Fundamentals of Financial Management (Concise 6th Edition)

Chapter 7 Bonds and Their Valuation 209

7-6 BONDS WITH SEMIANNUAL COUPONS

Although some bonds pay interest annually, the vast majority actually make pay-
ments semiannually. To evaluate semiannual bonds, we must modify the valu ation
model (Equation 7-1) as follows:

1. Divide the annual coupon interest payment by 2 to determine the dollars of
   interest paid each six months.


2. Multiply the years to maturity, N, by 2 to determine the number of semiannual
   periods.


3. Divide the nominal (quoted) interest rate, rd, by 2 to determine the periodic
   (semiannual) interest rate.
   On a time line, there would be twice as many payments, but each would be
   half as large as with an annual payment bond. Making the indicated changes re-
   sults in the following equation for! nding a semiannual bond’s value:

VB! ∑

t! 1

2N

__________(1 INT/2" r

d / 2)

t^ "^

___________M

(1 " rd / 2)2N^ 7-1a

To illustrate, assume that Allied Food’s 15-year bonds as discussed in Section 7-3
pay $50 of interest each 6 months rather than $100 at the end of each year. Thus,
each interest payment is only half as large but there are twice as many of them. We
would describe the coupon rate as “10% with semiannual payments.”^10
When the going (nominal) rate is rd! 5% with semiannual compounding, the
value of a 15-year, 10% semiannual coupon bond that pays $50 interest every
6 months is found as follows:

N I/YR PV PMT FV

2.5 50 1000

= –1,523.26

30

Output:

Inputs:

Enter N! 30, rd! I/YR! 2.5, PMT! 50, and FV! 1000; then press the PV key to
obtain the bond’s value, $1,523.26. The value with semiannual interest payments
is slightly larger than $1,518.98, the value when interest is paid annually as we

SEL

F^ TEST What is meant by the terms new issue and seasoned issue?

Last year a! rm issued 20-year, 8% annual coupon bonds at a par value of

$1,000.

(1) Suppose that one year later the going rate drops to 6%. What is the new price

of the bonds assuming they now have 19 years to maturity? ($1,223.16)

(2) Suppose that one year after issue, the going interest rate is 10% (rather

than 6%). What would the price have been? ($832.70)

Why do the prices of! xed-rate bonds fall if expectations for in" ation rise?

(^10) In this situation, the coupon rate of “10% paid semiannually” is the rate that bond dealers, corporate treasurers,
and investors generally discuss. Of course, if this bond were issued at par, its e! ective annual rate would be higher
than 10%.
EAR! EFF%! (^) ( 1 #
rNOM
M (^) )
M
$ 1! (^) ( 1 # 0.10 2 )^2 $ 1! (1.05)^2 $ 1! 10.25%
Since 10% with annual payments is quite di! erent from 10% with semiannual payments, we have assumed a change
in e! ective rates in this section from the situation in Section 7-3, where we assumed 10% with annual payments.