Leverages, EBIT-EPS analysis, financial break-even and indifference point
Operating leverage magnifies sales changes into EBIT changes; financial leverage magnifies EBIT changes into EPS changes. Combined leverage links sales directly to EPS.
Where each leverage acts
DOL covers sales to EBIT, DFL covers EBIT to EPS, and DCL covers the whole chain.
Three leverages
| Leverage | Formula | Risk it shows | Caused by |
|---|---|---|---|
| Operating (DOL) | Contribution ÷ EBIT | Business risk | Fixed operating costs |
| Financial (DFL) | EBIT ÷ EBT | Financial risk | Fixed financial charges: interest, preference dividend |
| Combined (DCL) | Contribution ÷ EBT = DOL × DFL | Total risk | Both |
Computing the leverages
Sales 10,000 units at ₹20; variable cost ₹12 per unit; fixed operating costs ₹30,000; interest ₹10,000.
- Sales = ₹2,00,000; variable cost = ₹1,20,000; contribution = ₹80,000
- EBIT = 80,000 − 30,000 = ₹50,000; EBT = 50,000 − 10,000 = ₹40,000
- DOL = 80,000 ÷ 50,000 = 1.6
- DFL = 50,000 ÷ 40,000 = 1.25
- DCL = 80,000 ÷ 40,000 = 2.0 (check: 1.6 × 1.25 = 2.0)
- So a 10% rise in sales lifts EBIT by 16% (to ₹58,000) and EPS by 20%
DOL 1.6; DFL 1.25; DCL 2.0.
EBIT-EPS indifference point
A firm needs ₹10,00,000. Plan A: all equity, 1,00,000 shares of ₹10. Plan B: 50,000 shares of ₹10 plus ₹5,00,000 of 10% debt. Tax 30%.
- Plan B interest = 10% × 5,00,000 = ₹50,000
- Set EPS equal: X(1 − 0.30) ÷ 1,00,000 = (X − 50,000)(1 − 0.30) ÷ 50,000
- Tax cancels: X ÷ 1,00,000 = (X − 50,000) ÷ 50,000, so X = 2X − 1,00,000
- X = ₹1,00,000
- Check: EPS under A = 1,00,000 × 0.70 ÷ 1,00,000 = ₹0.70; under B = 50,000 × 0.70 ÷ 50,000 = ₹0.70
- At EBIT ₹1,50,000: A gives ₹1.05 and B gives ₹1.40, so above the point the debt plan wins
Indifference EBIT = ₹1,00,000, where EPS is ₹0.70 under both plans.
Financial break-even point
Interest ₹40,000; preference dividend ₹21,000; tax 30%.
- Pre-tax earnings needed for the preference dividend = 21,000 ÷ (1 − 0.30) = ₹30,000
- Financial BEP = 40,000 + 30,000 = ₹70,000 of EBIT
- Check: at EBIT ₹70,000, EBT = ₹30,000; tax ₹9,000; PAT ₹21,000; after preference dividend ₹21,000, nothing is left for equity
Financial BEP = EBIT of ₹70,000; EPS is zero at this level.
Reading EBIT-EPS analysis
- Financial leverage is favourable (trading on equity works) when the return on assets exceeds the cost of debt.
- Above the indifference point, the plan with more debt gives higher EPS; below it, the equity plan does.
- Short cut without preference shares: indifference EBIT = (N1 × I2 − N2 × I1) ÷ (N1 − N2).
- On an EBIT-EPS chart, each plan's line meets the EBIT axis at its financial break-even point.
- DOL is very high just above operating break-even and falls as sales grow.
- High DOL with high DFL means very high total risk, so firms usually balance one against the other.
NET gives sales, costs and interest and asks for DOL, DFL or DCL, the EPS change from a sales change, the indifference EBIT of two plans or the financial break-even point.
Typical MCQ: “DOL is 2 and DFL is 1.5. If sales rise 10%, by how much does EPS rise?” DCL = 3, so EPS rises 30%. Trap: adding the leverages (3.5) instead of multiplying.
Typical MCQ: “What is EPS at the financial break-even point?” Zero. EBIT just covers interest and the pre-tax equivalent of the preference dividend.
Operating leverage: sales to EBIT. Financial leverage: EBIT to EPS. Multiply them for the whole chain.