Valuation of Bonds and Shares

Valuation of Bonds Bond A long-term debt instrument (a legal contract) in which a borrower agrees to make

payments of principal and interest, on specific dates, to the holders of the bond.Types of Bonds• Bonds with Maturity• Pure Discount Bonds• Perpetual Bonds

Issuers of Bonds1. Central Government2. State Government3. Municipalities4. PSUs 5. Private Sector Companies

• Bond Yields Coupon rate Current yield Yield to maturity Yield to call

TerminologyPar Value

The Value Stated on the face of Bond is called as Face Value.Coupon Rate

Bond carries a specific interest rate which is called the coupon rate.Maturity Period

The maturity of a bond indicates the length of time until the bond issuer returns the par value to the bond holder and terminates or redeems the bond.

Current YieldThe current yield on a bond refers to the ratio of the annual interest payment to the current market price .

Bonds with Call OptionThe bonds issued by some companies give the right to the company to redeem entire/part of the bond issue prior to maturity are called as callable bond or bond with call option.

Yield to MaturityThis is the rate of return that investors earn if they buy the bond at a specific price and hold it until maturity.

Yield to CallThis is the rate of return that investors earn if they buy the bond with a call option at a specific price and hold it till the company exercises its call option.

Yield to Maturity:

The yield-to-maturity (YTM) is the annualized rate of return on the investment that the investor expects to earn from the date of investment to the date of maturity. YTM is bond’s internal rate of return.

YTM = Lo + (m – p) /n 0.4(m) + 0.6(p)Where, I = Annual Interest m = Maturity Value p = Price of Bond n = Number of years to maturity

Valuation of Bonds Contd… Current Yield

Current yield is the annual interest divided by the bond’s current value.

It is calculated as:

ValueCurrent

PmtAnnualCY

Valuation of Bonds Contd…

Yield to Call:

The yield to call is the average annual rate of return that a bondholder will earn under the following assumptions: The bond is held to maturity The interest payments are reinvested at the YTM

YTC = FV + m – p n n1

0.4(m) + .0.6(p)

Where, FV = Face Value m = Maturity Value p = Price of Bond n = Number of years to maturity n1= Called Year

Valuation of Bonds Contd…

Pure Discount Bonds:

A pure discount bond makes a single payment at the maturity date of the bond. 

Value of pure discount bond = PV of the amount on maturity

Valuation of Bonds Contd…Perpetual Bonds:

A perpetual bond, is a bond with no maturity date. Therefore, it may be treated as equity, not as debt.

PV = A r

Where PV = Present Value of the Perpetuity, A = the Amount of the periodic payment, and r = yield , discount rate or interest rate.

Valuation of Preference Share Capital stock which provides a specific dividend that is paid before any

dividends are paid to common stock holders, and which takes precedence over common stock in the event of a liquidation. Like common stock, preference shares represent partial ownership in a company, although preferred stock shareholders do not enjoy any of the voting rights of common stockholders. Also unlike common stock, preference shares pay a fixed dividend that does not fluctuate, although the company does not have to pay this dividend if it lacks the financial ability to do so. In general, there are four different types of preferred stock: cumulative preferred, non-cumulative, participating, and convertible. also called preferred stock.

Po = Preference div ( PAVF Kp, n) + Pn (PVF Kp, n) Where, Kp = Cost of Preference Share or expected rate of return.

Pn = Maturity value of Preference shares at the end of n number of year.

Valuation of Equity

The valuation of ordinary or equity shares is relatively more difficult. The rate of dividend on equity shares is not known;

also, the payment of equity dividend is discretionary.

The earnings and dividends on equity shares are generally expected to grow, unlike the interest on bonds and preference dividend.

Dividend Discount Models

1 )1(tt

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DV

1 )1(tt

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DV

A procedure for valuing the price of a stock by using predicted dividends and discounting them back to present value. The idea is that if the value obtained from the DDM is higher than what the shares are currently trading at, then the stock is undervalued.

V0 = Value of Stock

Dt = Dividendk = required return

No Growth Model

VD

ko

D is the constant dividend k is the required rate of return Stocks that have dividends that are expected to

remain constant

Constant Growth Model

Dividends are expected to grow at a constant percent per period.

D0 is most recent dividend, D0(1+g) is next dividend

g = constant perpetual growth rate k = required rate of return

gk

gDV

)1(0

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Estimating Dividend Growth Rates

g ROE b

g = growth rate in dividends ROE = Return on Equity for the firm b = plowback or retention percentage rate. The

proportion of the firm’s earnings that is reinvested in the business. = (1- dividend payout rate)

Multi-Period Dividend-Discount Model

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kPD

kD

kDV N

NN

PN = expected sales price of stock at time N

N = number of years the stock is to be held

Multi-Period Earnings-Discount Model

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k NPNEb N

k

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k

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PN = expected sales price of stock at time N

N = number of years the stock is to be held

P/E Ratio and Growth Opportunities

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k b ROE

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k b ROE

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b = retention ration ROE = Return on Equity

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