Chapter 5
Valuing Bonds
Chapter 5 Topic Overview
Bond Characteristics
Annual and Semi-Annual Bond
Valuation
‹ Reading Bond Quotes
‹ Finding Returns on Bonds
‹ Bond Risk and Other Important Bond
Valuation Relationships
‹
‹
Bond Characteristics
Face (or Par) Value = stated face
value that is the amount the issuer
must repay, usually $1,000
| Coupon Interest Rate
| Coupon (cpn) = Coupon Rate x Face
Value
| Maturity Date = when the face value is
repaid.
| This makes a bond’s cash flows look
like this:
|
Characteristics of Bonds
• Bonds pay fixed coupon (interest)
payments at fixed intervals (usually
every 6 months) and pay the face
value at maturity.
cpn/2 cpn/2 cpn/2 cpn/2 … cpn/2+par
0
1
2
...
n
Bonds
WARNING
The 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.
Since the coupon rate is listed as a %, this
misconception is quite common.
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.
PV =
cpn
cpn
(cpn + par )
+
+....+
1
2
(1 + r ) (1 + r )
(1 + r ) t
Bond Valuation
|
Discount the bond’s cash flows at the
investor’s required rate of return.
z
z
z
cpn
0
1
the coupon payment stream (an annuity).
the face (par) value payment (a single
sum).
PV = cpn (PVAF r, t) + par /(1+r)t
cpn
2
cpn+par
...
n
Bond Valuation Example #1
‹
‹
Duff’s Beer has $1,000 par value bonds
outstanding that make annual coupon
payments. These bonds have an 8% annual
coupon rate and 12 years left to maturity.
Bonds with similar risk have a required
return of 10%, and Moe Szyslak thinks this
required return is reasonable.
What’s the most that Moe is willing to pay
for a Duff’s Beer bond?
Let’s Play with Example #1
‹ Homer
Simpson is interested in
buying a Duff Beer bond but
demands an 8 percent required
return.
‹ What is the most Homer would
pay for this bond?
Let’s Play with Example #1
some more.
‹ Barney
(belch!) Gumble is
interested in buying a Duff Beer
bond and demands on a 6
percent required return.
‹ What is the most Barney (belch!)
would pay for this bond?
Bond Prices and Interest Rates have
an inverse relationship!
($)M arket Value
Bond Values for 8% Annual Coupon Bonds
1400
1200
1000
800
600
400
200
0
12-yr Bond
0%
2%
4%
6%
8%
10%
12%
Required Return
Bonds with Semiannual
Coupons
‹
Double the number of years, and
divide required return and annual
coupon by 2.
VB = annual cpn/2
(PVAFr/2,2t) + par /(1+r/2)2t
cpn/2(PVAF
Semiannual Example
‹
A $1000 par value bond with an annual
coupon rate of 9% pays coupons
semiannually with 15 years left to maturity.
What is the most you would be willing to
pay for this bond if your required return is
8% APR?
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.
PV =
cpn
cpn
(cpn + par )
+
+....+
1
2
(1 + r ) (1 + r )
(1 + r ) t
Yield to Maturity Example
$1000 face value bond with a 10%
coupon rate paid annually with 20
years left to maturity sells for
$1091.29.
‹ What is this bond’s yield to maturity?
‹