chapter six bond and common share valuation j.d. han
TRANSCRIPT
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CHAPTER SIXCHAPTER SIX
Bond and Common Share Bond and Common Share ValuationValuation
J.D. HanJ.D. Han
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Learning ObjectivesLearning Objectives
1.1. Name the five variables of a debt contract.Name the five variables of a debt contract.
2.2. Describe how to estimate bond prices and Describe how to estimate bond prices and bond yields.bond yields.
3.3. Discuss the three leading theories on the Discuss the three leading theories on the term structure of interest rates, and term structure of interest rates, and explain how they differ.explain how they differ.
4.4. Explain the dividend discount model Explain the dividend discount model (DDM) and how financial officers use it to (DDM) and how financial officers use it to value shares.value shares.
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6. 1 Introduction6. 1 Introduction
Topics explored and discussed Topics explored and discussed include:include:
• Valuation of bonds and common Valuation of bonds and common share without risk premiumshare without risk premium
• Rates of ReturnsRates of Returns• Risk premiumsRisk premiums
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6.2 Valuation of Bonds6.2 Valuation of Bonds
BondBond – a debt instrument that entitles the owner – a debt instrument that entitles the owner to specified periodic interest payments and to specified periodic interest payments and eventually to the repayment of principle(face eventually to the repayment of principle(face value) at the stated date of maturity; sold at a value) at the stated date of maturity; sold at a market price(= face value +- premium or market price(= face value +- premium or discount)discount)
““What you see is not what you get”What you see is not what you get” Coupon rateCoupon rate – the rate specified on the original – the rate specified on the original
contract with the face valuecontract with the face value Effective yield or yield to maturityEffective yield or yield to maturity – the yield – the yield
investors realize by holding to maturity a debt investors realize by holding to maturity a debt contract bought at a particular market pricecontract bought at a particular market price
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Valuation of BondsValuation of Bonds
Debt contracts are characterized byDebt contracts are characterized by• The face valueThe face value• Stated interest rateStated interest rate• Time pattern of repayment under the Time pattern of repayment under the
debt contractdebt contract• Current market price of the debt Current market price of the debt
contractcontract• Effective yield of the debt contract, Effective yield of the debt contract,
based on its current pricebased on its current price
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Calculating Market Calculating Market PricePrice
Where:Where:B = current market price of the bondB = current market price of the bondF = face value of the bondF = face value of the bondI = interest or coupon paymentsI = interest or coupon paymentsr = yield to maturityr = yield to maturity
n
n
r
F
rr
IB
1
1
11
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Example: Calculating Example: Calculating Market PriceMarket Price
Where:Where:B = current market price of the bond= ?B = current market price of the bond= ?1000= face value of the bond1000= face value of the bondI = 80I = 80I = 0.1I = 0.1n= 20n= 20
16.8291.01
1000
1.01.01
11
80 20
20
B
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Different Payment Different Payment Intervals: Intervals:
In calculating the bond price for semi-In calculating the bond price for semi-annual(x times a year) coupons the following annual(x times a year) coupons the following changes must be recognized:changes must be recognized:
• Divide the annual coupon by two(x) to Divide the annual coupon by two(x) to determine the amount of semi-annual (x-ual) determine the amount of semi-annual (x-ual) couponcoupon
• Divide the market yield by two(x) to obtain Divide the market yield by two(x) to obtain the six-month (12/x month) market yieldthe six-month (12/x month) market yield
• Multiply the number of years(n) to maturity Multiply the number of years(n) to maturity by two(x) to obtain the number of semi-by two(x) to obtain the number of semi-annual periods to maturityannual periods to maturity
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Different Payment Different Payment Intervals: Intervals:
nx
nx
xr
F
xrxr
xIB/1/
/1
11
/
41.8282/1.01
1000
2/1.02/1.01
11
2/80
case above theofpayment coupon annual)
2.20
2.20
B
Ex
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Variations of BondsVariations of Bonds
Perpetual Bond Perpetual Bond Zero-coupon bond (or strip bond) do not Zero-coupon bond (or strip bond) do not
pay any interest during its life spay any interest during its life s Zeros are created when financial Zeros are created when financial
intermediaries buy traditional bonds and intermediaries buy traditional bonds and strip the cash flow from them and sell the strip the cash flow from them and sell the coupon and cash flow separatelycoupon and cash flow separately
Purchaser pays less for zeros and receives Purchaser pays less for zeros and receives face value at maturityface value at maturity
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Bond YieldsBond Yields
Yield to MaturityYield to Maturity - the ROR that - the ROR that investors realize by holding to investors realize by holding to maturity a debt contract that maturity a debt contract that they bought at a particular they bought at a particular market price. market price.
coupon income + capital gain or coupon income + capital gain or lossloss
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Two methods in calculating Two methods in calculating YTMYTM1. Linear interpolation1. Linear interpolation
2. Approximation formula2. Approximation formula
n
n
YTM
F
YTMYTM
IB
1
1
11
2/)(
/)(
BF
nBFIYTM
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Example:Example:
FV = 100; B = 98.25; Semi-annual I = FV = 100; B = 98.25; Semi-annual I = 6.3; n =76.3; n =7
14
14
1
1001
11
125.325.98YTMYTM
YTM
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Current YieldCurrent Yield
Current yieldCurrent yield – the ratio of annual – the ratio of annual coupon interest to the current coupon interest to the current market pricemarket price
B
interest AnnualCY
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6.3 Determinants of 6.3 Determinants of Interest RatesInterest Rates
The effective yield of a debt The effective yield of a debt contract is established by the contract is established by the general economic factors that general economic factors that effect the overall level of interest effect the overall level of interest rates and by such features of the rates and by such features of the debt contract as its maturity, debt contract as its maturity, currency denomination, and risk of currency denomination, and risk of default.default.
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Determinants of Determinants of Interest RatesInterest Rates
Interest Interest - the price paid for - the price paid for borrowing moneyborrowing money• Changes in interest is measured in Changes in interest is measured in
basis points.basis points.• One basis point = 1/100One basis point = 1/100thth of one of one
percentpercent
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Determinants of Determinants of Interest RatesInterest Rates
Loanable fund theoryLoanable fund theory –the –the relationship between the supply relationship between the supply and demand for funds where the and demand for funds where the supply of capital supply of capital with with interest interest rates and the demand for funds rates and the demand for funds as the costs as the costs . At equilibrium . At equilibrium interest rates are such that interest rates are such that demand equals supply.demand equals supply.
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Determinants of Determinants of Interest RatesInterest Rates
Real risk-free rate interestReal risk-free rate interest – the basic – the basic interest rate that must be offered to interest rate that must be offered to individuals to persuade them to save individuals to persuade them to save rather than consume and is not rather than consume and is not affected by price changes or risk affected by price changes or risk factorsfactors
Nominal interest ratesNominal interest rates – represent the – represent the real rate (RR) plus the expected real rate (RR) plus the expected inflationinflation
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Determinants of Determinants of Interest RatesInterest Rates
RF = RR + EIRF = RR + EI where:where:
RF = short-term treasury bill rate RF = short-term treasury bill rate
RR = the real risk-free rate of interestRR = the real risk-free rate of interest
EI = the expected rate of inflation EI = the expected rate of inflation over the term of the instrumentover the term of the instrument
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Term Structure of Term Structure of Interest RatesInterest Rates
Term Structure of Interest RatesTerm Structure of Interest Rates – – the relationship between time to the relationship between time to maturity and yields for a particular maturity and yields for a particular category of bonds at a particular category of bonds at a particular timetime
Yield curveYield curve – the graphical depiction – the graphical depiction of the relationship between yields of the relationship between yields and time to maturityand time to maturity
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Term Structure of Interest Term Structure of Interest RatesRates
The three most common term The three most common term structure of interest rate theories structure of interest rate theories include:include:
1.1. Expectations theoryExpectations theory
2.2. Liquidity preference theoryLiquidity preference theory
3.3. Market segmentation theoryMarket segmentation theory
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6.4 Common Share 6.4 Common Share ValuationValuation
Two basic approaches are used in Two basic approaches are used in fundamental security analysis:fundamental security analysis:
1.1. Present Value using the DDMPresent Value using the DDM
2.2. Relative valuation methods which Relative valuation methods which values shares relative to some values shares relative to some company characteristics based on a company characteristics based on a multiple that is deemed appropriatemultiple that is deemed appropriate
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Common Share Common Share ValuationValuation
Dividend discount model (DDM)Dividend discount model (DDM) – uses the – uses the expected future cash flows as the basis for expected future cash flows as the basis for valuing common sharesvaluing common shares
Where:Where:
PPo o == estimated price of a commonestimated price of a common share todayshare todayD = the dividends expected to be received for D = the dividends expected to be received for
each future periodeach future period
rrcs cs = the required rate of return= the required rate of return
10 1t cs
t
rDP
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No-Growth-Rate Version No-Growth-Rate Version of the DDMof the DDM
The fixed dollar dividend reduces to a The fixed dollar dividend reduces to a perpetual annuityperpetual annuity
Where:Where:
DD00 = the constant-dollar dividend = the constant-dollar dividend
rrcs cs = the required rate of return= the required rate of return
rPcs
D0
0
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The Constant-Growth-The Constant-Growth-Rate Version of the DDMRate Version of the DDM
Dividends are expected to grow at Dividends are expected to grow at a constant rate over timea constant rate over time
Where:Where:
DD11 = the dividend expected to be = the dividend expected to be received at the end of year 1received at the end of year 1
grDPcs
10
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Estimating the Growth Estimating the Growth Rate in Future DividendsRate in Future Dividends
Three estimates are required in order Three estimates are required in order to implement the constant-growth-rate to implement the constant-growth-rate of the DDM:of the DDM:
1.1. The expected dividend at the end of The expected dividend at the end of the yearthe year
2.2. The required rate of return by The required rate of return by shareholdersshareholders
3.3. The expected growth rate in The expected growth rate in dividendsdividends
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Estimating Growth Estimating Growth RatesRates
Internal growth rateInternal growth rate of earnings or of earnings or dividends:dividends:
g = ROE X (1- Payout ratio)g = ROE X (1- Payout ratio)
• Used where Used where gg can be estimated using data can be estimated using data for a particular year using long-term for a particular year using long-term averages or “normalized” figures for ROE averages or “normalized” figures for ROE and payout ratioand payout ratio