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C H A P T E R . 2. Analyzing Cost-Volume- Profit Relationships. CVP - What Questions Does It Answer?. What happens to profits if we change our selling price?. What happens to profits if we change the number of units sold?. How many units do we need to sell to break even?.

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## C H A P T E R

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C H A P T E R

2

Analyzing Cost-Volume-

Profit Relationships

CVP - What Questions Does It Answer?
• What happens to profits if we change our selling price?
• What happens to profits if we change the number of units sold?
• How many units do we need to sell to break even?
• How much sales revenue do we need to meet our pretax profit goal?
• What happens to profits if we change our advertising expenses?
• What happens to profits if we discontinue certain products?
CVP Key Variables
• Revenues– Price x Quantity
• Fixed costs– Independent of volume
• Variable costs– Dependent upon volume
• Volume– Level of activity
• Product mix– Different products
• Efficiency & quality of production
• Combinations of above
What are Variable Costs?

Costs that change in total in direct proportion to changes in activity level.

Unit Cost: Constant

Total Cost: Varies

Total Cost

Units Produced

Define Relevant Range and Curvilinear Costs

Relevant range:

The range of operating level, or volume of activity, over which the relationship between total costs (variable + fixed) and activity level is approximately linear.

Curvilinear costs:Variable costs that do not vary in direct proportion to changes in activity level but vary at decreasing or increasing rates due to economies of scale, productivity changes, and so on.

Define Fixed Costs

Costs that remain constant in total, regardless of activity level, at least over a certain range of activity.

Unit Cost: Varies

Total Cost: Constant

Total

Cost

UnitsProduced

Total fixed costs

(Sales price per unit - Variable cost per unit)

Fixed Costs are Used to Calculate Break-Even
• What does break-even mean?
• Break-even is the point where revenues equal all costs, neither profit nor loss is incurred.
• What is the formula for break-even?

Stepped costs change in total in a stair-step fashion (in large amounts) with changes in volume of activity.

Relevant Range

Cost

Over the relevant range, stepped costs may appear to be fixed.

Production Volume

Define Stepped Costs

Mixed costs contain both variable and fixed cost components.

For Example: A leased machine might cost \$1,000 per month (fixed) plus \$20 per hour of usage (variable).

Variable

Cost

Fixed

Production Volume

Define Mixed Costs

Regression Line

What is the Scattergraph (Visual-Fit) Method?

A method of segregating the fixed and variable components of a mixed cost by plotting on a graph total costs at several activity levels and drawing a regression line through the points.

Cost

Volume of Activity

Variable costs per unit are equal to the slope of the regression line.

Variable Costs

Scattergraph (Visual-Fit)

Fixed costs are represented by the intersection of the regression line and the vertical axis.

Cost

Fixed Costs

Volume of Activity

Define the High-Low Method

A method of segregating the fixed and variable components of a mixed cost by analyzing the costs at the highest and lowest activity levels within a relevant range.

Step 1:Identify the highest and lowest activity levels.

High-Low Method

Cost

Volume of Activity

High-Low Method

Cost

Volume of Activity

Step 3: Calculate the variable cost per unit by finding the slope of the regression line between the two points (which reflect total mixed costs).

High-Low Method

Cost

Variable Cost

per Unit

Rise

=

Run

Volume of Activity

Contribution Margin Approach

Contribution margin is the portion of sales revenue available to cover fixed costs and provide a profit.

Sales revenue

– Variable costs

= Contribution margin

– Fixed costs

= Profit

Total

Sales revenue \$1,000,000

Less variable costs 400,000

Contribution margin \$ 600,000

Contribution Margin Approach
• If a computer sells for \$2,000 with variable costs of \$800 per computer and fixed costs of \$350,000 per year:
• What is the total contribution margin on 500 computers?
Contribution Margin Approach
• If a computer sells for \$2,000 with variable costs of \$800 per computer and fixed costs of \$350,000 per year:
• What is the total contribution margin on 500 computers?
• What is the contribution margin per unit?

TotalPer Unit

Sales revenue \$1,000,000 \$2,000

Less variable costs 400,000 800 Contribution margin \$ 600,000\$1,200

Contribution Margin Approach
• If a computer sells for \$2,000 with variable costs of \$800 per computer and fixed costs of \$350,000 per year:
• What is the total contribution margin on 500 computers?
• What is the contribution margin per unit?
• What is the contribution margin ratio?

Total Per Unit Ratio

Sales revenue \$1,000,000 \$2,000 100%

Less variable costs 400,000 800 40%

Contribution margin \$ 600,000 \$1,200 60%

Total Per Unit Ratio

Sales revenue \$1,000,000 \$2,000 100%

Less variable costs 400,000 800 40%

Contribution margin \$ 600,000 \$1,200 60%

Less fixed costs 350,000

Profit \$ 250,000

Contribution Margin Approach

If a computer sells for \$2,000 with \$800 variable costs per computer and \$350,000 fixed costs per year:

• What is the total contribution margin on 500 computers?
• What is the contribution margin per unit?
• What is the contribution margin ratio?
• What is the total dollar profit after one year?

Sales price

x units

Variable cost

x units

Independent

of units

Target

Income

\$2,000(x) - \$800(x) - \$350,000 = 0

1,200(x) - \$350,000 = 0

1,200(x) = 350,000

x = 292 computers

The Break-Even Point

Example: How many computers will the store have to sell in order to break even if one computer sells for \$2,000, costs \$800 to make (variable cost), and fixed costs are \$350,000?

Multiple Variable Changes

Costs

independent

of units

Sales price

x units

Variable cost

x units

Zero for

break-even

OR

OR

etc.

Target Income = Revenue - variable - fixed

X = \$1,700(500) - \$700(500) - \$325,000

X = \$850,000 - \$350,000 - \$325,000

X = \$175,000 or a 30% decrease in profit

Multiple Variable Changes

Assume prior year profits of \$250,000 for The Store.

What if this year the price of our \$2,000 computers is reduced by 15 percent due to a decrease in variable costs from \$800 to \$700 per computer and a decrease in fixed costs from \$350,000 to \$325,000? What would be the effect on target income (or profit) assuming the production of 500 computers?

Revenue Line

Break-Even Point

Revenue

& Cost

\$584,000

Total Cost Line

Fixed Costs

(\$350,000)

292

Number of Computers Sold

The Graphic ApproachIdentify the Break-Even Point, Revenue Line, Total Cost Line, and Fixed Costs
What are the Limiting Assumptionsof C-V-P Analysis?
• The behavior of revenues and costs is linear throughout the relevant range.
• All costs can be categorized as either fixed or variable.
• Sales mix does not change.

If a change in quality or production time either increases cost or decreases production speed, careful consideration should be given to the change.

How Do Quality & Time Affect C-V-P Decisions?
• Change in Quality:
• - Will it increase cost?
• - Will it decrease production speed?
• Change in Production Time:
• - Will it increase cost?
• - Will it decrease production speed?
Expanded MaterialLearning Objective 8
• Explain the effects of sales mix on profitability.

Can Openers Microwaves Total

Amount % Amount % Amount %

=

=

Product Revenue

Total Revenue

5,000

30,000

17%

Sales Mix

Sales revenue \$5,000 100% \$25,000 100% \$30,000 100%

Less variable costs 3,000 60% 20,000 80% 23,000 77%

Contribution margin \$2,000 40% \$ 5,000 20% \$ 7,000 23%

Sales mix 17% 83% 100%

Sales Mix

To maximize profit in a company with multiple products, management should emphasize products with the highest contribution margin ratio. Which product should they choose?

Can Openers Microwaves Total

Amount % Amount % Amount %

Sales revenue \$5,000 100% \$25,000 100% \$30,000 100%

Less variable costs 3,000 60% 20,000 80% 23,000 77%

Contribution margin \$2,000 40% \$ 5,000 20% \$ 7,000 23%

Sales mix 17% 83% 100%

Expanded MaterialLearning Objective 9
• Describe how fixed and variable costs differ in manufacturing, service, merchandising, and e-commerce organizations, and illustrate these differences with the operating leverage concept.

The extent to which fixed costs are part of a company’s cost structure.

• The higher the proportion of fixed costs to variable costs, the faster income increases or decreases with sales volume.

Contribution

Margin

Net

Income

Operating

Leverage

Define Operating Leverage

Operating Leverage

For example: Assume the following data.

Total Per Unit Ratio

Sales revenue \$1,000,000 \$2,000 100%

Less variable costs 400,000 800 40%

Contribution margin \$ 600,000 \$1,200 60%

Less fixed costs 450,000

Net income \$ 150,000

• What is the operating leverage?

Operating leverage = 2.4

• What happens to net income if sales are increased by 20 percent?

Net income increases 48%

• Increase fixed costs to \$450,000. What is the operating leverage (no sales increase)?

Operating leverage = 4

• Now what happens to net income if sales are increased by 20 percent?

Net income increases 80%