Bond investors commonly look at yield to
maturity (YTM) -- the rate of return the
bond offers at a specified price, if held to maturity.
By computing bonds' YTM, it is possible to compare
bonds with different coupon rates and prices.
A bond's YTM can be calculated by using the bond
pricing formula and solving for the discount rate.
If you know --
- current price (B0)
- annual interest (I)
- par value (M)
- years to maturity (n)
the yield can be found. Business calculators
can make the calculation. Or you can use a process
of trial and error with a spreadsheet. |
Example
1
A 10.3% bond (par $1,000) sells for $1,090. That
is, it trades at a premium. Assuming interest
is paid semi-annually, and the bond has 7 years
to maturity, what is the bond's current yield?
Answer. You can use a spreadsheet
(computing yield either by trial and error until
present value equals $1090, or using a "goal
seek" function):
| Trading
at premium |
| Interest |
10.3% |
| Years to maturity |
7 |
| Par (principal) |
$1000.00 |
| Present value |
$1090.00 |
Remaining interest payments |
$534.01 |
Principal payment |
$555.99 |
| Yield (discount rate) |
8.56% |
Example 2
Assume the same 10.3% bond (par $1,000) sells
for $890. That is, it trades at a discount. Assuming
interest is paid semi-annually, and the bond has
7 years to maturity, what is the bond's current
yield?
Answer: You can use the same
spreadsheet (computing yield either by trial and
error until present value equals $890, or using
a "goal seek" function):
| Trading
at discount |
| Interest |
10.3% |
| Years to maturity |
7 |
| Par (principal) |
$1000.00 |
| Present value |
$ 890.00 |
Remaining interest payments |
$468.20 |
Principal payment |
$421.80 |
| Yield (discount rate) |
12.72% |
|
4.2.3 Behavior of Bond Prices