In this brief video, we discuss cost-volume-profit analysis with examples.
That is, how the cost of production and volume (or quantity) relate to profit.
In particular we discuss the special case where no profit or loss is made which we refer
to as Break-Even.
The break-even point refers to the minimum quantity of a product to sell without generating
a loss.
Or how much sales are required before a business starts making profit.
So, at break-even point, total revenue equals total cost.
In theory, the Total Cost is divided mainly into
Fixed Costs and Variable Costs
Fixed Costs are assumed to remain the same irrespective of the volume of production over
a period of time.
Examples are Rent, Property Tax, and Insurance
It does not matter the quantity of output; these fixed costs remain the same.
Variable Cost on the other hand changes as the volume of output changes.
They are directly proportional to the level of activity or volume of production.
That is, the more the units of output, the higher the total variable cost.
If the variable cost per unit of an item is $3 and 10 units of that item is produced,
then the total variable cost will be $3 times 10.
That is, $30.
That is, total variable cost equals variable cost per unit times the number of units produced,
which we denote here as x.
Examples of variable costs are cost of materials, shipping costs, and credit card fees.
These costs increase with increases in output.
We can now put the formula for Total Cost as the sum of the Fixed Cost and Total Variable
Cost.
Now, Total Revenue is selling price per unit times the number of items sold.
Note that Selling Price per unit is sometimes denoted simply as S or P and the number of
units as Q.
Another important concept in Cost-volume profit analysis is
The Contribution margin per unit: This is the simply the amount by which the
selling price per unit exceeds the variable cost per unit
So, if a smartwatch that sells for $60 has variable costs of $20, the contribution margin
per unit is simply $60 minus $20 which is $40.
Now at break even point, total revenue equals total cost.
That is, selling price per unit, times number of units, equals Fixed Cost, plus Variable
Cost, times number of units.
On solving for x, we have a formula for Break-Even in units which is simply Fixed Cost divided
by Contribution margin.
Finally, we have the Contribution rate or ratio which expresses the contribution margin
as a ratio (or percentage) of the selling price.
We can use it to determine the break-even dollars.
That is, the total cost or total revenue at break-even.
And that can be determined by dividing the Fixed Cost by Contribution ratio.
Now let’s look at some examples.
Here we want to determine the break-even point in units and in dollars.
Note that there are 2 variable costs here: production cost and selling cost.
We first combine them so we have a total variable cost function of15x.
The total cost function is therefore 4000 (the fixed cost) plus 15x (the total variable
cost).
From the selling price per unit of $40, we have the total revenue function of 40x.
To find break even units, we can solve for x in the Total Revenue equals Total Cost equation
or simply divide fixed cost by the unit contribution margin.
And that gives 160 units.
So, in order to break even, we must produce 160 units.
We can then find the break even point in dollars by substituting the break-even units value
of 160 into either the total cost function or the total revenue function; and that will
give $6400.
Now, suppose this business has a capacity to produce only 500 units.
Then we can calculate the break-even point as a percent of capacity by simply dividing
the break even point in units by the capacity units.
And that will give 32%.
In essence, we need to reach 32% of capacity before breaking even.
In the next example, we solve a profit-related problem.
A manufacturer has the capacity to produce 500 units of their product per month.
Selling price is $85 per unit (and that makes the total revenue function 85x where x is
the number of units).
Variable costs are $30 per unit and fixed costs are $6,875.
Thus, the Total Cost function is 6875 + 30x Now, what we’re calling profit here is actually
Net Income or Operating Profit.
That is, Total Revenue minus Total Cost, before deducting other expenses.
So, if 100 units are sold, total revenue will be $8500 and total cost will be $9875.
Since total cost is greater than total revenue, operating profit will be a loss of $1375.
In number ii), to realize the maximum profit, the manufacturer has to sell all 500 units
they are capable of producing.
So, Total Revenue will be $42,500 and Total Cost will be $21,875, giving a maximum profit
of $20,625.
Next, we want to calculate the number of units to be sold to realize a profit of $9800.
In other words, Total Revenue minus Total Cost equals 9800.
And on substituting and solving for x, we obtain 303.18 which we have to round up to
304.
Because we can’t sell fractions of a unit And we have to round to the next higher integer
because selling 303 units will generate slightly less than the required profit.
Note that we can also calculate the number of units directly by dividing Fixed Cost,
plus Profit, by the contribution margin.
And that’s it.
In the next video, I’ll be solving a problem involving the break-even chart.
Thanks for watching.