After-Tax EBIT-EPS Comparisons

Why Compare After-Tax EPS?

A financing plan affects both the income available to common shareholders and the number of shares among which that income is divided. Debt financing creates interest expense, which reduces pretax income; issuing equity increases the share count. Corporate taxes also affect the income left for shareholders, and deductible interest can reduce taxable income. An after-tax EBIT-EPS comparison brings these effects together.

The comparison is an accounting analysis at specified EBIT levels. It does not, by itself, establish which plan has the lower overall cost of capital or is preferable after considering risk, financing constraints, and other effects. Those questions require additional analysis.

Definition: EBIT is earnings before interest and taxes. For a financing plan with interest expense $I$, common shares outstanding $N$, and corporate tax rate $T$, earnings per share (EPS) is net income available to common shareholders divided by $N$. In the basic model, net income is calculated from EBIT after subtracting interest and corporate income tax.

The After-Tax EBIT-EPS Model

Use $E$ for EBIT, $I$ for annual interest expense, $T$ for the corporate tax rate, and $N$ for the number of common shares outstanding. For each financing plan, assume that EBIT and interest are stated for the same period, interest is deductible for tax purposes, and the tax rate is constant. Assume there are no preferred dividends, no other income or deductions, and no change in the tax rate between plans. Also assume that the stated share count represents the shares used to calculate EPS for the period.

When taxable income is positive, pretax income is $E-I$, corporate tax expense is $T(E-I)$, and net income available to common shareholders is the difference between pretax income and tax expense.

\text{Net income}=(E-I)-T(E-I)=(E-I)(1-T), \qquad \text{EPS}=\frac{(E-I)(1-T)}{N}.

This formula assumes $E-I>0$. If $E-I<0$, do not automatically treat multiplication by $1-T$ as the actual current-period tax result. A loss creates a tax benefit only if the applicable tax rules and the company’s circumstances allow that benefit to be used or recognized. If no benefit is available, current tax expense is zero and the loss remains $E-I$. If a benefit is available, its amount and timing should be specified.

Worked Example: Comparing Two Plans at Positive EBIT

A company is considering two ways to finance an expansion. Plan A has 100,000 common shares and no debt. Plan B has 60,000 common shares and $400,000 of debt at an annual interest rate of 8%. EBIT for the year is $200,000, and the corporate tax rate is 25%. Assume interest is deductible, both plans have positive taxable income, and there are no preferred dividends or other income or deductions. Calculate each plan’s tax, net income, and EPS, then identify which plan has higher EPS.

Method and setup. First calculate Plan B’s annual interest: $$400{,}000\times0.08=\$32{,}000$. Plan A has no interest, so its interest expense is $0. Taxable income is positive under both plans: Plan A has $200,000, and Plan B has $$200{,}000-\$32{,}000=\$168{,}000$.

Plan A. Tax is $$200{,}000\times0.25=\$50{,}000$. Net income is $$200{,}000-\$50{,}000=\$150{,}000$. EPS is $$150{,}000/100{,}000=\$1.50$ per share.

Plan B. Tax is $$168{,}000\times0.25=\$42{,}000$. Net income is $$168{,}000-\$42{,}000=\$126{,}000$. EPS is $$126{,}000/60{,}000=\$2.10$ per share.

Check and conclusion. Plan B has $24,000 less net income than Plan A, but it also has 40,000 fewer shares. Its EPS is therefore higher: $$2.10>\$1.50$. The calculation avoids comparing only net income or only the interest bill; both the after-tax numerator and the share-count denominator matter.

Why the Tax Factor May Cancel at Indifference

An EBIT-EPS indifference point is the EBIT level at which two plans produce equal EPS. Suppose Plan A has interest $I_A$ and shares $N_A$, while Plan B has interest $I_B$ and shares $N_B$. If both plans have positive taxable income and the same tax rate $T$, equality of EPS is

\frac{(E-I_A)(1-T)}{N_A} = \frac{(E-I_B)(1-T)}{N_B}.

Because positive taxable income is assumed and the same tax rate applies, $1-T$ is a common positive factor. Dividing both sides by it gives the pretax indifference equation. Cross-multiplying and collecting the terms in $E$ gives the following result, provided $N_A\ne N_B$:

\begin{aligned} \frac{E-I_A}{N_A}&=\frac{E-I_B}{N_B},\\ N_B(E-I_A)&=N_A(E-I_B),\\ E(N_B-N_A)&=N_BI_A-N_AI_B,\\ E^*&=\frac{N_BI_A-N_AI_B}{N_B-N_A}. \end{aligned}

This derivation explains an important feature of the basic model: if both plans face the same constant tax rate and are in the positive-taxable-income region, taxes reduce both EPS values by the same proportional factor. The tax rate therefore does not change their indifference EBIT. Taxes still change the EPS levels, and deductible interest changes taxable income, but the common tax factor cancels when solving for equality.

The formula must be used within its assumptions. If the proposed indifference EBIT leaves either plan with a loss, the positive-taxable-income model may not apply. If tax rates, deductions, tax-benefit availability, or other components of income differ between plans, the same factor may not cancel. If the plans have equal share counts, the displayed formula has a zero denominator; compare their EPS equations directly rather than using this expression.

Worked Example: Finding the After-Tax Indifference EBIT

Plan A has 100,000 shares and no debt. Plan B has 60,000 shares and $400,000 of debt at 8% interest. The tax rate is 25%. Assume the two plans have the same EBIT, interest is deductible, both plans have positive taxable income at the indifference point, and there are no preferred dividends or other income or deductions. Find the indifference EBIT and verify the EPS under both plans.

Method. Plan A has $N_A=100{,}000$ and $I_A=0$. Plan B has $N_B=60{,}000$ and annual interest $I_B=\$400{,}000\times0.08=\$32{,}000$. Use the indifference equation; because the tax rate is common and both plans are taxable at the solution, the factor $1-T$ cancels.

Solve. \[ E^*=\frac{(60{,}000)(0)-(100{,}000)(32{,}000)}{60{,}000-100{,}000} =\frac{-3{,}200{,}000{,}000}{-40{,}000} =\$80{,}000. \]

Verify Plan A. Taxable income is $80,000, tax is $$80{,}000\times0.25=\$20{,}000$, and net income is $60,000. EPS is $$60{,}000/100{,}000=\$0.60$.

Verify Plan B. Taxable income is $$80{,}000-\$32{,}000=\$48{,}000$. Tax is $$48{,}000\times0.25=\$12{,}000$, and net income is $36,000. EPS is $$36{,}000/60{,}000=\$0.60$. Both plans have positive taxable income, so the assumptions used to find the threshold are satisfied.

Check and interpretation. The independently calculated EPS values agree. The indifference EBIT is $80,000; at EBIT above or below this level, one plan’s EPS may exceed the other’s, subject to the model’s tax and income assumptions.

Losses and the Tax-Benefit Trap

A common error is to apply $(E-I)(1-T)$ mechanically when $E-I$ is negative. The arithmetic may be correct under an assumption that a tax benefit is usable, but that assumption is not automatic. For example, if pretax income is a loss of $90,000 and $T=30\%$, a fully usable tax benefit would be $$90{,}000\times0.30=\$27{,}000$. In that case, net loss is $-\$90{,}000+\$27{,}000=-\$63{,}000$. Equivalently, $(-\$90{,}000)(0.70)=-\$63{,}000$. The benefit is positive $27,000; the tax expense line, if shown as an expense, is negative $27,000.

If the company cannot use or recognize the benefit in the current period, current tax expense is zero and net loss remains $-\$90{,}000$. It is incorrect to report a $27,000 current tax benefit without a stated basis for its availability. In a real analysis, tax attributes, jurisdictional rules, and the timing of any future benefit require further information. For an exam-style comparison, use the tax treatment specified in the problem and state any necessary assumption.

Worked Example: Debt Plan Produces a Taxable Loss

A company compares Plan A, with 120,000 common shares and no debt, with Plan B, with 80,000 common shares and $1,000,000 of debt at 9% annual interest. EBIT is $0 and the tax rate is 30%. Assume no other income, deductions, or preferred dividends. The company cannot use or recognize a tax benefit from a current loss. Calculate EPS under both plans. Then calculate the alternative Plan B result if a current benefit at the full 30% rate were available.

Method and setup. Plan B’s interest is $$1{,}000{,}000\times0.09=\$90{,}000$. Plan A has pretax income of $$0-\$0=\$0$, so its tax and net income are both $0. Its EPS is $$0/120{,}000=\$0.00$.

Plan B with no usable current tax benefit. Pretax income is $$0-\$90{,}000=-\$90{,}000$. By assumption, current tax expense is $0, so net income is $-\$90{,}000-\$0=-\$90{,}000$. EPS is $-\$90{,}000/80{,}000=-\$1.125$, or $-\$1.13$ per share rounded to two decimal places.

Alternative if the benefit is currently usable. The tax benefit is $$90{,}000\times0.30=\$27{,}000$. Net income is therefore $-\$90{,}000+\$27{,}000=-\$63{,}000$, and EPS is $-\$63{,}000/80{,}000=-\$0.7875$, or $-\$0.79$ per share rounded to two decimal places.

Check and common mistake. Applying the 30% tax reduction gives $(-\$90{,}000)(0.70)=-\$63{,}000$, which assumes the $27,000 benefit is available. It does not describe the stated no-benefit case, where the loss is $-\$90{,}000$. In either case, Plan B’s share count is 80,000, not 120,000. The example shows why the loss-tax assumption must be settled before comparing after-tax EPS.

Common Mistakes and Practical Checks

Using EBIT as if it were net income. Subtract interest before calculating taxable income and net income.
Forgetting the share count. The plan with the greater total net income does not necessarily have the higher EPS.
Applying taxes to the wrong amount. Under this model, when taxable income is positive, tax is $T(E-I)$, not $TE$.
Assuming every loss creates an immediate tax benefit. Check whether the problem states that a loss benefit is usable or recognized.
Using the indifference formula outside its assumptions. Confirm that both plans have positive taxable income at the calculated threshold and that the same tax treatment applies.

A useful final check is to calculate EPS for each plan directly at the EBIT of interest, even after deriving an indifference point. This catches sign errors in interest, mistaken share counts, and thresholds that fall outside the assumed tax region. The comparison is aligned with the SOA VEE Accounting and Finance syllabus.

Check Your Understanding

For each problem, use the stated assumptions and check whether the tax treatment is appropriate before calculating EPS.

A company has EBIT of $300,000. Plan A has 150,000 shares and no debt. Plan B has 90,000 shares and $500,000 of debt at 9% annual interest. The tax rate is 30%; interest is deductible and both plans have positive taxable income. Calculate EPS under each plan and identify the higher EPS. (Answer: Plan A EPS = $1.40; Plan B EPS = $1.98; Plan B is higher.)
Plan A has 80,000 shares and no debt. Plan B has 50,000 shares and $300,000 of debt at 8% annual interest. Both plans have positive taxable income at indifference, and the same tax rate applies. Find the indifference EBIT. (Answer: $64,000.)
A company has EBIT of $50,000, interest of $70,000, and 40,000 shares. The tax rate is 20%, but no current tax benefit from the loss is available. Find EPS. Then find EPS if the full current tax benefit can be used. (Answer: $-\$0.50$ with no benefit; $-\$0.40$ with a usable benefit.)
Plan A has 100,000 shares and no debt; Plan B has 70,000 shares and $500,000 of debt at 8%. EBIT is $120,000, the tax rate is 25%, and both plans have positive taxable income. Calculate EPS under each plan and identify which is higher. (Answer: Plan A EPS = $0.90; Plan B EPS = $0.86 rounded to two decimals; Plan A is higher.)
Plan A has 90,000 shares and no debt. Plan B has 60,000 shares and $500,000 of debt at 6%. The common tax rate is 30%, and both plans are assumed to have positive taxable income at the indifference point. Find the indifference EBIT, then identify the higher-EPS plan at EBIT of $75,000. (Answer: Indifference EBIT = $90,000; at $75,000, Plan A has the higher EPS.)

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