Chap005 Valuaing Bonds
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Transcript of Chap005 Valuaing Bonds
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Chapter 5 Fundamentals of
Corporate Finance
Fifth Edition
Slid es by
Matthew W ill
McGraw-Hill/Irwin Copyright 2007 by The McGraw-Hill Companies, Inc. All rights reserved
V a luing Bo nd s
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T op ics Covere d
B ond Characteristicsreading the financial pages
Interest Rates and B ond PricesCurrent Yield and Yield to MaturityB ond Rates and ReturnsThe Yield CurveCorporate B onds and the Risk of Default
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Bo nd s
TerminologyB ond - Security that obligates the issuer tomake specified payments to the bondholder.
Coupon - The interest payments made to the bondholder.Face Value (Par Value or Principal Value) - Paymentat the maturity of the bond.Coupon Rate - Annual interest payment, as a
percentage of face value.
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Bo nd s
W ARNINGW ARNINGThe coupon rate IS NOT the discount rateused 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 %, thismisconception is quite common.
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Bo nd Pr icing
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 therequired rate of return.
PV cpn
r cpn
r cpn par
r t ! ( ) ( ) ....( )
( )1 1 11 2
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Bo nd Pr icing
ExampleWh at is t h e price of a 5.5 % annual coupon bond,wit h a $1,000 face value, w h ich matures in 3
years? Assume a required return of 3.5%.
03.056,1$)
035.1(
055,1
)035
.1(
55
)035
.1(
55321
!
!
PV
PV
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Copyright 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin
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Bo nd Cash F lows
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Bo nd Pr icing
Example (continued)What is the price of the bond if the required rateof return is 5.5 %?
000,1$
)055.1(
055,1)055.1(
55
)055.1(
55321
!
!
PV
PV
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Bo nd Pr icing
Example (continued)What is the price of the bond if the required rateof return is 15 %?
09.783$
)15.1(
055,1)15.1(
55
)15.1(
55321
!
!
PV
PV
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Bo nd Pr icing
Example (continued)What is the price of the bond if the required rateof return is 3.5% AND the coupons are paid semi-annually?
49.056,1$)0 175.1(
50.0 27,1)0 175.1(
50.27...
)0 175.1(
50.27)0 175.1(
50.276521
!
!
PV
PV
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Bo nd Pr icing
Example (continued)Q: How did t h e calculation c h ange, given semi-
annual coupons versus annual coupon payments?
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Bo nd Pr icing
Example (continued)Q: How did t h e calculation c h ange, given semi-
annual coupons versus annual coupon payments?
T ime Periods
Paying coupons twice a
year, instead of oncedoubles t h e total number of cas h flows to be discounted
in t h e PV formula.
Discount Rate
Since t h e time periods are
nowh
alf years, t h
ediscount rate is alsoch anged from t h e annual rate to t h e h alf year rate.
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Bo nd Yield s
Current Yield - Annual coupon paymentsdivided by bond price.
Yield To Maturity - Interest rate for whichthe present value of the bonds paymentsequal the price.
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Bo nd Yield s
Calculating Yield to Maturity (YTM=r)If you are given the price of a bond (PV)
and the coupon rate, the yield to maturitycan be found by solving for r.
PV cpn
r cpn
r cpn par
r t ! ( ) ( ) ....( )
( )1 1 11 2
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Bo nd Yield s
ExampleWh at is t h e YTM of a 5.5 % annual coupon bond,wit h a $1,000 face value, w h ich matures in 3
years? T h e market price of t h e bond is $1,056.03.
03.056,1$)1(
055,1
)1(
55
)1(
55321
!
!
PV r r r
PV
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Bo nd Yield s
W ARNINGW ARNINGCalculating YTM by hand can be very
tedious.
It is highly recommended that you learn to
use the IRR or YTM or i functions ona financial calculator.
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Bo nd Yield s
Rate of Return - Earnings per period per dollar invested.
Rate of returntotal incomeinvestment
Rate of returnoupon income + price change
investment
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Bo nd V a lu at ion Sprea dsheet
Valuing bonds using a spreadshee t
5.5 % coupon 5.5% couponma turing Ma y 2005 10-ye ar ma turity
Settlement date 5/15/05 1/1/05Maturity date 5/15/08 1/1/15
Annual coupon rate 0.055 0.055Yield to maturity 0.035 0.035Redemption value (% of face value) 100 100Coupon payments per year 1 1
Bond price (% of par) 105.603 116.633
=PRICE(B7,B8,B9,B10,B11,B12)
Esc and Double click on spreadsheet to access
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Bo nd Yield Sprea dsheet
Finding yield to ma turity using a spreadsheetMay 2008 maturity bond, coupon rate = 5.5%, ma turity = 3 yea rs
Annual coupons Semiannual coupons
Settlement date 5/15/05 5/15/05Maturity date 5/15/08 5/15/08
Annual coupon rate 0.055 0.055Bond price 105.603 105.603Redemption value (% of face value) 100 100Coupon payments per year 1 2
Yield to maturity (decimal) 0.035 0.0352
=YIELD(B7,B8,B9,B10,B11,B12)
Esc and Double click on spreadsheet to access
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I n terest Rate R isk
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
B o n
d P r i c e
Price path for Premium B ond
Price path for Discount B ondToday
Maturity
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I n terest Rate R isk
-
500
1,000
1,500
2,000
2,500
3,000
0 2 4 6 8 10
YTM
$ B
P r
30 yr bond
3 yr bond
W hen the interest rate equalsthe 5 .5 % coupon rate, both
bonds sell at face value
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N om in a l and Rea l rates
0
2
4
6
8
10
12
14
8 5 8 6 8 7 8 8 8 9 9 0 9 1 9 2 9 3 9 4 9 5 9 6 9 7 9 8 9 9 2 0
0 0 2 0
0 1 2 0
0 2 2 0
0 3 2 0
0 4 2 0
0 5
Yea r
e r e n t
Yield on UK nominal bonds
Yield on UK indexed bonds
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D efa ul t R isk
Credit risk Default premium
Investment gradeJunk bonds
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D efa ul t R isk Standa d
d ' s & 's Safet
Aaa AAA The s es ating; ability to epay intere st and principalis ery strong .
Aa AA Very strong likelihood that intere st and principal ill berepaid
A A Strong ability to repay , but some ulnerability to change s incircum stance s
Baa BBB Adequate capacity to repay; more ulnerability to change sin economic circum stance s
Ba BB onsiderable uncertainty about ability to repay .
B B L ikelihood of intere st and principal payment s over sustained period s is que stionable .
aa CCC Bonds in the Caa/CCC and Ca/CC classes may already beCa CC in default or in danger of imminent defaultC C C-rated bond s offer little pros pect for intere st or principal
on the debt ever to be repaid .
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Corporate Bo nd s
Z ero couponsFloating rate bonds
Convertible bonds
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T he Y ield C urve
Term Structure of Interest Rates - A listing of bond maturity dates and the interest ratesthat correspond with each date.
Yield Curve - Graph of the term structure.