Some
Indicators of a Firm's Risk
and Debt Capacity
Roger Clarke
& Grant McQueen Revised 2001
Introduction
One
notion of the riskiness of a firm is the extent to which the firm’s earnings
can fluctuate from period to period in response to changes in total firm
revenues. The variability of earnings relative to revenues is determined by
two categories of risk. The first source of risk is business risk
and is related to the basic industry and operating decisions of the firm.
Business risk depends on a number of factors including the variability of
demand for the firm’s products, the stability of sales prices and basic
product input prices, and the extent to which the firm’s costs are fixed.
Each of these factors is determined to some extent by the character of the
firm's industry, but each of them is also controllable to some degree
through the firm's strategic operating decisions.
The second source of risk is financial risk. This risk is related to
the firm’s financial policies, specifically the use of debt in financing
operations. The use of debt obligates a firm to make interest and principal
payments, regardless of profit levels. These fixed financial expenses
compound fluctuations in operating income (EBIT) and introduce additional
risk to stockholders. Separating business and financial risk convenient
illustrates the division between firm operating and financial policies.
Both are important and poor management in one area can easily undo good
management in the other.
Operating Leverage
Business risk depends in part on the extent to which a firm builds fixed
costs into its operations. If fixed costs are high, even a small change in
sales can result in a large change in EBIT. The measure of a firm's
operating risk is called operating leverage. If a high percentage of a
firm's operating costs is fixed, the firm will have a high degree of
operating leverage. As a result, a small change in sales will result in a
large change in EBIT. Operating leverage is defined as the ratio of the
percentage change in operating earnings (EBIT) to the percentage change in
sales. If Δ represents the change in a variable, S represents total sales,
VC represents total variable costs, and FC represents total fixed costs, the
degree of operating leverage (DOL) at a particular level of sales is
given by:
(1)
(1')
where v = VC/S is the fraction variable costs are of sales. This equation
is easily derived since EBIT = S‑VC‑FC. Conceptually operating leverage is
best understood and interpreted using equation (1). However, when
calculating DOL, equation (1') is easier to use since it requires only one
year of data and requires only one calculation—dividing contribution by EBIT.
(The specific form of Equation (1') does assume that unit prices and
variable costs are constant as sales change, however.)
As an example of operating leverage, at a sales level of $20 million,
variable costs equaling 60 percent of sales, and $4 million of fixed costs,
a firm's degree of operating leverage would be:
Consequently, the ratio of the percentage change in EBIT to a percentage
change in sales would be 2.0. With this degree of operating leverage a 100
percent increase in sales from $20 million to $40 million would result in a
100(2.0) = 200 percent increase in EBIT from $4 million to $12 million. The
greater the degree of operating leverage for a firm, the greater will be the
change in operating earnings as sales change. Not only will operating
earnings increase substantially as sales increase for high levels of
operating leverage, but they will likewise decrease substantially as sales
decrease. For example, with DOL = 2, a 10 percent decline in sales results
in a 20 percent drop in EBIT.
Operating Breakeven
Point
A concept associated with a firm's operating leverage is operating breakeven
point. When a firm has fixed costs of operation, a certain amount of
revenue must be generated to cover these fixed expenses before any operating
profits are available. The point at which the firm just earns enough to
cover its non‑financial fixed expenses is called the operating breakeven
point. The concept is illustrated in Figure 1. For a firm with fixed
operating costs (FOC) of $4 million and variable costs amounting to 60
percent of the $5.00 sales price P (v = 0.6 and P = $5), the firm must sell
2 million units (Q* = 2 mill.) or have sales revenue of $10 million before
it covers its fixed expenses and just breaks even. The firm's breakeven
point in units can be calculated since at the breakeven point EBIT* = 0.
Setting EBIT* to its break-even level of 0 and solving for Q* gives the
breakeven number of units as:
(2)
The breakeven level in units can be converted to dollar sales volume by
multiplying through by the sales price per unit: S* = PQ*. Notice that for
the same contribution margin (l‑v), the higher are the fixed costs, the
greater is the breakeven point. Since the level of fixed costs also
influences the operating leverage of the firm, the higher the firm's
breakeven point, the greater will be the firm's operating leverage for any
given level of output.
Financial Leverage
Operating leverage affects changes in EBIT while financial leverage affects
changes in the earnings available to common stockholders. Financial
leverage takes over where operating leverage leaves off, further magnifying
the effect of a change in sales on operating earnings because of the fixed
financial costs associated with the use of debt and preferred stock.
The degree of financial leverage (DFL) is defined as the ratio of the
percentage change in EPS (or profit after taxes) to the percentage change in
EBIT. If Int represents the firm's fixed interest expense, tx is the
corporate tax rate, and assuming no preferred stock is outstanding, the
degree of financial leverage is given by:
(3)
This relationship can be simplified since:
Therefore, for a firm with no preferred dividend payments, the degree of
financial leverage is given as:
(3')
Like DOL, DFL is better interpreted using equation (3) but easier calculated
using equation (3'). The following example illustrates both the calculation
and interpretation.
For a firm with $4 million of EBIT and interest charges of $1.2 million, the
degree of financial leverage would be:
Consequently, the ratio of the percentage change in EPS to the percentage
change of EBIT would be 1.43. A 100 percent increase in EBIT would result
in a 100(1.43) = 143 percent increase in EPS. Note also that if no debt or
preferred stock is used, the degree of financial leverage is 1.0 so that a
100 percent increase in EBIT would result in a 100 percent increase in
EPS--financial leverage has no effect. The greater the financial leverage
for a firm, the greater will be the increase in EPS as operating earnings
increase. Likewise, the greater the financial leverage the greater will be
the decrease in EPS as operating earnings decrease.
Combined Leverage
The combined effect of both operating
and financial leverage influences the total risk of the firm. Two firms
with the same combined leverage may have different degrees of operating and
financial leverage. A firm with high operating leverage may offset this by
using only moderate financial leverage while a firm with moderate operating
leverage can use much more financial leverage. The combined leverage is the
product of the two and is defined as the ratio of the percentage change in
EPS to the percentage change in sales. The degree of combined leverage
(DCL) for a firm with no preferred stock is given by:
(4)
(4')
For the firm in the previous examples, the degree of combined leverage is:
Consequently, the ratio of
the percentage change in EPS to the percentage change in sales is 2.86. A
100 percent increase in sales would result in a 100(2.86) = 286 percent
increase in EPS. The greater the firm's combined leverage, the greater the
increase or decrease in EPS as sales increase or decrease.
The usefulness of the degree of leverage concept lies in the fact that 1) it
enables a manager to tell what a change in sales will do to the firm EPS and
2) it illustrates the relationship between operating and financial leverage
and their role in affecting the total risk of the firm's earnings. The
consideration of these concepts suggests the tradeoffs a manager must make
between the business risk built into the operating decisions of the firm and
the degree of financial risk involved in financing those operations. A firm
with sizeable business risk because of variable sales and high operating
leverage will need to use relatively less financial leverage (more equity
financing) if the overall risk of the firm is to remain at moderate levels.
Likewise, a firm with small business risk could use relatively more
financial leverage in its financing plans and still leave the firm with
moderate overall risk.
The Effects of Financial Leverage on EPS: Financial Indifference Point
Financial leverage occurs because of the fixed charges associated with
sources of capital just as operating leverage results from fixed operating
costs. The firm's choice among capital sources will influence firm EPS. In
general, the firm’s EPS can be calculated by rewriting the standard vertical
income statement in the following horizontal form:
(5)
where the firm has no preferred stock and where:
EBIT = earnings before interest and taxes
Int = interest expense
tx = income tax rate
n = number of shares of common stock
The firm usually has several different alternative
sources of funds. The firm might raise sufficient funds for an investment
through debt or additional common stock. Since interest expenses are
generally a fixed dollar amount once the financing is completed, equation
(5) allows us to graph the relationship between EPS and EBIT. Figure 2
shows the EPS resulting from various levels of EBIT given two different
financial plans for raising funds. One shows the impact of incremental debt
financing and the second shows the impact of incremental equity financing.
Notice that the two lines have different slopes. Conceptually, the
difference in slopes is due to differing degrees of financial leverage
between alternatives. The more highly levered debt alternative will always
have the steeper slope. Mathematically, the difference in slopes is caused
by differing number of shares: under the equity alternative, operating gains
and losses are spread over a greater number of shares.
The point at which the debt and equity lines cross
gives the level of EBIT for which both alternatives result in the same EPS.
This point can be calculated by equating EPS in equation (5) for two
different alternatives and then solving for the indifference level of EBIT.
Because at the indifference level EPSe = EPSd, we
have:
where subscript e represents the incremental equity financing option and
subscript d represents the incremental debt financing option. Cross
multiplying in these expressions allows us to solve for the level of EBIT at
which the two EPS will be equal giving:
(6)
In many cases managers relate better to levels of
sales rather than to levels of EBIT. The indifference level of EBIT can be
converted to an indifference level of sales using the firm's fixed costs FC
and percentage contribution margin (l‑v) by the equation:
(7)
since S = VC + FC + EBIT and VC = vS.
Uncommitted EPS
The calculations that permitted us to solve for the
EBIT‑EPS indifference point made no explicit allowance for the repayment of
the bond principal. Many bond contracts require that sinking‑fund payments
be made to a trustee. Thus, some of a company's earnings are committed, and
consequently not available to stockholders. Many times the sinking‑fund
payment is a mandatory fixed amount and is required by a clause in the bond
indenture. Sinking‑fund payments can represent a sizable cash drain on the
firm's liquid resources. Moreover, sinking‑fund payments are a return of
borrowed principal, so they are not tax deductible to the firm.
Because of the cash drain caused by sinking‑fund
requirements, the financial manager might be concerned with the uncommitted
earnings per share related to each financing plan. The calculation of
uncommitted earnings per share recognizes that sinking‑fund commitments have
been honored and the remaining part can be used for discretionary
purposes‑‑such as the payment of cash dividends.
If the sinking fund payment is denoted by SF, and
if no preferred stock is used, the EBIT indifference point for uncommitted
EPS (EPSu) can be calculated as:
The uncommitted indifference point (EBIT*u) is found
by the same method as before except that the EPS after the sinking fund
commitments are paid are equated to each other.
(8)
Notice that the sinking fund payments are treated
differently than interest payments in the equation. This happens because
payments to a sinking fund are not tax deductible to the firm and more must
be earned before taxes in order to have enough left after taxes to make the
payments.
An Example
Suppose XYZ Corporation could raise an additional
$100,000 by selling stock at $100/share or by selling bonds at par with a 10
percent coupon rate. With 1,000 shares of stock already outstanding the
stock financing would double the number of shares to 2,000. The firm
currently has no debt so its total interest expense under the debt
alternative would be $10,000 per year. Using equation (6) gives the EBIT‑EPS
indifference point as:
resulting in EPS of $5.00. If the firm has $10,000 of fixed costs and its
percentage contribution margin is 10 percent, the indifference level of
sales is:
Besides the indifference point, at least one other
point is needed to find the EPS ‑ EBIT line for each financing alternative.
The easiest point to find is the x‑intercept. This point is found by
setting EPS under each option equal to zero and solving for EBIT:
Equity
Debt
0 = EPSe
0 = EPSd
EBIT
=
0
EBIT = 10,000
Having found a second point for each financing
alternative, a line can be drawn showing all combinations of EBIT and EPS
for each financing alternative. Figure 3 illustrates that as long as sales
are greater than $300,000 (or EBIT greater than $20,000), the debt
alternative would give the firm higher EPS.
Suppose that the debt alternative requires an
annual sinking fund payment of $5,000. The EBIT indifference point for
uncommitted EPS with a 50 percent tax rate is
This is equivalent to sales of $500,000 and EPS of $10.00.
Again, a second point on the x‑axis can be found by
setting EPSu equal to zero and solving for EBIT which results in
20,000. Thus, if the company chose the debt financing alternative the first
$10,000 in EBIT would cover the interest and the second $10,000 in EBIT
would cover the sinking fund and taxes. Only for an EBIT greater than
$20,000 would earnings be great enough to fund dividend payments to the
common stockholder. The dashed line shows the level of uncommitted earnings
per share under the debt financing alternative.
Although the debt alternative would give the firm
the highest EPS as long as sales are greater than $300,000 (or EBIT greater
than $20,000), sales would have to be at least $500,000 (or EBIT of at least
$40,000) before the debt alternative would result in higher uncommitted EPS
than the common stock alternative.
Capital Structure
Decisions—FRICTO Analysis
Having discussed the effect financial leverage has
on a firm, the costs and benefits of different sources of funds can be
evaluated. Although a firm can raise money through an increasing variety of
tools, basically the firm faces two choices: debt or equity. Funds raised
through debt must eventually be repaid, typically with interest. Funds
raised through equity do not have a maturity date, but represent ownership
with the accompanying risk. The firm's mix of debt and equity is known as
its capital structure.
A convenient framework for analyzing the many
different factors that affect the capital structure decision is provided by
the acronym FRICTO. The initials represent major factors that the manager
should consider.
F = Flexibility
R = Risk
I = Income
C = Control
T = Timing
O = Other
These factors are not listed in order of priority
or importance. (It is just that FRIC'.TO sounds better than ICT'.FOR).
For each firm, and in different economic environments, the relative
importance of the various factors will differ. However, the manager should
ensure that all the important factors have been analyzed.
The first factor, flexibility, refers
to the future financing options for management. As capital is raised, the
choice among alternatives for raising capital in the future may be
narrowed. For example, raising capital today through debt may impose fixed
obligations and restrictive covenants that eliminate the possibility of
issuing additional debt tomorrow. Thus, for a firm that has future
capital needs the relevant decision may not be "equity vs. debt" but "debt
now and equity later vs. equity now and a choice later."
Besides capital for growth, companies also want to
have a financing reserve or backup liquidity to be able to raise capital
quickly to fund unforeseen needs like lawsuits, strikes, unsuccessful
marketing programs, casualty losses, etc. Here again, raising funds through
equity now often allows the financial manager to meet unforeseen situations
with reserve borrowing capacity later.
Risk and income
are so interrelated they cannot be discussed separately. For the investor,
equity is inherently more risky than debt since debt holders receive a fixed
payment and are "in line" before equity holders in the case of liquidation.
Because of the higher risk associated with holding equity, stockholders
demand a higher return than debt holders. Consequently, from the
firm's perspective, the cost of equity is always higher than the cost of
debt.
In addition to its comparative low cost, debt
has the advantage that interest expense is tax deductible and dividends are
not. In effect, the government is subsidizing debt by requiring less taxes
from firms who pay interest than those who do not pay interest. Thus,
management should take advantage of the low‑cost debt to boost the owner's
return by applying debt to projects earning more than the cost of borrowing
the necessary funds.
The income benefits of debt can be seen in Figure 3
where the EPS (income) with incremental debt financing is higher than the
EPS with incremental equity financing at all levels of EBIT above the
indifference point. Similarly, the earlier examples on financial leverage
illustrated that using debt can yield large improvements in income (EPS)
with relatively small increases in EBIT. However, Figure 3 also illustrates
the risk disadvantages of debt.
Financial leverage, however, also magnifies
declines in EBIT and therefore increases the general riskiness of the firm.
When considering the effects of risk on capital structure decisions,
business risk, as well as financial risk must be looked at. Financial risk
is typically measured by using the following common ratios.
Debt
Ratio = Total Liabilities
Total Assets
Times
Interest = EBIT
Earned (XIE) Interest Expense
Fixed
Charge = EBIT + TDFC
Coverage Interest + TDFC
Debt
Service = EBIT + DEP + TDFC + NTDFC
Coverage Interest + TDFC + NTDFC/(1‑tx)
where:
TDFC
= Tax deductible fixed charges other than interest (lease payments,
etc.)
NTDFC
= Non‑tax deductible fixed charges (principal repayment, etc.)
The use of debt consequently has both a positive
and a negative effect on the value of a firm. Debt enhances value by
increasing income (as long as EBIT is above the indifference point) but debt
also diminishes value by increasing risk. The relative size of the
income‑risk effects of debt must be evaluated before making the capital
structure decision. Appendix B explains an additional tool to measure the
trade‑offs between risk and income.
Control of a firm is
ultimately decided by stockholders. If management has a majority of the
outstanding shares, they must consider the effects that additional debt or
equity financing will have on the control of the firm. If concerned about
control, management may choose debt to avoid the dilution of control
resulting from new equity. If, however, management is not concerned about
control, then the control considerations are irrelevant to the capital
structure decision.
Timing has become an
increasingly important consideration for managers in the past decade as the
stock and bond markets have undergone extreme fluctuations. A firm may shy
away from issuing long‑term debt in periods of high interest rates like in
1981 when the yield on AAA bonds jumped to an average of 14.2% for the
year. Perhaps, with expectations of declining rates, a manager may feel the
timing is such that short‑term debt is better than long‑term debt.
Similarly, negative conditions and trends in the overall stock market and in
a firm's stock price can affect the desirability of issuing stock. The
significant issue is to consider the current state of the capital markets
and what opportunities might reasonably be expected in the future.
Other issues besides
flexibility, risk, income, control, and timing must be considered before
making the capital structure decision. Each situation is different but some
common "other" considerations are:
1. Asset
structure—Are assets tangible, suitable for use as collateral?
2. Floatation
costs—How much a investment bank will charge to float the issue?
3. Speed—How
soon will the funds be needed?
4. Management
attitudes—Is management conservative?
5.
Exposure—Will additional stock increase the stock's value because of greater
exposure or liquidity?
6. Market
valuation—Is the stock valued fairly?
The FRICTO approach to financing decisions does not
give answers. It does, however, give a helpful, systematic approach to
analyzing capital structure decisions. The tools presented in this paper do
not tell a manager that a debt ratio of 43% is the optimal capital
structure. However, a good financial manager with an understanding of
breakeven points, degrees of operating and financial leverage, indifference
points, and FRICTO analysis can set an appropriate range for the capital
structure; for example, a debt ratio of 40 to 45%.
APPENDIX A
Financial Leverage with
Preferred Stock
The body of this paper, when
discussing financial leverage, assumed that preferred stock was not included
in the capital structure of the firm and that no preferred dividends (PD)
were paid. For firms using preferred stock the EPS of the firm would be:
Notice first that the use of preferred stock in
financing acts similar to the use of debt in affecting the risk of earnings
available for common stockholders. The higher the preferred dividend
payments, the greater the degree of financial leverage will be. Notice
second that in the uncommitted EPS calculation preferred dividends are
treated like sinking funds which are also not tax deductible to the firm.
With the addition of preferred dividend payments
the formula for DFL (3') takes on an additional term to become:
The degree of combined leverage (4') changes similarly to become:
Since preferred dividends are deducted before
calculating EPS, the indifference level of EBIT (formula (6)) where EPS are
equal under two financing plans, and the uncommitted EPS indifference point
(formula (8)) are also altered.
The net effect of the additional terms in the two
formulas will generally be to increase the indifference point between the
debt and equity alternatives.
APPENDIX B
The Impact on
Stock Price
If EBIT is greater than the
EBIT ‑ EPS indifference point, the more highly leveraged financial plan
promises to deliver a larger EPS. Strict application of the criterion of
selecting the financial plan promising the highest EPS might have the firm
issuing debt most of the time. The primary weakness of the EBIT ‑ EPS
analysis is that it ignores the effects of risk on the firm's stock price
and cost of equity.
An approach similar to the EBIT ‑ EPS indifference
analysis uses the change in the firm's price‑earnings ratio (m) to capture
the effect on the firm's future stock price. Since the future stock price
for the firm is equal to the product of future EPS and the firm's
price‑earnings ratio, equating the firm's stock price under two different
financial plans and solving for the indifference EBIT using the same
technique as before gives
(9)
If no preferred dividends are being paid, the
indifference EBIT reduces to
(9')
Only if EBIT is greater than this indifference
point would the more highly leveraged financial plan result in a greater
future stock price for the firm. Otherwise, the potentially higher EPS
using more leverage would not be sufficient to offset the increased risk
investors perceive as reflected in a decline in the firm's P/E ratio. The
result would be a decrease in the firm's stock price even though EPS might
increase.
An Example
The example of XYZ
Corporation used previously can be expanded to show the effects of financial
leverage on the stock price of the firm. Suppose the debt financing plan
increases the risk of the firm enough to reduce the firm's price‑earnings
ratio from 16 to 10. Using formula (9') the resulting EBIT indifference
level for the stock price is:
This is equivalent to $600,000 in sales and a stock
price of $200. At this indifference level, using debt the EPS would be
equal to $20.00, while with equity, the EPS would be $12.50.
Consequently, as illustrated in Figure 3, the debt
alternative would give the firm the highest EPS as long as EBIT is greater
than $20,000. However, EBIT would have to be at least $40,000 before the
debt alternative would result in higher uncommitted EPS than the common
stock alternative. Finally, since the debt alternative increases the risk
of the firm enough to result in a decline in the firm's price‑earnings
ratio, EBIT must be at least $50,000 before the future stock price of the
firm is greater under the debt plan than under the equity plan. This is
illustrated in Figure 4.
Summary of Key
Relationships
|
Degree of Operating Leverage
|
 |
(1') |
|
Degree of Financial Leverage
(no preferred stock)
|
 |
(3') |
|
Degree of Combined Leverage
(no preferred stock)
|
 |
(4') |
|
Operating Breakeven
|
 |
(2) |
|
EPS Indifference
(no preferred stock)
|
 |
(6) |
|
Uncommitted EPS Indifference
(no preferred stock)
|
 |
(8) |
|
Stock Price Indifference
(no preferred stock)
|
 |
(9') |
| |
|
|
|
∏=3.141592
|
Surface Area Formulas |
|
(Math
|
Geometry | Surface Area Formulas) |
(pi = 
=
3.141592...)
Surface Area Formulas
In general, the surface area is the sum of all the areas of all the shapes
that cover the surface of the object.
Cube |
Rectangular Prism |
Prism |
Sphere |
Cylinder |
Units
Note: "ab" means "a" multiplied by "b". "a2" means "a
squared", which is the same as "a" times "a".
Be careful!! Units count. Use the same units for all measurements.
Examples
|
Surface Area of a Cube = 6 a 2
|
(a
is the length of the side of each edge of the cube)
In words, the surface
area of a cube is the area of the six squares that cover it. The area of one
of them is a*a, or a 2 . Since these are all the same, you can
multiply one of them by six, so the surface area of a cube is 6 times one of
the sides squared.
|
Surface Area of a Rectangular Prism = 2ab + 2bc + 2ac
|
(a,
b, and c are the lengths of the 3 sides)
In words, the surface
area of a rectangular prism is the are of the six rectangles that cover it.
But we don't have to figure out all six because we know that the top and
bottom are the same, the front and back are the same, and the left and right
sides are the same.
The area of the top and
bottom (side lengths a and c) = a*c. Since there are two of them, you get
2ac. The front and back have side lengths of b and c. The area of one of
them is b*c, and there are two of them, so the surface area of those two is
2bc. The left and right side have side lengths of a and b, so the surface
area of one of them is a*b. Again, there are two of them, so their combined
surface area is 2ab.
|
Surface Area of Any Prism |
(b
is the shape of the ends)
Surface Area = Lateral
area + Area of two ends
(Lateral area) =
(perimeter of shape b) * L
Surface Area = (perimeter
of shape b) * L+ 2*(Area of shape b)
|
Surface Area of a Sphere = 4 pi r 2
|
(r
is radius of circle)
|
Surface Area of a Cylinder = 2 pi r 2 + 2
pi r h |
(h
is the height of the cylinder, r is the radius of the top)
Surface Area = Areas of
top and bottom +Area of the side
Surface Area = 2(Area of
top) + (perimeter of top)* height
Surface Area = 2(pi
r 2) + (2 pi r)* h
In words, the easiest way
is to think of a can. The surface area is the areas of all the parts needed
to cover the can. That's the top, the bottom, and the paper label that wraps
around the middle.
You can find the area of
the top (or the bottom). That's the formula for area of a circle (pi r2).
Since there is both a top and a bottom, that gets multiplied by two.
The side is like the
label of the can. If you peel it off and lay it flat it will be a rectangle.
The area of a rectangle is the product of the two sides. One side is the
height of the can, the other side is the perimeter of the circle, since the
label wraps once around the can. So the area of the rectangle is (2 pi
r)* h.
Add those two parts
together and you have the formula for the surface area of a cylinder.
Surface Area = 2(pi
r 2) + (2 pi r)* h
