cost-volume-profit relationships chapter 6. 6-2 learning objectives 1.explain how changes in...

Cost-Volume-Profit Relationships

Chapter

6

6-2

© McGraw-Hill Ryerson Limited., 2001

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.


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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.


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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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CM is used to cover fixed expenses.CM is used to cover fixed expenses.

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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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Each month Wind must generate at least $80,000 in total CM to break even.

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If Wind sells 400 units in a month, it will be operating at the break-even point.

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Less: fixed expenses 80,000 Net income 200$




If Wind sells one additional unit (401 bikes), net income will increase by $200.

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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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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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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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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$


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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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%


Total Per Unit PercentSales (500 bikes) 250,000$ 500$ 100%Less: variable expenses 150,000 300 60%Contribution margin 100,000$ 200$ 40%


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Equation Method

We calculate the break-even point as follows:


$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:


$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.


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.


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


$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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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



Break-even sales




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).

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

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cost-volume-profit relationships chapter 6. 6-2 learning objectives 1.explain how changes in...

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