How is the valuation of preference share done? Explain using a hypothetical example.

Posted By: February 08, 2025 Leave a Reply

 Q. How is the valuation of preference share done? Explain using a hypothetical example.

Valuation of Preference Shares

Preference shares, also known as preferred stock, are a type of equity instrument that combines features of both debt and equity. They represent ownership in a company but have preferential rights over common shares in terms of dividend payments and liquidation proceeds. In the valuation of preference shares, the focus is primarily on their ability to generate fixed dividends and their relative risk compared to other investments.



Key Characteristics of Preference Shares

Before diving into the valuation process, it is important to understand the key features of preference shares:

1.     Fixed Dividend: Preference shares typically come with a fixed dividend rate, expressed as a percentage of the face value or par value of the share.

2.     Priority in Dividend Payment: In the event of dividend distribution, preference shareholders are paid before common shareholders.

3.     Non-Participation in Profits: Preference shareholders generally do not participate in the company’s profits beyond the fixed dividend.

4.     Cumulative or Non-Cumulative: Cumulative preference shares entitle the shareholder to receive any missed dividends in subsequent periods, while non-cumulative preference shares do not.

5.     Convertible or Non-Convertible: Some preference shares may be converted into common shares at a certain point, while others may not.

Given these characteristics, the valuation of preference shares often relies on their fixed dividend payments and the rate of return demanded by investors, which reflects the risk associated with holding such shares.

Valuation Approach

The valuation of a preference share is similar to that of a bond because it represents a fixed stream of income (dividends) over a set period. The primary method for valuing preference shares is the Dividend Discount Model (DDM), where the value of the preference share is determined by calculating the present value of the future dividends.

The formula for valuing a preference share is:

P=DrP = \frac{D}{r}P=rD​

Where:

  • PPP is the price of the preference share,
  • DDD is the fixed dividend paid annually,
  • rrr is the required rate of return (or discount rate), which is the yield required by an investor.

    This formula assumes that the preference shares are perpetual (i.e., they pay dividends indefinitely) and the dividends are fixed.

    Steps to Valuation

    1.     Determine the Dividend Payment: The fixed annual dividend on a preference share is typically a percentage of the nominal (par) value of the share. If a preference share has a nominal value of $100 and a dividend rate of 6%, the annual dividend payment (DD) is:

    D=100×6%=6 dollars per share annuallyD = 100 \times 6\% = 6 \text{ dollars per share annually}D=100×6%=6 dollars per share annually

    2.     Establish the Required Rate of Return (r): The required rate of return or discount rate is the return that investors demand for holding the preference share. This rate depends on various factors, including the company’s creditworthiness, the interest rate environment, and the risk premium associated with the preference shares. For instance, if investors require a 5% return, the rate rr will be 0.05.

    3.     Apply the Formula: Using the dividend of $6 and a required return of 5%, the value of the preference share can be calculated as:

    P=60.05=120 dollarsP = \frac{6}{0.05} = 120 \text{ dollars}P=0.056​=120 dollars

    So, the price of the preference share in this case is $120.

    Hypothetical Example

    Let’s take a more detailed hypothetical example to illustrate how the valuation works:

    Example:

    Assume Company XYZ issues preference shares with the following details:

    • Nominal value of each preference share = $100
    • Dividend rate = 8% per annum
    • Required rate of return = 6%

    Step 1: Calculate the Annual Dividend Payment The fixed annual dividend is calculated as the dividend rate multiplied by the nominal value of the preference share:

    D=100×8%=8 dollars per share annuallyD = 100 \times 8\% = 8 \text{ dollars per share annually}D=100×8%=8 dollars per share annually

    Step 2: Determine the Required Rate of Return The required rate of return (or discount rate) is given as 6% (or 0.06). This is the return that investors expect to earn from investing in the preference share, given its risk level.

    Step 3: Apply the Valuation Formula Now, apply the formula for the price of the preference share:

    P=80.06=133.33 dollarsP = \frac{8}{0.06} = 133.33 \text{ dollars}P=0.068​=133.33 dollars

    So, the price of the preference share would be $133.33. This means that, based on the fixed dividend of $8 and the required return of 6%, the preference share is valued at $133.33.

    Considering Different Scenarios in Valuation

    The valuation of preference shares can vary based on several factors. Let’s explore how changes in dividend rates and required return impact the price of preference shares.

    Scenario 1: Change in Dividend Rate

    If the dividend rate increases, the price of the preference share would also increase, assuming the required rate of return remains constant. Conversely, if the dividend rate decreases, the price of the preference share would decrease.

    For example, if the dividend rate were to increase from 8% to 10%, while the required rate of return remains at 6%, the price of the preference share would change as follows:

    • New dividend payment: D=100×10%=10D = 100 \times 10\% = 10 dollars
    • New price of preference share:

    P=100.06=166.67 dollarsP = \frac{10}{0.06} = 166.67 \text{ dollars}P=0.0610​=166.67 dollars

    So, with an increase in the dividend rate, the price of the preference share increases from $133.33 to $166.67.

    Scenario 2: Change in Required Rate of Return

    If the required rate of return increases (i.e., investors demand a higher return due to an increase in interest rates or higher perceived risk), the price of the preference share will decrease.

    For example, if the required rate of return rises from 6% to 8%, the price of the preference share would change as follows:

    • Dividend payment: D=8D = 8 dollars (unchanged)
    • New required rate of return: r=8%r = 8\% or 0.08
    • New price of preference share:

    P=80.08=100 dollarsP = \frac{8}{0.08} = 100 \text{ dollars}P=0.088​=100 dollars

    So, with an increase in the required rate of return, the price of the preference share decreases from $133.33 to $100.

    Valuing Cumulative Preference Shares

    If the preference shares are cumulative, the valuation process remains mostly the same. However, in the case of cumulative preference shares, if dividends are not paid in any given year, the unpaid dividends accumulate and must be paid in the future before any dividends can be paid to common shareholders.

    For example, suppose a company issues cumulative preference shares with the following details:

    • Nominal value = $100
    • Dividend rate = 8%
    • Required rate of return = 6%
    • The company missed a dividend payment last year, but is expected to pay it in the current year along with the current year's dividend.

    In this case, the total dividend expected in the current year is:

    Dtotal=8 (current year)+8 (missed dividend)=16 dollarsD_{\text{total}} = 8 \text{ (current year)} + 8 \text{ (missed dividend)} = 16 \text{ dollars}Dtotal​=8 (current year)+8 (missed dividend)=16 dollars

    Now, using the same required rate of return of 6%, the price of the preference share would be:

    P=160.06=266.67 dollarsP = \frac{16}{0.06} = 266.67 \text{ dollars}P=0.0616​=266.67 dollars

    Thus, the price of the cumulative preference share would be higher because the shareholder is receiving the accumulated dividends in addition to the current year’s dividend.

    Valuing Convertible Preference Shares

    Convertible preference shares are those that can be converted into common shares after a certain period or upon the occurrence of certain events. The valuation of convertible preference shares is more complex than that of non-convertible preference shares, as it involves considering both the fixed dividend payments and the potential value of converting the preference shares into common shares.

    The valuation of convertible preference shares generally involves two components:

    1.     Dividend Yield: The portion of the value attributable to the preference share’s fixed dividend.

    2.     Conversion Value: The potential future value of the common shares that the preference shares can be converted into.

    The conversion value depends on the current price of the common shares and the conversion ratio. If the conversion ratio is 1:1, each preference share can be converted into one common share. If the market price of the common share is high, the conversion value will increase.

    For example, if the price of the common share is $50 and the conversion ratio is 1:1, the conversion value of the preference share would be $50.

    To value a convertible preference share, the total value would be the higher of:

    1.     The value derived from the fixed dividend payments (as done for regular preference shares), and

    2.     The conversion value, which is based on the price of the common shares.

    Conclusion

    Valuing preference shares involves calculating the present value of the expected dividends, which is generally done using the Dividend Discount Model (DDM). The valuation depends on several factors, including the dividend rate, the required rate of return, and the potential for changes in these variables. The value of preference shares can be sensitive to changes in the required rate of return and the dividend rate.

    In the case of cumulative preference shares, the valuation is adjusted to account for any unpaid dividends that accumulate over time. For convertible preference shares, the valuation includes both the fixed dividend payments and the potential value of converting the preference shares into common shares.

    By understanding these valuation techniques and factors, investors and analysts can make informed decisions about the value of preference shares and how they fit into their investment portfolios.




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