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Discussion on: valuation for a perpetual bond, preferred stock, and common stock with constant dividend

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DIPA_DHUNGANA

Valuation of security is the process of calculating the present value of the future cash flows offered by the security. The value of stocks or bonds is determined by discounting the expected cash flows to present value using appropriate discount rate. If the present value of the security higher than the market price, the security is underpriced and the security is overpriced if the market value exceeds the calculated present value. The investment decision is made by comparing the present value with the market price and the underpriced securities are considered as good investment options (Moyer, McGuigan, Rao, & Kretlow, 2012). The process of calculating present value of some of the securities is discussed below:

Valuation of Perpetual Bond

A perpetual bond is a bond with infinite term to maturity. It pays a specified amount of interest every year forever and never return the principle amount or face value. It is also known as irredeemable bind or consol bond. The value of perpetual bond is calculated by finding the present value of infinite series of interest, which is discounted at investor’s required rate of return. As per the formula,

V0 = I / KD

Where,

V0 = Value/Price of bond

I = Interest amount

KD = Required rate of return

Let us consider a bond that pays annual coupon of 10 % when the desired rate of return is 15%.

Here,

Face value of bond (M) = Rs. 1,000

Coupon rate (IR) = 10%

Coupon amount (I) = 10 % of Rs.1,000 = Rs.100

Required rate (KD) = 15%

Value of bond (V0) = ?

Using the formula,

V0 = I / KD

= Rs.100/0.15

= Rs.666.67

Valuation of Preferred Stock

Preferred stock is often considered as hybrid security since it possesses features of both equity and bond. It gets fixed rate of dividend determined before the issuance of stock. The valuation of preferred stock is done with the assumption that the stated dividend will be received each year till infinity. The present or intrinsic value of preferred stock is calculate by discounting the dividend amount with required rate of return. The formula for valuation of preferred stock is:

VPS = DPS / KPS

where,

VPS = Value of preferred stock

DPS = Preferred stock dividend

KPS = Required rate of return

Let us take an example of a preferred stock that pays 12% annual dividend when the required rate of return is 10%.

Here,
Par value of preferred stock § = Rs. 100

Preferred stock dividend (DPS) = 12% of Rs.100 = Rs.12

Required Rate of return (KPS) = 10%

Value of preferred stock (VPS) = ?

Using the formula,

VPS = DPS / KPS

= Rs.12/0.10

= Rs. 120

Valuation of Common Stock with Constant Dividend (Zero Growth)

The stock having constant earnings and dividends each year till infinity is known as zero growth stock. The valuation of common stock with constant dividend (zero growth) is done by discounting the amount of dividend at the appropriate required rate of return. If expressed in formula,

P0 = D / KE

Where,

P0 = Value of zero growth

D = Dividend per share

KE = Required rate of return

If we consider a zero growth bond that pays annual dividend Rs. 8 indefinitely when the investor requires 10% return on his investment.

Here,

Dividend per share (D) = Rs.8

Required Rate of return (KE) = 10%

Value of preferred stock (P0) = ?

Using the formula,

P0 = D / KE

= Rs.8/0.1
= Rs.80

Perpetual bonds, preferred stock and zero growth stock are expected to pay a constant return each year till indefinite period. So all three belong to perpetuity (Ghimire, 2011). The value of perpetuity is calculated by dividing the fixed annual return offered by the securities with the required rate of return. From the above calculations, we can see that the value of perpetual bond, preferred stock and zero growth bond are calculated following the same process, only the values are different. The required rate of return is used as denominator in all three cases while the numerator is the annual return offered by those securities in monetary terms. So we can say that valuation of these three securities are virtually identical.

References
Ghimire, S. R. (2011). Fundamentals of Financial Management. Kathmandu: K.P Pustak Bhandar.

Moyer, R. C., McGuigan, J. R., Rao, R., & Kretlow, W. J. (2012). Contemporary Financial Management (12th ed.). Oklahoma: Cengage Learning.