CP

You could substitute values for rduntil you find a value that “works” and forces the

sum of the PVs on the right side of the equal sign to equal $1,494.93. Alternatively,

you could substitute values of rdinto the third form of Equation 4-1 until you find a

value that works.

Finding rd 
 YTM by trial-and-error would be a tedious, time-consuming

process, but as you might guess, it is easy with a financial calculator.^8 Here is the setup:

Inputs: 14 1494.93 100 1000

Output: 
 5

Simply enter N 
14, PV 
1494.93, PMT 
100, and FV 
1000, and then press

the I key. The answer, 5 percent, will then appear.

The yield to maturity is identical to the total rate of return discussed in the pre-

ceding section. 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 the promised payments are

made. However, the yield to maturity equals the expected rate of returnonly if (1) the

probability of default is zero and (2) the bond cannot be called. If there is some default

risk, or if the bond may be called, then there is some probability that the promised

payments to maturity will not be received, in which case the calculated yield to matu-

rity will differ from the expected return.

The YTM for a bond that sells at par consists entirely of an interest yield, but if the

bond sells at a price other than its par value, the YTM will consist of the interest yield

plus a positive or negative capital gains yield. Note also that a bond’s yield to maturity

changes whenever interest rates in the economy change, and this is almost daily. One

who purchases a bond and holds it until it matures will receive the YTM that existed

on the purchase date, but the bond’s calculated YTM will change frequently between

the purchase date and the maturity date.

Yield to Call

If you purchased a bond that was callable and the company called it, you would not

have the option of holding the bond until it matured. Therefore, the yield to

maturity would not be earned. For example, if MicroDrive’s 10 percent coupon bonds

were callable, and if interest rates fell from 10 percent to 5 percent, then the company

could call in the 10 percent bonds, replace them with 5 percent bonds, and save

$100 $50 
$50 interest per bond per year. This would be beneficial to the com-

pany, but not to its bondholders.

If current interest rates are well below an outstanding bond’s coupon rate, then a

callable bond is likely to be called, and investors will estimate its expected rate of re-

turn as the yield to call (YTC)rather than as the yield to maturity. To calculate the

YTC, solve this equation for rd:

Price of bond
 a (4-2)

N

t
 1

INT

(1rd)t



Call price

(1rd)N

.

VB
$1,494.93

$100

(1rd)^1



$100

(1rd)^14



$1,000

(1rd)^14

.

Bond Yields 163

(^8) You could also find the YTM with a spreadsheet. In Excel,you would use the RATE function for this bond,
inputting Nper
14, Pmt
100, Pv
1494.93, Fv
1000, 0 for Type, and leave Guess blank.

Bonds and Their Valuation 159