T

$1,000 (1.06)
30
$174.11
4- 12
Equation
4- 13
Equation Yield to Maturity of an n-Year Zero-Coupon Bond
Example Yields for Different Maturities
4- 14
Example 8.1 Yields for Different Maturities
PV
16 1.045

16
1.045
2

16
1.045
3

16
1.045
4

216
1.045
5
243.57 Yen
4- 24
Valuing a Bond
Example - USA
In July 2006 you purchase a 3 year US Government bond. The bond has an annual coupon rate of 4%, paid semi-annually. If investors demand a 2.48% return on 6 month investments, what is the price of the bond?
The yield to maturity is the required market interest rate on the bond.
4- 5
Bonds
Face value is the stated value of an asset. In the case of a bond, the face value is usually $1000
4- 6
Treasury Bond – issued by the federal government. Corporate Bond – issued by corporations. Municipal Bonds – issued by state and local governments. Foreign Bonds – issued by either foreign governments or foreign corporations.
4- 11
Pure Discount Bonds: Example
Find the value of a 30-year zero-coupon bond with a $1,000 par value and a YTM of 6%.
$0
$0
$0
$1,000


0
1
2
29
30
PV
F (1 r )
4- 20
Valuing a Bond
Example If today is October 1, 2007, what is the value of the following bond? An IBM Bond pays $115 every September 30 for 5 years. In September 2012 it pays an additional $1000 and retires the bond. The bond is rated AAA (WSJ AAA YTM is 7.5%)
4- 4
Bonds (the indenture)
A bond is a legally binding agreement between a borrower and a lender that specifies the:
– – – – Par (face) value ---principal Coupon rate Coupon payment Maturity Date
– The face value is supposed to be paid back to the bondholders as the principal, no matter what the purchasing price of the bond
Coupon：annual interest payment Coupon rate: the stated rate of interest on a bond; or the annual interest payment divided by bond’s face value
Principles of Corporate Finance
Ninth Edition
Chapter 4
Valuing Bonds
4- 2
Topics Covered
Bonds Using The Present Value Formula to Value Bonds How Bond Prices Vary With Interest Rates The Term Structure and YTM
PV
115 1.075

115
1.075
2

115
1.075
3

115
1.075
4

1,115
1.075
5
$1,161.84
4- 22
Valuing a Bond
Example - Germany
In July 2006 you purchase 100 Euros of bonds in Germany which pay a 5% coupon every year. If the bond matures in 2012 and the YTM is 3.8%, what is the value of the bond?
PV 5 1.038 5
1.038
2

5
1.038
3

5
1.038
4

5
1.038
5

105
1.038
6
106.33 Euros
4- 23
Valuing a Bond
Another Example - Japan
In July 2006 you purchase 200 Yen of bonds in Japan which pay a 8% coupon every year. If the bond matures in 2011 and the YTM is 4.5%, what is the value of the bond?
4- 17
Bond Price
Yield-to-maturity (YTM)
7-17
4- 18
Valuing a Bond
PV
C1 (1 r )
1

C2 (1 r )
2
...
1,000 C N (1 r )
N
4- 19
Coupon bonds
Like zero-coupon bonds, coupons bonds pay investors their face value at maturity. In addition, these bonds make regular coupon interest payments.
4- 7
Government Bonds
U.S. Government Bonds
– Treasury bills – pure discount bonds with original maturity of one year or less – T-notes – coupon debt with original maturity between one and ten years
4- 9
Zero-coupon bonds
Suppose that a one-year, risk-free, zero coupon bond with a 100,000 face value has an initial price of $96,618.36Year0 1-$96,618.36
PV
20 1.0248

20
1.0248
2

20
1.0248
3

20
1.0248
4

20
1.0248
5

1020
1.0248
6
$973.54
4- 25
Valuing a Bond
Example continued - USA
Take the same 3 year US Government bond. The bond has an annual coupon rate of 4%, paid semi-annually. If investors demand a 1.50% return on 6 month investments, what is the new price of the bond?
Cash Flows Sept 08 09 10 11 12 115 115 115 115 1115
4- 21
Valuing a Bond
Example continued
If today is October 1, 2007, what is the value of the following bond? An IBM Bond pays $115 every September 30 for 5 years. In September 2012 it pays an additional $1000 and retires the bond. The bond is rated AAA (WSJ AAA YTM is 7.5%)