Cost-Volume-Profit Relationships

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Cost-Volume-Profit Relationships

• UAA ACCT 202 Principles of Managerial
  Accounting Dr. Fred Barbee

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Introduction

• We have learned . . .
• How to identify costs as fixed, variable, and
  mixed
• How each of these behave when changes take place
  and
• How to separate them into their component parts.

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Introduction

• Understanding these relationships help managers
  to
• Predict future conditions (planning) and
• Explain, evaluate, and act on past results
  (control)

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Introduction

• Today we will focus on gaining an understanding
  of how . . .
• Costs
• Volume, and
• Profits
• Interact

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Cost-Volume-Profit (CVP)

• CVP is the systematic examination of the
  relationships among . . .
• Selling prices,
• Volume of Sales and Production
• Cost,
• Expenses, and
• Profits

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What happens here?
As changes occur here.
Graphically
Total Revenues
Total Revenue
Output
Sales Price
Total Cost
Total Cost
Variable Costs
Operating Income
Operating Income
Fixed Costs
4
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CVP - For-Profit Firms

• How many photocopies must the College Avenue Copy
  Shop produce to earn a profit of 20,000?
• At what sales volume will Burger Kings total
  costs and total revenues equal?

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CVP - For-Profit Firms

• What will happen to profits in Joes Diner if . .
  .
• There is a 20 increase in the cost of food and
• A 10 increase in the selling price of meals?

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CVP - Not-For-Profit Firms

• How many meals can the Salvation Army serve with
  an annual budget of 150,000?
• How many tickets must be sold for the benefit
  concert to raise 15,000?

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CVP is Useful in . . .

• Choice of product lines
• Pricing of products
• Developing marketing strategies
• Utilization of productive facilities

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Traditional Statement

• Costs are grouped by functional classifications -
  such as
• Production,
• Selling Administration
• With both fixed and variable costs being included
  in each category.

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Absorption-Costing I/S
Production FC VC
Selling FC VC
Administrative FC VC
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Contribution Format

• The focus of the contribution format income
  statement is the contribution margin . . .

Contribution Margin Net Sales -
Variable Costs
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Contribution Format I/S

• Groups costs by behavior
• Fixed, and
• Variable
• Rather than into the functional categories of
  production, marketing and administration.

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Variable-Costing I/S
Variable Costs
(xx)
Fixed Costs
(xx)
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Income Statements . . .
Traditional
Contribution Format
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Sourdough Alaska, Inc.
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Sourdough Alaska, Inc. Traditional Income
Statement For Year Ended December 31, 2002
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What if . . .

• You were asked to project the effect on net
  income of
• A 20 increase in sales volume
• With no change in selling prices.
• How would you go about doing it?

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Sourdough Alaska, Inc. Contribution Format Income
Statement For Year Ended December 31, 2002
Net Income
290,000
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NOW . . . What if . . .

• You were asked to project the effect on net
  income of
• A 20 increase in sales volume
• With no change in selling prices.
• How would you go about doing it?

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Sourdough Alaska, Inc. Projected Increase in Net
Income For Year Ended December 31, 2002
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Breakeven Analysis
2

• Can be computed two ways
• The equation method
• The contribution margin method

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Breakeven Analysis
2

• Can be computed in two forms

• Number of units required to break even or
• Sales dollars required to break even.

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The Equation Method

• Exhaustion Unlimited An Illustration

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Exhaustion Unlimited

• Exhaustion Unlimited makes and distributes high
  end exercise equipment.
• One of their best selling products is an exercise
  bike Model IMATRD-1

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Exhaustion Unlimited Info
Per Bike Percent
SP 500 100
VC 300 60
CM 200 40
Fixed Costs 80,000 Fixed Costs 80,000 Fixed Costs 80,000
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• The equation method centers on the contribution
  approach to the income statement.

Sales xxx
Variable Costs (xx)
Contribution Margin xxx
Fixed Costs (xx)
Net Operating Income xxx
Profit Sales - VC - FC
Sales Profit VC FC
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Sales Profit VC FC

• At breakeven profit 0

Sales Profit VC FC

• The equation becomes

BES VC FC
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• Use our BE Equation and
• Let X BE Point in Bikes

Sales VC FC
Sales
FC
VC
500X 300X 80,000
200X 80,000
X 400 Bikes
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• Use our BE Equation and
• Let X BE Point in Sales

Sales VC FC
Sales
FC
VC
1X .6X 80,000
.4X 80,000
X 200,000
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Exhaustion Unlimited Income Statement For Year Ended 12/31/01 Exhaustion Unlimited Income Statement For Year Ended 12/31/01
Sales (400 x 500) 200,000
VC (400 x 300) 120,000
CM 80,000
FC 80,000
Net Income -0-
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The Unit Contribution Method

• Exhaustion Unlimited An Illustration

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Unit-Contribution Method

• Is a variation of the equation method.
• The method may be just a bit more intuitive than
  the equation method.

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Unit-Contribution Method

• The approach centers on the idea that each unit
  sold provides a certain amount of CM that goes
  toward covering fixed costs.

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Unit-Contribution Method

• The Formula . . .

Fixed Expenses BEP
Unit Contribution Margin BEP
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Fixed Costs
BEP in Units
Unit CM
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Fixed Costs
BEP in
CM
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Unit Contribution Method

• Lets look at a series of income statements that
  graphically point out the concept of a
  contribution margin.

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Exhaustion Unlimited Income Statement Exhaustion Unlimited Income Statement Exhaustion Unlimited Income Statement Exhaustion Unlimited Income Statement Exhaustion Unlimited Income Statement
1 Bike 2 Bikes 400 Bikes 401 Bikes
Sales 500 1,000 200,000 200,500
VC 300 600 120,000 120,300
CM 200 400 80,000 80,200
FC 80,000 80,000 80,000 80,000
NI (79,800) (79,600) -0- 200
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Break-Even Analysis

• Target Net Profit Analysis

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Target Net Profit Analysis

• A firms targeted NI is the amount of income the
  firm wishes to make . . .
• Pre-Tax OI or
• After-Tax NI

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Target Net Profit Analysis

• Recall the BE formula

Sales FC VC Profits
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Target Net Profit Analysis

• Using data from Exhaustion Unlimited.
• Assume the firm wants to make a before-tax profit
  of 40,000.

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Exhaustion Unlimited Info
Per Bike Percent
SP 500 100
VC 300 60
CM 200 40
Fixed Costs 80,000 Fixed Costs 80,000 Fixed Costs 80,000
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• Use our BE Equation and
• Let X BE Point in Bikes

Sales VC FC Profits
Sales
FC
VC
500X 300X 80,000 40,000
Desired Profit
200X 120,000
X 600 Bikes
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• Use our BE Equation and
• Let X BE Point in Sales

Sales VC FC Profits
Sales
FC
VC
1X .6X 80,000 40,000
Desired Profit
.4X 12,000
X 300,000
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Exhaustion Unlimited Income Statement For Year Ended 12/31/01 Exhaustion Unlimited Income Statement For Year Ended 12/31/01
Sales (600 x 500) 300,000
VC (600 x 300) 180,000
CM 120,000
FC 80,000
Net Income 40,000
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Target Before-Tax Profit Analysis

• The Unit Contribution Method

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Unit-Contribution Method

• The Formula . . .

Add Targeted Before-Tax OI (TI) to the Fixed
Expenses
Add Targeted Before-Tax OI (TI) to the Fixed
Expenses
Fixed Expenses BEP
Unit Contribution Margin BEP
Fixed Expenses TI BEP
Unit Contribution Margin BEP
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Desired BT OI (TI)
Fixed Costs
BEP in Units
Unit CM
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Desired BT OI
Fixed Costs
BEP in
CM
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Target Net Profit Analysis

• What About Taxes?

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• At breakeven profit 0

Remember this?
Sales Profit VC FC

• The equation becomes

BES VC FC
Sales Profit VC FC
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Tax Effects . . .
NI OI - Taxes
OI - (TR x OI)
OI(1 - TR)
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This, then, is our handy-dandy formula to
calculate an after-tax net income (ATNI).
Net Income OI ------------------
(1 TR)
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Target Net Profit Analysis

• Back to Exhaustion Unlimited
• Assume management wants 40,000 after taxes
• Tax Rate 30

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Sales VC FC ATNI
Sales
FC
VC
Targeted ATNI
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Sales VC FC ATNI
Bikes
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Bikes
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Limiting Assumptions

• CVP assumes a linear revenue and cost function.
• CVP analysis assumes a relevant range.
• CVP assumes that production equals sales.

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Limiting Assumptions

• Sales mix remains constant.
• Sales prices and costs are known with certainty.