9-1 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Cost-Volume- Profit Analysis:...

9-1Copyright © 2004 by Nelson, a division of Thomson Canada Limited.

Cost-Volume-Cost-Volume-Profit Analysis: Profit Analysis: A Managerial A Managerial Planning ToolPlanning Tool

99

PowerPresentation® prepared by PowerPresentation® prepared by

David J. McConomy, Queen’s UniversityDavid J. McConomy, Queen’s University


Learning ObjectivesLearning Objectives

Determine the number of units that must be sold to break even or to earn a targeted profit.

Determine the amount of revenue required to break even or to earn a targeted profit.


Learning Objectives (continued)Learning Objectives (continued)

Apply cost-volume-profit analysis in a multiple-product setting.

Prepare a profit-volume graph and a cost-volume-profit graph and explain the meaning of each.


Learning Objectives (continued)Learning Objectives (continued)

Explain the impact of risk, uncertainty, and changing variables on cost-volume-profit analysis.

Discuss the impact of activity-based costing on cost-volume-profit analysis.


Sample Questions Raised and Sample Questions Raised and Answered by CVP AnalysisAnswered by CVP Analysis

1. How many units must be sold (or how much sales revenue must be generated) in order to break even?

2. How many units must be sold to earn a before-tax profit equal to $60,000? A before-tax profit equal to 15 percent of revenues? An after-tax profit of $48,750?

3. Will total profits increase if the unit price is increased by $2 and units sold decrease 15 percent?

4. What is the effect on total profit if advertising expenditures increase by $8,000 and sales increase from 1,600 to 1,750 units?


Sample Questions Raised and Sample Questions Raised and Answered by CVP Analysis Answered by CVP Analysis

(continued)(continued)

5. What is the effect on total profit if the selling price is decreased from $400 to $375 per unit and sales increase from 1,600 units to 1,900 units?

6. What is the effect on total profit if the selling price is decreased from $400 to $375 per unit, advertising expenditures are increased by $8,000, and sales increased from 1,600 units to 2,300 units?

7. What is the effect on total profit if the sales mix is changed?


CVP: A Short-Term Planning CVP: A Short-Term Planning and Analysis Tooland Analysis Tool

Assists in establishing prices of products.

Assists in analyzing the impact that volume has on short-term profits.

Assists in focusing on the impact that changes in costs (variable and fixed) have on profits.

Assists in analyzing how the mix of products affects profits.

Benefits of CVP:


Cost-Volume-Profit GraphCost-Volume-Profit Graph

RevenueTotal Revenue

Total Cost

Units soldX

Y

Loss

Profit

X = Break-even point in unitsY = Break-even point in revenue


Simple CVP ExampleSimple CVP Example

Fixed costs (F) = $40,000Selling price per unit (P) = $10Variable cost per unit (V) = $6Tax rate = 40%

1. What is the break-even point in units?

2. What is the break-even point in dollars?


Simple CVP Example: BEPSimple CVP Example: BEP

1. Let X = break-even point in units

Operating income = Sales revenue -Variable expenses - Fixed expenses

0 =$10X -$6X - $40,000$10X - $6X =$40,000

$4X =$40,000X =10,000 units

2. Break-even point in sales dollars is:

10,000 x $10 or $100,000

This can be shown with a variable-costing income statement.


Variable-Costing Income Variable-Costing Income StatementStatement

Sales (10,000 x $10) $100,000

Less: Variable costs (10,000 x $6) 60,000

Contribution margin $ 40,000

Less: Fixed costs 40,000

Profit before taxes $0

Less: Income taxes 0

Profit after taxes $ 0=====


Sales Revenue ApproachSales Revenue Approach

Alternative approach: break-even point in sales dollars:

Let X equal break-even sales in dollarsOperating income = Sales revenue - Variable expenses -

Fixed expenses0 = X - 0.6X - $40,000

X - 0.6X = $40,000

0.4X = $40,000

X = $100,000

Note: V is the variable cost percentage which is found by:

Variable Cost per Unit 6

Selling Price per Unit 10

= 0.6


CVP Example: CVP Example: Targeted Pretax IncomeTargeted Pretax Income

Let X = break-even point in units

Sales $ = $10XLess: Variable costs = 6XContribution margin $60,000 = $ 4XLess: Fixed costs 40,000Profit before taxes $20,000

====

What sales in units and dollars are needed to obtain atargeted profit before taxes of $20,000?

Therefore, $60,000 = $4X

15,000 units= X

Sales in dollars is (15,000 x $10) = $150,000.

Check this by completing the variable-costing income statement.


CVP Example: CVP Example: Targeted Pretax Income (continued)Targeted Pretax Income (continued)

Sales $150,000 = 15,000 x $10Less: Variable costs 90,000 = 15,000 x $6Contribution margin $ 60,000Less: Fixed costs 40,000Profit before taxes $ 20,000

=======

It checks!


CVP Analysis: CVP Analysis: Targeted After-Tax IncomeTargeted After-Tax Income

Let X = break-even point in units

Sales $ = $10X

Less: Variable costs $ = 6X

Contribution margin $ = $ 4X

Less: Fixed costs 40,000

Profit before taxes $

Less income taxes

Profit after taxes $24,000 ======

We have the same problem as PPT 9-13 assuming we are able to find the profit before taxes.

What sales in units and dollars are needed to obtain atargeted profit after taxes of $24,000?


CVP Analysis:CVP Analysis:Targeted After-Tax Income (continued)Targeted After-Tax Income (continued)

The Approach:

AFTER = Profit after taxes

BEFORE = Profit before taxes

AFTER = (1 - tax rate) x BEFORE

$24,000 = (1 - .4) x BEFORE

$24,000/.6 = BEFORE

$40,000 = BEFORE


CVP Analysis:CVP Analysis:Targeted After-Tax Income (continued)Targeted After-Tax Income (continued)

Therefore,

Sales $ = $10XLess: Variable costs = $ 6X

Contribution margin $80,000 = $ 4X

Less: Fixed costs 40,000Profit before taxes $40,000Less: Income taxes 16,000 = 40% of $40,000

Profit after taxes $24,000======

$4X = $80,000X = $80,000/$4X = 20,000 units

Sales in dollars is (20,000 x $10) or $200,000


CVP Analysis:CVP Analysis: Targeted After-Tax Income (continued)Targeted After-Tax Income (continued)

The income statement below illustrates that $200,000 in sales will give you an after-tax profit of $24,000.

Sales $200,000Less: Variable costs 120,000Contribution margin $ 80,000Less: Fixed costs 40,000Profit before taxes $ 40,000Less: Income taxes 16,000Profit after taxes $ 24,000

======


CVP Analysis:CVP Analysis: Targeted Pretax IncomeTargeted Pretax Income

Let X = sales in dollars

Sales $ = 1.0XLess: Variable costs = 0.6XContribution margin $40,000 + .2X = 0.4XLess: Fixed costs $40,000Profit before taxes .2X

What sales in dollars is needed to obtain a targeted profit before taxes equal to 20 percent of sales?

.4X = $40,000 + .2X

.2X = $40,000

X = $40,000/.2

X = $200,000


CVP Analysis: CVP Analysis: Targeted Pretax Income (continued)Targeted Pretax Income (continued)

The following variable-costing income statement can be used to check the solution.

Sales $200,000Less: Variable costs 120,000 = .6 ($200,000)Contribution margin $ 80,000 = .4 ($200,000)Less: Fixed costs 40,000Profit before taxes $ 40,000

=======

$40,000 is 20% of $200,000. It checks!


CVP Analysis:CVP Analysis: Targeted After-Tax IncomeTargeted After-Tax Income

Let X = sales in dollars

Sales $ = 1.0XLess: Variable costs = 0.6XContribution margin $ = 0.4XLess: Fixed costs 40,000Profit before taxes $ Less: Income taxesProfit after taxes $ .06X

=====

What sales in dollars is needed to obtain a targeted profit after taxes equal to 6 percent of sales?


CVP Analysis: CVP Analysis: Targeted After-Tax Income (continued)Targeted After-Tax Income (continued)

Use the method from PPT 9-16AFTER = (1- tax rate) x BEFORE

0.06X = (1 - .4) x BEFORE0.06X / 0.6 = BEFORE

0.1X = BEFORETherefore,

Sales $ = 1.0XLess: Variable costs = 0.6XContribution margin $ 40,000 + .1X = 0.4XLess: Fixed costs 40,000Profit before taxes 0.10XLess: Income taxes 0.04XProfit after taxes 0.06X

======

.4X = 40,000 + .1X

.3X = 40,000X = $40,000/.3X = $133,333


CVP Analysis:CVP Analysis:Targeted After-Tax IncomeTargeted After-Tax Income (continued)(continued)

The following income statement checks the solution:

Sales $133,333Less: Variable costs 80,000 = .6 x $133,333Contribution margin $ 53,333Less: Fixed costs 40,000Profit before taxes $ 13,333Less: Income taxes 5,333 = .4 x $13,333Profit after taxes $ 8,000

=======

$8,000 is 6% of $133,333. It Checks!


Multiple-Product ExampleMultiple-Product Example

Product P - V = CM x Mix = Total CMA $10 - $6 = $4 x 3 = $12

B 8 - 5 = 3 x 2 = 6

Total CM per package $18

===

Total fixed expenses = $180,000


Multiple-Product Example Multiple-Product Example (continued)(continued)

Break-even point:

X = Fixed cost / Unit contribution margin

= $180,000 / $18

= 10,000 packages to break even

Each package contains 3 units of A and 2 units of B. Therefore, to break even, we need to sell the following units of A and B:

A: 3 x10,000 = 30,000 units

B: 2 x10,000 = 20,000 units


Assume the following:

Regular Deluxe Total PercentUnits sold 400 200 600 ----

Sales price per unit $500 $750 ---- ----

Sales $200,000 $150,000 $350,000 100.0%

Less: Variable expenses 120,000 60,000 180,000 51.4

Contribution margin $ 80,000 $ 90,000 $170,000 48.6%

Less: Fixed expenses 130,000

Net income $ 40,000 =======

1. What is the break-even point?

2. How much sales-revenue of each product must be generated to earn a before tax profit of $50,000?

Another Multiple-Product Another Multiple-Product ExampleExample


Another Multiple-Product Another Multiple-Product Example: BEPExample: BEP

BEP = Fixed cost / CM ratio for sales mix

= $130,000 / 0.486

= $267,490 for the firm

BEP for Regular Model:

(400/600) x $267,490 = $178,327

BEP for Deluxe Model:

(200/600) x $267,490 = $89,163


Another Multiple-Product Another Multiple-Product Example: Example: Targeted RevenueTargeted Revenue

BEP = (Fixed Costs + Targeted income) / CM ratio per sales mix

= ($130,000 + $50,000) / 0.486

= $370,370 for the firm

BEP for Regular Model:

(400/600) x $370,370 = $246,913

BEP for Deluxe Model:

(200/600) x 370,370 = $123,457


Profit-Volume GraphProfit-Volume Graph

Profit I = (P-V)X-F

Slope = P-V

Profit

loss break-even point UNITS

in units

-F


The Limitations of CVP The Limitations of CVP AnalysisAnalysis

A number of limitations are commonly mentioned with respect to CVP analysis:

1. The analysis assumes a linear revenue function and a linear cost function.

2. The analysis assumes that price, total fixed costs, and unit variable costs can be accurately identified and remain constant over the relevant range.

3. The analysis assumes that what is produced is sold.

4. For multiple-product analysis, the sales mix is assumed to be known.

5. The selling prices and costs are assumed to be known with certainty.


Margin of SafetyMargin of Safety

Assume that a company has the following projected income statement:

Sales $100,000

Less: Variable expenses 60,000

Contribution margin $ 40,000

Less: Fixed expenses 30,000

Income before taxes $ 10,000=======

Break-even point in dollars (R):

R = $30,000/.4 = $75,000

Safety margin = $100,000 - $75,000 = $25,000


Degree of Operating Leverage Degree of Operating Leverage (DOL)(DOL)

DOL = $40,000/$10,000 = 4.0

Now suppose that sales are 25% higher than projected. What is the percentage change in profits?

Percentage change in profits = DOL x percentage change in sales

Percentage change in profits = 4.0 x 25% = 100%


DOL (continued)DOL (continued)

Proof:

Sales $125,000Less: Variable expenses 75,000Contribution margin $ 50,000Less: Fixed expenses 30,000Income before taxes $ 20,000

======


CVP and ABCCVP and ABC

Assume the following:Sales price per unit

$15Variable cost

5Fixed costs (conventional)

$180,000Fixed costs (ABC) 100,000 with $80,000 subject to ABC analysis

Other Data:Unit

Level ofVariableActivity

Activity Driver CostsDriver

Setups $500100

Inspections 50600

1. What is the BEP under conventional analysis?

2. What is the BEP under ABC analysis?

3. What is the BEP if setup cost could be reduced to $450 and inspection cost reduced to $40?


CVP and ABC (continued)CVP and ABC (continued)

1. Break-even units (conventional analysis)

BEP = $180,000/$10

= 18,000 units

2. Break-even units (ABC analysis)

BEP = [$100,000 + (100 x $500) + (600 x $50)]/$10

= 18,000 units

3. BEP = [$100,000 + (100 x $450) + (600 x $40)]/$10

= 16,900 units What implications does ABC have for improving performance?

9-1 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Cost-Volume- Profit Analysis:...

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