Download - Bond
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Group 06
Habiba MustafaSumaiya NishanMuhammad KashifHafiz Aamir SohailAltaf Hussain
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BOND VALUATION
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BOND: long term debt
A security that pays a stated amount of interest to the investor, period after period until its maturity.
Face valueCouponmaturity
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BOND VALUE PV(bond)=PV(coupon payments)+PV(final payment)
PV= PMT(1-1/(1+i)^n)/i + MV/(1+i)^n
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Factors affecting Bond prices
Credit QualityInterest RateYieldTax Status
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Interest rate
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yieldYield is a figure that shows the return you get
on a bond.
Simplest versionYield= coupon amount/price
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YIELD (Linking price and yield)
• Most important thing to remember!!!!**When prevailing interest rates rise, prices of
outstanding bonds fall to bring the yield of older bonds into line with higher-interest new issues
**When prevailing prices fall, prices of outstanding bonds rise, until the yield of older bonds is low enough to match the lower interest rate on new issues.
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BOND VOLATILITY
Volatility refers to the amount of uncertainty or risk about the size of changes in security’s value.
Volatility=Duration/1+yield
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BOND DURATION
• Duration is a weighted measure of the length of time the bond will pay out.
• Unlike maturity, duration takes into account interest payments that occur throughout the course of holding the bond.
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Cont’d…
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Term structure/Yield Curve
A "term structure of interest rates,“ also known as yield curve is a graph that plots the yield/spot rates of bonds against their maturities, ranging from shortest to longest.
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Forms of yield curve
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Cont’d…
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EXPECTATION THEORY
The expectation theory says that:
“Bonds are priced so that an investor who holds a succession of short bonds can expect the same
return as another investor who holds a long bond.”
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INTRODUCING RISK In expectation theory risk factor must
be considered. If predicted future level of interest rates, select strategy offering highest return.
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Inflation and Term structure
• Suppose u are saving for your retirement. which of the following strategies is the more risky?
• Invest in one-year or invest in 20-year bond?
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Inflation and nominal interest rates
• How does inflation affect the nominal rate of interest?
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FISHER’S THEORY
“A change in the expected inflation rate will cause the same proportionate change in the nominal interest rate; no effect on the required real interest rate”.
1+rnominal=(1+rreal)(1+i)
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REAL & NOMINAL INTEREST RATE
In Real interest rate no inflation factor while in Nominal interest rate inflation factor exists.
Inflation rate higher real return will be lower.
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NOMINAL INTEREST RATEReal cash flowt=nominal cash flowt/1+inflation
rate)t
FOR EXAMPLE:
If u were to invest $1,000 in a 20-year bond with a 10% coupon, final payment would be $1,100.
if inflation rate=6% then real value would be
=1,100/1.0620=$342.99
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INDEXED BONDS
Bonds promised you a fixed nominal rate of interest.
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Valuation of common stock
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How Common Stocks are Traded
• Primary MarketTrading through bank and OTC• Secondary MarketTrading through Stock Exchange
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How Common Stocks are valued
• PV(stock) = PV(expected future dividends)• Today’s PriceThe cash payoff to the owners of common stocks
comes in two forms• Cash dividends• Capital gains or losses
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Conti…d
• Expected return = r = Divi1 + p1-p0/p0Example Suppose Fledgling Electronics stock is selling for
$100 a share (p0=100). Investors expect a $5 cash dividend over the next year (Div1=5). They also expect stock to sell for $110 a year (p1=110)
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Conti’d
Expected return = r = 5+(110-100)/100 r = 0.15 or 15%On the other hand, if you are given investors
forecasts of dividend and price and the expected return is same then you can predict today’s price.
Price = po = Div1+p1/(1+r)
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Conit’d
• If DIV1=5 and p1=110 and r=15%, then today's price should be 100:
P0 = 5+110/1.15 =$100
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But what determines the Next Year’s Price
• P1 = DIV2 + P2/(1+r)
That is, a year from now investor will be looking out at dividends in year 2 and price at the end of year 2. thus we can forecast p1 by forecasting DIV2 and p2 and we can express po in terms of DIV1, DIV2, and p2:
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Conit…’d
• Po=1/1+r(DIV1+p1)=1/1+r(DIV1+DIV2+p2/1+r)=DIV1/(1+r) + DIV2+p2/(1+r)*2ExampleSuppose they are looking today for dividends of
$5.5 in year 2 and subsequent price of $121. that implies a price at the end of the year 1 of
P1 = 5.50+121/1.15 = $110
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Conti…d
• From our expended formulaP0 = 5/1.15 + 5.50+121/(1.15)*2 = $100
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Estimating the Cost of Equity Capital
• Po = DIV1/ (r-g)
• r = (DIV 1/p0) + g
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Danger lurk in Constant-Growth formula
• Dividend growth rate = plowback ratio*ROE
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The link between stock price and Earning per share
• Growth stock• Income stockExpected return =dividend yield=earning-p ratioIf dividend is $10 a share and stock price is $100
then:Expected return=DIV1/P0 = 10/100 = .10
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Conti..d
The price equalsP0= DIV1/r = EPS1/r = 10/.10 =100
Po =EPS1/r+PVGOSo,EPS/Po= r ( 1- PVGO/Po)It will underestimate r if PVGO is +ve and
overestimate it if PVGO is -ve
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Calculating PV of Growth Opportunities
• Po= DIV1/r-g• Payout ratio = DIV1/EPS1• Growth rate= g = plowback ratio*ROE• Present value of level stream of earnings= EPS/r• PVGO = NPV1/r-g• Share price = EPS1/r +PVGO
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Valuing a Business by Discounting Cash Flow
• In this you forecast dividend per share or total free cash flow of a business.
• Value today always equals future cash flow discounted at the opportunity cost of capital
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Valuing the Concatenator Business
• PV= FCF/1+r + FCF2/(1+r)^2 +….+FCF/(1+r)^H + PV/(1+r)^H
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Estimating Horizon Value
• Forecasting reasonable horizon is particularly difficult. The usual assumption is moderate long rum growth after the horizon, which allow us to growing-perpatuity DCF formula.
• It can also be calculated normal price-earnings or market-book ratios at the horizon date
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