?The McGraw-Hill Companies,Inc.,2001
4- 1
Irwin/McGraw-Hill
Chapter 4Fundamentals of Corporate FinanceThird Edition
Valuing Bonds
Brealey Myers Marcus
slides by Matthew Will
?The McGraw-Hill Companies,Inc.,2001
4- 2
Irwin/McGraw-Hill
Topics Covered
?Bond Characteristics
?reading the financial pages
?Bond Prices and Yields
?Bond prices and interest rates
?YTM vs,current yield
?Rate of Return
?Interest Rate Risk
?The Yield Curve
?Nominal and Real Rates of Interest
?Default Risk
?The McGraw-Hill Companies,Inc.,2001
4- 3
Irwin/McGraw-Hill
Bonds
Terminology
?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 Maturity Value) - Payment
at the maturity of the bond.
?Coupon Rate - Annual interest payment,as a
percentage of face value.
?The McGraw-Hill Companies,Inc.,2001
4- 4
Irwin/McGraw-Hill
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.
?The McGraw-Hill Companies,Inc.,2001
4- 5
Irwin/McGraw-Hill
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 c p n
r
c p n
r
c p n par
r t
?
?
?
?
? ? ?
?( ) ( )
.,,, ( )
( )1 1 11 2
?The McGraw-Hill Companies,Inc.,2001
4- 6
Irwin/McGraw-Hill
Bond Pricing
Example
What is the price of a 6 % annual coupon bond,
with a $1,000 face value,which matures in 3
years? Assume a required return of 5.6%,
77.010,1$
)056.1(
060,1
)056.1(
60
)056.1(
60
321
?
???
PV
PV
?The McGraw-Hill Companies,Inc.,2001
4- 7
Irwin/McGraw-Hill
Bond Pricing
Example (continued)
What is the price of the bond if the required rate
of return is 6 %?
0 0 0,1$
)06.1(
0 6 0,1
)06.1(
60
)06.1(
60
321
?
???
PV
PV
?The McGraw-Hill Companies,Inc.,2001
4- 8
Irwin/McGraw-Hill
Bond Pricing
Example (continued)
What is the price of the bond if the required rate
of return is 15 %?
51.7 9 4$
)15.1(
0 6 0,1
)15.1(
60
)15.1(
60
321
?
???
PV
PV
?The McGraw-Hill Companies,Inc.,2001
4- 9
Irwin/McGraw-Hill
Bond Pricing
Example (continued)
What is the price of the bond if the required rate
of return is 5.6% AND the coupons are paid semi-
annually?
91.010,1$
)028.1(
030,1
)028.1(
30
...
)028.1(
30
)028.1(
30
6521
?
?????
PV
PV
?The McGraw-Hill Companies,Inc.,2001
4- 10
Irwin/McGraw-Hill
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.
?The McGraw-Hill Companies,Inc.,2001
4- 11
Irwin/McGraw-Hill
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.
?The McGraw-Hill Companies,Inc.,2001
4- 12
Irwin/McGraw-Hill
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 c p n
r
c p n
r
c p n par
r t
?
?
?
?
? ? ?
?( ) ( )
.,,, ( )
( )1 1 11 2
?The McGraw-Hill Companies,Inc.,2001
4- 13
Irwin/McGraw-Hill
Bond Yields
Example
What is the YTM of a 6 % annual coupon bond,
with a $1,000 face value,which matures in 3
years? The market price of the bond is $1,010.77
77.0 1 0,1$
)1(
0 6 0,1
)1(
60
)1(
60
321
?
?
?
?
?
?
?
PV
rrr
PV
?The McGraw-Hill Companies,Inc.,2001
4- 14
Irwin/McGraw-Hill
Bond Yields
WARNING
Calculating YTM by hand can be very
tedious,
It is highly recommended that you learn to
use the,IRR” or,YTM” or,i” functions on
a financial calculator,
?The McGraw-Hill Companies,Inc.,2001
4- 15
Irwin/McGraw-Hill
Bond Yields
Rate of Return - Earnings per period per
dollar invested.
R at e o f re t u rn =
t o t al i n co me
i n v est m en t
R at e o f re t u rn =
C o u p o n i n c o m e + p ri ce ch an ge
i n v est m en t
?The McGraw-Hill Companies,Inc.,2001
4- 16
Irwin/McGraw-Hill
Interest Rate Risk
880
900
920
940
960
980
1,0 0 0
1,0 2 0
1,0 4 0
1,0 6 0
1,0 8 0
0 5 10 15 20 25 30
T i m e to M atu r i ty
B
o
n
d
Pr
i
ce
Premium Bond
Discount Bond
?The McGraw-Hill Companies,Inc.,2001
4- 17
Irwin/McGraw-Hill
Interest Rate Risk
-
500
1,0 0 0
1,5 0 0
2,0 0 0
2,5 0 0
3,0 0 0
0 2 4 6 8 10
YT M
$
B
o
n
d
Pr
i
c
e
30 yr bond
3 yr bond
?The McGraw-Hill Companies,Inc.,2001
4- 18
Irwin/McGraw-Hill
Nominal and Real rates
0
2
4
6
8
10
12
14
16
82 85 88 91 94 97
Year
Per
cen
t
Yield on UK
nominal bonds
Yield on UK
indexed bonds
?The McGraw-Hill Companies,Inc.,2001
4- 19
Irwin/McGraw-Hill
Default Risk
?Credit risk
?Default premium
?Investment grade
?Junk bonds
?The McGraw-Hill Companies,Inc.,2001
4- 20
Irwin/McGraw-Hill
Default Risk
S t a n d a r d
Mo o d y ' s & P o o r ' s S a f e t y
A a a AAA T h e s t r o n g e s t r a t i n g ; a b i l i t y t o r e p a y i n t e r e s t a n d p r i n c i p a l
i s v e r y s t r o n g,
Aa AA V e r y s t r o n g l i k e l i h o o d t h a t i n t e r e s t a n d p r i n c i p a l w i l l b e
r e p a i d
A A S t r o n g a b i l i t y t o r e p a y,b u t s o m e v u l n e r a b i l i t y t o c h a n g e s i n
c i r c u m s t a n c e s
B a a BBB A d e q u a t e c a p a c i t y t o r e p a y ; m o r e v u l n e r a b i l i t y t o c h a n g e s
i n e c o n o m i c c i r c u m s t a n c e s
Ba BB C o n s i d e r a b l e u n c e r t a i n t y a b o u t a b i l i t y t o r e p a y,
B B L i k e l i h o o d o f i n t e r e s t a n d p r i n c i p a l p a y m e n t s o v e r
s u s t a i n e d p e r i o d s i s q u e s t i o n a b l e,
C a a CCC B o n d s i n t h e C a a / C C C a n d C a / C C c l a s s e s m a y a l r e a d y b e
Ca CC i n d e f a u l t o r i n d a n g e r o f i m m i n e n t d e f a u l t
C C C - r a t e d b o n d s o f f e r l i t t l e p r o s p e c t f o r i n t e r e s t o r p r i n c i p a l
o n t h e d e b t e v e r t o b e r e p a i d,
?The McGraw-Hill Companies,Inc.,2001
4- 21
Irwin/McGraw-Hill
Corporate Bonds
?Zero coupons
?Floating rate bonds
?Convertible bonds
?The McGraw-Hill Companies,Inc.,2001
4- 22
Irwin/McGraw-Hill
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 McGraw-Hill Companies,Inc.,2001
4- 23
Irwin/McGraw-Hill
Web Resources
www.finpipe.com
www.investinginbonds.com
www.bloomberg.com/markets/C13.html
www.bondmarkets.com/publications/IGCORP/what.htm
www.moodys.com
www.standardandpoors.com/ratings
Click to access web sites
Internet connection required
4- 1
Irwin/McGraw-Hill
Chapter 4Fundamentals of Corporate FinanceThird Edition
Valuing Bonds
Brealey Myers Marcus
slides by Matthew Will
?The McGraw-Hill Companies,Inc.,2001
4- 2
Irwin/McGraw-Hill
Topics Covered
?Bond Characteristics
?reading the financial pages
?Bond Prices and Yields
?Bond prices and interest rates
?YTM vs,current yield
?Rate of Return
?Interest Rate Risk
?The Yield Curve
?Nominal and Real Rates of Interest
?Default Risk
?The McGraw-Hill Companies,Inc.,2001
4- 3
Irwin/McGraw-Hill
Bonds
Terminology
?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 Maturity Value) - Payment
at the maturity of the bond.
?Coupon Rate - Annual interest payment,as a
percentage of face value.
?The McGraw-Hill Companies,Inc.,2001
4- 4
Irwin/McGraw-Hill
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.
?The McGraw-Hill Companies,Inc.,2001
4- 5
Irwin/McGraw-Hill
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 c p n
r
c p n
r
c p n par
r t
?
?
?
?
? ? ?
?( ) ( )
.,,, ( )
( )1 1 11 2
?The McGraw-Hill Companies,Inc.,2001
4- 6
Irwin/McGraw-Hill
Bond Pricing
Example
What is the price of a 6 % annual coupon bond,
with a $1,000 face value,which matures in 3
years? Assume a required return of 5.6%,
77.010,1$
)056.1(
060,1
)056.1(
60
)056.1(
60
321
?
???
PV
PV
?The McGraw-Hill Companies,Inc.,2001
4- 7
Irwin/McGraw-Hill
Bond Pricing
Example (continued)
What is the price of the bond if the required rate
of return is 6 %?
0 0 0,1$
)06.1(
0 6 0,1
)06.1(
60
)06.1(
60
321
?
???
PV
PV
?The McGraw-Hill Companies,Inc.,2001
4- 8
Irwin/McGraw-Hill
Bond Pricing
Example (continued)
What is the price of the bond if the required rate
of return is 15 %?
51.7 9 4$
)15.1(
0 6 0,1
)15.1(
60
)15.1(
60
321
?
???
PV
PV
?The McGraw-Hill Companies,Inc.,2001
4- 9
Irwin/McGraw-Hill
Bond Pricing
Example (continued)
What is the price of the bond if the required rate
of return is 5.6% AND the coupons are paid semi-
annually?
91.010,1$
)028.1(
030,1
)028.1(
30
...
)028.1(
30
)028.1(
30
6521
?
?????
PV
PV
?The McGraw-Hill Companies,Inc.,2001
4- 10
Irwin/McGraw-Hill
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.
?The McGraw-Hill Companies,Inc.,2001
4- 11
Irwin/McGraw-Hill
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.
?The McGraw-Hill Companies,Inc.,2001
4- 12
Irwin/McGraw-Hill
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 c p n
r
c p n
r
c p n par
r t
?
?
?
?
? ? ?
?( ) ( )
.,,, ( )
( )1 1 11 2
?The McGraw-Hill Companies,Inc.,2001
4- 13
Irwin/McGraw-Hill
Bond Yields
Example
What is the YTM of a 6 % annual coupon bond,
with a $1,000 face value,which matures in 3
years? The market price of the bond is $1,010.77
77.0 1 0,1$
)1(
0 6 0,1
)1(
60
)1(
60
321
?
?
?
?
?
?
?
PV
rrr
PV
?The McGraw-Hill Companies,Inc.,2001
4- 14
Irwin/McGraw-Hill
Bond Yields
WARNING
Calculating YTM by hand can be very
tedious,
It is highly recommended that you learn to
use the,IRR” or,YTM” or,i” functions on
a financial calculator,
?The McGraw-Hill Companies,Inc.,2001
4- 15
Irwin/McGraw-Hill
Bond Yields
Rate of Return - Earnings per period per
dollar invested.
R at e o f re t u rn =
t o t al i n co me
i n v est m en t
R at e o f re t u rn =
C o u p o n i n c o m e + p ri ce ch an ge
i n v est m en t
?The McGraw-Hill Companies,Inc.,2001
4- 16
Irwin/McGraw-Hill
Interest Rate Risk
880
900
920
940
960
980
1,0 0 0
1,0 2 0
1,0 4 0
1,0 6 0
1,0 8 0
0 5 10 15 20 25 30
T i m e to M atu r i ty
B
o
n
d
Pr
i
ce
Premium Bond
Discount Bond
?The McGraw-Hill Companies,Inc.,2001
4- 17
Irwin/McGraw-Hill
Interest Rate Risk
-
500
1,0 0 0
1,5 0 0
2,0 0 0
2,5 0 0
3,0 0 0
0 2 4 6 8 10
YT M
$
B
o
n
d
Pr
i
c
e
30 yr bond
3 yr bond
?The McGraw-Hill Companies,Inc.,2001
4- 18
Irwin/McGraw-Hill
Nominal and Real rates
0
2
4
6
8
10
12
14
16
82 85 88 91 94 97
Year
Per
cen
t
Yield on UK
nominal bonds
Yield on UK
indexed bonds
?The McGraw-Hill Companies,Inc.,2001
4- 19
Irwin/McGraw-Hill
Default Risk
?Credit risk
?Default premium
?Investment grade
?Junk bonds
?The McGraw-Hill Companies,Inc.,2001
4- 20
Irwin/McGraw-Hill
Default Risk
S t a n d a r d
Mo o d y ' s & P o o r ' s S a f e t y
A a a AAA T h e s t r o n g e s t r a t i n g ; a b i l i t y t o r e p a y i n t e r e s t a n d p r i n c i p a l
i s v e r y s t r o n g,
Aa AA V e r y s t r o n g l i k e l i h o o d t h a t i n t e r e s t a n d p r i n c i p a l w i l l b e
r e p a i d
A A S t r o n g a b i l i t y t o r e p a y,b u t s o m e v u l n e r a b i l i t y t o c h a n g e s i n
c i r c u m s t a n c e s
B a a BBB A d e q u a t e c a p a c i t y t o r e p a y ; m o r e v u l n e r a b i l i t y t o c h a n g e s
i n e c o n o m i c c i r c u m s t a n c e s
Ba BB C o n s i d e r a b l e u n c e r t a i n t y a b o u t a b i l i t y t o r e p a y,
B B L i k e l i h o o d o f i n t e r e s t a n d p r i n c i p a l p a y m e n t s o v e r
s u s t a i n e d p e r i o d s i s q u e s t i o n a b l e,
C a a CCC B o n d s i n t h e C a a / C C C a n d C a / C C c l a s s e s m a y a l r e a d y b e
Ca CC i n d e f a u l t o r i n d a n g e r o f i m m i n e n t d e f a u l t
C C C - r a t e d b o n d s o f f e r l i t t l e p r o s p e c t f o r i n t e r e s t o r p r i n c i p a l
o n t h e d e b t e v e r t o b e r e p a i d,
?The McGraw-Hill Companies,Inc.,2001
4- 21
Irwin/McGraw-Hill
Corporate Bonds
?Zero coupons
?Floating rate bonds
?Convertible bonds
?The McGraw-Hill Companies,Inc.,2001
4- 22
Irwin/McGraw-Hill
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 McGraw-Hill Companies,Inc.,2001
4- 23
Irwin/McGraw-Hill
Web Resources
www.finpipe.com
www.investinginbonds.com
www.bloomberg.com/markets/C13.html
www.bondmarkets.com/publications/IGCORP/what.htm
www.moodys.com
www.standardandpoors.com/ratings
Click to access web sites
Internet connection required
