## Calculating Maximum Number of Shares That Can Be Bought Back
The maximum permissible buy back is the least result from the three mandatory tests below. Each test gives a maximum number of shares; the binding constraint is the smallest.
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### Test 1 — Shares Outstanding Test
> Maximum shares = 25% of total paid-up equity shares outstanding
$$\text{Max shares} = \text{Total equity shares outstanding} \times 25\%$$
This is a pure quantity test — market price and reserves are irrelevant here.
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### Test 2 — Resources Test
> Maximum amount for buy back = 25% of (Paid-up Capital + Free Reserves)
$$\text{Max shares} = \frac{\text{Paid-up Capital} + \text{Free Reserves}}{\text{Buy-Back Price}} \times 25\%$$
Free Reserves include: General Reserve, Securities Premium, Revenue Reserve, Profit & Loss balance, and similar distributable reserves.
Always round down to the nearest whole share — you cannot buy back a fraction of a share.
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### Test 3 — Debt-Equity Ratio Test
> Post buy-back Debt : Equity must not exceed 2:1
Definitions for this test:
- Total Debt = All secured + unsecured borrowings (long-term + short-term)
- Equity = Paid-up Capital + Free Reserves (post buy back)
#### Step-by-Step Method (Simultaneous Equations)
Let:
- x = Amount to be transferred to CRR
- y = Maximum amount available for buy back
Equation 1 — Relationship between x and y:
$$x = y \times \frac{\text{Face Value}}{\text{Buy-Back Price}}$$
(Because: shares bought back = y ÷ BB price; CRR = shares × face value = y × FV/BB price)
Equation 2 — D/E constraint:
$$\text{Present Equity} - x - y = \text{Minimum Post-BB Equity}$$
$$\text{where Minimum Post-BB Equity} = \frac{\text{Total Debt}}{2}$$
Substitute Eq 1 into Eq 2 and solve for y, then:
$$\text{Max shares (D/E test)} = \frac{y}{\text{BB Price}}$$
#### Shortcut Formula (Faster in Exam)
$$\boxed{\text{Max Shares (D/E test)} = \frac{\text{Present Equity} - \text{Min Post-BB Equity}}{\text{BB Price} + \text{Face Value}}}$$
Proof: From the two equations, $x + y = \text{Present Eq} - \text{Min Eq}$. Since $x = y \cdot \frac{FV}{BB}$, we get $y \cdot \frac{BB+FV}{BB} = \text{Present Eq} - \text{Min Eq}$, so $\frac{y}{BB} = \frac{\text{Present Eq} - \text{Min Eq}}{BB + FV}$.
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### Summary: Final Answer
| Test | Max Shares |
|---|---|
| 1 — Shares Outstanding | 25% × total shares |
| 2 — Resources | 25% × (PC + FR) ÷ BB price, rounded down |
| 3 — Debt-Equity | (Present Eq − Min Eq) ÷ (BB price + FV) |
| Maximum permissible buy back | LEAST of the above three |