Roger Clarke
Grant McQueen
Revised 2001
Some Indicators of a Firm's Risk
and 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 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: