# Cost Behavior and Cost-Volume-Profit Analysis >>Okay, today’s lecture is called Cost
Behavior and Cost Volume Profit Analysis. This is not a difficult topic
and the concepts in this chapter, probably some of the most useful concepts
that you’ll take with you to business and they’re going to follow this
for 102 and most of this program. And so, it’s an important chapter but it’s
not that difficult a chapter and it evolves around basic concepts and that is cost
volume profit meaning how does cost behave when there’s changes in production levels. Let’s just take a look at
the three primary components. We have variable costs, fixed
costs and mixed costs. Variable costs vary as production
quantities vary. As you produce more you incur
more variable costs. Raw materials, direct materials
are variable costs. Okay, supplies variable costs. Direct labor is kind of unique. In this class we’ll consider it a
variable cost but there’s an argument to be made that it’s a fixed cost. But we’re going to consider it
to be a variable cost recognizing that some companies will classify
it in one of the two categories. Alright, now fixed costs don’t change. Your rent each month is fixed. So, if I rent a production factory,
whether I manufacture 10 units, 100 units or 1000 units,
my rent will stay the same. Straight line depreciation,
we call it straight line because it’s fixed, it doesn’t change, okay. And then we have something called mixed. Your book may use the term
semi-variable costs and this has– these costs have a fixed component
and a variable component and most of you are actually familiar with the
concept if you’ve ever rented a U-Haul or a Ryder rent-a-truck it’s
something like 29 bucks a day or 39 bucks a day plus 50, 60, 70 cents a
mile. That’s a mixed cost because
the 39 in the slide is fixed. The 75 cents per mile is variable, which
is why we don’t want to make any more trips than is necessary because that
mileage starts to run up a tab. Your cell phone, many cell phone plans for
example are 49 dollars per month plus 30, 40, 50 cents per minute once you’ve
whatever they call it. Okay, and so these are the three different
types of cost that we have in any business. Okay, now I would like you to know these graphs. I’m not going to ask you to prepare a graph,
but I could ask you to analyze a graph. Let’s just take a look at these graphs. Notice this is total variable costs and
variable costs per unit produced, okay. The more cars we produce, the
more engines we need, okay. So, we incur increasing costs
as production increases. However, if I buy the engines or tires or
some other car component from one of my vendors, I’ve contracted to pay fixed price per unit. Okay, now don’t confuse the terms. Variable costs per unit stay roughly the same. Now, remember these are assumptions
we’re making. Anytime you make assumptions there’s always
the chance that the assumptions will not hold. But, in many businesses have a relatively
stable environment it’s not an unreasonable assumption. Okay, that your variable costs on a
per unit basis stay the same, okay. And again, recognizing that in certain
circumstances if you didn’t order enough, you have to rush shipped goods,
your variable costs may increase. But, as a general rule of thumb variable
costs stay the same on a per unit basis and they increase as we produce more items. Okay, fixed costs, fixed
costs in total don’t change. If you’re paying 10,000 dollars rent
for your factory then regardless of how much you produce your total
fixed costs will stay the same. Now notice what happens to
fixed cost per unit and you have to interpret the information correctly. If I manufacture one item and my
rent is 10,000 than I have to charge that product 10,000 dollars
if I want to recover my costs. If I can produce two units than
I can divide the 10,000 dollars between the two units and
it will be 5000 per unit. If I can produce 1000 units, then 10,000
divided by 1000 units, then I have to make sure that the cost of my product
includes 10 dollars of rent per unit. If I produce 10,000 units than
I only have to charge one dollar for each unit produced to
recover my fixed rent cost. As a result the more we produce the
fixed cost per unit decreases, okay. And these are important concepts
for any business to understand is which costs are variable
and which costs are fixed. Now let’s take a look at the mixed
cost graph using your cell phone plan, renting a U-Haul truck as an example. Costs that have both a variable
component and a fixed component, so there’s the fixed cost
component at the 50,000 dollar level and than there’s the variable
point, the variable cost component, the red line going from the 50,000 dollar
mark. Okay, so even if you didn’t use
your phone one single minute, you’d still be charged 50
dollars for example, okay. If you stayed within your 600 anytime
minutes then you get hit for 50 bucks. If you run over, so you have 700-800 minutes,
than that red line starts to kick in. And the more minutes you exceed
your limit then, of course, the higher your bill is going to be, okay. So, there are a lot of different costs or
mixed costs and you can look at various departments, for example, the quality control department. That department has a lot
of different costs in it, some of which are variable
and some of which are mixed. So, the department, most departments are
mixed costs and what we have to do is we have to separate mixed costs or a
department with mixed costs into the variable components
and into the fixed components. Then we’re left with two neat, clean
categories, variable costs, fixed costs and then we can start doing what’s called
break even analysis, cost volume profit analysis, what we call “what if” analysis and
its very useful for many businesses. Another term you need to be familiar with
is this concept called the relevant range. This is the production level that we expect
to produce under normal operating conditions. Normal operating conditions
takes into account imperfections in human beings and in running a business. Notice we have ideal capacity. This is under perfect conditions,
which rarely if ever happens. I’m going to say never happens and then we
have normal expected capacity when we factor in that sometimes work a little inefficiently. Sometimes machines break down. They have routine maintenance, maybe
there’s a power outage, who knows. Maybe raw materials get jammed in the machines. Okay, but you factor in a
certain amount of insufficiency. You’re not justifying the inefficiency. Your goal is, of course, to
minimize or eliminate inefficiencies, but recognizing that until you reach
that point, which most likely is never, okay then normal expected capacity is
the concept in which we’re going to use to define the relevant range, okay. And the four graphs that we saw, really the
five graphs including the mixed cost graph are assumptions we make within the relevant range. Let’s take a look at this graph here. Notice total variable costs the purple
column in the middle is our relevant range. This is where we typically expect to
operate okay in normal operating conditions and notice it’s a relatively
straight line; it’s linear. Now in reality, there will
always be exceptions to the rule, but again with many businesses this
is a reasonable assumption to make, because their business is somewhat predictable. Okay, now fixed costs; look
at the graph with fixed costs. If I exceed the relevant range, for
example, if I’m going to produce or if I want to produce more than my factory is capable
of at full capacity, then I’m going to have to knock out a wall or I’m going to have to move
into a larger building or buy more machines and my fixed costs are not going to inch up,
they’re going to jump up by a measurable amount. Okay, so while we’re in that relevant range
the expected capacity, our fixed costs remain
fixed. If we exceed that than our fixed
cost structure will change. So, we’re going to stick
within the relevant range. Now, there are several techniques
we can use to separate a mixed cost into its variable and its fixed components. One is called regression analysis. We’re not going to look at that. You’ll look at that in your
probability and statistics class, scatter graphs which the book may discuss. Okay, we’re going to focus on this estimation
technique called the high-low method. Okay, and what we do is we identify
the months or the time periods and we want to define time periods. In this case, months which had the most
activity, the high month and we compare it to the month that had the lowest activity. So, let’s take a look at this graph. We’ll easily identify the
high month and the low month. Okay, the high month looks like August. Notice we produce the most units;
we incurred the most total cost. And remember I’m going to abbreviate variable
costs plus fixed costs equal total costs. All of our costs will be categorized
as either variable or fixed. Okay, and our mixed costs we’re going
to separate it into its variable and its mixed components
using this high-low method. Okay, the low month, the
least activity was October. The lowest amount produced,
lowest cost incurred. So, we’re going to first identify variable
costs per unit and what we’re going to do is the numerator, we’re going to take
the high month cost and subtract the low month
cost. And in the denominator we’re going
to take the high month activity, subtract the low month activity,
okay let’s take a look at that. There’s some yellow ink here. You probably can’t see that. It says difference in total
costs in the numerator there. Okay, here’s what we’re looking for. Okay, so in the month of August we produced
2100 units, incurred 61,500 in costs. October, produced 750 units,
incurred 41,250 in costs. So, the numerator high cost
minus low cost, okay. There was a difference of 20,250. And in terms of the difference in
activity between the high month and the low month was 21,000 minus 750, okay. There was a difference of 13,050 units. Now, let’s you need to think
about now what is this telling us, because if you just memorize a formula,
yes you’ll come up with an answer, but it helps to know what it means okay
otherwise you’re going to get tripped up. Notice that when we produced an additional
1350 units we incurred an additional 20,250 in
costs. Okay, what does that sound like to you? That sounds like variable costs. Now, as production increased,
some of those costs increased. Well, those had to be variable costs, because remember fixed costs don’t
change within the relevant range. So, that 20,250 are additional variable costs
we incurred as production level increased. And if you refer back to your variable costs
in total graph, it’s a linear line going up,
okay. Therefore, we divided 20,250
by 1350 units and we identify, and by the way the denominator
here says a difference in, so 20,250 divided by 1350 equals a variable
cost per unit of 15 dollars per unit. Now, review your variable cost
per unit graph and remember within the relevant range its straight, right. We assume, for example, that when Ford Motor
Company signs a contract with Goodyear Tire and Rubber, they’re going to buy
several million tires for X number of dollars per unit; it’s in a contract. The cost per unit stays the same. So, we can now rely on this 15 dollar per
unit variable cost and now we’re going to be able to separate the 61,500 into its variable
component and its fixed component. [ Silence ]>>Okay, in the high month
we produced 2100 units. Variable cost is 15 dollars per unit. So, if I multiply 2100 units times
15 dollars per unit, I get 31,500. Now, we know that in the high
month our total cost was 61,500 and we know variable plus fixed equals total. If 61,500 is total, 31,500 is variable, the
difference or 30,000 has to be our fixed cost. Let’s look at the low month;
31,250 is our total cost. We produce 750 units at a variable cost per
unit of 15 dollars per unit, variable cost 11,250. The 11,250 plus X equals 41,250 and notice
our fixed cost, which after all is fixed, stayed the same; it’s 30,000 units. Okay, now again this is an estimation technique
and if you were to plug in the other three or four months, it wouldn’t be exact. But if it was a normal operating
month, it would get you pretty close. Now, if there was something unusual
that happened in any given month, than your cost behavior would
have changed somewhat. But in normal operating conditions
then this formula for this particular company will
generate reasonably consistent results. Again, being an estimation technique
it won’t be right smack on the money, but it will be pretty darn close. Okay, so now what we’ve done is
we’ve separated our total costs into a variable component, fixed cost component. And now, all of our mixed costs have
been pushed into those two categories. All costs are now neatly
classified as variable or fixed. We can now start doing some analysis. Okay, now we want to introduce
an important concept in this whole process called
the contribution margin. How much does the sale of each unit contribute
towards first covering fixed costs and then after we’ve covered fixed costs, how
much does each sale contribute to profit? Okay, so for each one dollar of
revenue what percent goes to covering– first we subtract variable costs. That leaves us with something called
contribution margin and that’s the amount that we’re going to contribute
to covering fixed costs. Once they’re covered, that’s profit. Take a look at this new format. We haven’t seen this before. This is called the contribution margin
format for the income statement. And notice in parentheses we put not gap;
we can only use this for internal analysis. That’s what this is class is about, managerial
accounting, analyzing our business to make sure that we’re running it as efficiently
and effectively as possible. This type of information is
not for outside eyes, okay. A gap formatted financial statement
which should look familiar is over there. Its operating income will still be the same. We’re simply rearranging our costs to
help us analyze our business, okay. Sales minus variable costs
equals contribution margin, CM minus fixed costs equals operating income. Okay and what we’ll see is that your costs
of goods sold has a variable and a fixed component and your operating expenses has
a variable and a fixed component. Okay, so we’ve separated variable and fixed,
so this number variable costs here includes part of cost of goods sold, part
of operating expenses. Fixed costs will include part of costs to
goods sold, part of operating expenses, okay. So, sales minus variable costs
equals contribution margin. We also have to calculate what’s
called the contribution margin ratio. The contribution margin divided by sales
gives us the contribution margin ration and this is the percentage of each
dollar of revenue that contributes to covering fixed costs, and then once
fixed costs are covered how much profit for each dollar of sales. Okay, so one dollar of revenue, we subtract
whatever the variable cost is per unit, which is a fixed number remember that. It stayed the same. That gives us contribution margin per unit. We can do this on a total basis, sales minus
variable costs equals contribution margin and we can do it on a per
unit basis as well, okay. And then contribution margin, which
again is sales minus variable costs. The contribution margin divided by sales
tells us the percentage of each dollar revenue that helps to contribute
to cover our fixed costs. Now, we’re going to do some examples. The break even point, when revenue equals
expenses and all of our expenses are separated into variable and fixed components,
we’re not making money. We’re not losing money, we’re breaking even. How many units do we need to sell to break
even? That’s a useful piece of
information for a business. What would revenue be at the break even point? How many units do we need to sell if I want
to achieve a profit of 50,000, a 100,000 a million; useful information for a business. We can also then figure out what would happen? What happens to break even if we
raise the selling price a little bit, if we have to drop the selling price,
if variable costs go up or down, if fixed costs go up or down, because
let’s face it, over time things change. Your energy costs may change. Your materials cost, your labor cost may change. You may buy new equipment. You may move into a new building. So, nothing stays the same forever but this
formula allows us to modify our equations and our break even points will
change under these circumstances, but we can still figure that out. Okay, so let’s take a look at this example. Our sales price for each unit we sell is 200. Our variable cost per unit, things like direct
materials, direct labor, supplies, utilities, etc., leaving us the contribution
margin of 50, 200 minus 150 equals 50. Fixed costs in total are
500,000 and just think of rent, straight line depreciation,
maybe property tax, insurance. Okay, our contribution margin ratio,
therefore, is 50 divided by 200. Twenty-five percent of each sale contributes to covering our fixed costs,
what’s the break even point. Let’s plug in this formula. Notice, each unit gets sold for 200 dollars. X represents the number of units we will
sell to break even, to cover our costs. Each unit that we sell we know the
variable cost per unit is 150 and we know that our fixed costs in total are 500,000. So, now let’s take this the algebraic path;
200, let’s isolate X. So, let’s subtract 150X from both sides and we’re left with 50X, which by the way is our contribution
margin equals 500,000 divide both sides by 50X equals 10,000 units of product that
we have to sell to break even, to cover our costs. So, our break even point is
10,000 units of production. We don’t really need to do these three steps. We can eliminate this first step by simply saying here’s fixed
costs, here’s contribution margin. We can simply say fixed cost, divided by
contribution margin per unit gives us the number of units we have to sell
at the break even point. And there it is, 500,000
divided by 50– 10,000 units. Now, we can use a slight
variation of this formula to figure out how much revenue we would bring in
at the break even point, 10,000 units. And we take the fixed cost and we divide
it by the contribution margin ratio, which we previously figured out was .25, remember contribution margin
divided by 200 sales per unit. And we would achieve two
million dollars in revenue at the break even point, which is easily proven. We know we sell each unit for 200. Break even in units is 10,000; 10,000 times
200 dollars per unit our total revenue would be two million. So, these are simply nice shortcuts that
we can use to calculate break even in units and break even in dollars of revenue. From this, we can also factor
in what we call target profit and don’t let fancy terms get you rattled. This simply says hey if I want to make
100 grand or 100,000 dollars in profit, how many units do I have to sell. If I want to make a million dollars in profit,
how many more units would I have to sell? And we just do a slight modification of
the formula and we can figure this out. And look what we did. We said fixed costs plus target
profit, add those two numbers together, that’s your numerator and divide it
by the contribution margin, okay. Now, from the previous example, notice what
it says and if we want to achieve a target profit of 250, then fixed costs of 500 plus the 250
target profit divided by the contribution margin of 50 dollars per unit, we’d
have to sell 15 thousand units to achieve a 250,000 dollar profit. And, how much revenue would we bring in at
that point where we’re achieving 250 in profits. Well, fixed costs plus target
profit your numerator, divided by the contribution margin ratio of
.25 we bring in three million dollars of revenue. Okay, so it’s actually a very simple
formula, but it’s very useful. Okay and now we can do all sorts
of what we call what if analysis. Okay, we can say what happens
if we raise the sales price? What happens if we lower the sales price? What happens if we raise the sales price in
response to an increase in variable costs? What if we bought a new machine that
makes our fixed costs go higher, but as a result we use less labor
so our variable cost goes lower. So, you can do all these different scenarios
once you know your variable and fixed costs. Okay, so now we can do a
variety of what if scenarios. Let’s go ahead and take a look at these. Let’s go ahead and change the
sales price from 200 to 210. Well, literally just plug the new number into
the formula, 210 sales minus 150 variable cost; contribution margin is now 60 dollars per
unit. Use the formula, 500 fixed cost divided by the new contribution ratio,
8333 units to break even. Okay, hey it makes sense. If you can raise the price without your
price going up you’re going to make, you’re going to achieve profitability
sooner, less units to break even. Okay, now whether or not you can
pull that off in the real world with competition demand remains to be seen. What if variable costs go up by 15 dollars
per unit, we keep the original sales price. Okay, original sales 200, new variable cost
165, contribution margin is now only 35 per unit. Notice our formula is going to take
over 14,000 units to break even. Okay, continuing what if
fixed costs increase to 575 and we bought some new machines,
better technology. But, as a result we use less direct labor
and now variable costs went from 150 down to 135 and we dropped the price,
sales price to 190 per unit. All three elements change, well just put
all three elements into the formula, okay. Our contribution margin is 190 minus 135. Okay, now fixed cost 575 divided by the new
contribution margin 10,454 units of break even. And using this particular data here, if I want to achieve 100,000 dollar profit
575 plus target profit of 100 divided by the contribution margin 55, I have to
sell 12,273 units to accomplish that profit. Now, we can also do this if we have two,
three, four, many multiple products. So, this is called the sales mix: determining
break even with two or more products. Assume that a company is two products
that it sells, products A and B and in normal business most of our business,
70 percent of our product sales relate to product
A and about 30 percent for product B.
You’ll have your sales price information, your variable costs. Therefore, you have contribution
margin and here’s the key here. We can still figure out break even,
but we need to plug the sales mix, the 70/30 split between products
A and B into the equation. Okay now, if you don’t have a consistent
sales mix you can’t use this technique. But a lot of companies do. They have a primary product and
they have secondary products. So, what we do, and here’s the trick here, is we’re going to multiply the contribution
margin per unit times the sales mix for each product; \$1.50 times 70 percent and
\$2.00 times 30 percent and then we’re going to plug it back into our formula. Let’s take a look. Contribution margin times sales
mix percentage gives us WACM, which is simply the weighted
average contribution margin. Okay, your book presents this as product
E or product some– gives it a new letter. This is simply a weighted
average contribution margin when you blend the two products,
given the 70/30 mix. So, 150 times .7 is \$1.05; \$2.00 times .3
is .6. Now add them together and the weighted average
contribution margin is \$1.05 plus 60 cents equals \$1.65. Take your fixed costs, which in the
previous slide we sold over 330, divided by your weighted average
contribution margin and we have to sell a total of 200,000 units. Now this 200,000 units is comprised of products
A and B. We got to separate product A and B and for this we got back to our sales mix,
200,000 times .7, 70 percent of that 200,000 or 140 units will be product A and 30 percent
of the 200 units or 60,000 units will be product
B. And if we were to plug these in and multiply
the number of units times the sales price, variable costs, etc. we would see
that we do, in fact, break even. In fact, here it is okay. Total sales for A, that’s the break even
unit times the sales price per unit. Okay, variable costs per unit
times the units sold at break even. You can go back on your own and you an plug
these in and in fact, it’s a good idea for you to do that and then plug in these numbers
and you will see that the contribution margin in total for the two products, 210 plus 120
gives you a combined contribution margin of 330. There’s our fixed cost, 330;
we did, in fact, break even. Okay, so it’s useful even when you
have two, three, four, five products, providing you have a reliable sales mix. Last item, concept called operating
leverage, based on a company’s cost structure, the percent to variable cost versus
the percentage of fixed costs. We can tell what an increase in sales
will do for the profit of the company. Companies with a higher fixed cost, more fixed costs than variable costs
will have a higher break even point, but will have more operating leverage. And what that means is, as sales increase
your profit increases by a greater degree. We’ll see this momentarily. Companies with a high variable cost,
higher variable costs and fixed costs, have a lower break even point, but
they have less operating leverage. So, as their revenue increases,
their profitability will increase, but not as much in percentage point as
a company with high operating leverage. Let’s see it in action. Here’s our formula. This comes straight from the contribution
margin formatted income statement. Remember sales minus variable costs equals
contribution margin minus fixed costs equals operating income our formula
is contribution margin divided by operating income gives us what
we call operating leverage, okay. Company A has sales of 100,000. Variable costs 60,000 giving
you a contribution margin of 40. Total fixed cost is 30, operating income 10,
therefore 40,000 contribution margin divided by operating income of 10,000, this
company has operating leverage of 4. And what that means is for every one
percentage point that revenue increases, operating income will increase
four times as much. If sales increase 10 percent,
profit will increase by 40 percent. So, let’s go ahead. Let’s plug that in. If sales increase by 10 percent
variable costs would go up by 10 percent. Contribution margin goes up by 10
percent, fixed cost does not change. That’s the key here. So, 110 minus 66, contribution margin is 44,000,
fixed costs do not change; they’re fixed. Operating income is now 14,000. Now, this year operating income is 14,000. Last year it was 10,000;
that’s a 4000 dollar increase. And let’s just do the math, profits
did, in fact, go up by 40 percent because our leverage was four times. So, revenue went up 10 percent, 10
times 4, profit goes up 40 percent. Our formula would be the current year
profit minus previous year profit [Writing on board] divided by previous year
profit, there’s our 40 percent increase. Now, you’re operating leverage will change
from year to year, but it’s still a useful tool. Companies, for example, health spas
like LA Fitness, 24-Hour Fitness, most of their costs are fixed costs. So, each additional they sign
up, that’s mostly profit, okay. Give you a little bit of negotiating
power when you sign up for a gym. Okay folks, that’ll do it; study.

#### 1 Comment

1. Amira Ibrahim says: