Cost-Volume-Profit Analysis

The Contribution Format

Used primarily forexternal reporting.

Used primarily bymanagement.

Total Per UnitSales (500 bicycles) 250,000$ 500$ Less: variable expenses 150,000 300 Contribution margin 100,000 200$

Less: fixed expenses 80,000 Operating income 20,000$

Racing Bicycle CompanyContribution Income Statement

For the Month of June

Total Per Unit PercentSales (500 bicycles) 250,000$ 500$ 100%Less: variable expenses 150,000 300 60%Contribution margin 100,000$ 200$ 40%

Less: fixed expenses 80,000 Operating Income 20,000$

Contribution-Margin Ratio

Sales revenue, variable expenses and contribution for Racing Bicycles can be expressed as a percentage of sales

Contribution Margin Method

The contribution margin method has two key equations.

Fixed expensesCM per unit

=Break-even point

in units sold

Fixed expenses CM ratio

=Break-even point in

total sales dollars

-

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

450,000

- 100 200 300 400 500 600 700 800

CVP Graph

Fixed expenses

Units

Dol

lars Total Expenses

Total Sales

-

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

450,000

- 100 200 300 400 500 600 700 800

Units

Dol

larsCVP Graph

Break-even point

Profit Area

Loss Area

Break-even Reduction

Racing Bicycles is currently selling 500 bicycles per month. Break-even units are 400 per month under the current cost structure.

What would be the break-even units if fixed costs decrease to $70,000?

What would be the break-even units if variable costs were reduced to $250?

What would be the break-even units if selling price was increased to $513.33?

Target Operating Profit Analysis

The equation and contribution margin methods can be used to determine the sales volume

needed to achieve a target profit.

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

earn a profit of $100,000.

The Contribution Margin Approach

The contribution margin method can be used to determine that 900 bikes must be sold to earn

the target operating profit of $100,000.

Fixed expenses + Target profit CM per unit

=Unit sales to attain

the target profit

$80,000 + $100,000 $200/bike

= 900 bikes

Net income = Operating profit – Income taxes

= Operating profit – (Tax rate x Operating profit)

After-Tax Profit TargetsAfter-Tax Profit TargetsAfter-Tax Profit TargetsAfter-Tax Profit Targets

= Operating profit (1 – Tax rate)

Or

Operating profit =Net income

(1 – Tax rate)

After-Tax Profit TargetsAfter-Tax Profit TargetsAfter-Tax Profit TargetsAfter-Tax Profit Targets

Fisher Company has a selling price of $40 for its only product. Variable cost per unit is $24, and fixed costs are $800,000 for the year. The Company wants

to achieve an annual net income (after taxes) of $487,500. How many units must it sell if its income

tax rate is 35 percent.

Changes in Fixed Costs and Sales Volume

What is the profit impact if Racing can increase unit sales from 500 to 540 by

increasing the monthly advertising budget by $10,000?

Change in Variable Costs and Sales Volume

What is the profit impact if Racing can use higher quality raw materials, thus increasing variable costs per unit by $10, to generate an

increase in unit sales from 500 to 580?

Change in Fixed Cost, Sales Price and Volume

What is the profit impact if Racing (1) cuts its selling price $20 per unit, (2) increases its

advertising budget by $15,000 per month, and (3) increases sales from 500 to 650 units per

month?

Change in Variable Cost, Fixed Cost and Sales Volume

What is the profit impact if Racing (1) pays a $15 sales commission per bike sold instead of paying salespersons flat salaries that currently total $6,000 per month, and (2) increases unit

sales from 500 to 575 bikes?

Change in Regular Sales Price

If Racing has an opportunity to sell 150 bikes to a wholesaler without disturbing sales to other

customers or fixed expenses, what price would it quote to the wholesaler if it wants to increase

monthly profits by $3,000?

The Margin of Safety

The margin of safety is the excess of actual (or budgeted) sales over the break-even volume

of sales.

Margin of safety = Total sales - Break-even salesMargin of safety = Total sales - Break-even sales

Let’s look at Racing Bicycle Company and determine the margin of safety.

The Margin of Safety

If we assume that Racing Bicycle Company has actual sales of $250,000, given that we have already determined the break-even sales to be $200,000, the margin of safety is

$50,000 as shown.

Break-even sales

400 unitsActual sales

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$

Break-even sales

400 unitsActual sales

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$

The Margin of Safety

The margin of safety can be expressed as 20% of sales.

($50,000 ÷ $250,000)

Break-even sales

400 unitsActual sales

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$

Break-even sales

400 unitsActual sales

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$

The Margin of Safety

The margin of safety can be expressed in terms of the number of units sold. The margin of safety at Racing is $50,000, and each bike sells for

$500.

Margin ofSafety in units = = 100 bikes

$50,000$500

Cost Structure and Profit Stability

Cost structure refers to the relative proportion of fixed and variable costs in an organization.

Managers often have some latitude in determining their organization’s cost structure.

Cost Structure and Profitability

Alpha Beta Gamma

Amount % Amount % Amount %

Sales $800,000 100% $800,000 100% $800,000 100%

Variable Expenses

400,000 50% 300,000 37.5% 200,000 25%

Contribution Margin

400,000 50% 500,000 62.5% 600,000 75%

Fixed Expenses

300,000 400,000 500,000

Op. Income $ 100,000 $ 100,000 $ 100,000

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 fixedcost structure is that incomewill be higher in good years

compared to companieswith lower proportion of

fixed costs.

An advantage of a high fixedcost structure is that incomewill be higher in good years

compared to companieswith lower proportion of

fixed costs.

A disadvantage of a high fixedcost structure is that incomewill be lower in bad yearscompared to companieswith lower proportion of

fixed costs.

A disadvantage of a high fixedcost structure is that incomewill be lower in bad yearscompared to companieswith lower proportion of

fixed costs.

Definition of Operating Leverage

The relative mix of a firm’s fixed and variable costs determines its operating leverage.

At a given level of sales: Degree of operating = Contribution Margin leverage Operating Income

The higher a firm’s fixed cost as compared to its variable cost, the greater its operating leverage.

Operating leverage acts like a multiplier. The greater the operating leverage, the greater the change in operating income for a given change in sales.

Let’s calculate the operating leverage for each firm.

Application of Operating Leverage

At a given level of sales, the operating leverage is a measure of how a given percentage change in sales will affect operating profits.

In fact, the operating profit will increase by the operating leverage times the percentage change in sales.

For a 10% increase in sales , Firm Alpha’s operating income increased 40% (4 times 10%).

For a 10% increase in sales , Firm Beta’s operating income increased 50% (5 times 10%).

For a 10% increase in sales , Firm Gamma’s operating income increased 60% (6 times 10%).

The Concept of Sales Mix

Sales mix is the relative proportion in which a company’s products are sold.

Different products have different selling prices, cost structures, and contribution margins.

Break-even Analysis (in Units) with Multiple Products

Curl Company provides us with the following information:

Fixed cost is $120,000. What is the break-even point in units? What are the sales of Surfboards and Sailboards at the break-even point?

Break-even Analysis (in Sales Dollars) with Multiple Products

Curl’s Contribution Margin income statement is shown below:

Surfboards Sailboards TotalSales 300,000$ 100% 150,000$ 100% 450,000$ 100.0%Var. exp. 210,000 70% 90,000 60% 300,000 66.7%Contrib. margin 90,000$ 30% 60,000$ 40% 150,000 33.3%

Fixed exp. 120,000 Operating income 30,000$

Sales mix 300,000$ 67% 150,000$ 33% 450,000$ 100.0%

$150,000 $450,000

= 33.3%

What is the break-even point in Sales? What are the sales of Surfboards and

Sailboards at the break-even point?