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8/13/2019 Fund.finance Lecture 3 Valuing Bond 2011 Revised
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Present Value of Future Cash Flows
Link Risk & Return
Expected Returnon Assets
Valuation2
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)r+(1CF+...+
)r+(1CF+
)r+(1CF=P n
n
2
2
1
10
P0 = Price of asset at time 0 (today)
CFt = Cash flow expected at time t
r = Discount rate (reflecting assets risk)
n = Number of discounting periods (usually years)
This model can express the price of any asset at
t = 0 mathematically.
Marginal benefitof owningthe asset: right to receive the
cash flows
Marginal cost:opportunitycost of owning the asset3
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A bond is a long term security that obligates the
issuer to make specified interest and principal
payments to the holder on specified dates.
Bonds are sometimes called fixedincome securities.
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The face valueof a bond, which the borrower repaysat maturity.
Par value
The datewhen a bonds life endsand the borrower
must make the final interest payment and repay theprincipal/par value.
Maturity Date
A fixed amount of interestthat a bond promises to payinvestors each period.
Coupon payments
The rate derived by dividing the bonds annual coupon
payment by its par value.
Coupon interest rate
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WARNING
The coupon rate IS NOTthe discount rate used in the
Present Value calculations.
The coupon rate merely tells us what cash flow the bondwill produce.
Since the coupon rate is listed as a %, this misconceptionis quite common.
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Based onissuer
Governmentbonds
Municipalbonds
Corporatebonds
Foreign bonds
Based oncouponrate
Fixed rate
Floating rate
Zerocoupon
Based onprotection
Secured
Unsecured
Based onotherfeatures
Convertible
Exchangeable
Etc.
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Issued by Federal governments Have no default risk but still have interest rate risk Used to fund budget deficits If 1 year < maturity < 10 years: Treasury Notes Maturity > 10 years: Treasury Bonds
Treasury Bonds
Issued by corporations Have default risk and interest rate risk Different corporate bonds have different levels of
default risk
Corporate Bonds
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Issued by local and state government Have default risk and interest risk. In general, interest on municipal bonds tax-free
Municipal Bonds
Issued by either foreign governments or foreign
corporations. Have default risk and interest rate risk. Can issued in either in a currency or in investors home
currency Can be exposed to currency risk
Foreign Bonds
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Coupon payments are fixedat stated rate
Fixed
Rate Bonds
coupon tied to prime rate, LIBOR, Treasury rate or other interestrate
Floating rate = benchmark rate + spread Floating rate can also be tied to the inflation rate: TIPS, for example
Floating Rate Bonds
Zero-coupon bonds pay no interest Also known as Discount bonds or pure discount bonds Sell below par value Treasury Bills (Tbills) Treasury STRIPs
Zero Coupon Bonds
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Unsecured bonds (debentures) are backed only by general faithand credit of issuer
Secured bonds are backed by specific assets (collateral) Mortgage bonds, collateral trust bonds, equipment trust
certificates
Secured vs. Unsecured Bonds
A provision in a bond contract that gives the issuer the right toredeem the bonds under specified terms prior to normal
maturity dates
Call provision
A provision in a bond contract that requires the issuers to retire
a portion of the bond issue each year.
Sinking Funds
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Convertible bonds, in addition to paying coupon, offers the right to convert the bondinto common stock of the issuer of the bond
Exchangeable bonds are convertible in shares of a company other than the issuers
Convertible and Exchangeable Bonds
Callable bonds: bond issuer has the right to repurchase the bonds at a specified price(call price).
Firms could retire and reissue debt if interest rates fall. Putable bonds: the investors have the right to sell the bonds to the issuer at the put
price.
Callable and Putable Bonds
Sinking fund provisions: the issuer is required to gradually repurchase outstandingbonds.
Protective covenants: requirements the bond issuer must meet Positive and negative covenants
Protection from Default Risk
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A bond that pay interest only if it is earned
Income bond
A bond that has interest payments based on
an inflation index so as to protect hodlers frominflation
Indexed/purchasing power bond
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Assuming annual interest:
)r+(1
M
+)r+(1
C
+...+)r+(1
C
+)r+(1
C
=P nn210
)r+(1M
+rr
C=
nn
1
11
Bond Price = PV of coupons + PV of principal
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Example
What is the price of a 5.5 % annual coupon bond, with a$1,000 face value, which matures in 3 years? Assume arequired return of 3.5%.
03.056,1$
)035.1(
055,1
)035.1(
55
)035.1(
55321
PV
PV15
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Example (continued)
What is the price of the bond if the required rate of return is 5.5%?
000,1$
)055.1(
055,1
)055.1(
55
)055.1(
55
321
PV
PV
Example (continued)
What is the price of the bond if the required rate of return is 15 %?
09.783$
)15.1(
055,1
)15.1(
55
)15.1(
55321
PV
PV16
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6% coupon ratefor both
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Bond prices move inversely to yields (interest rates)
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r > Coupon InterestRate
P0< par value DISCOUNT
r < Coupon InterestRate
P0 > par value PREMIUM
r = Coupon Interest
Rate
P0 =par value PAR VALUE
What happens to bond values if the required return is not equal tothe coupon rate?
The bond's price will differ from its par value.
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880
900
920
940
960
980
1,000
1,020
1,040
1,060
1,080
0 5 10 15 20 25 30
Bond
Price
Time to Maturity
Price path for Premium
Bond
Price path for DiscountBond
TodayMaturity
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Bond prices converge to par value (plus final coupon) with
passage of time
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SEMIANNUAL COMPOUNDING
Example (continued)
Determine the price of a 5.5 % annual coupon bond, with a$1,000 face value, which matures in 3 years?
What is the price of the bond if the required rate of return is3.5% AND the coupons are paid semi-annually?
49.056,1$
)0175.1(
50.027,1
)0175.1(
50.27...)0175.1(
50.27
)0175.1(
50.276521
PV
PV
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SEMIANNUAL COMPOUNDING (CONT.)
Example (continued)
Question:How did the calculation change, given semi-annual coupons versus annual coupon payments?
Time Periods
Paying coupons twice a year,
instead of once doubles the total
number of cash flows to be
discounted in the PV formula.
Discoun t Rate
Since the time periods are now
half years, the discount rate is
also changed from the annual
rate to the half year rate.
nr
MC
r
C
r
C
r
C
2321 )2
1(
2....
)2
1(
2
)2
1(
2
)2
1(
2Price
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SEMIANNUAL COMPOUNDING (CONT.)
nr
MC
r
C
r
C
r
C
2321 )2
1(
2....
)2
1(
2
)2
1(
2
)2
1(
2Price
22
)r+(1M
+
rr
C=
nn 22
221
11
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Interest rate for which the presentvalue of the bonds couponpayments and principal equal thebond price.
YTM
Estimate the rate of return
investors earn if they buy at P0and hold it until maturity
YTM
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n
r
MC
r
C
r
CPV
)1(
)(....
)1()1( 21
YIELD TO MATURITY (YTM) (CONT.)
Calculating Yield to Maturity (YTM=r)
If you are given the price of a bond (PV) and the coupon rate,
the yield to maturity can be found by solving for r.
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YIELD TO MATURITY (YTM) (CONT.)
Example
What is the YTM of a 5.5 % annual coupon bond, with a
$1,000 face value, which matures in 3 years? The market price
of the bond is $1,056.03.
03.056,1$
)1(
055,1
)1(
55
)1(
55
321
PV
rrr
PV
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WARNING
Calculating YTM by hand can be very tedious.
It is highly recommended that you learn to use the IRR
or YTM or i functions on a financial calculator.
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The amount obtained by dividing the bondscoupon by its current market price (which
does not always equal its par value).
CurrentYield
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Interest rate risk: the risk of a decline in bonds value(bond price)due to an increase in interest rate.
Interest rate risk is higher on bonds with long maturitiesthan on those maturing in near future.
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C Discount Rate
Bon
dValue
Par
Short Maturity Bond
Long Maturity Bond
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For a given change in yields, longer maturity bonds have
largerprice changes. Bond price volatility is positively relatedto maturity
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Discount Rate
BondV
alue
High Coupon Bond
Low Coupon Bond
30
For a given change in yields, higher coupon issues showsmaller price fluctuation . Bond price volatility is inverselyrelated to coupon.
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Reinvestment rate risk: the risk of decline in income froma bond portfolio due to the decrease in interest rate.
Reinvestment rate risk is higher on bonds with shortmaturities than those with longer maturities.
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Interest rate risk
Interest rate risk relates tothe value of the bond
portfolio.
Investors hold long-termbonds will face significantinterest rate risk, but will
not face muchreinvestment rate risk.
Reinvestmentrisk
Reinvestment rate riskrelates to the i ncomeof the
bond portfolio.
Otherwise, investors holdshort- termbonds will face
significant reinvestmentrate risk, but will not facemuch interest rate risk.
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Approximately, the difference between an
investments stated or nominal return and theinflation rate.
Real return
The stated return offered by an investmentunadjusted for the effects of inflation.
Nominal return
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Bond ratings: grades assigned to bond issues based ondegree of default risk
Investment-grade bonds
Moodys Aaa to Baa3 ratings S&P and Fitch AAA to BBB-
ratings
Junk bonds Moodys Ba1 to Caa1 or lower
S&P and Fitch BB to CCC+ orlower
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TUTORIALQUESTIONS
CHAPTER 5TEXTBOOK:
QUESTIONS FOR REVIEW CHAPTER 1, 2, 3, 4, 5
PRATICE PROBLEMS 7, 17, 20, 21, 22, 23 AND 25
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