Roger ClarkeGrant McQueen

Revised 2001

Some Indicators of a Firm's Riskand Debt Capacity

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

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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

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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.

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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:

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(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

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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:

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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:

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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

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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.

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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:

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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.

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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

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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

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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.

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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?

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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%.

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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.

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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.

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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')

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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.

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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')

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