Measures of leverage This is a short reading in which
we talk about leverage, business risk and financial
risk. Leverage is the use of fixed costs in a company's
cost structure. If a company has high fixed costs
then we say it has high leverage. Leverage has two
components: operating leverage and financial leverage.
If a company has high operating fixed costs, in other
words high amount of property, plant and equipment,
then we say that the company has high operating leverage.
If a company has high financial costs because
it has taken a lot of debt then we say that the company
has high financial leverage. For highly leveraged
firms a small change in sales will have a big impact
on earnings. I want to make a small clarification here,
in general throughout the CFA level 1 course when
we talk about leverage we are generally referring
to financial leverage but in this reading we are
taking a broader look at leverage and when we say
leverage in this reading we mean both operating
leverage and financial leverage. To understand
the concept of leverage let's consider two companies
HL which stands for high leverage and LL which stands
for low leverage. They have the same revenue and
net income but a different cost structure. The cost
structure and operating performance are shown over here.
The income statement is on the right. Look at these
numbers carefully and identify how the cost structure
is different, here is what you shall notice, the fixed
operating costs for high leverage firm HL are much more than the fixed operating
cost for LL and the financing costs are also two times
larger than LL so clearly we can say that this firm
has higher leverage. At this level of sales, hundred
units, it turns out that the revenue is the same and
the net income is the same. But I want you to do a little
experiment before you go to the next slide. What
if the sales numbers are higher? If each company sold
120 units then how will the income statement be impacted?
Then what will happen if the sales number is only
80? So come up with the income statement under these scenarios.
Here is roughly what you should come up with. This blue
line represents the net income for different number
of units sold for the high leverage company. This
intercept over here is going to be minus 60 because
this point represents zero sales, if there are zero
sales than the net income is -60 because of these
two numbers, but as sales increase the net income
increases at a relatively high rate. The black line
represents the low leverage firm, if there are no
sales then the loss is only 20. As sales increase the
net income increases but at a lower rate. This point
represents the sales at which the net income is the
same for both companies, but notice as sales increase
beyond hundred the benefit is much more to HL and
that is another way of saying that HL has
higher leverage. A 1% increase in sales will have
a higher percent increase in net income for the high
leverage firm relative to the low leverage firm. Leverage
increases volatility of a company's earnings and
cash flows and also increases the risk of lending
or owning a company. You are now taking an analyst perspective.
When you are evaluating a company and you want to
determine the level of risk one of the most important
things to look at is the degree of leverage. Clearly,
the high leverage firm is more risky because if sales
are high then net income increases a lot but if sales
are lower than expected then the losses will be much
greater for the high leverage firm. So clearly high-leverage
implies higher risk, higher risk would imply that we use a higher
discount rate when we do valuation. So all else
equal the high-risk has a negative impact on valuation.
Coming now to business risk and financial risk. Within business
risk we have sales risk and operating risk. Sales
risk deals with the variability and profits due to
uncertainty of sales price and volume. Operating
risk is the risk due to the operating cost structure.
If a company has high fixed costs then we say that
the operating risk is high. As I just mentioned sales
risk and operating risk collectively are referred
to as business risk. Financial Risk is the risk due
to debt financing. If a company has a lot of debt financing
then that means the company has to make large interest
payments and the financial risk is high. Now we will
talk about how to measure risk and we will start with
operating risk. We measure operating risk using
degree of operating leverage or DOL. This is a quantitative
measure of operating risk. Degree of operating
leverage is equal to the percentage change in operating
income divided by percentage change in sales. If
you have a situation where of one percent change
in sales causes a 3% change in operating income then
the degree of operating leverage is 3, if for another
company 1% change in sales causes a 5% change in operating
income then this company has a degree of operating
leverage of 5. Clearly a higher number implies a
higher degree of operating leverage. The curriculum
shows us how degree of operating leverage can be
written as follows, degree of operating leverage
is equal to the quantity or the number of units sold
into the contribution margin, which is the price
minus the variable cost divided by Q into the contribution
minus the fixed operating costs. You don't need
to understand the derivation, but you definitely
need to memorize this formula and you need to understand
and remember this interpretation for degree of
operating leverage. Just to make sure you know how
to do this, I want you to compute the degree of operating
leverage for the HL company and the LL company. Here
is what you should come up with and as you would expect
the number for the high leverage firm is larger than
the number for the low leverage firm. Now I want you
to do example one from the curriculum which illustrates
this concept. Financial Risk, degree of financial
leverage or DFL is a quantitative measure of financial
risk. Degree of financial leverage is the percentage
change in net income divided by the percentage change
in operating income. If a given company has a 1% change
in operating income and this creates a 2% change
in net income then we say that the company has a degree
of financial leverage equal to 2. The formula that
you need to remember is given right here: degree of
financial leverage is quantity sold into the margin
P minus variable cost minus the fixed operating
costs divided by quantity into margin minus the
fixed operating cost minus the fixed financial
cost. The C stands for financial cost. Here again
I want you to compute the DFL for both companies.
These are the numbers you should get notice again
that the DFL for the high leverage firm is higher
and to consolidate this concept do example 2 from
the curriculum. Now we will consider the effect
of financial leverage on net income and return on
equity. Remember return on equity is equal to net
income divided by equity. High leverage leads to
higher ROE volatility. Volatility refers to the
changes in ROE and high leverage also potentially
leads to higher ROE levels and we'll understand
why we use the term potentially. Let us consider
an example say you have two companies company A and
company B. Company A is 100% financed by equity. So equity
is 200 and assets are 200 so there is no debt. For simplicity
we'll say that there are no taxes. Company B however
is financed by both equity and debt, 50% equity and 50% debt.
On the debt the company pays an interest of 10%. What
this table simply shows is for both companies on
the left we have company A and on the right we have company B.
So for both companies, we have a given EBIT.
this EBIT is the same for both companies and we are
computing the net income for both companies and
the ROE for both companies. The EBIT is the same
but net income will not be the same because company A
does not have interest so net income is the same
as EBIT but with company B, there is debt so there
is interest income and net income will obviously
be lower. The ROE is the net income divided by equity,
for company A we are going to divide net income by
the equity which is 200, for company B we are going
to divide net income by a much lower equity number
of 100. So because the equity number is lower, that in general
is going to have a positive impact on ROE. That is why you notice that for
relatively high EBIT numbers the ROE for company
B is more than the ROE for company A. However if the
EBIT numbers are very low, let's says 0 or close to zero
then notice what happens. For company A the net
income is 0 and ROE is 0, but company B still needs to make
interest payments. The interest payment is 10
so the net income is -10 if the operating income
is 0, and the ROE is negative. This demonstrates
the fact that high-leverage firms are more risky.
And you can also look at the range of ROE which is one
measure of riskiness, ROE for these numbers ranges
between - 10% and 70%. So that's an 80% range, whereas for company
A the range is only half of that from 0 to 40%. So this
should make sense now. High-leverage leads to high
ROE volatility and potentially higher ROE levels,
the potentially higher means that when you have
high operating income when you have higher ROE levels
for low operating income you can actually have lower
ROE levels. Total leverage, degree of total leverage combines
degree of operating leverage and degree of financial
leverage. Degree of total leverage is the percentage
change in net income divided by the percentage change
in sales. It can be shown that the degree of total
leverage is simply the product of degree of operating
leverage and degree of financial leverage and the
formula is given right here. The numerator is Q into
(P - V) and the denominator is Q*(P - V) minus
the total cost, both operating and financial. Just
to make sure you understand this I want you to know
compute the DTL for both companies. Here are the
numbers you should get and notice that for the high leverage
firm we come up with 4 using this formula. And if
you also multiply the degree of operating leverage
with the degree of financial leverage you get 4.
Low leverage firm has a degree of total leverage equal
to 2 and you could also arrive at this number by multiplying
the degree of operating leverage with the degree
of financial leverage. Now, I want you to do example
4 from the curriculum. Break-even points and
operating break-even points. Break-even point is
the point where the number of units sold is such that
the net income is equal to zero. Generally this
point is referred to as QBE for break-even quantity.
This is equal to the total cost which is your fixed
operating cost plus the fixed financial cost divided
by the contribution margin, which is the sales
price minus the variable cost. The operating break-even
point is the point where EBIT or operating profit
is zero. This is given by the fixed operating cost
divided by the contribution margin. This is a very
simple concept but just to make sure you practice
this and understand this I want you to calculate
the breakeven points for both companies as well
as the operating break-even points. Here are the
numbers that you should get and now I want you to do
example 5 from the curriculum. That brings us to the
end of this relatively short and simple reading.
I will summarize the most important points. Degree
of operating leverage is the percentage change
in operating income divided by the percentage change
in sales and here is the formula: Degree of financial
leverage is the percentage change in net income
divided by the percentage change in operating income
and here is the formula. Just to help you remember
this notice that in the numerator we are subtracting
the fixed operating cost and then in the denominator,
we are subtracting the total cost. Degree of total
leverage is the percentage change in net income
divided by the percentage change in sales and the
formula is given right where the numerator is the
same as a numerator for DOL and the denominator is
the same as the denominator for DFL. Notice that when
you multiply DOL with DFL you are going to get the
degree of total leverage. As we have discussed high
financial leverage leads to high ROE volatility
and potentially higher ROE levels. Another point
I want to highlight here is the following, if you consider
a very simple income statement you have revenue
and then you have operating costs, then you have financial
costs such as interest and finally you come up with
net income. Degree of operating leverage is showing
the relationship between revenue and operating
costs or you can think of it as follows, degree of operating
leverage is showing the relationship between revenue
and operating income where operating income is revenue
minus operating costs. Degree of financial leverage
is showing the relationship between operating
income and net income, which obviously is based
on financial costs. Then the formulas for the break-even
point and the operating break-even point are given
right here. My contention is that this slide illustrates
all that you really need to know for this particular
reading. So when you are revising just make sure
that you are on top of all the formulas and the information
shown on this slide. As always read the summary, review
the learning objectives. The examples are good. That's
why I have asked you to do all the examples in this
reading, do the practice problems from the curriculum
and also try to do practice problems from other sources.