The next area we're going to talk about deals with Cost Volume Profit, or Break even Analysis.
With Break even Analysis, the purpose of this is to determine the volume of product and
sales, of production and sales, necessary to break even.
But in life, do you want to break even?
Does breaking even get you friends, dates, fun vacations?
I don't think so.
We need to not only break even, but, hey, let's make a little bit of profit on this,
as well.
That's why we call it Cost Volume Profit Analysis, or Break even Analysis.
That's what we're looking at.
Now, in looking at Breakeven Analysis, a couple of assumptions, first of all, that we're within
the relevant range, the range in which your cost assumptions remain valid, which means
fixed are fixed in total, so they remain the same, and variable costs are fixed per unit
and they occur at a constant rate.
Those are some of the things we're looking at.
Now, in doing this, we are not looking at a GAAP income statement.
We're looking at a Contribution Margin Income Statement.
Remember what a Contribution Margin Income Statement looked like?
It was sales minus variable cost is contribution margin, minus fixed cost equals your profit.
Now, if we're trying to break even, profit is zero, right?
That means, sales minus variable cost is contribution margin.
That means contribution margin equals fixed cost, equals zero.
That's what we're looking at.
With Breakeven Analysis, breakeven occurs where what?
Where total revenues equal total costs.
Let's look at this.
Total revenue equals total cost, okay.
What's total revenue?
How about sales price times x, which is the number of units you've sold, equals ... What's
total cost?
Let's see ... Total cost, it was fixed plus variable times x.
Oh yeah, that's right.
Fixed plus variable times x.
Let's divide through, bring this over, come over here, bring the fixed, what do you end
up with?
You end up with your formula, as you'll see in your notes, which is ... Breakeven in units
equals fixed cost over sales price minus variable cost.
That is your formula.
What is it?
Breakeven in units.
Remember, breakeven in units is dollars over dollars.
Dollars over dollars is non-dollars.
So breakeven, in units, is fixed dollars, fixed costs, divided by sales price minus
variable costs.
What do we call sales price minus variable cost?
How about CM, contribution margin?
That's going to be the contribution margin per unit.
Fixed cost in total, contribution margin per unit, equals breakeven in units.
All right, so dollars over dollars is non-dollars.
That is the formula we're going to use.
Let's say, for example, I want to write a brand-new CPA Review book.
Let's say the sales price is going to be 20 bucks.
Variable costs are $12.
Let's say my fixed costs are $60,000.
The question is, how many do I have to sell in order to break even?
Well, in doing this, breakeven in units is ... equals fixed costs, 60,000, over sales
price, 20, minus 12.
We know 20 minus 12 is eight bucks.
60 over eight gives me 7,500 units.
If I sell 7,500 units, I should break even.
Let's see if this really works out.
Let's come back over here.
We'll do an income statement.
Let's see, sales are going to be 7,500 at 20, which is $150,000.
Variable costs are going to be 7,500 at 12, which is 90,000.
That gives me a contribution margin of 60.
I've got fixed costs of 60.
I've got profit of zero.
Profit is zero, I broke even.
I got no money, I got no friends.
All right?
Another very important formula is breakeven in sales dollars.
That equals your fixed costs over your CM ratio.
Now, what is a CM ratio?
This is dollars over non-dollars, is dollars.
So what is this CM ratio?
CM ratio's going to be your CM over sales price.
In this case, let's come back over here, your contribution margin is eight bucks over 20
is 40 percent.
Four time two is eight, 40 percent.
That's your CM ratio.
Your CM is eight bucks, but your CM ratio is eight over sales price, 40 percent.
Bringing that back over here, we end up with 60,000 ... I'll do it up here.
60,000 over CM ratio, which is eight over 20, or 40 percent.
40 percent of something is 60.
40 percent of 150 is 60, becausecarry the two, is 60,000.
That works, boom, boom, boom.
Notice that gives me breakeven in sales dollars.
Hm, two important formulas: breakeven in units, breakeven in sales dollars.
Breakeven in units is fixed costs over CM.
Breakeven in sales dollars is what?
Fixed costs over CM ratio.