McGraw-Hill/Irwin
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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
6-2
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.
6-3
Bond Pricing: Example
Treasury bond prices are quoted in 32nds
rather than in decimals.
Example:
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% + (06/32) = 103.1875% of face value
(1.031875) * ($1,000) = $1,031.875
6-4
Bond Pricing
coupon coupon
(coupon  par )
PV 

 .... 
1
2
t
(1  r )
(1  r )
(1  r )
6-5
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%.
6-6
Bond Pricing
A bond is a package of two investments: an annuity
and a final repayment.
PVBond  PVCoupons  PVParValue
PVBond  coupon  ( Annuity Factor )  par value  ( Discount Factor )
1  (1  r )  t
where Annuity Factor 
r
1
and Discount Factor 
(1  r )t
6-7
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%.
PVBond
1  (1  .04) 3
1
 $90 
 $1, 000 
.04
(1  .04)3
 $1,138.75
6-8
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%?
6-9
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
6-10
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?
6-11
Yield to Maturity
Yield to Maturity:
coupon coupon
(coupon  par )
PV 

 .... 
1
2
(1  r )
(1  r )
(1  r )t
6-12
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
$60
($60  $1,000)
$1,150 


1
2
(1  r )
(1  r )
(1  r ) 3
6-13
Rate of Return
6-14
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?
6-15
The Yield Curve: Example
6-16
Interest Rates & Inflation
In the presence of inflation, an investor’s real interest
rate is always less than the nominal interest rate.
6-17
Interest Rates & Inflation
If you invest in a security that pays 10% interest
annually and inflation is 6%, what is your real
interest rate?
6-18
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
6-19
The Risk of Default
When investing in bonds, there is always the
risk that the issuer may default.
 Default risk
 Default premium
6-20
The Risk of Default
Bonds come in many categories, with returns
commensurate with risk.
 Credit agency
 Investment-grade bonds
 Junk bonds
6-21
Types of Corporate Bonds
Zero-Coupon Bonds
Floating-Rate Bonds
Convertible Bonds
6-22
Appendix A: Treasury Bond
Rates
10-year U.S. Treasury bond interest rates, 1900-2010
6-23
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
6-24
Appendix C: Credit Ratings
6-25