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Cost-Volume-Profit Analysis

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Cost-Volume-Profit Analysis

Chapter

22

- Purpose of C-V-P Analysis
- Identifying Cost Behavior
- Measuring Cost Behavior
- Using Break-Even Analysis
- Applying C-V-P Analysis
- Decision Analysis:
- Degree of Operating Leverage

CVP analysis is used to answer questionssuch as:

- How much must I sell to earn my desired income?
- How will income be affectedif I reduce selling prices toincrease sales volume?
- How will income be affectedif I change the sales mixof my products?

Total fixed costs remain unchangedwhen activity changes.

Monthly Basic Telephone Bill

Your monthly basictelephone bill probablydoes not change whenyou make more local calls.

Number of Local Calls

Fixed costs per unit declineas activity increases.

Monthly Basic Telephone Bill per Local Call

Your average cost perlocal call decreases asmore local calls are made.

Number of Local Calls

- Total variable costs changewhen activity changes.

Total Long DistanceTelephone Bill

Your total long distancetelephone bill is basedon how many minutesyou talk.

Minutes Talked

Variable costs per unit do not changeas activity increases.

Per MinuteTelephone Charge

The cost per long distanceminute talked is constant.For example, 7cents per minute.

Minutes Talked

Mixed costs contain a fixed portion that is incurred even when facility is unused, and a variable portion that increases with usage.

Example: monthly electric utility charge

- Fixed service fee
- Variable charge perkilowatt hour used

Total mixed cost

Variable Utility Charge

Total Utility Cost

Fixed MonthlyUtility Charge

Activity (Kilowatt Hours)

Total cost remainsconstant within anarrow rangeofactivity.

Cost

Activity

Total cost increases to a new higher cost for the next higher range of activity.

Cost

Activity

Costs that increase when activity increases, but in a nonlinearmanner.

Total Cost

Activity

The objectiveis to classify all costs as either fixed or variable.

A scatter diagram of past cost behavior may be helpful in analyzing mixed costs.

20

*

*

*

*

*

*

*

*

Total Cost in1,000’s of Dollars

*

*

10

0

0 1 2 3 4

Activity, 1,000’s of Units Produced

Scatter Diagram

Plot the data points on a graph (total cost vs. activity).

20

*

*

*

*

*

*

*

*

Total Cost in1,000’s of Dollars

*

*

10

0

0 1 2 3 4

Activity, 1,000’s of Units Produced

Scatter Diagram

Draw a line through the plotted data points so that about equal numbers of points fall above and below the line.

Estimated fixed cost = 10,000

in costin units

Unit Variable Cost = Slope =

20

*

*

*

*

*

*

*

*

Total Cost in1,000’s of Dollars

*

*

10

0

0 1 2 3 4

Activity, 1,000’s of Units Produced

Scatter Diagram

Vertical distance is the change in cost.

Horizontal distance is the change in activity.

Exh.

22-6

The following relationships between salesand costs are observed:

Using these two levels of activity, compute:

- the variable cost per unit.
- the total fixed cost.

$8,500$50,000

in costin units

- Unit variable cost = = = $0.17 per $

The High-Low Method

Exh.

22-6

$8,500$50,000

in costin units

- Unit variable cost = = = $0.17 per $
- Fixed cost = Total cost – Total variable

The High-Low Method

Exh.

22-6

$8,500$50,000

in costin units

- Unit variable cost = = = $0.17 per $
- Fixed cost = Total cost – Total variable cost Fixed cost = $29,000 – ($0.17 per sales $ × $67,500) Fixed cost = $29,000 – $11,475 = $17,525

The High-Low Method

Exh.

22-6

- Least-squares regression is usually covered in advanced cost accounting courses. It is commonly used with computer software because of the large number of calculations required.

The objective of the cost analysis remains the same: determination of total fixed cost and the variable unit cost.

Let’s extend ourknowledge ofcost behavior to break-even analysis.

The break-even point (expressed in units of product or dollars of sales) is the unique sales level at which a company earns neither a profit nor incurs a loss.

Contribution margin is amount by which revenue exceeds thevariable costsof producing the revenue.

Computing Break-Even Point

How much contribution margin must this company have to cover its fixed costs (break even)?

Answer: $30,000

Computing Break-Even Point

How manyunits must this company sell to cover its fixed costs (break even)?

Answer: $30,000 ÷ $20 per unit = 1,500 units

Fixed costs

Break-even point in units =

Contribution margin per unit

Exh.

22-8

We have just seen one of the basic CVP relationships – the break-evencomputation.

Unit sales price less unit variable cost($20 in previous example)

Fixed costs

Break-even point in dollars =

Contribution margin ratio

Computing Break-Even Point

Exh.

22-9

The break-even formula may also be expressed in sales dollars.

Unit contribution margin Unit sales price

Computing Break-Even Point

ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to break even?

a. 100,000 units

b. 40,000 units

c. 200,000 units

d. 66,667 units

Unit contribution = $5.00 - $3.00 = $2.00

Fixed costsUnit contribution

$200,000$2.00 per unit

=

= 100,000 units

Computing Break-Even Point

ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to break even?

a. 100,000 units

b. 40,000 units

c. 200,000 units

d. 66,667 units

Computing Break-Even Point

Use the contribution margin ratio formula to determine the amount of sales revenue ABC must have to break even. All information remains unchanged: fixed costs are $200,000; unit sales price is $5.00; and unit variable cost is $3.00.

a. $200,000

b. $300,000

c. $400,000

d. $500,000

Computing Break-Even Point

Use the contribution margin ratio formula to determine the amount of sales revenue ABC must have to break even. All information remains unchanged: fixed costs are $200,000; unit sales price is $5.00; and unit variable cost is $3.00.

a. $200,000

b. $300,000

c. $400,000

d. $500,000

Unit contribution = $5.00 - $3.00 = $2.00

Contribution margin ratio = $2.00 ÷ $5.00 = .40

Break-even revenue = $200,000 ÷ .4 = $500,000

Total costs

- Draw the total cost line with a slopeequal to the unit variable cost.

- Plot total fixed costs on the vertical axis.

Total fixed costs

Costs and Revenuein Dollars

Volume in Units

- Starting at the origin, draw the sales line with a slope equal to the unit sales price.

Sales

Total fixed costs

Costs and Revenuein Dollars

Total costs

Break-even Point

Volume in Units

- A limited range of activity called therelevant range, where CVP relationships are linear.
- Unit selling price remains constant.
- Unit variable costs remain constant.
- Total fixed costs remain constant.

- Production = sales (no inventory changes).

Exh.

22-12

Income (pretax) = Sales – Variable costs – Fixed costs

Exh.

22-13

Rydell expects to sell 1,500 units at $100 each next month. Fixed costs are $24,000 per month and the unit variable cost is $70. What amount of income should Rydell expect?

Income (pretax) = Sales – Variable costs – Fixed costs

= [1,500 units × $100]– [1,500 units × $70] – $24,000

= $21,000

Break-even formulas may be adjusted to show the sales volume needed to earnany amount of income.

Fixed costs +Target income

Unit sales =

Contribution margin per unit

Fixed costs +Target income

Dollar sales =

Contribution margin ratio

Computing Sales for a Target Income

ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to earn income of $40,000?

a. 100,000 units

b. 120,000 units

c. 80,000 units

d. 200,000 units

Unit contribution = $5.00 - $3.00 = $2.00

Fixed costs + Target income Unit contribution

$200,000 + $40,000 $2.00 per unit

= 120,000 units

Computing Sales for a Target Income

ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to earn income of $40,000?

a. 100,000 units

b. 120,000 units

c. 80,000 units

d. 200,000 units

Target netincome is income after income tax.

Exh.

22-14

Fixed Target net Incomecosts income taxes

+

+

Dollar sales =

Contribution margin ratio

To convert target net income to before-tax income, use the following formula:

Target net income

Before-tax income =

1 - tax rate

Rydell has a monthly target net income of $18,000. The unit selling price is $100. Monthly fixed costs are $24,000, the unit variable cost is $70, and the tax rate is 25 percent.

- What is Rydell’s before-tax income andincome tax expense?

Target net income

Before-tax income =

1 - tax rate

$18,000

Before-tax income = = $24,000

1 - .25

Rydell has a monthly target net income of $18,000. The unit selling price is $100. Monthly fixed costs are $24,000, the unit variable cost is $70, and the tax rate is 25 percent.

- What is Rydell’s before-tax income andincome tax expense?

Income tax = .25 × $24,000 = $6,000

Rydell has a monthly target net income of $18,000. The unit selling price is $100. Monthly fixed costs are $24,000, the unit variable cost is $70, and the tax rate is 25 percent.

- What monthly sales revenue will Rydellneed to earn the target net income?

Fixed Target net Incomecosts income taxes

+

+

Dollar sales =

Contribution margin ratio

$24,000 + $18,000 + $6,000

Dollar sales = = $160,000

30%

- What monthly sales revenue will Rydellneed to earn the target net income?

The formula for computing dollar sales may be used to compute unit sales by substituting contribution per unit in the denominator.

Fixed Target net Incomecosts income taxes

+

+

Unit sales =

Contribution margin per unit

$24,000 + $18,000 + $6,000

Unit sales = = 1,600 units

$30 per unit

Exh.

22-16

Margin of safety is the amount by which sales may decline before reaching break-even sales.

Margin of safety may be expressed as a percentage of expected sales.

Margin of safety Expected sales - Break-even sales percentage Expected sales

=

Exh.

22-17

Margin of safety Expected sales - Break-even sales percentage Expected sales

=

Exh.

22-17

If Rydell’s sales are $100,000 and break-even sales are $80,000, what is the margin of safety in dollars and as a percentage?

Margin of safety Expected sales - Break-even sales percentage Expected sales

=

Margin of safety $100,000 - $80,000 percentage $100,000

= = 20%

Exh.

22-17

If Rydell’s sales are $100,000 and break-even sales are $80,000, what is the margin of safety in dollars and as a percentage?

Margin of safety = $100,000 - $80,000 = $20,000

The basic CVP relationships may be used to analyze a number of situations such as changing sales price, changing variable cost, or changing fixed cost.

Consider the following example.

Continue

Rydell Company is considering buying a new machine that would increase monthly fixed costs from $24,000 to $30,000, but decrease unit variable costs from $70 to $60. The $100 per unit selling price would remain unchanged.

What is the new break-even point in dollars?

Revised Break-evenpoint in dollars

Revised fixed costsRevised contribution margin ratio

=

Revised Break-evenpoint in dollars

$30,00040%

=

= $75,000

Exh.

22-18

Rydell Company is considering buying a new machine that would increase monthly fixed costs from $24,000 to $30,000, but decrease unit variable costs from $70 to $60. The $100 per unit selling price would remain unchanged.

The CVP formulas may be modified for use when a company sells more than one product.

The unit contribution margin is replaced with the contribution margin for acomposite unit.

A composite unit is composed of specific numbers of each product in proportion to the productsales mix.

Sales mix is the ratio of the volumes of the various products.

Exh.

22-19

The resulting break-even formulafor composite unit sales is:

Fixed costsContribution marginper composite unit

Break-even pointin composite units

=

Consider the following example:

Continue

Hair-Today offers three cuts as shown below. Annual fixed costs are $96,000. Compute the break-even point in composite units and in number of units for each haircut at the given sales mix.

Hair-Today offers three cuts as shown below. Annual fixed costs are $96,000. Compute the break-even point in composite units and in number of units for each haircut at the given sales mix.

A 4:2:1 sales mix means that if there are 500 budget cuts, then there will be 1,000 ultra cuts, and 2,000 basic cuts.

Step 1: Compute contribution margin percomposite unit.

Step 1: Compute contribution margin percomposite unit.

Contribution margin per composite unit

Fixed costsContribution marginper composite unit

Break-even pointin composite units

=

Exh.

22-19

Step 2: Compute break-even point incomposite units.

Fixed costsContribution marginpercompositeunit

Break-even pointincompositeunits

=

$96,000$32.00 percompositeunit

Break-even pointincompositeunits

=

Exh.

22-19

Step 2: Compute break-even point incomposite units.

Break-even pointincompositeunits

= 3,000compositeunits

Step 3: Determine the number of each haircut that must be sold to break even.

Exh.

22-20

Step 4: Verify the results.

Contribution margin

Net income

= Degree of operating leverage

A measure of the extent to which fixed costsare being used in an organization.

A measure of how a percentage change in sales will affect profits.

Contribution margin

Net income

= Degree of operating leverage

$48,000

$24,000

= 2.0

If Rydell increases sales by 10percent, what will the percentageincrease in income be?

End of Chapter 22