1. Valuing Bonds
Chapter Six

2. Bond Terminology
 Bond
• A security that obligates the issuer to make fixed payments
to the bondholder until the maturity of the bond (fixed
income security)
 Face Value (par, principal or maturity value)
• Payment made at the maturity of the bond. In the US it is
usually $1,000
 Coupon
• The interest payments made to the bondholder. In the USA
coupons are paid twice a year
 Coupon Rate
• Total annual interest payment as percent of bond face
value. Only used to calculate coupon. Not used as
discount rate, but upon issuance the coupon rate is usually
close or equal to the discount or required rate of return.

3. Bond Terminology and Pricing
 Bond Price
• Equals the present value of all future coupon payments and
the future par value payment.
 Bond Yield
• The annualized (APR) discount rate used to calculate the
bond’s present value. Also known as the yield to maturity
or required rate of return.
 Current Yield
• Annual coupon payments divided by bond price.
coupon coupon ( coupon + par )
PV = + + .... +
(1 + r ) 1
(1 + r ) 2
(1 + r ) t

4. 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%.
50 50 1,050
PV = + +
(1.0215) (1.0215) (1.0215) 3
1 2
PV = $1,081.95
Calculator: N=3, I/Y=2.15, PMT=.05x1,000=50,
FV=1,000, PV=?

5. Bond Cash Flows

6. Bond Pricing Example
What is the price of the bond if the required rate of
return is 2.15% and the coupons are paid semi-
annually?
25 25 25 1,025
PV = 1
+ 2
+ ... + 5
+ 6
(1.01075) (1.01075) (1.01075) (1.01075)
PV = $1,082.37
Calculator: N=3 years x 2 payments/year=6,
I/Y=2.15/2 payments/year = 1.075,
PMT=.05x1,000/2 payments/year=25, FV=1,000,
PV=?

7. Semi-Annual Coupons
How did the calculation change, given semi-annual
coupons versus annual coupon payments?
Time Periods Discount Rate
Paying coupons twice a year, Since the time periods are
instead of once doubles the now half years, the
total number of cash flows to discount rate is also
be discounted in the PV changed from the annual
formula. rate to the half year rate.

8. Bond Pricing Example
What is the price of the annual bond if the
required rate of return is 5.0 %?
50 50 1,050
PV = 1
+ 2
+ 3
(1.050) (1.050) (1.050)
PV = $1,000

9. Bond Pricing Example
What is the price of the annual bond if the
required rate of return is 8 %?
50 50 1,050
PV = + +
(1.08) (1.08) (1.08) 3
1 2
PV = $922.69

10. Interest Rate Risk
 The value of an existing bond falls as interest
(discount) rates rise
1,200
1,100
1,000
900
B
p
d
n
o
$
e
c
r
)
(
i
800
700
0 2 4 6 8 10 12 14 16
Interest rate (%)

11. Interest Rate Risk
 The value of an existing bond falls as interest
(discount) rates rise.
 The intuition is that, when buying a bond, we
agree on a fixed interest payment.
 Afterwards, when current interest rates go
up, our bond pays less interest than newer
bonds, making our bond worth less.

12. 
bonds
Yield %
0
2
4
6
8
10
12
14
16
1900
1905
1910
1915
1920
1925
1930
1935
Treasury Yields
1940
1945
1950
1955
Year
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
The interest rate on 10-year U.S. Treasury

13. Pricing of Zero-Coupon Bonds
 Price a 10 year zero-coupon bond at a
12% discount rate.
PV = CFt / (1 + r)t = 1000 / (1 + .12)10
 Price = 1000 / (1+0.12)10 = $321.97

14. Bond Yield or
Yield to Maturity (YTM)
 When a normal coupon bond is initially issued its
coupon rate should be close to or equal to its yield to
maturity (discount rate)
 But market conditions like changing interest rates can
cause the bond prices and yields to change over time
while the coupon rate stays constant
 If given the bond price, you can calculate its YTM by
solving for r below.
coupon coupon ( coupon + par )
PV = + + .... +
(1 + r ) 1 (1 + r ) 2 (1 + r ) t

15. 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.
50 50 1,050
PV = + +
(1 + r ) (1 + r )
1 2
(1 + r ) 3
PV = $1,081.95
YTM = 2.15%

16. 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.

17. The Yield Curve
Treasury zero coupon bonds (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.
6
5
4
Yield %
3
2
1
0
11
13
15
17
19
21
23
25
27
29
1
3
5
7
9
Maturity (years)

18. Bond Rates of Return
Rate of Return – actual earnings of an
investor during a certain period of time per
dollar invested in a bond.
(coupons + change in price)
Rate of return =
investment
(coupons + Price 1 – Price 0 )
Rate of return =
Price 0

19. Bonds and Credit Risks
Credit risk is the risk of default by the issuer, which is the
inability to pay coupons or face value at maturity. US
Government debt has no credit risk by convention.
Investors require higher yields on riskier bonds.
The default premium is the difference between the yields on
government bonds and corporate bonds with the same
maturity, but more default risk.

20. Default Risk and Ratings
• Rating companies
– Moody’s Investor Service
– Standard & Poor’s
– Duff and Phelps
• Rating Categories
– Investment grade = BBB, Baa and above
– Speculative grade or Junk bonds = BB and
below

21. Bond Ratings
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
repaid
A 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.

22. Default Risk
Yield spreads between corporate and 10-year Treasury
bonds
12
10
Yield spread %
8 Junk bonds
6
4 Baa-rated
bonds
2
Aaa-rated bonds
0
80
83
86
89
92
95
98
01
04
07
19
19
19
19
19
20
19
19
20
20