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Valuation of Bonds and Shares
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Valuation of BondsBondA 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 BondsBonds with MaturityPure Discount BondsPerpetual BondsBond
YieldsCoupon rateCurrent yieldYield to maturityYield to call
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Valuation of Bonds Contd
Bonds with Maturity:
Bond value = Present value of interest after n number of year +
Present value of maturity after n number of year.
Therefore, Bond Value = I ( PVIAF Kd, n) + F ( PVIF Kd, n)
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Valuation of Bonds ContdYield to Maturity:
The yield-to-maturity (YTM) is the measure of a bonds rate of
return that considers both the interest income and any capital gain
or loss. YTM is bonds internal rate of return.
YTM = I + (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
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Valuation of Bonds ContdCurrent Yield
Current yield is the annual interest divided by the bonds
current value.
It is calculated as:
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Valuation of Bonds ContdYield 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 maturityThe 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
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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
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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.
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Valuation of Preference ShareCapital 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.
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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.
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Dividend Discount Models 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 StockDt = Dividendk = required return
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No Growth ModelD is the constant dividendk is the required rate
of returnStocks that have dividends that are expected to remain
constant
VDko=
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Constant Growth ModelDividends are expected to grow at a
constant percent per period.D0 is most recent dividend, D0(1+g) is
next dividendg = constant perpetual growth ratek = required rate of
return
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Estimating Dividend Growth Ratesg = growth rate in dividendsROE
= Return on Equity for the firmb = plowback or retention percentage
rate. The proportion of the firms earnings that is reinvested in
the business. = (1- dividend payout rate)gROEb=
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Multi-Period Dividend-Discount Model PN = expected sales price
of stock at time NN = number of years the stock is to be held
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Multi-Period Earnings-Discount Model PN = expected sales price
of stock at time NN = number of years the stock is to be held
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P/E Ratio and Growth Opportunities b = retention ration ROE =
Return on EquityPDkgEbkbROEPEbkbROE0110111=-=--=--()()()
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THANK YOUGroup NoH3Debojit RoyH66Neeraj SharmaH30Biswajit
GhoshH12Sritanu Das MahapatraH57Abhisek SahuH03Krishnakant
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