Q. How is the valuation of preference share done? Explain using a hypothetical example.
Valuing preference
shares, often referred to as preferred stock, involves determining the present
value of the future dividend payments associated with the shares. Preference
shares represent a type of equity security that typically offers a fixed
dividend to shareholders before any dividends are paid to common shareholders.
These dividends are often paid at a constant rate, which simplifies the
valuation process relative to common stock. Valuing preference shares can be
approached using different methods, depending on whether the preferred stock is
perpetual (has no maturity date) or has a finite life.
The primary method
for valuing preference shares is the Dividend
Discount Model (DDM),
particularly when the preference shares are perpetual, and dividends are paid
at a fixed rate indefinitely. This model is based on the concept that the value
of an asset is the present value of its future cash flows. For preference
shares, the future cash flows are the dividends that will be paid periodically.
The formula for valuing perpetual preference shares is:
P0=DrP_0
= \frac{D}{r}P0=rD
Where:
- P0P_0P0 is the price
or value of the preference share.
- DDD is the
annual dividend paid on the preference share.
- rrr is the
required rate of return or discount rate (also known as the cost of equity
for the preference shares).
Assumptions for Valuation
Before diving into
the specifics of the example, it's important to understand the assumptions
underlying this model:
1.
Constant
Dividend: Preference shares
usually have a fixed dividend amount, meaning the value of each preference
share depends on this fixed payment.
2.
Perpetuity: If the preferred
stock is perpetual, it means the company is expected to continue paying
dividends indefinitely.
3.
Market
Discount Rate: The required rate of return, rrr, is typically determined
by the risk associated with the preferred stock. This rate reflects the
market’s perception of the company’s creditworthiness, the stability of its
dividends, and the risk relative to other investments.
Example: Valuing a Perpetual
Preference Share
Let’s take a
hypothetical example to demonstrate how to value preference shares. Suppose
Company XYZ has issued preference shares that pay a fixed annual dividend of $5
per share. An investor requires a rate of return of 8% on this type of
investment, based on the company’s risk profile and the prevailing interest
rates in the market. To calculate the value of one preference share, we can
apply the Dividend Discount Model.
Step 1: Identify the Known Variables
From the problem,
we know the following:
- The
annual dividend D=$5D = \$5D=$5.
- The
required rate of return r=8%=0.08r = 8\% = 0.08r=8%=0.08.
Step 2: Apply the Formula
The formula for
valuing a preference share is:
P0=DrP_0
= \frac{D}{r}P0=rD
Substituting the
known values:
P0=50.08=62.50P_0
= \frac{5}{0.08} = 62.50P0=0.085=62.50
So, the value of
each preference share is $62.50. This means that, given the fixed annual
dividend of $5 and a required rate of return of 8%, the fair price of the
preference share is $62.50.
Interpretation of the Result:
The value of
$62.50 represents the price an investor would be willing to pay for a
preference share that pays a fixed $5 dividend annually, assuming the investor
requires an 8% return. If the price of the preference share were higher than
$62.50, the effective yield (or dividend yield) would be lower than 8%, and if
the price were lower, the effective yield would exceed 8%. Thus, the price of
the preference share reflects the investor’s return expectations.
Adjustments for Other Features of
Preference Shares
While the basic
Dividend Discount Model works well for perpetual preference shares, in
practice, preference shares may have additional features that affect their
valuation. These include callable features, convertible features, or maturity
dates.
1. Callable Preference Shares
Callable
preference shares allow the issuer to redeem the shares before the maturity
date, typically at a predetermined price. When valuing callable preference
shares, it is important to consider the possibility that the company may buy
back the shares early if interest rates decline. This early redemption would
limit the investor's upside potential. In such cases, the price of the callable
preference shares will generally be lower than that of non-callable preference
shares.
To adjust for the
callable feature, you may estimate the value of the preference share assuming
it is redeemed at the call price, and compare that to the value calculated
using the perpetual model. If the current market price exceeds the call price,
the issuer might choose to call the shares, capping the investor's return.
2.
Convertible Preference Shares
Convertible
preference shares allow the holder to convert the preference shares into a
predetermined number of common shares at certain times or under certain
conditions. Valuing convertible preference shares requires an additional layer
of complexity, as it involves considering both the fixed dividend payments and
the potential value derived from the conversion option.
To value
convertible preference shares, analysts typically use a hybrid model that
incorporates both the fixed dividend stream and the value of the conversion
option. The conversion option adds value because, if the common stock price
rises significantly, the investor could convert the preference shares into
common shares and participate in the potential capital appreciation of the
common stock.
The valuation of
convertible preference shares can therefore involve:
- Valuing the preference
shares as if they were non-convertible, using the
Dividend Discount Model.
- Valuing the conversion
option
separately, often using option pricing models such as the Black-Scholes
model or a binomial model, depending on the complexity of the conversion
terms.
The overall value
of the convertible preference share is the sum of the two components (the
non-convertible preference value and the value of the conversion option).
3. Maturity Date for
Preference Shares
In cases where the
preference shares are not perpetual but have a fixed maturity date (i.e., they
are redeemable after a set number of years), the valuation process needs to
incorporate the fact that the investor will receive both the dividends and the
redemption price at maturity.
The valuation of
redeemable preference shares with a fixed maturity date can be calculated as
the present value of the dividends plus the present value of the redemption
price. The formula for valuing redeemable preference shares is:
P0=∑t=1nD(1+r)t+F(1+r)nP_0
= \sum_{t=1}^{n} \frac{D}{(1+r)^t} + \frac{F}{(1+r)^n}P0=t=1∑n(1+r)tD+(1+r)nF
Where:
- P0P_0P0 is the
present value of the preference share.
- DDD is the
annual dividend.
- rrr is the
discount rate.
- nnn is the
number of periods until maturity.
- FFF is the face
or redemption value of the preference share (the amount paid back to the
investor at maturity).
This formula
considers both the stream of dividend payments over the life of the preference
share and the lump sum redemption payment at the end of the term.
Example:
Valuing Redeemable Preference Shares
Let’s extend our
example to a redeemable preference share. Suppose Company XYZ issues preference
shares with the following terms:
- Annual
dividend D=$5D = \$5D=$5.
- The
required rate of return r=8%r = 8\%r=8%.
- The
face value (redemption price) F=$100F = \$100F=$100.
- The
maturity date is 5 years from today.
The value of the
preference share is calculated by adding the present value of the dividend
payments and the redemption value. Using the formula for redeemable preference
shares, we get:
P0=∑t=155(1+0.08)t+100(1+0.08)5P_0
= \sum_{t=1}^{5} \frac{5}{(1+0.08)^t} + \frac{100}{(1+0.08)^5}P0=t=1∑5(1+0.08)t5+(1+0.08)5100
First, we
calculate the present value of the dividends:
5(1.08)1+5(1.08)2+5(1.08)3+5(1.08)4+5(1.08)5=4.63+4.29+3.97+3.68+3.41=20.98\frac{5}{(1.08)^1}
+ \frac{5}{(1.08)^2} + \frac{5}{(1.08)^3} + \frac{5}{(1.08)^4} +
\frac{5}{(1.08)^5} = 4.63 + 4.29 + 3.97 + 3.68 + 3.41 = 20.98(1.08)15+(1.08)25+(1.08)35+(1.08)45+(1.08)55=4.63+4.29+3.97+3.68+3.41=20.98
Next, we calculate
the present value of the redemption price:
100(1.08)5=1001.4693=68.05\frac{100}{(1.08)^5}
= \frac{100}{1.4693} = 68.05(1.08)5100=1.4693100=68.05
Adding these two
components together:
P0=20.98+68.05=89.03P_0
= 20.98 + 68.05 = 89.03P0=20.98+68.05=89.03
Thus, the value of
the redeemable preference share is $89.03, considering the fixed dividend
payments and the redemption price at maturity.
Conclusion
Valuing preference
shares requires careful consideration of the nature of the dividends, the
required rate of return, and any special features such as callability,
convertibility, or maturity. For perpetual preference shares, the Dividend
Discount Model provides a straightforward method for valuation by calculating
the present value of future dividend payments. For redeemable preference
shares, the calculation involves both the present value of the dividend stream
and the redemption value. Callable or convertible preference shares require
more sophisticated valuation techniques, incorporating the potential for early
redemption or the value of the conversion option.
The process of
valuing preference shares is crucial for investors to assess whether the price
of the preference shares in the market offers an adequate return relative to
the associated risks and the required rate of return. By understanding the
valuation mechanics, investors can make more informed decisions when purchasing
or selling preference shares, ensuring that their investments are aligned with
their financial goals and market expectations.
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