© 2012 mcgrawhill ryerson ltd. chapter 6 - the coupon rate is the annual interest payment divided...
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© 2012 McGrawHill Ryerson Ltd. Chapter 6 -
The coupon rate is the annual interest payment divided by the face value of the bond
The interest rate (or discount rate) is the rate at which the cash flows from the bond are discounted to determine its present value
The coupon rate and the discount rate are NOT necessarily the same! When they are not, the price of the bond is not the same as its face value
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© 2012 McGrawHill Ryerson Ltd. Chapter 6 -
The price of a bond is the present value of all its future cash flows, that is, it is the present value of the coupon payments and the face value of the bond. In calculating the PV, the ‘appropriate’ opportunity cost has to be used.
Example: Calculate the current price of a 6.5 % annual coupon bond, with a $1,000 face value which matures in 3 years. Assume a required return of 5.1%.
◦ In this case, the first coupon payment is $65 (6.5% of $1,000), the second payment is the same and the third payment is the final payment: a coupon of $65 plus the face value $1,000.
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© 2012 McGrawHill Ryerson Ltd. Chapter 6 -
0 1 2
$65$65
3
$1,065
05.038,1$
)051.1(
065,1
)051.1(
65
)051.1(
65321
PV
PV
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© 2012 McGrawHill Ryerson Ltd.
ExampleCalculate the current price of a 6.5 % annual coupon bond, with a $1,000 face value which matures in 3 years. Assume a required return of 6.5%.
0 1 2
$65$65
3
$1,065
000,1$
)065.1(
065,1
)065.1(
65
)065.1(
65321
PV
PV
Chapter 6 -4LO2
© 2012 McGrawHill Ryerson Ltd.
ExampleCalculate the current price of a 6.5 % annual coupon bond, with a $1,000 face value which matures in 3 years. Assume a required return of 15%.
0 1 2
$65$65
3
$1,065
93.805$
)15.1(
065,1
)15.1(
65
)15.1(
65321
PV
PV
Chapter 6 -5LO2
© 2012 McGrawHill Ryerson Ltd Chapter 6 -
From the three examples shown, notice how bond price varies with interest rates. When interest rate goes up, bond price decreases.
Coupon Rate Interest RatePrice of
Bond 6.5% 5.1%$1,038.05
6.5% 6.5%$1,000.00
6.5% 15.0% $ 805.93
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© 2012 McGrawHill Ryerson Ltd. Chapter 6 -
When the coupon rate is equal to the required return, the bond sells at face value (at par)
When the coupon rate is higher than the required return, the bond sells above face value (at a premium)
When the coupon rate is lower than the required return, the bond sells below face value (at a discount)
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© 2012 McGrawHill Ryerson Ltd. Chapter 6 -
The relationship between bond price and the discount rate
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© 2012 McGrawHill Ryerson Ltd. Chapter 6 -
Semi-annual payments:◦ Semi-annual coupon payments implies that the annual
coupon payment is paid in two equal installments, every six months
◦ Thus, the time line must be in six-month periods◦ And, you need to compute the six-month required return
Example: Calculate the current price of a 6.5 % semi-annual coupon bond, with a $1,000 face value which matures in 3 years. Assume a required return of 6%
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© 2012 McGrawHill Ryerson Ltd. Chapter 6 -
0 2 4
$32.50
6 1 3 5
$32.50 $32.50 $32.50$32.50 $1,032.50
540131
031
500321
031
5032
031
5032
031
50326521
.,$PV
).(
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).(
....
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.
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.PV
10LO2
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