How Financial Leverage Changes Return on Equity

Why Borrowing Can Change Shareholder Returns

A company can finance its assets with common equity, debt, or a combination of both. Borrowing does not by itself improve the operating performance of those assets: it does, however, add interest charges that must be paid before common shareholders receive any residual earnings. Because debt can also reduce the amount of equity needed to finance the assets, it changes the relationship between company earnings and the common shareholders’ equity supporting them.

The effect depends importantly on how the operating return compares with the cost of debt. If the assets earn more than the debt costs, the earnings left after interest may support a higher return on the smaller equity base. If the assets earn less than the debt costs, interest can reduce the return available to common shareholders. The comparison is useful, but it must be made with consistent assumptions about taxes, time period, and the equity measure used.

Definition: Return on equity (ROE) is net income available to common shareholders divided by common shareholders’ equity for the period. In these examples, equity is treated as constant during the period, so the stated common equity is the denominator. In financial statements, average common equity is often used when equity changes over the period. The operating return on assets used here is operating income before interest and taxes divided by total assets.

The calculations below assume that the company has no preferred shares, pays the stated interest for a full year, and applies the stated tax rate to positive income before tax. In the unleveraged comparisons, the same assets earn the same operating income, but debt is replaced by equity. Unless stated otherwise, all dollar amounts are annual and all equity figures are common equity. These are simplified comparisons: actual taxes, financing terms, and balance-sheet values can vary.

From Operating Income to Common Shareholders’ ROE

Interest is a financing charge, not an operating expense in the comparisons here. Start with operating income, subtract interest to obtain income before tax, then subtract tax to obtain net income. Dividing that net income by common equity gives ROE.

\begin{aligned} \text{Income before tax} &= \text{Operating income} - \text{Interest expense},\\ \text{Net income} &= \text{Income before tax} - \text{Income tax},\\ \text{ROE} &= \frac{\text{Net income}}{\text{Common equity}}. \end{aligned}

This calculation follows directly from the order in which the claims are paid. Lenders receive the contracted interest before the residual earnings belong to common shareholders. When taxable income is positive and the tax rate is $T$, the tax amount in this simplified model is $T$ times income before tax. Therefore, net income is income before tax multiplied by $1-T$. If income before tax is zero or negative, or if tax rules treat deductions and losses differently, that simple tax calculation may not apply.

Calculation rule: With positive income before tax and a constant tax rate $T$, calculate common shareholders’ net income as $(\text{Operating income} - \text{Interest expense})(1-T)$. Then divide by common equity. Do not subtract interest twice, and do not apply the tax rate to operating income before accounting for interest.

Worked Example: Operating Return Above the Debt Cost

A hypothetical firm owns assets of $1,000,000 that generate annual operating income of $120,000. Compare an all-equity financing with a financing that includes $400,000 of debt at 8% interest. The leveraged firm’s remaining financing is common equity. Use a 25% tax rate, and assume positive taxable income.

Method. Calculate operating income once, then calculate net income and ROE for each financing mix. This isolates the financing effect: the assets and operating income do not change.

All-equity case. There is no interest expense, and common equity is $1,000,000. Income before tax is $120,000. Tax is $0.25 \times \$120,000=\$30,000$, so net income is $\$120,000-\$30,000=\$90,000$. Thus:

\text{ROE}_{\text{all equity}}=\frac{\$90{,}000}{\$1{,}000{,}000}=9.00\%.

Leveraged case. Interest expense is $0.08 \times \$400,000=\$32,000$. Common equity is $\$1,000,000-\$400,000=\$600,000$. Income before tax is $\$120,000-\$32,000=\$88,000$. Tax is $0.25 \times \$88,000=\$22,000$, so net income is $\$88,000-\$22,000=\$66,000$. Therefore:

\text{ROE}_{\text{leveraged}}=\frac{\$66{,}000}{\$600{,}000}=11.00\%.

The operating return on assets is $\$120,000/\$1,000,000=12.00\%$, above the 8% debt cost. Borrowing reduces net income from $90,000 to $66,000, but it also reduces common equity from $1,000,000 to $600,000. In this case, the smaller equity base more than offsets the lower net income, so ROE rises from 9.00% to 11.00%. The calculation avoids the mistake of treating higher ROE as higher operating income: operating income remains $120,000.

When the Debt Cost Exceeds the Operating Return

The direction can reverse. If borrowing costs more than the return earned on the assets, interest consumes more of the operating income relative to the funds borrowed. The company still has to pay its interest, even when operations are weak. This makes the difference between operating performance and financing cost particularly important when judging a proposed debt level.

Worked Example: Operating Return Below the Debt Cost

A hypothetical company has $1,000,000 of assets and earns $60,000 of annual operating income. Compare all-equity financing with $400,000 of debt at 9% and $600,000 of common equity. Use a 25% tax rate.

Method. Use the same operating income in both cases, and calculate interest, tax, net income, and ROE separately. This prevents the financing comparison from being confused with a change in asset performance.

All-equity case. There is no interest expense. Tax is $0.25 \times \$60,000=\$15,000$, so net income is $\$60,000-\$15,000=\$45,000$. ROE is $\$45,000/\$1,000,000=4.50\%$.

Leveraged case. Interest is $0.09 \times \$400,000=\$36,000$. Income before tax is $\$60,000-\$36,000=\$24,000$. Tax is $0.25 \times \$24,000=\$6,000$, leaving net income of $\$18,000$. With common equity of $600,000:

\text{ROE}_{\text{leveraged}}=\frac{\$18{,}000}{\$600{,}000}=3.00\%.

The operating return on assets is $\$60,000/\$1,000,000=6.00\%$, below the 9% debt cost. Leveraged ROE is 1.50 percentage points lower than the all-equity ROE of 4.50%. A common error is to compare $60,000 of operating income directly with $36,000 of interest and stop there. That comparison indicates the company can cover interest in this example, but it does not calculate common shareholders’ return; taxes and the equity denominator still matter.

Same Debt, Different Operating Outcomes

A single forecast can obscure the fact that operating performance may vary. The following example holds the financing mix fixed while changing the operating return. The comparison helps locate the point at which operating income just covers interest, while also showing how ROE responds on either side of that point.

Worked Example: A Range of Operating Returns

A hypothetical firm has $1,200,000 of assets, financed with $400,000 of debt at 8% and $800,000 of common equity. Its tax rate is 25%. Compare annual operating returns on assets of 5%, 8%, and 12%, and calculate the leveraged ROE in each case. Also compare each result with the all-equity ROE at the same operating return.

Method. Interest remains fixed at $0.08 \times \$400,000=\$32,000$. For each operating return, multiply the rate by $1,200,000 to find operating income. Then subtract interest, calculate tax on positive income before tax, and divide net income by equity. In the all-equity case, interest is zero and equity is $1,200,000.

At a 5% operating return: operating income is $0.05 \times \$1,200,000=\$60,000$. Leveraged income before tax is $\$60,000-\$32,000=\$28,000$; tax is $0.25 \times \$28,000=\$7,000$; net income is $21,000. Leveraged ROE is $\$21,000/\$800,000=2.625\%$. All-equity net income is $\$60,000 \times 0.75=\$45,000$, giving ROE of $\$45,000/\$1,200,000=3.750\%$. Leverage lowers ROE.

At an 8% operating return: operating income is $0.08 \times \$1,200,000=\$96,000$. Leveraged income before tax is $\$96,000-\$32,000=\$64,000$; tax is $16,000; net income is $48,000; and leveraged ROE is $\$48,000/\$800,000=6.000\%$. All-equity net income is $\$96,000 \times 0.75=\$72,000$, so all-equity ROE is $\$72,000/\$1,200,000=6.000\%$. The operating return equals the debt cost, and the two ROEs match.

At a 12% operating return: operating income is $0.12 \times \$1,200,000=\$144,000$. Leveraged income before tax is $\$144,000-\$32,000=\$112,000$; tax is $28,000; net income is $84,000; and leveraged ROE is $\$84,000/\$800,000=10.500\%$. All-equity net income is $\$144,000 \times 0.75=\$108,000$, giving ROE of $\$108,000/\$1,200,000=9.000\%$. Leverage raises ROE.

The check is consistent across all three cases: interest is fixed at $32,000, equal to 8% of the $400,000 of debt. Operating income is below that cost per dollar of assets at 5%, matches it at 8%, and exceeds it at 12%. No intermediate result has been rounded.

How to Compare Financing Outcomes

A disciplined comparison keeps operating performance separate from financing and makes the relevant denominator explicit. The process is useful for a hypothetical financing decision or for interpreting a stated ROE.

Fix the operating case.
Specify the assets and operating income, or state the operating return and total assets. Use the same operating assumptions when comparing financing alternatives.

Calculate the financing charge.
Multiply debt principal by its annual interest rate for a full-year charge, adjusting the calculation if the debt is outstanding for only part of the year.

Find net income.
Subtract interest from operating income, then apply the stated tax treatment. Do not assume the tax rate applies to negative income unless the problem specifies that treatment.

Divide by common equity.
Use the equity attributable to common shareholders for that financing alternative and period. State whether the problem gives beginning, ending, or average equity.

Interpret, then check.
Compare the operating return with the debt cost and explain how both net income and the equity denominator changed. Verify that interest and taxes were each counted once.

Interpretation and Common Exam Traps

When the simplified assumptions in these examples apply, comparing the operating return on assets with the debt cost indicates the direction of the leverage effect. An operating return above the debt cost tends to raise ROE relative to all-equity financing; a return below the debt cost tends to lower it; and equality produces the same ROE. The comparison is not a promise of a particular realized return. It depends on the operating result, the debt terms, and the equity base.

ROE is an accounting return to common equity, not a complete measure of shareholder value or risk. Borrowing can increase the sensitivity of common shareholders’ earnings to changes in operating income because interest is a fixed financing charge. Thus a favorable ROE in one scenario does not establish that the financing choice is safe or that debt will remain affordable in a weaker scenario.

Comparing the wrong rates. Compare the operating return on the assets financed with the cost of debt, not net income per share with the interest rate.
Changing operating assumptions between cases. To isolate financial leverage, hold assets and operating income constant.
Ignoring the denominator. Debt usually reduces the equity needed to fund a given asset base. A higher ROE can occur even while net income falls.
Mixing pre-tax and after-tax quantities. State whether the comparison uses operating income before tax or net income after tax, and apply a consistent tax assumption.
Using total equity without checking the claim. ROE concerns common shareholders. Preferred claims, if present, must be handled before determining income and equity attributable to common shareholders.
Confusing positive earnings with favorable leverage. A firm may earn enough to pay interest yet still have lower ROE than it would without debt, as the second worked example shows.

Key takeaway: Calculate ROE from net income available to common shareholders divided by common equity. Borrowing can raise that ratio when operating returns exceed borrowing costs, but it can lower the ratio when operating returns fall short. Always show both the earnings calculation and the equity denominator.

Check Your Understanding

For each problem, assume annual interest, no preferred shares, and the stated tax rate on positive income before tax. Compare with all-equity financing only when requested.

A hypothetical firm has $800,000 of assets earning 8% before interest and taxes. It borrows $300,000 at 7%, with the rest financed by common equity. At a 25% tax rate, calculate leveraged net income and ROE, then compare ROE with the all-equity case. (Answer: leveraged net income $32,250 and ROE 6.45%; all-equity ROE 6.00%, so leverage raises ROE by 0.45 percentage points.)
A hypothetical business has $1,500,000 of assets earning $90,000 before interest and taxes. It finances $500,000 with debt at 8% and $1,000,000 with common equity. At a 20% tax rate, calculate leveraged ROE and all-equity ROE, and state which is higher. (Answer: leveraged ROE 4.00%; all-equity ROE 4.80%, so leverage lowers ROE by 0.80 percentage points.)
A hypothetical insurer’s investment assets total $2,000,000 and produce annual operating income of $220,000. It has $800,000 of debt at 5% and $1,200,000 of common equity. With a 30% tax rate, calculate net income, leveraged ROE, and all-equity ROE. (Answer: net income $126,000; leveraged ROE 10.50%; all-equity ROE 7.70%, so leverage raises ROE by 2.80 percentage points.)
A hypothetical firm has $900,000 of assets, $300,000 of debt at 9%, and $600,000 of common equity. It earns a 6% operating return on assets. At a 25% tax rate, calculate leveraged and all-equity ROE, then compare the operating return with the debt cost. (Answer: operating income $54,000; interest $27,000; leveraged net income $20,250 and ROE 3.375%; all-equity net income $40,500 and ROE 4.500%. The 6% operating return is below the 9% debt cost, so leverage lowers ROE by 1.125 percentage points.)

What You'll Learn