## Diluted EPS — Convertible Preference Shares
### Why Convertible Preference Shares Are Potential Equity Shares (PES)
Convertible preference shares can be exchanged for equity shares at a pre-agreed ratio. Because they may become equity shares in the future, they are classified as Potential Equity Shares (PES) and must be considered when computing diluted EPS.
---
### Effect on the Two Components of Diluted EPS
| Component | Adjustment | Reason |
|---|---|---|
| Numerator (EAFESH) | Add back preference dividend | Dividend is saved when pref. shares convert to equity |
| Denominator (WANES) | Add equity shares from conversion (No. of pref. shares × conversion ratio) | Potential shares that would be issued on conversion |
> Critical rule — No tax adjustment on preference dividend savings. Preference dividend is declared and paid from post-tax profits. Unlike interest on debentures (which reduces taxable income), preference dividend creates no tax shield. Therefore, the full dividend amount is added back without any tax grossing-up.
---
### Step-by-Step Process
Step 1 — Basic EPS
$$\text{Basic EPS} = \frac{\text{EAFESH}}{\text{WANES}}$$
Step 2 — Diluted EPS (Working Notes)
WN 1 — Adjusted Numerator:
$$\text{Adj. EAFESH} = \text{EAFESH} + (\text{Pref. Shares} \times \text{Face Value} \times \text{Dividend Rate})$$
WN 2 — Adjusted Denominator:
$$\text{Adj. WANES} = \text{WANES} + (\text{Pref. Shares} \times \text{Conversion Ratio})$$
Step 3 — Compute and Test
$$\text{Diluted EPS} = \frac{\text{Adj. EAFESH}}{\text{Adj. WANES}}$$
- If Diluted EPS < Basic EPS → Dilutive → include in reported diluted EPS
- If Diluted EPS > Basic EPS → Anti-Dilutive → exclude; report Basic EPS = Diluted EPS
---
### Contrast: Preference Dividend vs. Debenture Interest (Tax Treatment)
| Instrument | Numerator Adjustment | Tax Adjustment? |
|---|---|---|
| Conv. Pref. Shares | Add back preference dividend | No — post-tax item |
| Conv. Debentures | Add back interest expense | Yes — pre-tax item; multiply by (1 − tax rate) |
For debentures: Adj. EAFESH = EAFESH + Interest × (1 − Tax Rate)