Value of Redeemable Preference Shares Formula

To understand the value of redeemable preference shares, it's crucial to comprehend both the theoretical and practical aspects involved. Redeemable preference shares are a type of equity security issued by companies that offer a fixed dividend and are redeemable by the company at a future date. This provides a degree of security to the investor, as they have the option to sell the shares back to the company under predetermined conditions.

The value of redeemable preference shares can be calculated using a formula that factors in the present value of their future cash flows. Here's a step-by-step breakdown of how to calculate it:

1. Identify Key Variables:

   • Dividend Payment (D): This is the fixed amount paid periodically to the preference shareholders.
   • Redemption Value (R): The amount paid to the shareholders when the shares are redeemed.
   • Redemption Period (n): The time period until the shares are redeemed.
   • Discount Rate (r): The rate of return required by the investor.

2. Present Value of Dividends: To calculate the present value of the dividends, use the formula for the present value of an annuity:

   $P{V}_{dividends}=D\times \left(\frac{1-(1+r{)}^{-n}}{r}\right)$PVdividends​=D×(r1−(1+r)−n​)

3. Present Value of Redemption Value: The redemption value needs to be discounted to its present value using the formula:

   $P{V}_{redemption}=R\times (1+r{)}^{-n}$PVredemption​=R×(1+r)−n

4. Total Value of Redeemable Preference Shares: The total value of the redeemable preference shares is the sum of the present value of the dividends and the present value of the redemption value:

   $Value=P{V}_{dividends}+P{V}_{redemption}$Value=PVdividends​+PVredemption​

For example, if a redeemable preference share offers a fixed dividend of $5, a redemption value of $100, a redemption period of 10 years, and the discount rate is 8%, the value of the preference share can be computed as follows:

• Present Value of Dividends:

  $P{V}_{dividends}=5\times \left(\frac{1-(1+0.08{)}^{-10}}{0.08}\right)=5\times 6.7101=33.55$PVdividends​=5×(0.081−(1+0.08)−10​)=5×6.7101=33.55

• Present Value of Redemption Value:

  $P{V}_{redemption}=100\times (1+0.08{)}^{-10}=100\times 0.4632=46.32$PVredemption​=100×(1+0.08)−10=100×0.4632=46.32

• Total Value of Preference Shares:

  $Value=33.55+46.32=79.87$Value=33.55+46.32=79.87

In summary, the value of redeemable preference shares is derived from the present value of expected dividends plus the present value of the redemption value. This approach provides a comprehensive understanding of how these financial instruments are valued and how they can be compared to other investments.