## Capital Redemption Reserve (CRR) Calculation
When a company buys back its own shares using free reserves, it must transfer an amount equal to the nominal (face) value of the shares bought back to the Capital Redemption Reserve (CRR).
This ensures the company's permanent capital base is not permanently eroded.
---
### Why a Simultaneous Equation is Needed
In Test 3 (D:E Ratio), you need to find the maximum buyback amount. The problem is that:
- Funding the buyback from free reserves → reduces equity
- Transferring to CRR also reduces free reserves → reduces equity
- Both happen at the same time, so you cannot compute one without the other
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### Setting Up the Equations
Let x = amount transferred to CRR (₹)
Let y = maximum buyback amount available from free reserves (₹)
Equation 1 — equity constraint:
```
Present Equity − x − y = Minimum Equity post-buyback
```
Equation 2 — ratio of y to x equals ratio of BB Price to FV:
```
y / x = BB Price / Face Value
```
Because for each share: you pay BB Price (this is y/n) and set aside FV for CRR (this is x/n).
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### Solving the System
Substitute Eq 2 into Eq 1:
```
Present Equity − x − (BB Price/FV)·x = Min Equity
Gap × FV / (BB Price + FV) = x ← CRR
Gap × BB Price / (BB Price + FV) = y ← BB Amount
```
where Gap = Present Equity − Minimum Equity
---
### Shortcut Formula
> Max Shares = Gap ÷ (BB Price + FV)
Then directly:
- CRR = Max Shares × FV
- BB Amount = Max Shares × BB Price
- Verify: BB Amount + CRR = Gap ✓
Intuition: Each share bought back "consumes" (BB Price + FV) rupees from the equity gap — BB Price flows to the shareholder, FV flows into CRR. The gap is divided exactly in the ratio BB Price : FV.
---
### Effect of Securities Premium Covering the Premium
If the premium on buyback is funded from Securities Premium:
- Securities Premium absorbs the premium portion → free reserves are only used for the FV portion
- CRR transfer = FV × n (unchanged) — it is always the full nominal value of shares bought back
- The simultaneous equation approach is not needed in this case; CRR = FV × actual shares bought back