional advertising cost 15,000
Reduction in net income (7,000)
NO
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APPLICATIONS
A plan to switch sales people from flat salary ($6,000 per month) to a sales commission of $15 per speaker could increase sales by 15%. Good idea?
Expected total CM (400x115%x$85) $39,100
Current total CM (400x$100) 40,000
Decrease in total CM (900)
Salaries avoided if commission paid 6,000
Increase in net income $5,100
YES
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APPLICATIONS
A wholesaler is willing to buy 150 speakers if we will give him a discount off our price. The sale will not disturb regular sales and will not change fixed costs. We want to make $3,000 on this sale. What price should we quote?
Variable cost per speaker $150
Desired profit on order (3,000/150) 20
Quoted price per speaker $170
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Break-Even Analysis
Break-even analysis can be approached in two ways:Equation methodContribution margin method.
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Equation Method
Profits = Sales – (Variable expenses + Fixed expenses)
Sales = Variable expenses + Fixed expenses + Profits
OR
At the break-even point profits equal zero.
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Equation Method
Here is the information from Wind Bicycle Co.:
Total Per Unit PercentSales (500 bikes) 250,000$ 500$ 100%Less: variable expenses 150,000 300 60%Contribution margin 100,000$ 200$ 40%
Less: fixed expenses 80,000 Net income 20,000$
Total Per Unit PercentSales (500 bikes) 250,000$ 500$ 100%Less: variable expenses 150,000 300 60%Contribution margin 100,000$ 200$ 40%
Less: fixed expenses 80,000 Net income 20,000$
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Equation Method
We calculate the break-even point as follows:
Sales = Variable expenses + Fixed expenses + Profits
$500Q = $300Q + $80,000 + $0
Where:Q = Number of bikes sold$500 = Unit sales price$300 = Unit variable expenses$80,000 = Total fixed expenses
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Equation Method
We calculate the break-even point as follows:
Sales = Variable expenses + Fixed expenses + Profits
$500Q = $300Q + $80,000 + $0
$200Q = $80,000
Q = 400 bikes
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Equation Method
We can also use the following equation to compute the break-even point in sales dollars.
Sales = Variable expenses + Fixed expenses + Profits
X = 0.60X + $80,000 + $0 Where:
X = Total sales dollars0.60 = Variable expenses as a
percentage of sales$80,000 = Total fixed expenses
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Equation Method
We can also use the following equation to compute the break-even point in sales dollars.
Sales = Variable expenses + Fixed expenses + Profits
X = 0.60X + $80,000 + $0
0.40X = $80,000
X = $200,000
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Contribution Margin Method
The contribution margin method is a variation of the equation method.
Fixed expenses Unit contribution margin
=Break-even point
in units sold
Fixed expenses CM ratio
=Break-even point intotal sales dollars
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CVP Relationships in Graphic Form
Viewing CVP relationships in a graph gives managers a perspective that can be obtained in no other way. Consider the following information for Wind Co.:
Income 300 units
Income 400 units
Income 500 units
Sales 150,000$ 200,000$ 250,000$ Less: variable expenses 90,000 120,000 150,000 Contribution margin 60,000$ 80,000$ 100,000$ Less: fixed expenses 80,000 80,000 80,000 Net income (loss) (20,000)$ -$ 20,000$
Income 300 units
Income 400 units
Income 500 units
Sales 150,000$ 200,000$ 250,000$ Less: variable expenses 90,000 120,000 150,000 Contribution margin 60,000$ 80,000$ 100,000$ Less: fixed expenses 80,000 80,000 80,000 Net income (loss) (20,000)$ -$ 20,000$
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50,000
100,000
150,000
200,000
250,000
300,000
350,000
400,000
- 100
200
300
400
500
600
700
800
CVP Graph
Fixed expenses
Units
Dol
lars
Total Expenses
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50,000
100,000
150,000
200,000
250,000
300,000
350,000
400,000
- 100
200
300
400
500
600
700
800
Units
Dol
lars
CVP Graph
Total Sales
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50,000
100,000
150,000
200,000
250,000
300,000
350,000
400,000
- 100
200
300
400
500
600
700
800
Units
Dol
lars
CVP Graph
Break-even point
Profit Area
Loss Area
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Target Profit Analysis
Suppose Wind Co. wants to know how many bikes must be sold to earn a profit
of $100,000.
We can use our CVP formula to determine the sales volume needed to achieve a
target net profit figure.
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The CVP Equation
Sales = Variable expenses + Fixed expenses + Profits
$500Q = $300Q + $80,000 + $100,000
$200Q = $180,000
Q = 900 bikes
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The Contribution Margin Approach
We can determine the number of bikes that must be sold to earn a profit of $100,000 using the contribution margin approach.
Fixed expenses + Target profit Unit contribution margin
=Units sold to attain
the target profit
$80,000 + $100,000 $200
= 900 bikes
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The Margin of Safety
Excess of budgeted (or actual) sales over the break-even volume of sales. The
amount by which sales can drop before losses begin to be incurred.
Margin of safety = Total sales - Break-even sales
Let’s calculate the margin of safety for Wind.
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The Margin of Safety
Wind has a break-even point of $200,000. If actual sales are $250,000, the margin of
safety is $50,000 or 100 bikes.Break-even
sales 400 units
Actual sales 500 units
Sales 200,000$ 250,000$ Less: variable expenses 120,000 150,000 Contribution margin 80,000 100,000 Less: fixed expenses 80,000 80,000 Net income -$ 20,000$
Break-even sales
400 unitsActual sales
500 unitsSales 200,000$ 250,000$ Less: variable expenses 120,000 150,000 Contribution margin 80,000 100,000 Less: fixed expenses 80,000 80,000 Net income -$ 20,000$
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Break-even sales
400 unitsActual sales
500 unitsSales 200,000$ 250,000$ Less: variable expenses 120,000 150,000 Contribution margin 80,000 100,000 Less: fixed expenses 80,000 80,000 Net income -$ 20,000$
Break-even sales
400 unitsActual sales
500 unitsSales 200,000$ 250,000$ Less: variable expenses 120,000 150,000 Contribution margin 80,000 100,000 Less: fixed expenses 80,000 80,000 Net income -$ 20,000$
The Margin of Safety
The margin of safety can be expressed as 20 percent of sales.($50,000 ÷ $250,000)
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Operating Leverage
A measure of how sensitive net income is to percentage changes in sales.
With high leverage, a small percentage increase in sales can produce a much larger percentage increase in net income.
Contribution margin Net income
Degree ofoperating leverage =
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Operating Leverage
Actual sales 500 Bikes
Sales 250,000$ Less: variable expenses 150,000 Contribution margin 100,000 Less: fixed expenses 80,000 Net income 20,000$
Actual sales 500 Bikes
Sales 250,000$ Less: variable expenses 150,000 Contribution margin 100,000 Less: fixed expenses 80,000 Net income 20,000$
$100,000 $20,000
= 5
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Operating Leverage
With a measure of operating leverage of 5, With a measure of operating leverage of 5, if Wind increases its sales by 10%, net if Wind increases its sales by 10%, net
income would increase by 50%.income would increase by 50%.
Percent increase in sales 10%Degree of operating leverage × 5Percent increase in profits 50%
Here’s the proof!
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Operating Leverage
10% increase in sales from$250,000 to $275,000 . . .
10% increase in sales from$250,000 to $275,000 . . .
. . . results in a 50% increase inincome from $20,000 to $30,000.. . . results in a 50% increase in
income from $20,000 to $30,000.
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The Concept of Sales Mix
Sales mix is the relative proportions in which a company’s products are sold.
Different products have different selling prices, cost structures, and contribution margins.
Let’s assume Wind sells bikes and carts and see how we deal with break-even analysis.
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The Concept of Sales Mix
Wind Bicycle Co. provides us with the following information:
Bikes Carts TotalSales 250,000$ 100% 300,000$ 100% 550,000$ 100%Var. exp. 150,000 60% 135,000 45% 285,000 52%Contrib. margin 100,000$ 40% 165,000$ 55% 265,000 48%
Fixed exp. 170,000 Net income 95,000$
$265,000 $550,000
= 48% (rounded)
$170,000 $170,000 0.480.48
= $354,167 (rounded)= $354,167 (rounded)
Break-even point in sales dollars:
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Assumptions of CVP Analysis
Selling price is constant throughout the entire relevant range.
Costs are linear throughout the entire relevant range.
In multi-product companies, the sales mix is constant.
In manufacturing companies, inventories do not change (units produced = units sold).
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Cost-Volume-Profitwith uncertainty
Appendix
6A
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CVP with uncertaintyUse a decision tree to simplify
calculationsThe decision tree is used to calculate
profits under various alternativesA second decision tree can be used to
calculate the probabilities of the various scenarios to further determine a reasonable estimate of profit
A computer can be used to save time
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End of Chapter 6
We madeit!