Transcript No Slide Title

6- 1
Fundamentals
of Corporate
Finance
Chapter 5
Valuing Bonds
Sixth Edition
Richard A. Brealey
Stewart C. Myers
Alan J. Marcus
Slides by
Matthew Will
McGraw
McGraw Hill/Irwin
Hill/Irwin
Copyright ©Copyright
2009 by The
McGraw-Hill
Companies, Inc.
All rights
reserved
© 2009
by The McGraw-Hill
Companies,
Inc.
All rights reserved
6- 2
Topics Covered
 The Bond Market
 Interest Rates and Bond Prices
 Current Yield and Yield to Maturity
 Bond Rates and Returns
 The Yield Curve
 Corporate Bonds and the Risk of Default
6- 3
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 Principal Value) - Payment
at the maturity of the bond.
 Coupon Rate - Annual interest payment, as a
percentage of face value.
6- 4
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.
6- 5
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.
cpn
cpn
(cpn  par )
PV 

....
1
2
t
(1  r ) (1  r )
(1  r )
6- 6
Bond Cash Flows
6- 7
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
2
(1.0215) (1.0215) (1.0215)3
PV  $1,081.95
6- 8
Bond Pricing
Example (continued)
Q: How did the calculation change, given semi-annual
coupons versus annual coupon payments?
6- 9
Bond Pricing
Example (continued)
What is the price of the bond if the required rate of
return is 2.15% AND the coupons are paid semiannually?
25
25
25
1,025
PV 

 ... 

1
2
5
(1.01075) (1.01075)
(1.01075) (1.01075) 6
PV  $1,082.37
Year
2005
2000
1995
1990
1985
1980
1975
1970
1965
1960
1955
1950
1945
1940
1935
1930
1925
1920
1915
1910
1905
1900
Yield %
6- 10
Treasury Yields
 The interest rate on 10-year U.S. Treasury bonds
16
14
12
10
8
6
4
2
0
6- 11
Bond Pricing
Example (continued)
What is the price of the 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
6- 12
Bond Pricing
Example (continued)
What is the price of the bond if the required rate of
return is 8 %?
50
50
1,050
PV 


1
2
(1.08) (1.08) (1.08)3
PV  $922.69
6- 13
Bond Pricing
Example (continued)
Q: How did the calculation change, given semiannual coupons versus annual coupon payments?
Time Periods
Discount Rate
Paying coupons twice a
year, instead of once
doubles the total number of
cash flows to be discounted
in the PV formula.
Since the time periods are
now half years, the
discount rate is also
changed from the annual
rate to the half year rate.
6- 14
Interest Rate Risk
 The value of the 5% bond falls as interest rates rise
1,200
Bond price ($)
1,100
1,000
900
800
700
0
2
4
6
8
10
Interest rate (%)
12
14
16
6- 15
Interest Rate Risk
3,000
When the interest rate equals
the 5.0% coupon rate, both
bonds sell at face value
2,500
30 yr bond
$ Bond Price
2,000
1,500
3 yr bond
1,000
500
-
0
2
4
6
YTM
8
10
6- 16
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.
6- 17
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.
cpn
cpn
(cpn  par )
PV 

....
1
2
t
(1  r ) (1  r )
(1  r )
6- 18
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
2
3
(1  r ) (1  r ) (1  r )
PV  $1,081.95
YTM = 2.15%
6- 19
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.
6- 20
Bond Yields
Rate of Return - Earnings per period per dollar
invested.
total income
Rate of return =
investment
Coupon income + price change
Rate of return =
investment
6- 21
Bond Valuation Spreadsheet
Valuing bonds using a spreadsheet
5.0 % coupon
maturing Feb 2011
Settlement date
Maturity date
Annual coupon rate
Yield to maturity
Redemption value (% of face value)
Coupon payments per year
Bond price (% of par)
2/15/08
2/15/11
0.05
0.0215
100
1
108.195
6.0% coupon
10-year maturity
1/1/00
1/1/10
0.06
0.07
100
1
92.976
=PRICE(B7,B8,B9,B10,B11,B12)
Esc and Double click on spreadsheet to access
6- 22
Interest Rate Risk
1,400
Price path for
Premium Bond
1,300
Bond Price
1,200
1,100
1,000
Price path for
Discount Bond
900
800
Today
Maturity
700
600
0
5
10
15
Time to Maturity
20
25
30
6- 23
Bond Yield Spreadsheet
Finding yield to maturity using a spreadsheet
Feb 2011 maturity bond, coupon rate = 5.0%, maturity = 3 years
Annual coupons
Semiannual coupons
Settlement date
Maturity date
Annual coupon rate
Bond price
Redemption value (% of face value)
Coupon payments per year
2/15/08
2/15/11
0.05
108.195
100
1
2/15/08
2/15/11
0.05
108.195
100
2
Yield to maturity (decimal)
0.0215
0.0216
=YIELD(B7,B8,B9,B10,B11,B12)
Esc and Double click on spreadsheet to access
6- 24
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.
6- 25
The Yield Curve
Treasury 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
4
3
2
1
Maturity (years)
29
27
25
23
21
19
17
15
13
11
9
7
5
3
0
1
Yield %
5
6- 26
Corporate Bonds
 Zero coupons
 Floating rate bonds
 Convertible bonds
6- 27
Nominal and Real rates
14
12
Yield on UK
nominal bonds
Percent
10
8
6
Yield on UK
indexed bonds
4
2
0
Year
6- 28
Default Risk
 Credit risk
 Default premium
 Investment grade
 Junk bonds
6- 29
Default Risk
Moody' s
Standard
& Poor's
Aaa
AAA
Aa
AA
A
A
Baa
BBB
Ba
B
BB
B
Caa
Ca
C
CCC
CC
C
Safety
The strongest rating; ability to repay interest and principal
is very strong.
Very strong likelihood that interest and principal will be
repaid
Strong ability to repay, but some vulnerability to changes in
circumstances
Adequate capacity to repay; more vulnerability to changes
in economic circumstances
Considerable uncertainty about ability to repay.
Likelihood of interest and principal payments over
sustained periods is questionable.
Bonds in the Caa/CCC and Ca/CC classes may already be
in default or in danger of imminent default
C-rated bonds offer little prospect for interest or principal
on the debt ever to be repaid.
6- 30
Default Risk
Yield spreads between corporate and 10-year Treasury bonds
10
8
Junk bonds
6
4
2
0
Baa-rated
bonds
Aaa-rated bonds
19
80
19
83
19
86
19
89
19
92
19
95
19
98
20
01
20
04
20
07
Yield spread %
12
6- 31
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