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Fundamentals of Corporate
Finance
Chapter 6
Valuing Bonds
Topics CoveredThe Bond MarketInterest Rates and Bond PricesCurrent Yield and Yield to MaturityBond Rates and ReturnsThe Yield CurveCorporate Bonds and the Risk of Default
BondsTerminology Bond - Security that obligates the issuer to make specified
payments to the bondholder. Coupon - The interest payments made to the bondholder. Face Value (Par Value or Principal Value) - Payment at the maturity
of the bond. Coupon Rate - Annual interest payment, as a percentage of
face value.
WARNINGWARNINGThe 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.
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.
PVcpn
r
cpn
r
cpn par
r t
( ) ( )
....( )
( )1 1 11 2
Bond Cash Flows
Bond Pricing
Example
What is the price of a 5.0 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume a required return of 2.15%.
Bond Pricing
Example
What is the price of a 5.0 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume a required return of 2.15%.
95.081,1$
)0215.1(
050,1
)0215.1(
50
)0215.1(
50321
PV
PV
Bond Pricing
Example (continued)
Q: How did the calculation change, given semi-annual coupons versus annual coupon payments?
Bond Pricing
Example (continued)
What is the price of the bond if the required rate of return is 2.15% AND the coupons are paid semi-annually?
37.082,1$
)01075.1(
025,1
)01075.1(
25...
)01075.1(
25
)01075.1(
256521
PV
PV
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 once
doubles the total number of cash flows to be discounted
in the PV formula.
Discount Rate
Since the time periods are now half years, the discount rate is also
changed from the annual rate to the half year rate.
Bond Pricing
Example (continued)
What is the price of the bond if the required rate of return is 5.0 %?
000,1$
)050.1(
050,1
)050.1(
50
)050.1(
50321
PV
PV
Bond Pricing
Example (continued)
What is the price of the bond if the required rate of return is 8 %?
69.922$
)08.1(
050,1
)08.1(
50
)08.1(
50321
PV
PV
Interest Rate Risk
The value of the 5% bond falls as interest rates rise
700
800
900
1,000
1,100
1,200
0 2 4 6 8 10 12 14 16
Interest rate (%)
Bo
nd
pri
ce (
$)
Interest Rate Risk
-
500
1,000
1,500
2,000
2,500
3,000
0 2 4 6 8 10
YTM
$ B
on
d P
ric
e
30 yr bond
3 yr bond
When the interest rate equals the 5.0% coupon rate, both
bonds sell at face value
Bond Yields
Current Yield - Annual coupon payments divided by bond price.
Yield To Maturity - Interest rate for which the present value of the bond’s payments equal the price.
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.
PVcpn
r
cpn
r
cpn par
r t
( ) ( )
....( )
( )1 1 11 2
Bond Yields
Example
What is the YTM of a 5.0 % annual coupon bond, with a $1,000 face value, which matures in 3 years? The market price of the bond is $1,081.95.
95.081,1$
)1(
050,1
)1(
50
)1(
50321
PV
rrrPV
YTM = 2.15%
Bond Yields
Rate of Return - Earnings per period per dollar invested.
Rate of return =total income
investment
Rate of return =Coupon income + price change
investment
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.
The Yield Curve
0
1
2
3
4
5
61 3 5 7 9
11
13
15
17
19
21
23
25
27
29
Maturity (years)
Yie
ld %
Treasury strips are bonds that make a single payment. The yields on Treasury strips in February 2008 show that investors received a higher yield on longer term bonds.
Default Risk
Credit (default) risk: the risk that a bond issuer may default on its bonds
Default premium: The additional yield on a bond that investors require for bearing credit risk
Investment grade: Bonds rated Baa or above by Moody’s or BBB or above by S&P
Junk bonds: Bond with a rating below Baa or BBB
Default Risk
StandardMoody' s & Poor's Safety
Aaa AAA The strongest rating; ability to repay interest and principalis very strong.
Aa AA Very strong likelihood that interest and principal will berepaid
A A Strong ability to repay, but some vulnerability to changes incircumstances
Baa BBB Adequate capacity to repay; more vulnerability to changesin 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 beCa CC in default or in danger of imminent defaultC C C-rated bonds offer little prospect for interest or principal
on the debt ever to be repaid.
Default Risk
0
2
4
6
8
10
12Y
ield
sp
read
%
Junk bonds
Baa-rated bonds
Aaa-rated bonds
Yield spreads between corporate and 10-year Treasury bonds