Cost Volume Profit Analysisor

Break Even AnalysisDr. R. Jayaraj, M.A., Ph.D.,

Break-Even Analysis

• Break-even analysis helps managers find the combination of costs, output, and selling price that permits the firm to break even, with no profits and losses

• Break even point is nothing but where TR is equal to TC (Zero)

Selling Price

Output Costs

Vocabulary• Gross Margin = Revenue - Cost of goods sold.

All costs are manufacturing costs. Some of them are fixed costs.

• Contribution margin = Revenue - Variable costsSome variable costs are manufacturing costs, but some may be non-manufacturing costs. None are fixed costs.

• Gross margin percent = Gross margin/Revenue

• Contribution margin percent = Contribution margin/Revenue

Safety margin:• Actual Sales volume- Breakeven sales volume

Or• Actual sales in currency- Breakeven sales in

currency

• The dollar amount by which sales revenue exceeds what is required to break even.

• The number of units by which sales exceed what is required to break even.

Your boss asks…

How many of these things do we have to sell before we start making money?

Then your boss asks…

If we sell 100,000 units, what will our profit be?

Finally, your boss asks…

How much do we make on one of these?

Are you going to have the answers?

Surprisingly, it is pretty easy to answer these questions...

If you know how.

In fact, those who become good at this can answer these questions in their heads.

Here is how it is done…

Here is the formula you can use to solve every break-even problem.

SP-VC CM-FC NI

Here is what “SP” means:

SP = Selling Price-VC CM-FC NI

Selling Price is usually stated on a per unit basis. For example, A football might sell for $25.00, a car might sell for $25,000.

“VC” means:

SP-VC = Variable Cost CM-FC NI

There will be a more detailed discussion on variable cost, but for now… variable costs are costs such as labor to build or assemble the product and the materials used in the product. They are costs that increase or decrease in proportion to how many product units are made or sold.

“CM” means:

SP-VC CM = Contribution Margin-FC NI

Selling price less the cost to make or buy the product equals the contribution margin. For example, suppose a company sells a football for $25.00 and it costs the company $15.00 to make the football. The contribution margin would be $10.00.

“FC” means:

SP-VC CM-FC = Fixed Costs NI

Fixed costs are those costs that stay the same regardless of how many products are sold or made (within a reasonable range of sales or production). Some examples may include property taxes, administrator’s salaries, and insurance.

“FC” means:

SP-VC CM-FC NI = Net Income

• Net income is simply the contribution margin minus fixed costs.

• The break-even point is when net income equals zero.

Here is specific info on how to solve these problems:

SP List selling price on a per unit basis.

-VC CM-FC NI

Most of the time you will know what a product sells for. Sometimes you might you might be told that sales are expected to be $250,000 and it is expected that sales will be 10,000 units. With that information, it is easy to find the per unit sales price. If it is impossible to determine what the per unit selling price is, do not worry. It is still possible to solve these types of problems.

Step #1: If possible, list the Selling Price (SP) on a per unit basis.

SP $200 -VC CM-FC NI

For example, suppose our company makes high-end custom running shoes. The total sales is expected to be $1,000,000 and we expect to make 5,000 shoes. The selling price per unit = $200 per pair of shoes.

Step #2: If possible, list the Variable Costs (VC) on a per unit basis.

SP $200 -VC 40 CM-FC NI

In our running shoes example, suppose the cost of materials and the labor to make the 5,000 shoes totals $200,000. That would be $40 per pair of shoes.

Step #3: Calculate the Contribution Margin on a Per Unit Basis

SP $200 -VC 40 CM 160-FC NI

The contribution margin is simply Sales Price – Variable Cost.

Step #4: Include the Total Fixed Costs in the Formula

SP $200 -VC 40 CM 160-FC 600,000 NI

Fixed costs must be listed on a grand total basis. Do not use fixed cost on a per unit basis. For example, in our custom running shoe example, the total fixed cost = $600,000

Step #5: What We Have So Far

SP $200 -VC 40 CM 160-FC 600,000 NI

Right now the numbers in the formula might look a little strange. Everything except Fixed Costs are listed on a per unit basis and so it would not make any sense to subtract $600,000 from $160. That would not tell us anything useful. However, the information in this format can tell us something very interesting: The Breakeven Point.

Step #6: Breakeven Point

SP $200 -VC 40 CM 160-FC 600,000 NI

Finding the breakeven point is simple. You need to realize that each pair of shoes sold contributes $160 towards covering fixed costs and making a profit. In order to breakeven, you just need to cover your fixed costs. Here is how you figure it out.

The breakeven point = Total fixed costs divided by the contribution margin.

$600,000 / $160 = 3,750 units

This means, that if we make 3,750 pairs of shoes, the company will just cover its fixed costs and have a net income of zero. The company will just breakeven. It is important to know that the answer is in units and not $.

How Many Do We Need to Sell to Make a $300,000 Profit?

SP $200 -VC 40 CM 160-FC 600,000 NI 300,000

This is also easy. Include the $300,000 desired profit in the formula.

Instead of just covering fixed costs, we want to make an additional $300,000. This means that we need a total of $900,000. Here is how you calculate the number of pairs of shoes that need to be sold.

$900,000 / $160 = 5,625 units

If the company can sell 5,625 units, it will make a profit of $300,000.

Other Ways of Saying the Same Thing

SP 100% -VC 20% CM 80%-FC 600,000 NI

Sometimes a problem might specify percentages rather than dollars. If that is the case, Selling Price is always listed as 100%.

Everything still works the same. If you want to find the breakeven point, just divide fixed costs be the Contribution Margin.

$600,000 / 80% (80/100= 0.8) = $750,000

This time the breakeven point is listed in $ and not units.

Other Ways of Saying the Same Thing

SP $400 -VC 30%CM ? -FC NI

Sometimes problems will be given in a combination of dollars and percentages. Usually the problems are still easy to figure out. For example, from the information given, can you figure out the contribution amount in either % or $?

If the Variable Costs are 30%, the Contribution Margin will be 70%. It all needs to add up to 100%. Also, the Variable costs are 30% of the Selling Price and so variable costs = $120. The Contribution Margin must equal $280. From there it is simple to find the breakeven point.

Break-Even Analysis

Costs/Revenue

Output/Sales

Initially a firm will incur fixed costs, these do not depend on output or sales.

FC

As output is generated, the firm will incur variable costs – these vary directly with the amount produced

VC

The total costs therefore (assuming accurate forecasts!) is the sum of FC+VC

TCTotal revenue is determined by the price charged and the quantity sold – again this will be determined by expected forecast sales initially.

TR The lower the price, the less steep the total revenue curve.

TR

Q1

The Break-even point occurs where total revenue equals total costs – the firm, in this example would have to sell Q1 to generate sufficient revenue to cover its costs.

Break-Even AnalysisCosts/Revenue

Output/Sales

FC

VCTCTR (p = £2)

Q1

If the firm chose to set price higher than £2 (say £3) the TR curve would be steeper – they would not have to sell as many units to break even

TR (p = £3)

Q2

Break-Even AnalysisCosts/Revenue

Output/Sales

FC

VCTCTR (p = £2)

Q1

If the firm chose to set prices lower (say £1) it would need to sell more units before covering its costs

TR (p = £1)

Q3

Break-Even AnalysisCosts/Revenue

Output/Sales

FC

VC

TCTR (p = £2)

Q1

Loss

Profit

Break-Even AnalysisCosts/Revenue

Output/Sales

FC

VC

TCTR (p = £2)

Q1 Q2

Assume current sales at Q2

Margin of Safety

Margin of safety shows how far sales can fall before losses made. If Q1 = 1000 and Q2 = 1800, sales could fall by 800 units before a loss would be made

TR (p = £3)

Q3

A higher price would lower the break even point and the margin of safety would widen

Costs/Revenue

Output/Sales

FC

VC

TR

Eurotunnel’s problem

High initial FC. Interest on debt rises each year – FC rise therefore

FC 1

Losses get bigger!

Break-Even Analysis• Remember:• A higher price or lower price does not mean that break even

will never be reached! • The BE point depends on the number of sales needed to

generate revenue to cover costs – the BE chart is NOT time related!

Break-Even Analysis

• Importance of Price Elasticity of Demand:• Higher prices might mean fewer sales to break-

even but those sales may take a longer time to achieve.

• Lower prices might encourage more customers but higher volume needed before sufficient revenue generated to break-even

Break-Even Analysis

Links of BE to pricing strategies and elasticity• Penetration pricing – ‘high’ volume, ‘low’ price –

more sales to break even• Market Skimming – ‘high’ price ‘low’ volumes –

fewer sales to break even• Elasticity – what is likely to happen to sales when

prices are increased or decreased?

Thanks