[MUSIC] I'm Larry Walther,
this is principlesofaccounting.com, Chapter 18.
And in this module, we will extend what we've previously learned about
definitions of fixed and variable costs.
And show how this information can be used in break-even analysis and
target income analysis.
So, first of all let's define Cost-Volume-Profit Analysis.
Cost-Volume-Profit Analysis is where we look at cost structure,
our volume, and determine the effect on profitability CVP, in other words.
The contribution margin is defined as revenues minus all variable expenses.
Those variable costs can arise from producing a product such as direct
material, direct labor, variable manufacturing overhead.
But they can also derive from period costs such as the salesman's commission that
varies with each unit sold.
Do not confuse the contribution margin with the gross profit.
Remember, gross profit is sales minus costs of goods sold.
And in a manufacturing context, costs of good sold includes direct material,
direct labor, and all manufacturing overhead, whether fixed or variable.
We can express this in the aggregate or we can express it on a per unit basis.
Or we can even speak to it on a ratio basis.
Let's look at an example of how we can use this information for break even analysis.
Let's assume that Leyland Sports manufactures score boards.
The production cost is $500 per sign and
sales representatives are paid $300 commission per sign.
Each sign is assumed to sell for $2,000.
By the way the entities total fixed cost of $1,200,000.
So variable cost are $800 per sign, $500 manufacturing and $300 elated to selling.
Therefore, the contribution margin is $1,200 per sign.
The $2,000 selling price minus the $800 variable cost.
So let's see how we use contribution margin information and
fixed cost information margin in calculations.
And let's look at how sales affects our total profitability, with this example for
Leyland Sports.
In this first example, we're going to assume that sales were 1,000 units
at $2,000 per unit, so we have total sales of $2 million.
In the second example, sales are only 500 units at $2,000 a unit,
so total sales are $1 million.
And then in the last of the three illustrations were sending were selling
2,000 units at total sales of $4,000,000.
Notice how in each of the three cases, the contribution
margin per unit and the contribution margin ratio are unaffected.
Now we can see that the breakeven point is 1,000 units.
So when we sold 1,000 units we had a total contribution margin of 1,200,000 from
which we subtracted our total fixed cost of 1,200,000 and we broke even.
Obviously when we sold less than 1,000 units we lost money.
And when we sold more than 2,000 units we made a profit, because we were more
than able to cover our fixed costs, with our contribution margin.
Let's look at the analysis for Leyland Sports using a graphical representation.
Here on the horizontal axis,
I have total units sold, on the vertical axis I simply have dollar amounts.
And I've got various amounts plotted on the graph.
For example I have a horizontal line at the $1,200,000 level and
that continuous all way across the graph.
That represents our fixed cost area.
We incur 1,200,000 of fixed cost no matter the level of production.
If we look at our sales line we start at 0 and
we rise with each unit sold at $2,000 a unit.
So for example, at 1,000 units we have 2,000 in sales on this sales line.
At 2,000 units we've got $4 million in sales.
So sales is increasing on a linear basis, okay.
I've added on top of that one more line, a total cost line,
and you can see that that that rises with each additional unit.
That line is increasing at $800 per unit.
So for example at our 1000 units, we have variable costs that were $800,000,
which is that area, adding to the 1,200,000 fixed cost gave us total
cost of 2 million and total sales of 2 million, our break even point.
When sales increased beyond that level we had a profit area and
when sales were less than that, the red area represents a loss areas.
So let's continue along here,
break-even occurs definitionally when there is no profit or loss.
Break-even sales, in other words, equal our total cost
whether they consist of variable components of fixed components.
And so, our analysis for Leyland shows,
algebraically we solve here to find that break-even sales are 1,000 units.
There are several shortcut formulas for calculating break even.
The first one I'm showing is break-even in units,
where we divide total fixed cost by the contribution margin per unit.
In our example, $1,200,000 of fixed cost divided by $1,200
per unit contribution margin yielded us 1,000 units for break-even.
Another example is we can calculate break-even point in sales dollars.
This would be the total fixed cost divided by the contribution margin ratio.
In other words, $1,200,000 divided by
the 0.60 contribution margin ratio would equal sales in dollars of $2 million.
So those two shortcut formulas one returns the value in units and
one returns the value in total sales dollars to break even.
[MUSIC]