Combined Operating and Financial Leverage

Why Combine Operating and Financial Leverage?

A change in sales can affect common shareholders’ earnings through two separate layers. Fixed operating costs make a change in sales produce a larger percentage change in operating income (EBIT). Fixed interest expense can then make that EBIT change produce a still larger percentage change in earnings available to common shareholders. Combined leverage measures the overall relationship between a percentage change in sales and the resulting percentage change in common earnings.

The calculation brings together the degree of operating leverage (DOL) and the degree of financial leverage (DFL). These measures are most useful when interpreted at a specified baseline: the same fixed costs and interest expense can imply different leverage at different sales levels. For an actuarial finance candidate, the key is to calculate each measure using its correct earnings denominator, then check whether the model’s assumptions support the estimate. This method is aligned with the SOA VEE Accounting and Finance syllabus.

Definition: The degree of combined leverage (DCL) is the percentage change in earnings available to common shareholders, or in earnings per common share when the number of common shares is fixed, divided by the percentage change in sales. Under the standard model below, DCL equals DOL multiplied by DFL.

The Model and the Leverage Measures

Assume a firm sells one product, or has a constant sales mix. Let $S$ be sales revenue, $V$ variable operating costs, $F$ fixed operating costs, and $I$ interest expense. The contribution margin is $S-V$, and EBIT is contribution margin less fixed operating costs. Assume unit selling price and variable cost per sales dollar are constant, while fixed operating costs and interest expense do not change over the relevant sales range.

For the formulas that include taxes and preferred dividends, let $T$ be a constant tax rate between zero and one, and let $PD$ be a fixed preferred dividend. Assume EBIT exceeds interest, taxable income is positive, and the firm has enough earnings to pay the stated preferred dividend. Common earnings are then $(EBIT-I)(1-T)-PD$. The number of common shares is fixed if the result is interpreted as a percentage change in earnings per share.

At a baseline with positive EBIT and positive earnings available to common shareholders, the three degrees of leverage are:

DOL=\frac{S-V}{EBIT}, \qquad DFL=\frac{EBIT(1-T)}{(EBIT-I)(1-T)-PD}, \qquad DCL=DOL\times DFL.

When there are no preferred dividends, the constant tax factor cancels from DFL, giving $DFL=EBIT/(EBIT-I)$. When preferred dividends are present, the tax factor does not cancel against the fixed dividend. Equivalently, provided $T<1$, the DFL denominator can be expressed as $EBIT-I-PD/(1-T)$.

Multiplying the DOL and DFL formulas gives another useful form:

DCL=\frac{(S-V)(1-T)}{(EBIT-I)(1-T)-PD}.

If there are no preferred dividends, this simplifies to $DCL=(S-V)/(EBIT-I)$. Use the version that matches the firm’s financing and the definition of earnings being analyzed; do not include preferred dividends when none are specified.

Why the Product Formula Holds

The product relationship follows from the chain of percentage changes. DOL compares the percentage change in EBIT with the percentage change in sales. DFL compares the percentage change in common earnings with the percentage change in EBIT. Multiplying cancels the intermediate EBIT percentage change.

\frac{\%\Delta EBIT}{\%\Delta S} \times \frac{\%\Delta E_c}{\%\Delta EBIT} = \frac{\%\Delta E_c}{\%\Delta S} =DCL,

where $E_c$ denotes earnings available to common shareholders. The formula can also be checked directly. Let $m$ be the contribution margin per sales dollar, so $S-V=mS$. If sales change by $\Delta S$, and the firm stays within the stated operating range, EBIT changes by $m\Delta S$. With a constant tax rate and fixed interest and preferred dividends, common earnings change by $(1-T)m\Delta S$. Therefore:

\frac{\Delta E_c}{E_c} = \frac{(1-T)mS}{E_c}\frac{\Delta S}{S} = DCL\frac{\Delta S}{S}.

This derivation explains why the percentage estimate is exact in the stated linear model when the same baseline is used and the firm remains in the same positive-income tax and dividend conditions. In practice, the estimate may only be approximate if selling prices, variable cost rates, fixed costs, taxes, or financing change as sales change.

Worked Calculations

Worked Example: A Sales Increase With No Preferred Dividends

A hypothetical manufacturer has annual sales of $1,200,000, variable operating costs of $720,000, fixed operating costs of $300,000, and annual interest expense of $60,000. Its tax rate is 25%, it has no preferred dividends, and its common share count is fixed. Estimate the change in common earnings if sales increase by 2%, then verify the estimate using the revised figures.

Method. First calculate the baseline contribution margin, EBIT, taxable income, and common earnings. Then calculate DOL, DFL, and DCL. The fixed-cost and fixed-interest assumptions allow the leverage estimate to be checked against a full recalculation.

Contribution margin is $S-V=\$1{,}200{,}000-\$720{,}000=\$480{,}000$. EBIT is $\$480{,}000-\$300{,}000=\$180{,}000$. Earnings before tax are $\$180{,}000-\$60{,}000=\$120{,}000$. Tax is $0.25(\$120{,}000)=\$30{,}000$, so common earnings are $\$120{,}000-\$30{,}000=\$90{,}000$.

The degrees of leverage are:

DOL=\frac{\$480{,}000}{\$180{,}000}=2.6667,\qquad DFL=\frac{\$180{,}000}{\$120{,}000}=1.5,

so $DCL=2.6667(1.5)=4.0$. The estimated common-earnings change is $4.0(2\%)=8\%$.

Verification. A 2% sales increase is $\$1{,}200{,}000(0.02)=\$24{,}000$, giving new sales of $1,224,000. Variable costs rise by $0.60(\$24{,}000)=\$14{,}400$, because the baseline variable-cost ratio is $\$720{,}000/\$1{,}200{,}000=0.60$. Contribution margin rises by $\$24{,}000-\$14{,}400=\$9{,}600$, and EBIT becomes $\$180{,}000+\$9{,}600=\$189{,}600$. Earnings before tax are $\$189{,}600-\$60{,}000=\$129{,}600$. Tax is $\$32{,}400$, so common earnings are $\$97{,}200$. The increase is $\$97{,}200-\$90{,}000=\$7{,}200$, or $\$7{,}200/\$90{,}000=8\%$. The check agrees with DCL.

Common mistake avoided: DOL uses EBIT, not earnings before tax, as its denominator. Using $\$480{,}000/\$120{,}000$ would incorrectly include interest in the operating leverage measure.

Worked Example: A Sales Decline and the Earnings Check

A hypothetical service company has sales of $800,000, variable operating costs of $480,000, fixed operating costs of $200,000, and interest expense of $40,000. Its tax rate is 30%, it has no preferred dividends, and its share count is unchanged. Estimate the effect on common earnings of a 5% decline in sales and verify it.

Method. Compute leverage at the original sales level. Apply the combined percentage estimate to baseline earnings, then recompute earnings after the sales decline to check the result.

The contribution margin is $\$800{,}000-\$480{,}000=\$320{,}000$, and EBIT is $\$320{,}000-\$200{,}000=\$120{,}000$. Earnings before tax are $\$120{,}000-\$40{,}000=\$80{,}000$. Tax is $0.30(\$80{,}000)=\$24{,}000$, so baseline common earnings are $\$56{,}000$.

DOL=\frac{\$320{,}000}{\$120{,}000}=2.6667,\qquad DFL=\frac{\$120{,}000}{\$80{,}000}=1.5,\qquad DCL=4.0.

The estimated common-earnings change is $4.0(-5\%)=-20\%$, a decline of 20%.

Verification. Sales fall by $0.05(\$800{,}000)=\$40{,}000$, to $760,000. The variable-cost ratio is $0.60$, so variable costs fall by $0.60(\$40{,}000)=\$24{,}000$, to $456,000. Contribution margin is now $\$760{,}000-\$456{,}000=\$304{,}000$, down by $16,000. EBIT is $\$304{,}000-\$200{,}000=\$104{,}000$. Earnings before tax are $\$104{,}000-\$40{,}000=\$64{,}000$, tax is $0.30(\$64{,}000)=\$19{,}200$, and common earnings are $44,800. The change is $\$44{,}800-\$56{,}000=-\$11{,}200$, which is $-\$11{,}200/\$56{,}000=-20\%$. The verification agrees.

Common mistake avoided: A decline in sales does not reduce EBIT by the same percentage as sales when fixed operating costs remain in place. The DOL factor captures that difference; applying only the sales decline to earnings would miss the operating and financing effects.

Worked Example: Preferred Dividends and Common Earnings

A hypothetical equipment supplier has contribution margin of $600,000, fixed operating costs of $360,000, interest expense of $40,000, a tax rate of 25%, and fixed preferred dividends of $30,000. Estimate the change in common earnings if sales increase by 4%. Assume the tax rate and all fixed amounts remain unchanged.

Method. Because preferred dividends reduce earnings available to common shareholders after tax, include them in the DFL denominator. Then verify by recalculating common earnings after the sales change.

EBIT is $\$600{,}000-\$360{,}000=\$240{,}000$. Earnings before tax are $\$240{,}000-\$40{,}000=\$200{,}000$, and tax is $0.25(\$200{,}000)=\$50{,}000$. Net income after tax is $150,000, so earnings available to common shareholders are $\$150{,}000-\$30{,}000=\$120{,}000$.

DOL=\frac{\$600{,}000}{\$240{,}000}=2.5,\qquad DFL=\frac{\$240{,}000(0.75)}{\$120{,}000}=1.5, \qquad DCL=2.5(1.5)=3.75.

A 4% sales increase therefore implies a common-earnings increase of $3.75(4\%)=15\%$.

Verification. The contribution margin rises by $0.04(\$600{,}000)=\$24{,}000$, so EBIT becomes $264,000. Earnings before tax are $\$264{,}000-\$40{,}000=\$224{,}000$, and tax is $\$56{,}000$. Net income is $168,000; after the unchanged $30,000 preferred dividend, common earnings are $138,000. The increase is $\$138{,}000-\$120{,}000=\$18{,}000$, and $\$18{,}000/\$120{,}000=15\%$. The result agrees with DCL.

Common mistake avoided: DFL is not $EBIT/(EBIT-I)$ when fixed preferred dividends are part of the common-earnings calculation. That simpler form applies here only when there are no preferred dividends.

Interpretation, Scope, and Exam Traps

A DCL of 4 means that, at the baseline and under the model assumptions, a 1% sales change corresponds to a 4% change in common earnings. It does not mean common earnings change by four percentage points, nor does it mean the firm’s sales change by four times the earnings change. The sign of the sales change carries through: a sales decrease implies an earnings decrease when the firm remains in the positive-income range.

The measure depends on the baseline. In particular, if EBIT or earnings available to common shareholders are close to zero, a leverage ratio can become very large and the percentage-change interpretation can be unstable. If the baseline common earnings are zero, the percentage change in those earnings is undefined. If taxable income becomes negative, losses alter the tax calculation; if preferred dividends are not paid or are variable, the stated formula also needs adjustment.

A useful calculation sequence is to keep operating and financing quantities separate:

Build the operating baseline.
Calculate contribution margin as sales less variable costs, then subtract fixed operating costs to obtain EBIT.

Build the common-earnings baseline.
Subtract interest, apply the assumed tax rate, and subtract fixed preferred dividends if present.

Calculate the leverage measures.
Use contribution margin divided by EBIT for DOL, the appropriate common-earnings formula for DFL, and multiply them for DCL.

Apply and check the estimate.
Multiply the sales percentage change by DCL. When the model assumptions hold, recalculate the changed figures to confirm the result.

One frequent trap is to use earnings before tax as the DOL denominator. Interest is a financing cost, not an operating cost; including it in DOL incorrectly mixes the two leverage effects. Another is to apply the tax rate to preferred dividends. In this model, tax is applied to earnings after interest, and preferred dividends are then deducted to find common earnings. Keeping those steps in order prevents both errors.

Key takeaway: Under a constant contribution margin, fixed operating costs, fixed interest, and stable tax and preferred-dividend conditions, $DCL=DOL\times DFL$ translates a sales percentage change into a common-earnings percentage change. State the baseline and check that the assumptions still hold before interpreting the result.

Check Your Understanding

For each hypothetical firm, use the stated baseline and assumptions. Treat the requested leverage estimates as applying at that baseline.

A firm has sales of $500,000, variable costs of $300,000, fixed operating costs of $120,000, and interest expense of $20,000. It has no preferred dividends and a constant tax rate. Calculate DOL, DFL, and DCL, then estimate the common-earnings change for a 3% sales increase. (Answer: DOL = 2.5; DFL = 1.3333; DCL = 3.3333; estimated common-earnings increase = 10%.)
A firm has sales of $1,000,000, variable costs of $650,000, fixed operating costs of $250,000, and interest expense of $25,000. It has no preferred dividends. Estimate the common-earnings change if sales fall by 2%. (Answer: DOL = 3.5; DFL = 1.3333; DCL = 4.6667; estimated common-earnings decrease = 9.3333%.)
A firm has contribution margin of $420,000, fixed operating costs of $180,000, interest expense of $40,000, a 30% tax rate, and fixed preferred dividends of $28,000. Calculate DOL, DFL, and DCL, then estimate the common-earnings change for a 2% sales increase. (Answer: Baseline common earnings = $112,000; DOL = 1.75; DFL = 1.5; DCL = 2.625; estimated increase = 5.25%.)
A firm has sales of $750,000, variable costs of $450,000, fixed operating costs of $210,000, and interest expense of $30,000. It has no preferred dividends. If sales fall by 4%, calculate DCL and verify the estimated percentage change by finding revised common earnings; assume taxes are constant and positive. (Answer: Baseline EBIT = $90,000; baseline earnings before tax = $60,000; DOL = 3.3333; DFL = 1.5; DCL = 5; common earnings decrease by 20%.)
A firm has sales of $600,000, variable costs of $360,000, fixed operating costs of $150,000, and interest expense of $30,000. It has no preferred dividends, fixed shares, and a constant tax rate. What sales percentage increase is needed for an estimated 12% increase in common earnings? (Answer: DOL = 2.6667; DFL = 1.5; DCL = 4; required sales increase = 3%.)

What You'll Learn