204 Part 3 Financial Assets
publications. To! nd the YTM, all you need to do is solve Equation 7-1 for rd as
follows:VB! _______INT
(1 " rd)^1
" _______INT
(1 " rd)^2
"... " _______INT
(1 " rd)N
" _______M
(1 " rd)N$1,494.93! _______$100
(1 # rd)^1
"... " ________$100
(1 # rd)^14
" ________$1,000
(1 # rd)^14
You can substitute values for rd until you! nd a value that “works” and force the
sum of the PVs in the equation to equal $1,494.93. However,! nding rd! YTM by
trial and error would be a tedious, time-consuming process. However, as you
might guess, the calculation is easy with a! nancial calculator.^7 Here is the setup:N I/YR PV PMT FV14 –1494.93 100 1000Output: = 5Inputs:Simply enter N! 14, PV! $1494.93, PMT! 100, and FV! 1000; then press the
I/YR key. The answer, 5%, will appear.
The yield to maturity can also be viewed as the bond’s promised rate of return,
which is the return that investors will receive if all of the promised payments are
made. However, the yield to maturity equals the expected rate of return only when
(1) the probability of default is zero and (2) the bond cannot be called. If there is
some default risk or the bond may be called, there is some chance that the prom-
ised payments to maturity will not be received, in which case the calculated yield
to maturity will exceed the expected return.
Note also that a bond’s calculated yield to maturity changes whenever interest
rates in the economy change, which is almost daily. An investor who purchases a
bond and holds it until it matures will receive the YTM that existed on the pur-
chase date, but the bond’s calculated YTM will change frequently between the
purchase date and the maturity date.7-4b Yield to Call
If you purchase a bond that is callable and the company calls it, you do not have
the option of holding it to maturity. Therefore, the yield to maturity would not be
earned. For example, if Allied’s 10% coupon bonds were callable and if interest
rates fell from 10% to 5%, the company could call in the 10% bonds, replace them
with 5% bonds, and save $100 $ $50! $50 interest per bond per year. This would
be bene! cial to the company but not to its bondholders.
If current interest rates are well below an outstanding bond’s coupon rate, a
callable bond is likely to be called; and investors will estimate its most likely rate
of return as the yield to call (YTC) rather than the yield to maturity. To calculate
the YTC, we modify Equation 7-1, using years to call as N and the call price rather
than the maturity value as the ending payment. Here’s the modi! ed equation:7-2 Price of bond! ∑
t! 1N
_______(1 INT" r
d)
t^ "^Call price
________(1 " r
d)
N^Here N is the number of years until the company can call the bond; call price is the
price the company must pay in order to call the bond (it is often set equal to the par
value plus one year’s interest); and rd is the YTC.Yield to Call (YTC)
The rate of return earned
on a bond when it is called
before its maturity date.Yield to Call (YTC)
The rate of return earned
on a bond when it is called
before its maturity date.(^7) You can also " nd the YTM with a spreadsheet. In Excel, you use the Rate function, inputting N
per^! 14,
Pmt! 100, Pv! $1494.93, Fv! 1000, and 0 for Type and leaving Guess blank.