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McGraw-Hill /Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.

Cost-Volume-Profit Relationships

April 22, 2014


Agenda

n  A deeper look at Contribution Analysis n  Break even

n  Cost-Volume-Profit

n  Variable Costing and Decision Making


Basics of Cost-Volume-Profit Analysis

Contribution Margin (CM) is the amount remaining from sales revenue after variable expenses have been deducted.

Sales (500 bicycles) 250,000$ Less: Variable expenses 150,000 Contribution margin 100,000 Less: Fixed expenses 80,000 Net operating income 20,000$

Racing Bicycle CompanyContribution Income Statement

For the Month of June

The contribution income statement is helpful to managers in judging the impact on profits of changes in selling price,

cost, or volume. The emphasis is on cost behavior.


Basics of Cost-Volume-Profit Analysis

CM is used first to cover fixed expenses. Any remaining CM contributes to net operating income.

Sales (500 bicycles) 250,000$ Less: Variable expenses 150,000 Contribution margin 100,000 Less: Fixed expenses 80,000 Net operating income 20,000$




Total Per UnitSales (400 bicycles) 200,000$ 500$ Less: Variable expenses 120,000 300 Contribution margin 80,000 200$ Less: Fixed expenses 80,000 Net operating income -$



The Contribution Approach

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


CVP Relationships in Equation Form

This equation can be used to show the profit RBC earns if it sells 401. Notice, the answer of

$200 mirrors our earlier solution.

Profit = (Sales – Variable expenses) – Fixed expenses

401 units × $500 401 units × $300

$80,000

Profit = ($200,500 – $120,300) – $80,000 $200 = ($200,500 – $120,300) – $80,000


$0

$50,000

$100,000

$150,000

$200,000

$250,000

$300,000

$350,000

0 100 200 300 400 500 600

Sales

Total expenses

Fixed expenses

Preparing the CVP Graph

Break-even point (400 units or $200,000 in sales)

Units

Dol

lars

Loss Area

Profit Area


Contribution Margin Ratio (CM Ratio)

Total Per Unit CM RatioSales (500 bicycles) 250,000$ 500$ 100%Less: Variable expenses 150,000 300 60%Contribution margin 100,000 200$ 40%Less: Fixed expenses 80,000 Net operating income 20,000$



$100,000 ÷ $250,000 = 40%

The CM ratio is calculated by dividing the total contribution margin by total sales.


400 Units 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 operating income -$ 20,000$


A $50,000 increase in sales revenue results in a $20,000 increase in CM ($50,000 × 40% = $20,000).

If Racing Bicycle increases sales from 400 to 500 bikes ($50,000), contribution margin will increase by $20,000 ($50,000 × 40%).

Here is the proof:


Break-Even in Unit Sales: Equation Method

$0 = $200 × Q + $80,000

Profits = Unit CM × Q – Fixed expenses Suppose RBC wants to know how many

bikes must be sold to break-even (earn a target profit of $0).

Profits are zero at the break-even point.


Break-Even in Unit Sales: Formula Method

Let’s apply the formula method to solve for the break-even point.

Unit sales = 400

$80,000 $200 Unit sales =

Fixed expenses CM per unit = Unit sales to

break even


Contribution Analysis

n  Below is a Contribution Income Statement for the Go Fast Car Company

n  The Contribution Margin is $52 million, $4,727 per unit, or 39% n  With this analysis in place, we can test different volume scenarios

Go Fast Car CompanyContribution Income Statement

Sales $ per unit Units # 11,000 Unit Price 12,000 Sales 132,000,000 12,000 100% Less Variable Costs 80,000,000 7,273 61%

Contribution Margin 52,000,000 4,727 39%

Less Fixed Costs 38,000,000 3,455 29%Operating Income 14,000,000 1,273 11%


Calculating Break Even

n  Under a Contribution Analysis framework, calculating break-even becomes very straight forward n  Break Even Volume = Fixed Costs / Unit Contribution Margin n  Break Even Sales = Break Even Volume * Unit Sales Price

n  At sales volume of $96.5 million, Go Fast Car Co will make $0 n  For every additional sale, the company will add $4.7k to its

operating income

Go Fast Car CompanyBreak Even Calculations

Fixed Costs 38,000,000 Contribution Margin 4,727 Break Even (units) 8,038 Sales Price 12,000 Break Even (sales) 96,461,538


Target Profit: Formula Method

The formula uses the following equation.

Target profit + Fixed expenses CM per unit = Unit sales to attain

the target profit


Target Profit Analysis in Terms of Unit Sales

Suppose Racing Bicycle Company wants to know how many bikes must be sold

to earn a profit of $100,000.

Target profit + Fixed expenses CM per unit = Unit sales to attain

the target profit

Unit sales = 900

$100,000 + $80,000 $200 Unit sales =


Contribution Margin Ratio

n  The Contribution margin ration is:

n  For Go Fast Car Co n  52,000,000 / 132,000,000 = 39%

n  For every additional $1 sold, the company will see 39 cents go to Operating Income

Total CM Total sales CM Ratio =



The relationship between profit and the CM ratio can be expressed using the following equation:

Profit = (CM ratio × Sales) – Fixed expenses

Profit = (40% × $250,000) – $80,000 Profit = $100,000 – $80,000 Profit = $20,000

If Racing Bicycle increased its sales volume to 500 bikes, what would management expect profit or net

operating income to be?


Cost Structure and Profit Stability

There are advantages and disadvantages to high fixed cost (or low variable cost) and low fixed cost (or high variable

cost) structures.

An advantage of a high fixed cost structure is that income will be higher in good years

compared to companies with lower proportion of

fixed costs.

A disadvantage of a high fixed cost structure is that income

will be lower in bad years compared to companies with lower proportion of

fixed costs.

Companies with low fixed cost structures enjoy greater stability in income across good and bad years.


Operating Leverage

Operating leverage is a measure of how sensitive net operating income is to

percentage changes in sales. It is a measure, at any given level of sales, of how a

percentage change in sales volume will affect profits.

Contribution margin Net operating income

Degree of operating leverage =


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$

$100,000 $20,000 = 5

Degree of Operating Leverage

=

To illustrate, let’s look at the contribution income statement for RBC.


Operating Leverage

With an operating leverage of 5, if RBC increases its sales by 10%, net

operating income would increase by 50%.

Percent increase in sales 10%Degree of operating leverage × 5Percent increase in profits 50%

Here’s the verification!


Operating Leverage

Actual sales (500)

Increased sales (550)

Sales 250,000$ 275,000$ Less variable expenses 150,000 165,000 Contribution margin 100,000 110,000 Less fixed expenses 80,000 80,000 Net operating income 20,000$ 30,000$

10% increase in sales from $250,000 to $275,000 . . .

. . . results in a 50% increase in income from $20,000 to $30,000.


Multiple Volume Scenarios & Cost Volume Profit

n  The Variable Cost Model allows us to easily test a multitude of volume scenarios and assess the impact on income

n  What would Operating Income be at unit sales of 20,000? n  Graph the company’s CVP (X axis -$s; Y axis – units)

Go Fast Car CompanyContribution Income Statement

Sales $ Units # 6,000 8,038 11,000 Unit Price 12,000 12,000 12,000 Sales 72,000,000 96,461,538 132,000,000 100% Less Variable Costs 43,636,364 58,461,538 80,000,000 61%

Contribution Margin 28,363,636 38,000,000 52,000,000 39%

Less Fixed Costs 38,000,000 38,000,000 38,000,000 Operating Income 9,636,364-‐ -‐ 14,000,000


Assumptions and Shortcomings

n  The Contribution Model can be very helpful, but it does make a number of simplifying assumptions n  Selling price is constant n  Costs are linear n  Sales/product mix is constant n  Inventories do not change (production = sales)

n  Ultimately, reliable models will be much more detailed n  Nonetheless, and certainly within certain bounds, these

concepts are most helpful


Decision Making

n  The VP Sales wants to undertake a $3 million promotional campaign

n  How many more cars would Go Fast have to sell to justify that level of expenditure?


Decision Making

n  How many more cars would Go Fast have to sell to justify that level of expenditure?

COST OF CAMPAIGN / UNIT CONTRIBUTION ($)

= INCREMENTAL # OF UNITS REQUIRED


Decision Making

n  Analysis of how many cars would need to be sold to justify a $3 million promotional expenditure

n  In this case, if the VP Sales signed up to selling more than 635 incremental cars, the company should proceed n  The VP Sales compensation should be driven by the

success of this n  Of course, the company would only do this for substantially

more than break even

Go Fast Car CompanyAnalysis of Required Incremental SalesCost of Promotional Campaign 3,000,000 Unit Contribution Margin 4,727 Incremental Unit Sales Required 635


Decision Making

n  An economist reported that demand for Go Fast’s cars is highly elastic n  A decrease in price of 2% would increase unit sales volume

by 10% n  Would Go Fast Car Co be better off by doing this?


Decision Making

n  Analysis of a 2% decrease in price resulting in 10% increase in unit sales

n  Results in a decrease in Contribution per car, but an increase in operating income

Go Fast Car CompanyOriginal Plan Price down 2%, Sales up 10%Sales $ per unit per unit Units # 11,000 12,100 Unit Price 12,000 11,760 Sales 132,000,000 12,000 100% 142,296,000 11,760 100% Less Variable Costs 80,000,000 7,273 61% 88,000,000 7,273 62%

Contribution Margin 52,000,000 4,727 39% 54,296,000 4,487 38%

Less Fixed Costs 38,000,000 3,455 29% 38,000,000 3,140 27%Operating Income 14,000,000 1,273 11% 16,296,000 1,347 11%


Multi-Product Companies and Sales Mix

n  Analysis of a multi-product company

n  What is break-even? n  Which product would the company rather sell and why?

Go Fast Car Company

Sales $ Units # 11,000 25,000 36,000 Unit Price 12,000 5,000 Sales 132,000,000 100% 125,000,000 100% 257,000,000 100%

Less Variable Costs 80,000,000 61% 85,000,000 68% 165,000,000 64%

Contribution Margin 52,000,000 39% 40,000,000 32% 92,000,000 36%

Less Fixed Costs 53,000,000 Operating Income 39,000,000 15%

Cars Motorbikes Total



n  Break even sales = Fixed Costs/Contribution Margin n  $53 million / .36 = $147 million

n  The company would rather sell a car as they contribute more in absolute dollars and profitability

Go Fast Car Company

Sales $ Units # 11,000 25,000 36,000 Unit Price 12,000 5,000 Sales 132,000,000 100% 125,000,000 100% 257,000,000 100% Less Variable Costs 80,000,000 61% 85,000,000 68% 165,000,000 64%

Contribution Margin 52,000,000 39% 40,000,000 32% 92,000,000 36%

Less Fixed Costs 53,000,000 Operating Income 39,000,000 15%

Cars Motorbikes Total



Break even sales =

Fixed Costs/Contribution Margin


Structuring Sales Commissions

Companies generally compensate salespeople by paying them either a commission based on

sales or a salary plus a sales commission. Commissions based on sales dollars can lead to

lower profits in a company.

Let’s look at an example.



Pipeline Unlimited produces two types of surfboards, the XR7 and the Turbo. The XR7 sells for $100 and generates a contribution

margin per unit of $25. The Turbo sells for $150 and earns a contribution margin per unit of $18.

The sales force at Pipeline Unlimited is compensated based on sales commissions.

Which product would you prefer to sell if you were a salesperson?



If you were on the sales force at Pipeline, you would push hard to sell the Turbo even though the XR7

earns a higher contribution margin per unit.

To eliminate this type of conflict, commissions can be based on contribution margin rather than on selling

price alone.


Review

n  A deeper look at Contribution Analysis n  Break even

n  Cost-Volume-Profit

n  Variable Costing and Decision Making


Tutorial

n  Case Studies

n  Additional Ratios

n  Income Statement n  Trends / Growth n  Comparative Income Statement

n  Balance Sheet n  Days AR/Inventory/AP

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April 22, 2014 - UWCENTRE · Here is the proof: ... Formula Method Letʼs apply the formula method...

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