Your boss asks

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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?
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Finally, your boss asks
How much do we make on one of
these?
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Are you going to have
the answers?
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Surprisingly, it is pretty easy to
answer these questions... If you know how.
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In fact, those who become good at this
can answer these questions in their heads.
Here is how it is done
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Here is the formula you can use to solve every
break-even problem.
SP -VC CM -FC NI
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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, and a 50
yacht might sell for 250,000.
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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.
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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.
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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, administrators salaries, and insurance.
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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.
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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.
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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 200 -VC CM -FC NI
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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 200 -VC 40 CM -FC
NI
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Step 3 Calculate the Contribution Margin on a
Per Unit Basis
The contribution margin is simply Sales Price
Variable Cost.
SP 200 -VC 40 CM
160 -FC NI
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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 200 -VC 40 CM
160 -FC 600,000 NI
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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 200 -VC 40 CM
160 -FC 600,000 NI
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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 200 -VC 40 CM
160 -FC 600,000 NI
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 .
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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 200 -VC 40 CM
160 -FC 600,000 NI 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.
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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 100 -VC 20 CM
80 -FC 600,000 NI
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.
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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.
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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. Lets 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.)
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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.
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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

12.00 Rubber for the bottom of the shoes
1.00
Shoestrings

.50 Shoe boxes

.50 Labor to make each pair of shoes

20.00 Electricity to run the shoe machines

.50 Glue to hold parts of the shoe together
.50 Sales
person commission if paid according to the
quantity sold 5.00
Total Variable Cost per pair of shoes
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.
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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
presidents salary. The president has a salary
of 100,000 per year. The presidents 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.
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The End
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SP -VC CM -FC NI