Borrowing and Earnings Per Share

Why Financing Choice Changes Earnings Per Share

A company can obtain funds by borrowing or by issuing common shares. Borrowing creates interest expense but does not, by itself, increase the number of common shares. A common-stock issue avoids that additional interest expense but increases the share count. Because earnings per share (EPS) depends on both net income and common shares, the financing method can change reported EPS even when the funds support the same business.

The comparison is meaningful only when the operating assumptions are held consistent. In particular, use the same EBIT, tax rate, financing amount, and reporting period for both alternatives. EPS is an accounting measure of earnings allocated to each common share; it is not, by itself, a measure of the company’s value or a complete basis for choosing a financing plan.

Definition: Earnings per share is net income available to common shareholders divided by the weighted-average number of common shares outstanding during the reporting period. In the basic model used here, there are no preferred dividends or other adjustments to earnings available to common shareholders. If the common-share count is unchanged throughout the period, the weighted-average share count equals that constant count.

The EPS Model for the Two Financing Alternatives

Assume a hypothetical company has EBIT, denoted $E$, and $N$ common shares outstanding for the full year. It needs to raise $F$ dollars for that year. Under the debt alternative, it borrows $F$ for the full year at an annual interest rate $r$, so the additional annual interest expense is $rF$. Under the equity alternative, it issues $q$ new common shares at the beginning of the year. Assume the issue has no fees, the shares are outstanding for the full year, and the company has no other financing changes.

Let $I_0$ be any interest expense that is already present under both alternatives. Let the corporate tax rate be $\tau$. For the formulas below, assume that earnings before tax are positive under each alternative, the tax rate is the same in both cases, and all interest shown is tax-deductible. Thus, taxes equal $\tau$ times earnings before tax. These assumptions matter: if one alternative produces a tax loss, actual tax treatment may not equal a simple tax-rate calculation.

\text{EPS}_{D} = \frac{(E-I_0-rF)(1-\tau)}{N}, \qquad \text{EPS}_{E} = \frac{(E-I_0)(1-\tau)}{N+q}

The subscripts $D$ and $E$ refer to debt financing and equity financing, respectively. The debt-financed company deducts both its existing interest and the new borrowing’s interest before calculating tax. Its common-share count remains $N$. The equity-financed company has no new interest from this funding choice, but its share count becomes $N+q$. If the issue price is $P$ dollars per share and the company must raise $F$, then $q=F/P$, provided the share issue is made at that price.

Set the operating result.
Use the same EBIT for both financing alternatives unless the problem explicitly states that financing changes operations.

Find each alternative’s interest expense.
Add the new borrowing’s interest to any interest expense common to both alternatives. Do not add borrowing interest to the equity-financed case.

Calculate taxes and net income.
For positive earnings before tax, multiply earnings before tax by $1-\tau$ to obtain net income under the stated assumptions.

Use the matching share count.
Divide debt-financed net income by the existing shares and equity-financed net income by existing shares plus newly issued shares.

Why the Formula Works

The formula follows from the sequence used to determine earnings available to common shareholders. Start with EBIT, subtract interest to obtain earnings before tax, subtract taxes to obtain net income, and divide by the weighted-average common shares. In this model, the debt alternative has interest $I_0+rF$, whereas the equity alternative has interest $I_0$.

\begin{aligned} \text{Earnings before tax under debt} &= E-I_0-rF,\\ \text{Taxes under debt} &= \tau(E-I_0-rF),\\ \text{Net income under debt} &=(E-I_0-rF)-\tau(E-I_0-rF)\\ &=(E-I_0-rF)(1-\tau). \end{aligned}

Dividing this net income by $N$, the unchanged common-share count, gives $\text{EPS}_{D}$. Under equity financing, the same steps give net income $(E-I_0)(1-\tau)$, but the new shares increase the denominator to $N+q$. This establishes both expressions and shows why a comparison must account for the numerator and denominator together.

Worked Comparisons

Worked Example: Comparing a $900,000 Borrowing With a Share Issue

A hypothetical company has EBIT of $900,000, 300,000 common shares outstanding, and no existing interest expense. It needs $900,000 for a full year. It can borrow at 10% or issue 60,000 common shares. The tax rate is 25%. Assume positive taxable earnings, deductible interest, no fees or preferred dividends, and that the new shares are outstanding for the full year. Calculate EPS under both alternatives and identify which produces the higher EPS. Report EPS to the nearest cent.

Method. Calculate interest and after-tax net income separately for each financing choice, then divide by that choice’s share count. This avoids applying the debt alternative’s share denominator to the equity alternative.

Debt alternative. Annual interest is $0.10\times \$900{,}000=\$90{,}000$. Earnings before tax are $\$900{,}000-\$90{,}000=\$810{,}000$. Taxes are $0.25\times \$810{,}000=\$202{,}500$, so net income is $\$810{,}000-\$202{,}500=\$607{,}500$. The share count remains 300,000. Therefore, EPS is $\$607{,}500/300{,}000=\$2.025$, or $2.03 per share to the nearest cent.

Equity alternative. There is no new interest expense. Earnings before tax are $900,000, taxes are $0.25\times \$900{,}000=\$225{,}000$, and net income is $\$900{,}000-\$225{,}000=\$675{,}000$. The share count is $300{,}000+60{,}000=360{,}000$. EPS is $\$675{,}000/360{,}000=\$1.875$, or $1.88 per share to the nearest cent.

Check and conclusion. The debt alternative has the lower net income, $607,500 versus $675,000, but also has fewer shares. Its exact EPS of $2.025 exceeds the equity alternative’s exact EPS of $1.875, so debt produces the higher EPS in this example. The displayed cents are rounded only after the full calculation.

Worked Example: Carrying Existing Interest Through Both Alternatives

A hypothetical company has EBIT of $1,200,000, 240,000 common shares, and existing annual interest expense of $120,000. It needs $600,000 for a full year. It can borrow the funds at 8% or issue 40,000 common shares. The tax rate is 30%. Assume positive taxable earnings, deductible interest, no fees or preferred dividends, and that the shares are outstanding for the full year. Calculate both EPS amounts to the nearest cent.

Method. Keep the existing $120,000 interest in both cases. Add the new borrowing interest only in the debt case. This prevents an existing financing cost from disappearing in the equity calculation.

Debt alternative. New interest is $0.08\times \$600{,}000=\$48{,}000$. Total interest is $\$120{,}000+\$48{,}000=\$168{,}000$. Earnings before tax are $\$1{,}200{,}000-\$168{,}000=\$1{,}032{,}000$. Taxes are $0.30\times \$1{,}032{,}000=\$309{,}600$, leaving net income of $\$1{,}032{,}000-\$309{,}600=\$722{,}400$. The share count remains 240,000, so EPS is $\$722{,}400/240{,}000=\$3.01$.

Equity alternative. Total interest remains $120,000. Earnings before tax are $\$1{,}200{,}000-\$120{,}000=\$1{,}080{,}000$. Taxes are $0.30\times \$1{,}080{,}000=\$324{,}000$, leaving net income of $756,000. The share count is $240{,}000+40{,}000=280{,}000$. EPS is $\$756{,}000/280{,}000=\$2.70$.

Check and conclusion. Equity financing gives $33,600 more net income, and it also adds 40,000 shares. After including both effects, debt EPS is $3.01 and equity EPS is $2.70. Debt produces the higher EPS for the stated assumptions. The existing interest expense was included in both earnings-before-tax calculations.

Worked Example: When Equity Financing Produces Higher EPS

A hypothetical company has EBIT of $300,000, 200,000 common shares, and no existing interest expense. It needs $500,000 for a full year. The debt alternative is a loan at 9%; the equity alternative is a share issue at $25 per share. The tax rate is 20%. Assume positive taxable earnings, deductible interest, no fees or preferred dividends, and that new shares are outstanding for the full year. Find EPS under both alternatives to the nearest cent.

Method. Convert the equity proceeds into the number of new shares, then calculate the after-tax earnings and EPS for each case. This example also checks the mistaken assumption that borrowing must always produce higher EPS.

Debt alternative. Annual interest is $0.09\times \$500{,}000=\$45{,}000$. Earnings before tax are $\$300{,}000-\$45{,}000=\$255{,}000$. Taxes are $0.20\times \$255{,}000=\$51{,}000$, so net income is $\$255{,}000-\$51{,}000=\$204{,}000$. EPS is $\$204{,}000/200{,}000=\$1.02$.

Equity alternative. The new share count is $\$500{,}000/\$25=20{,}000$. Earnings before tax remain $300,000 because this alternative adds no interest expense. Taxes are $0.20\times \$300{,}000=\$60{,}000$, leaving net income of $240,000. The total share count is $200{,}000+20{,}000=220{,}000$, so EPS is $\$240{,}000/220{,}000=\$1.090909\ldots$, or $1.09 per share to the nearest cent.

Check and conclusion. The equity alternative produces higher EPS: $1.09 compared with $1.02 under debt. Its higher net income more than offsets the additional shares in this case. Thus, the direction of the EPS comparison depends on the inputs; neither financing method must always produce the higher EPS.

Common Mistakes and Limits of the Comparison

A frequent error is to use the equity-financed share count in the debt calculation, or the debt-financed share count in the equity calculation. In the first worked example, this incorrect debt calculation would be $\$607{,}500/360{,}000=\$1.6875$, because it wrongly includes the 60,000 shares that are issued only under the equity alternative. The correct debt calculation is $\$607{,}500/300{,}000=\$2.025$. Each numerator must be paired with the shares outstanding under that same alternative.

Other checks help keep the comparison sound:

Do not omit interest. Subtract borrowing interest before computing taxes and net income.
Do not tax the same amount twice. Calculate tax on earnings before tax, then subtract tax once to obtain net income.
Carry through common interest. Existing interest remains in both alternatives unless the problem says it changes.
Convert proceeds to shares carefully. For a share issue, divide the amount raised by the issue price to find the new shares.
Respect the reporting period. If shares are issued during a year, the denominator is weighted for the time those shares are outstanding, not automatically treated as if all were outstanding for the full year.

The model also has boundaries. A tax-rate shortcut such as $(E-I)(1-\tau)$ assumes positive taxable earnings and the same applicable tax rate. It may not describe a loss-making company, where tax-loss carryforwards, tax credits, or other rules affect taxes. Likewise, fees, preferred dividends, changing operations, or other financing terms must be incorporated if the problem supplies them.

Key takeaway: To compare borrowing with a common-share issue, calculate after-tax earnings under each alternative and divide by its own weighted-average common shares. Higher EPS is a result for the stated assumptions, not a general guarantee that one financing method is superior.

Check Your Understanding

For each hypothetical company, assume the stated tax rate applies to positive earnings before tax, interest is deductible, there are no fees or preferred dividends, and any newly issued shares are outstanding for the full year unless noted. Round final EPS to the nearest cent.

A company has EBIT of $720,000 and 180,000 common shares, and needs $300,000. It can borrow at 6% or issue shares at $30 each. The tax rate is 25%. Calculate EPS under each alternative and state which is higher. (Answer: Debt EPS = $2.93; equity EPS = $2.84; debt is higher.)
A company has EBIT of $640,000, 160,000 common shares, and existing annual interest expense of $40,000. It needs $400,000, which it can borrow at 10% or raise by issuing shares at $20 each. The tax rate is 25%. Calculate both EPS amounts. (Answer: Debt EPS = $2.63; equity EPS = $2.50; debt is higher.)
A company has EBIT of $250,000, 100,000 common shares, and no existing interest. It needs $200,000, available as debt at 12% or equity issued at $10 per share. The tax rate is 30%. Calculate both EPS amounts and identify the higher result. (Answer: Debt EPS = $1.58; equity EPS = $1.46; debt is higher.)
A company has net income available to common shareholders of $300,000 for the year. It had 100,000 common shares outstanding from January 1 through June 30, then issued 20,000 shares on July 1. Find the weighted-average shares and EPS. (Answer: Weighted-average shares = 110,000; EPS = $2.73.)
A company has EBIT of $300,000, 200,000 common shares, and no existing interest. It needs $500,000, available as debt at 9% or equity issued at $25 per share. The tax rate is 20%. Calculate both EPS amounts and state which is higher. (Answer: Debt EPS = $1.02; equity EPS = $1.09; equity is higher.)

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