# Segments of Return on Equity (ROE)
ROE can be broken down to show where each rupee of equity return comes from — the firm's own equity-funded assets, plus the residual return earned on preference and debt funds.
## The three-segment decomposition
> ROE = (E/E) × ROI(1 − t) + (P/E) × [ROI(1 − t) − Pref Div Rate] + (D/E) × [(ROI − Kd) × (1 − t)]
Reading the three segments:
1. Equity-on-equity: (Equity / Equity) × post-tax ROI = the direct post-tax return on assets funded by equity itself.
2. Preference contribution: (Preference / Equity) × [ROI(1−t) − Pref Div]. Positive if post-tax ROI exceeds the preference dividend rate.
3. Debt contribution: (Debt / Equity) × [(ROI − Kd) × (1 − t)]. Positive if ROI exceeds the pre-tax cost of debt (the classic trading on equity gain).
## When the decomposition is useful
- Explaining why ROE is high or low.
- Showing the impact of a proposed capital structure change before any actual numbers move.
- Linking back to favourable vs. unfavourable financial leverage: if (ROI − Kd) < 0, the debt segment becomes a deduction from ROE, not an addition.
## Three companion ratios — keep them distinct
| Ratio | Numerator | Denominator | What it tells you |
|---|---|---|---|
| ROI / ROCE | EBIT | Capital Employed (Equity + LT Debt) | Operating efficiency of the entire capital base |
| Return on Shareholders' Funds | PAT | Equity + Preference + Reserves | Return to all providers of ownership capital |
| ROE | EAES (PAT − Pref Div) | Equity capital + reserves attributable to equity | Return to equity shareholders specifically |
Mixing these up is the most common error in this section.