BMM Ch4 Valuing Bonds
Transcript of BMM Ch4 Valuing Bonds
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Chapter 4Fundamentals of Corporate Finance
Third Edition
Valuing Bonds
Brealey Myers Marcus
slides by Matthew Will
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Topics Covered
Bond Characteristicsreading the financial pages
Bond Prices and Yields
Bond prices and interest rates
YTM vs. current yield
Rate of Return
Interest Rate Risk
The Yield Curve
Nominal and Real Rates of Interest
Default Risk
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Bonds
TerminologyBond - Security that obligates the issuer to
make specified payments to the bondholder.
Coupon - The interest payments made to thebondholder.
Face Value (Par Value or Maturity Value) - Payment
at the maturity of the bond.Coupon Rate - Annual interest payment, as a
percentage of face value.
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Bonds
WARNING
The coupon rate IS NOT the discount rate
used in the Present Value calculations.
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Bonds
WARNING
The coupon rate IS NOT the discount rate
used in the Present Value calculations.
The coupon rate merely tells us what cash flow the
bond will produce.
Since the coupon rate is listed as a %, this
misconception is quite common.
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Bond Pricing
The price of a bond is the Present Value of
all cash flows generated by the bond (i.e.
coupons and face value) discounted at the
required rate of return.
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Bond Pricing
The price of a bond is the Present Value of
all cash flows generated by the bond (i.e.
coupons and face value) discounted at the
required rate of return.
PV
cpn
r
cpn
r
cpn par
r t
( ) ( ) ....
( )
( )1 1 11 2
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Bond Pricing
Example
What is the price of a 6 % annual coupon bond,
with a $1,000 face value, which matures in 3
years? Assume a required return of 5.6%.
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Bond Pricing
Example
What is the price of a 6 % annual coupon bond,
with a $1,000 face value, which matures in 3
years? Assume a required return of 5.6%.
77.010,1$
)056.1(
060,1
)056.1(
60
)056.1(
60321
PV
PV
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Bond Pricing
Example (continued)
What is the price of the bond if the required rate
of return is 6 %?
000,1$
)06.1(
060,1
)06.1(
60
)06.1(
60321
PV
PV
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Bond Pricing
Example (continued)
What is the price of the bond if the required rate
of return is 15 %?
51.794$
)15.1(
060,1
)15.1(
60
)15.1(
60321
PV
PV
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Bond Pricing
Example (continued)
What is the price of the bond if the required rate
of return is 5.6% AND the coupons are paid semi-
annually?
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Bond Pricing
Example (continued)
What is the price of the bond if the required rate
of return is 5.6% AND the coupons are paid semi-
annually?
91.010,1$
)028.1(
030,1
)028.1(
30...
)028.1(
30
)028.1(
306521
PV
PV
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Bond Pricing
Example (continued)
Q: How did the calculation change, given semi-
annual coupons versus annual coupon payments?
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Bond Pricing
Example (continued)
Q: How did the calculation change, given semi-
annual coupons versus annual coupon payments?
Time Periods
Paying coupons twice a
year, instead of oncedoubles the total number of
cash flows to be discounted
in the PV formula.
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Bond Pricing
Example (continued)
Q: How did the calculation change, given semi-
annual coupons versus annual coupon payments?
Time Periods
Paying coupons twice a
year, instead of oncedoubles the total number of
cash flows to be discounted
in the PV formula.
Discount Rate
Since the time periods are
now half years, thediscount rate is also
changed from the annual
rate to the half year rate.
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Bond Yields
Current Yield - Annual coupon payments
divided by bond price.
Yield To Maturity - Interest rate for which
the present value of the bonds payments
equal the price.
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Bond Yields
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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Bond Yields
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.
PV
cpn
r
cpn
r
cpn par
r t
( ) ( ) ....
( )
( )1 1 11 2
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Bond Yields
Example
What is the YTM of a 6 % annual coupon bond,
with a $1,000 face value, which matures in 3
years? The market price of the bond is $1,010.77
77.010,1$)1(
060,1
)1(
60
)1(
60321
PVrrr
PV
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Bond Yields
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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Bond Yields
Rate of Return - Earnings per period per
dollar invested.
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Bond Yields
Rate of Return - Earnings per period per
dollar invested.
Rate of return = total incomeinvestment
Rate of return =Coupon income + price change
investment
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Interest Rate Risk
880
900
920
940
960
980
1,000
1,020
1,040
1,060
1,080
0 5 10 15 20 25 30
Time to Maturity
Bond
Pric
e
Premium Bond
Discount Bond
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Interest Rate Risk
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500
1,000
1,500
2,000
2,500
3,000
0 2 4 6 8 10
YTM
$Bond
Price
30 yr bond
3 yr bond
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Nominal and Real rates
0
2
4
6
8
10
12
14
16
82
85
88
91
94
97
Year
Percent
Yield on UK
nominal bonds
Yield on UK
indexed bonds
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Default Risk
Credit risk
Default premium
Investment grade
Junk bonds
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Default Risk
Standard
Moody' s & Poor's Safety
Aaa AAA The strongest rating; ability to repay interest and principal
is very strong.
Aa AA Very strong likelihood that interest and principal will be
repaidA A Strong ability to repay, but some vulnerability to changes in
circumstances
Baa BBB Adequate capacity to repay; more vulnerability to changes
in economic circumstances
Ba BB Considerable uncertainty about ability to repay.
B B Likelihood of interest and principal payments over sustained periods is questionable.
Caa CCC Bonds in the Caa/CCC and Ca/CC classes may already be
Ca CC in default or in danger of imminent default
C C C-rated bonds offer little prospect for interest or principal
on the debt ever to be repaid.
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The Yield Curve
Term Structure of Interest Rates - A listing of
bond maturity dates and the interest rates
that correspond with each date.
Yield Curve - Graph of the term structure.
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Web Resources
www.finpipe.com
www.investinginbonds.com
www.bloomberg.com/markets/C13.html
www.bondmarkets.com/publications/IGCORP/what.htm
www.moodys.com
www.standardandpoors.com/ratings
Click to access web sites
Internet connection required
http://www.finpipe.com/http://www.investinginbonds.com/http://www.bloomberg.com/markets/C13.htmlhttp://www.bondmarkets.com/publications/IGCORP/what.htmhttp://www.moodys.com/http://www.standardandpoors.com/ratingshttp://www.ibm.com/investor/FinancialGuidehttp://www.ibm.com/investor/FinancialGuidehttp://www.standardandpoors.com/ratingshttp://www.moodys.com/http://www.bondmarkets.com/publications/IGCORP/what.htmhttp://www.bloomberg.com/markets/C13.htmlhttp://www.investinginbonds.com/http://www.finpipe.com/