EBIT-EPS Analysis and Indifference Point Between Debt and Equity

Understand EBIT-EPS Analysis and Indifference Point

Key rules to remember

EPS for a plan

EPS = [(EBIT − I)(1 − t) − PD] ÷ N

I = interest, t = tax rate, PD = preference dividend (not tax-deductible), N = number of equity shares. Subtract PD after multiplying by (1 − t), then divide the whole result by N.

Indifference point (two plans)

[(X − I₁)(1 − t) − PD₁] ÷ N₁ = [(X − I₂)(1 − t) − PD₂] ÷ N₂

X is the indifference EBIT. Solve for X. Use total interest and total shares under each plan, including existing ones. This equation method works in every case, so prefer it.

Indifference point (no preference shares)

X = (N₂ × I₁ − N₁ × I₂) ÷ (N₂ − N₁)

Tax cancels out when PD is zero for both plans. Plan 2 is the plan with the larger share count (N₂ > N₁). This shortcut only works when there is no preference dividend.

Indifference point with preference shares

X = (N₂ × I₁ − N₁ × I₂) ÷ (N₂ − N₁) + [PD₁ × N₂ − PD₂ × N₁] ÷ [(1 − t)(N₂ − N₁)]

Use only if you are sure of the numbering: N₂ is the larger share count, and PD₁, I₁, N₁ belong to the same plan (plan 1). Preference dividend is paid after tax, so it is divided by (1 − t). In the exam, equating the two EPS expressions is safer than recalling this.

Decision rule

EBIT > X: choose plan with more fixed-cost funds. EBIT < X: choose plan with more equity.

Applies when comparing a debt-heavy plan with an equity-heavy plan.

How to solve EBIT-EPS Analysis and Indifference Point questions

1. 1List each plan separately. For every plan, find the total equity shares, total interest and any preference dividend, including existing capital.
2. 2Find new shares as new equity amount ÷ issue price. Find new interest as new debt × interest rate. Add to existing figures.
3. 3Write the EPS formula for each plan: [(EBIT − interest)(1 − t) − PD] ÷ shares.
4. 4If asked for EPS at a given EBIT, put the value in and compute for each plan. Show the working in a neat table.
5. 5If asked for the indifference point, equate the two EPS expressions, replace EBIT with X, and solve. Check by putting X back in both plans.
6. 6Compare the expected EBIT with X. State which plan gives higher EPS and why.
7. 7Add a one-line comment on risk, since higher debt means higher fixed charges and financial risk.

Quickest way: Fast route for MCQs and written answers

Common mistakes in EBIT-EPS Analysis and Indifference Point

• Forgetting existing shares and existing debt.

  Students focus on the new financing and only use the new amounts.

  Fix: Always add the new amounts to the existing capital. Total shares and total interest drive EPS.

• Deducting preference dividend before tax.

  Students treat it like interest.

  Fix: Preference dividend is not tax-deductible. Compute profit after tax first, then subtract it.

• Using the no-tax shortcut formula when preference shares are present.

  The shortcut is easy to remember, so it is applied everywhere.

  Fix: Use the shortcut only when PD is zero for both plans. Otherwise equate the full EPS expressions.

• Reversing the decision rule.

  Students forget which side of the crossover favours debt.

  Fix: Above the indifference point, the debt-heavy plan gives higher EPS. Below it, equity gives higher EPS.

• Calculating new shares with face value instead of issue price.

  The question gives both values and students pick the wrong one.

  Fix: New shares = amount raised ÷ issue price. Face value is used only for dividend or paid-up capital.

• Stopping at the number and giving no conclusion.

  Students think the calculation is the answer.

  Fix: State which plan is better at the expected EBIT and mention financial risk in a line.

Worked examples