Your boss asks…
How many of these things do
we have to sell before
we start making money?
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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
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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, and a 50’ yacht might sell for
$250,000.
“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
-VC
CM
-FC
NI
List selling price on a per unit basis.
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.
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.
SP
-VC
CM
-FC
NI
$200
Step #2: If possible, list the Variable Costs (VC) on a per
unit basis.
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.
SP
-VC
CM
-FC
NI
$200
40
Step #3: Calculate the Contribution Margin on a Per Unit
Basis
The contribution margin is simply Sales Price – Variable Cost.
SP
-VC
CM
-FC
NI
$200
40
160
Step #4: Include the Total Fixed Costs in the Formula
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
SP
-VC
CM
-FC
NI
$200
40
160
600,000
Step #5: What We Have So Far
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.
SP
-VC
CM
-FC
NI
$200
40
160
600,000
Step #6: Breakeven Point
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.
SP
-VC
CM
-FC
NI
$200
40
160
600,000
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?
This is also easy. Include the $300,000 desired profit in the formula.
SP
-VC
CM
-FC
NI
$200
40
160
600,000
300,000
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
Sometimes a problem might specify percentages rather than dollars. If that is
the case, Selling Price is always listed as 100%.
SP
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CM
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NI
100%
20%
80%
600,000
Everything still works the same. If you want to find the breakeven point, just
divide fixed costs be the Contribution Margin.
$600,000 / 80%
=
$750,000
This time the breakeven point is listed in $ and not units.
Other Ways of Saying the Same Thing
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 $?
SP $400
-VC
30%
CM
?
-FC
NI
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.
A closer Look At Variable Costs
As you can see, the math is simple. The tricky part for students is
recognizing variable costs. Once you see how to do it, it is pretty simple.
The Key: If a cost goes up proportionally with increased sales or
production, the cost is probably a variable cost. Of course the opposite is
true also. Costs that go down proportionally with decreased sales or
production are also probably variable costs.
Let’s take the custom running shoe as an example. As more running shoes
are made and sold the following costs are going to go up…
Leather and fabric
Rubber for the bottom of the shoes
Shoestrings
Shoe boxes
Labor to make the shoes
Electricity to run the shoe machines
Glue to hold parts of the shoe together
Sales person commission if paid according to the quantity sold
Etc. (You might be able to think of more variable costs.)
Variable Costs on a per Unit Basis
In order to solve breakeven problems, you need to be able to recognize
variable costs and then be able to assign variable costs on a per unit basis.
For example: if a business plans on spending $60,000 on shoe leather and
fabric, and at the same time, plans to make 5,000 shoes, the cost of shoe
leather and fabric would = $12 per shoe. Getting the variable cost on a per
unit basis is important. That is how the formula in all of the previous
slides works.
Adding Up Variable Costs
So now you know that shoe leather and fabric is $12 per shoe. For each
variable cost you need to find the variable cost per unit and then add up
them up for a grand total. (each cost is per pair of shoes basis)
Leather and fabric
Rubber for the bottom of the shoes
Shoestrings
Shoe boxes
Labor to make each pair of shoes
Electricity to run the shoe machines
Glue to hold parts of the shoe together
Sales person commission if paid according to the quantity sold
Total Variable Cost per pair of shoes
$12.00
1.00
.50
.50
20.00
.50
.50
5.00
$40.00
You would use $40 as “VC” in the formula to find the breakeven point.
Just as we have been doing in the previous examples.
A Fixation on Fixed Costs
Fixed costs remain relatively unchanged as sales and production increases
or decreases. For example: the custom running shoe factory produces
between 4,000 and 8,000 shoes a year. This range is the normal operating
range of the factory.
As for fixed costs, take property taxes on the factory building. Each year
the property taxes are $5,000. It does not matter if production is slow or
fast. The property taxes remain the same (fixed).
Another example might be the president’s salary. The president has a
salary of $100,000 per year. The president’s salary is set by the board of
directors and does not change as production changes.
Any cost that does not change as sales and production increases or
decreases, is called a fixed cost. A fixed cost should stay relatively the
same as long as the business is operating in its normal operating range.
Make sure you find the Total Fixed Costs and not the fixed cost per unit.
In order to make the formula work correctly, you need to have a grand
total of fixed costs. The total fixed costs is usually a pretty big number.
The End
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SP
-VC
CM
-FC
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