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Unformatted text preview: alue (that is,
B0 M) will always equal the coupon interest rate. When the bond value differs
from par, the yield to maturity will differ from the coupon interest rate.
Assuming that interest is paid annually, the yield to maturity on a bond can
be found by solving Equation 6.7 for kd. In other words, the current value, the
annual interest, the par value, and the years to maturity are known, and the
required return must be found. The required return is the bond’s yield to maturity. The YTM can be found by trial and error or by use of a financial calculator.
The calculator provides accurate YTM values with minimum effort. The Mills Company bond, which currently sells for $1,080, has a 10% coupon
interest rate and $1,000 par value, pays interest annually, and has 10 years to
maturity. Because B0 $1,080, I $100 (0.10
$1,000), M $1,000, and
n 10 years, substituting into Equation 6.7a yields
$1,080 $100 (PVIFAk )
d,10yrs $1,000 (PVIFk )
d,10yrs Our objective is to solve the equation for kd, the YTM.
Trial and Error Because we know that a required return, kd, of 10% (which
equals the bond’s 10% coupon interest rate) would result in a value of $1,000,
the discount rate that would result in $1,080 must be less than 10%. (Remember
that the lower the discount rate, the higher the present value, and the higher the
discount rate, the lower the present value.) Trying 9%, we get
$100 (PVIFA9%,10yrs) $1,000 (PVIF9%,10yrs)
$100 (6.418) $1,000 (0.422)
Because the 9% rate is not quite low enough to bring the value up to $1,080, we
next try 8% and get
$100 (PVIFA8%,10yrs) $1,000 (PVIF8%,10yrs)
$100 (6.710) $1,000 (0.463)
Because the value at the 8% rate is higher than $1,080 and the value at the 9%
rate is lower than $1,080, the bond’s yield to maturity must be between 8% and CHAPTER 6 Input
10 9%. Because the $1,063.80 is closer to $1,080, the YTM to the nearest whole
percent is 9%. (By using interpolation, we could eventually find the more precise
YTM value to be 8.77%.)15 Function
N 1080 PV 100 291 Interest Rates and Bond Valuation PMT 1000 Calculator Use [Note: Most calculators re...
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