This document provides an overview of key concepts for valuing and analyzing bonds, including: - Bond basics like face value, coupon, and coupon rate - How to calculate the price of a bond using principles of present value - How bond prices change with interest rates - Methods for calculating bond yields like current yield and yield to maturity - The relationship between interest rates and inflation and how this affects real returns - The risks of default and how bonds are categorized based on their default risk.

1. McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

2. 6-
2
Valuing Bonds
A bond is a debt instrument issued by
governments or corporations to raise money
The successful investor must be able to:
• Understand bond structure
• Calculate bond rates of return
• Understand interest rate risk
• Differentiate between real and nominal returns

3. 6-
3
Bond Basics
When governments or companies issue bonds, they promise to
make a series of interest payments and then repay the debt.
Bond
• Security that obligates the issuer to make specified payments to
the bondholder.
Face Value
• Payment at the maturity of the bond.
Coupon
• The interest payments paid to the bondholder.
Coupon Rate
• Annual interest payment as a percentage of face value.

4. 6-
4
Bond Pricing: Example
Treasury bond prices are quoted in 32nds
rather than in decimals.
For a $1000 face value bond with a bid price of 103:05 and
an asked price of 103:06, how much would an investor pay
for the bond?
103% 6 103.1875%
+ æç ö¸ = of face value è 32
ø
( ) ( )
´ =
1.031875 $1,000 $1,031.875

5. 6-
5
Bond Pricing
PV = coupon + coupon + + coupon +
par
1 2
.... ( )
(1 + r ) (1 + r ) (1 +
r
)t

6. 6-
6
Bond Pricing: Example
What is the price of a 9% annual coupon bond with a par
value of $1,000 that matures in 3 years? Assume a required
rate of return of 4%.

7. 6-
7
Bond Pricing
A bond is a package of two investments: an annuity
and a final repayment.
PV = PV +
PV
Bond Coupons ParValue
PV = coupon ´ Annuity Factor + par value ´
Discount Factor
( ) ( )
Annuity Factor r
where 1 (1 )
and 1
(1 )
Bond
t
r
t
Discount Factor
r
-
= - +
=
+

8. ( ) ( ) bond PV = coupon ´ annuity factor + par value´ discount factor
6-
8
Bond Pricing: Example
What is the value of a 3-year annuity that pays $90 each year and an
additional $1,000 at the date of the final repayment? Assume a
discount rate of 4%.
3
3
$90 1 (1 .04) $1,000 1
.04 (1 .04)
$1,138.75
Bond PV
- + - = ´ + ´
+
=

9. 6-
9
Bond Prices & Interest Rates
As interest rates change, so do bond prices.
What is the present value of a 4% coupon bond with face value
$1,000 that matures in 3 years? Assume a discount rate of 5%.
What is the present value of this same bond at a discount rate of 2%?

10. 6-
10
Bond Yields
To calculate how much we earn on a bond investment,
we can calculate two types of bond yields:
Current Yield
Yield to Maturity

11. 6-
11
Current Yield: Example
Suppose you spend $1,150 for a $1,000 face value
bond that pays a $60 annual coupon payment for 3
years.
What is the bond’s current yield?

12. 6-
12
Yield to Maturity
Yield to Maturity:
coupon par
+ + +
.... ( )
r t
coupon
(1 )1 (1 r
)2 +
PV coupon
r
(1 )
+
+
+
=

13. 6-
13
Yield to Maturity: Example
Suppose you spend $1,150 for a $1,000 face value bond
that pays a $60 annual coupon payment for 3 years.
What is the bond’s yield to maturity?
($60 $1,000)
$60
1 2 (1 )3
r (1 r )
+r
$1,150 $60
(1 )
+ +
+
+
+
=

14. 6-
14
Rate of Return

15. 6-
15
Rate of Return: Example
Suppose you purchase a 5% coupon bond, par value $1,000,
with 5 years until maturity, for $975.00 today. After one year
you sell the bond for $965.00.
What was the rate of return during the period?

16. 6-
16
The Yield Curve

17. 6-
17
Interest Rates & Inflation
In the presence of inflation, an investor’s real interest
rate is always less than the nominal interest rate.

18. 6-
18
Interest Rates & Inflation
If you invest in a security that pays 10% interest
annually and inflation is 6%, what is your real
interest rate?

19. 6-
19
Interest Rates & Inflation:
Example
Treasury Inflation Protected Securities (TIPS)
Example:
If you invest in 5% coupon, 3 year TIPS and inflation is 3% each
year, what are your real annual cash flows?
Year 1 2 3
Real cash flows $50 $50 $1,050

20. 6-
20
The Risk of Default
When investing in bonds, there is always the
risk that the issuer may default.
Default risk
Default premium

21. 6-
21
The Risk of Default
Bonds come in many categories, with returns
commensurate with risk.
Credit agency
Investment-grade bonds
Junk bonds

22. 6-
22
Types of Corporate Bonds
Zero-Coupon Bonds
Floating-Rate Bonds
Convertible Bonds

23. 6-
23
Appendix A: Treasury Bond
Rates
10-year U.S. Treasury bond interest rates, 1900-2010

24. 6-
24
Appendix B: Real vs. Nominal Yields
Red line – Real yield on long-term UK indexed bonds
Blue line – Nominal yield on long-term UK bonds

25. 6-
25
Appendix C: Credit Ratings