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 (D) is:
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 r 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:
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:
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:
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%=10 dollars
- New
price of preference share:
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=8
dollars (unchanged)
- New
required rate of return: r=8%
or 0.08
- New
price of preference share:
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:
Now, using the
same required rate of return of 6%, the price of the preference share would be:
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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