Choosing Debt or Equity Across EBIT Scenarios

Why Compare Financing Plans Across EBIT Scenarios?

A financing plan can look attractive when operating income is strong and less attractive when it is weak. Debt reduces the number of shares that must divide earnings, but interest is a fixed obligation. All-equity financing avoids interest, but typically requires more shares. Comparing the plans at only one EBIT level can conceal these differences.

A useful comparison therefore tracks each plan across low, base, and high EBIT outcomes. It examines earnings per share (EPS), the ability of operating income to cover interest, and how widely EPS varies among the scenarios. This analysis, aligned with the SOA VEE Accounting and Finance syllabus, informs a financing decision; it does not make EPS alone a complete measure of shareholder value.

Definition: EBIT is earnings before interest and taxes. Under a financing plan with fixed interest expense $I$, earnings before tax are $EBIT-I$. EPS is earnings available to common shareholders divided by the number of common shares outstanding. Interest coverage is EBIT divided by interest expense, when interest expense is positive.

To make the comparison precise, use the following simplified model: EBIT is specified for each scenario; interest expense and the number of shares are fixed within each plan; there are no preferred dividends; and the corporate tax rate $T$ applies to positive taxable income. Unless a problem says otherwise, assume losses receive no immediate tax benefit. The plans finance the same operating assets, so their scenario EBIT values are comparable.

Model result: If taxable income is positive, net income under a plan with interest $I$ is $(EBIT-I)(1-T)$, and $EPS=(EBIT-I)(1-T)/N$, where $N$ is common shares outstanding. If taxable income is negative and there is no immediate tax benefit, net income equals $EBIT-I$, not $(EBIT-I)(1-T)$. For an all-equity plan, set $I=0$.

Interest is deducted before calculating tax because it reduces taxable income in this model. Interest coverage is calculated separately as $EBIT/I$; it is not a measure of net income or EPS. When a plan has no interest expense, the ratio is undefined rather than a finite coverage multiple.

A Three-Scenario Comparison

The first example compares two plans at low, base, and high EBIT. The assigned probabilities also allow a calculation of expected EPS and scenario variance. Expected EPS summarizes the probability-weighted earnings per share; the variance describes how dispersed those EPS outcomes are around their mean.

Worked Example: Low, Base, and High EBIT

A hypothetical company considers two ways to finance the same operations. EBIT is $30,000 with probability 0.25, $60,000 with probability 0.50, and $90,000 with probability 0.25. Plan A is all-equity financing with 20,000 shares and no interest. Plan B has 12,000 shares and annual interest of $24,000. The tax rate is 25%, and all scenarios have positive taxable income. Compare EPS and interest coverage, then calculate expected EPS and EPS standard deviation under each plan.

Method. For each scenario, calculate taxable income, apply the 25% tax rate, and divide net income by the plan’s share count. Then weight the EPS outcomes by their probabilities. The common mistake to avoid is comparing only the high-EBIT EPS and overlooking the debt plan’s fixed interest burden at low EBIT.

Plan A, EBIT of $30,000. Taxable income is $30,000, tax is $0.25(30{,}000)=\$7{,}500$, and net income is $22,500. Thus EPS is $\$22{,}500/20{,}000=\$1.125$.

Plan A, EBIT of $60,000. Tax is $0.25(60{,}000)=\$15{,}000$, net income is $45,000, and EPS is $\$45{,}000/20{,}000=\$2.25$.

Plan A, EBIT of $90,000. Tax is $0.25(90{,}000)=\$22{,}500$, net income is $67,500, and EPS is $\$67{,}500/20{,}000=\$3.375$.

Plan B, EBIT of $30,000. Earnings before tax are $\$30{,}000-\$24{,}000=\$6{,}000$. Tax is $0.25(6{,}000)=\$1{,}500$, so net income is $4,500 and EPS is $\$4{,}500/12{,}000=\$0.375$. Interest coverage is $\$30{,}000/\$24{,}000=1.25$.

Plan B, EBIT of $60,000. Earnings before tax are $36,000, tax is $9,000, and net income is $27,000. EPS is $\$27{,}000/12{,}000=\$2.25$. Interest coverage is $\$60{,}000/\$24{,}000=2.50$.

Plan B, EBIT of $90,000. Earnings before tax are $66,000, tax is $16,500, and net income is $49,500. EPS is $\$49{,}500/12{,}000=\$4.125$. Interest coverage is $\$90{,}000/\$24{,}000=3.75$.

The probabilities give Plan A expected EPS of $0.25(1.125)+0.50(2.25)+0.25(3.375)=\$2.25$. Plan B expected EPS is $0.25(0.375)+0.50(2.25)+0.25(4.125)=\$2.25$. The expected EPS is equal, even though the scenario outcomes differ.

For Plan A, deviations from the expected EPS are $-\$1.125,\$0,\$1.125$. Its EPS variance is $0.25(1.125^2)+0.50(0^2)+0.25(1.125^2)=0.6328125$ dollars-squared per share, giving a standard deviation of $\sqrt{0.6328125}=\$0.7955$. For Plan B, deviations are $-\$1.875,\$0,\$1.875$; variance is $0.25(1.875^2)+0.50(0^2)+0.25(1.875^2)=1.7578125$, and standard deviation is $\sqrt{1.7578125}=\$1.3258$. Both standard deviations are rounded to four decimal places.

Check. At the base EBIT of $60,000, both plans produce EPS of $2.25. Plan B has the greater spread of EPS and its lowest EPS is smaller, while its highest EPS is larger. The calculations show why equal expected EPS does not imply equal shareholder earnings risk.

Why an EPS Indifference EBIT Exists

When both plans have positive taxable income and the same tax rate, their after-tax EPS expressions can be equated to find the EBIT at which EPS is equal. For an all-equity plan with $N_E$ shares and a debt plan with $N_D$ shares and interest $I$, the equality is:

\frac{EBIT(1-T)}{N_E} = \frac{(EBIT-I)(1-T)}{N_D}

Because $1-T$ is the same positive factor on both sides, it cancels. Rearranging the remaining equality gives:

N_D \, EBIT=N_E(EBIT-I) \qquad\Longrightarrow\qquad EBIT=\frac{N_E I}{N_E-N_D}

This threshold is valid under the stated conditions: the plans have the assumed fixed share counts and interest, and both plans have positive taxable income at the threshold. Below or above the threshold, the relative EPS ordering may change. If a plan has taxable losses, a different tax treatment can change the expressions, so the threshold must be reconsidered rather than applied mechanically.

In the first example, $N_E=20{,}000$, $N_D=12{,}000$, and $I=\$24{,}000$. The threshold is $20{,}000(24{,}000)/(20{,}000-12{,}000)=\$60{,}000$, matching the base scenario where both EPS values were $2.25.

Expected EPS, Coverage, and Downside Risk

Expected EPS is the probability-weighted average of scenario EPS values. For outcomes $EPS_j$ with probabilities $p_j$, where the probabilities sum to 1, the calculation is:

E[EPS]=\sum_j p_j EPS_j

The variance is $\sum_j p_j(EPS_j-E[EPS])^2$; its square root is the standard deviation. These measures describe dispersion in the specified scenarios, not every source of risk faced by shareholders. A scenario table should also keep the individual outcomes visible: two plans can have the same expected EPS but materially different low and high outcomes.

Interest coverage adds a separate diagnostic. A coverage ratio close to 1 means EBIT only slightly exceeds interest expense in that scenario. Coverage below 1 means EBIT is less than interest expense; it does not, by itself, establish that the company has defaulted, but it signals that operating earnings do not cover the stated interest charge. Coverage should be interpreted at each EBIT level, not as a guarantee about future payment.

Worked Example: Expected EPS With Two EBIT Outcomes

A hypothetical company’s EBIT is $25,000 or $55,000, each with probability 0.50. Under a debt plan, it has 10,000 shares, $15,000 of interest, and a 20% tax rate. Both outcomes have positive taxable income. Find EPS in each outcome, expected EPS, and the EPS standard deviation.

Method. Subtract interest from EBIT, apply the tax rate to positive taxable income, and divide by 10,000 shares. Then calculate the equally weighted mean and dispersion. This avoids treating the lower EBIT as if it were already net of interest.

At EBIT of $25,000, taxable income is $\$25{,}000-\$15{,}000=\$10{,}000$. Tax is $0.20(10{,}000)=\$2{,}000$, leaving net income of $8,000. EPS is $\$8{,}000/10{,}000=\$0.80$. Coverage is $\$25{,}000/\$15{,}000=1.6667$.

At EBIT of $55,000, taxable income is $40,000. Tax is $8,000, net income is $32,000, and EPS is $\$32{,}000/10{,}000=\$3.20$. Coverage is $\$55{,}000/\$15{,}000=3.6667$.

Expected EPS is $0.50(0.80)+0.50(3.20)=\$2.00$. Each outcome is $1.20 from the mean, so variance is $0.50(1.20^2)+0.50(1.20^2)=1.44$, and standard deviation is $\sqrt{1.44}=\$1.20$.

Check. The mean of $0.80 and $3.20 is $2.00, and both outcomes are exactly $1.20 from that mean. The coverage calculations also exceed 1 in both scenarios.

Taxes, Financing Choice, and a Common Trap

A frequent error is to calculate tax on EBIT before deducting interest. In the debt plan of the preceding example, that incorrect order would give tax of $0.20(25{,}000)=\$5{,}000$, then earnings after tax and interest of $\$25{,}000-\$5{,}000-\$15{,}000=\$5{,}000$, and EPS of $0.50. The model instead taxes EBIT less interest: tax is $0.20(25{,}000-15{,}000)=\$2{,}000$, so EPS is $(\$10{,}000-\$2{,}000)/10{,}000=\$0.80$. Interest comes out before tax in this calculation.

Another trap is multiplying a negative taxable income by $1-T$ when the problem says there is no immediate tax benefit for losses. For example, if EBIT is $8,000 and interest is $12,000, taxable income is $-\$4,000$. Under that assumption net income is $-\$4,000$, not $-\$4,000(1-T)$. If tax-loss carryforwards or another tax treatment are specified, use those facts instead.

A plan with the greatest high-scenario EPS is not automatically the best choice. A decision-maker should compare the low-scenario EPS, expected EPS when probabilities are supplied, coverage under weak operating conditions, and the variability of earnings. The scenario model does not capture every financing consequence, and its results depend on the assumptions about taxes, interest, share counts, and operating outcomes.

Key takeaway: Compare financing plans across the same EBIT scenarios. Calculate interest before tax, check coverage in each scenario, and consider both expected EPS and its spread. A high EPS in one outcome is not, by itself, sufficient reason to select debt or equity financing.

Worked Example: Comparing Expected EPS Across Plans

A hypothetical company forecasts EBIT of $15,000 with probability 0.25 and $45,000 with probability 0.75. An all-equity plan has 30,000 shares. A debt plan has 20,000 shares and $10,000 of interest. The tax rate is 20%, and both plans have positive taxable income in both scenarios. Compare expected EPS.

Method. Calculate each plan’s EPS at each EBIT, then take the probability-weighted average. Avoid applying the tax rate to EBIT before deducting interest in the debt plan.

Under all-equity financing, at EBIT of $15,000 tax is $0.20(15{,}000)=\$3{,}000$, net income is $12,000, and EPS is $\$12{,}000/30{,}000=\$0.40$. At EBIT of $45,000, tax is $9,000, net income is $36,000, and EPS is $\$36{,}000/30{,}000=\$1.20$. Expected EPS is $0.25(0.40)+0.75(1.20)=\$0.10+\$0.90=\$1.00$.

Under debt financing, at EBIT of $15,000 earnings before tax are $\$15{,}000-\$10{,}000=\$5{,}000$. Tax is $1,000, net income is $4,000, and EPS is $\$4{,}000/20{,}000=\$0.20$. At EBIT of $45,000, earnings before tax are $35,000, tax is $7,000, net income is $28,000, and EPS is $\$28{,}000/20{,}000=\$1.40$. Expected EPS is $0.25(0.20)+0.75(1.40)=\$0.05+\$1.05=\$1.10$.

Check. The debt plan has lower EPS in the low scenario and higher EPS in the high scenario. Since the high scenario has probability 0.75, its expected EPS is higher in this example: $1.10 versus $1.00.

Check Your Understanding

For each problem, apply the stated tax and financing assumptions before comparing outcomes.

An all-equity plan has 10,000 shares, EBIT of $40,000, and a 25% tax rate. Find EPS. (Answer: $3.00 per share.)
A debt plan has 6,000 shares, $6,000 of interest, EBIT of $24,000, and a 25% tax rate. Find EPS and interest coverage. (Answer: EPS is $2.25 per share; coverage is 4.00.)
A debt plan has 10,000 shares and $15,000 interest. EBIT is $20,000 with probability 0.40 and $50,000 with probability 0.60. The tax rate is 20%, and taxable income is positive in both outcomes. Find expected EPS. (Answer: $1.84 per share.)
An all-equity plan has 16,000 shares. A debt plan has 10,000 shares and $30,000 interest. The tax rate is 25%. EBIT is $40,000 or $80,000, each with probability 0.50. Find expected EPS under each plan. (Answer: All-equity $2.8125 per share; debt plan $2.25 per share.)
A debt plan has 8,000 shares and $12,000 interest. EBIT is $8,000 or $28,000, each with probability 0.50. The tax rate is 30%, and losses receive no immediate tax benefit. Find EPS in each outcome, expected EPS, and coverage in each outcome. (Answer: EPS is $-\$0.50$ and $1.40; expected EPS is $0.45; coverage is 0.6667 and 2.3333, respectively.)

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