Now suppose interest rates in the economy fell after the MicroDrive bonds were
issued, and, as a result, rdfell below the coupon rate,decreasing from 10 to 5 percent.
Both the coupon interest payments and the maturity value remain constant, but now 5
percent values for PVIF and PVIFA would have to be used in Equation 4-1. The value
of the bond at the end of the first year would be $1,494.93:
With a financial calculator, just change rdI from 10 to 5, and then press the PV key
to get the answer, $1,494.93. Thus, if rdfell belowthe coupon rate, the bond would sell
above par, or at a premium.
The arithmetic of the bond value increase should be clear, but what is the logic be-
hind it? The fact that rdhas fallen to 5 percent means that if you had $1,000 to invest,
you could buy new bonds like MicroDrive’s (every day some 10 to 12 companies sell
new bonds), except that these new bonds would pay $50 of interest each year rather
than $100. Naturally, you would prefer $100 to $50, so you would be willing to pay
more than $1,000 for a MicroDrive bond to obtain its higher coupons. All investors
would react similarly, and as a result, the MicroDrive bonds would be bid up in price
to $1,494.93, at which point they would provide the same rate of return to a potential
investor as the new bonds, 5 percent.
Assuming that interest rates remain constant at 5 percent for the next 14 years,
what would happen to the value of a MicroDrive bond? It would fall gradually from
$1,494.93 at present to $1,000 at maturity, when MicroDrive will redeem each bond
for $1,000. This point can be illustrated by calculating the value of the bond 1 year
later, when it has 13 years remaining to maturity. With a financial calculator, merely
input the values for N, I, PMT, and FV, now using N 13, and press the PV key to
find the value of the bond, $1,469.68. Thus, the value of the bond will have fallen
from $1,494.93 to $1,469.68, or by $25.25. If you were to calculate the value of the
bond at other future dates, the price would continue to fall as the maturity date ap-
proached.
Note that if you purchased the bond at a price of $1,494.93 and then sold it one
year later with rdstill at 5 percent, you would have a capital loss of $25.25, or a to-
tal return of $100.00$25.25$74.75. Your percentage rate of return would con-
sist of aninterest yield(also called acurrent yield) plus acapital gains yield,calculated as
follows:
Interest, or current, yield $100/$1,494.93 0.0669 6.69%
Capital gains yield $25.25/$1,494.93 0.0169 1.69%
Total rate of return, or yield $74.75/$1,494.93 0.0500 5.00%
Had interest rates risen from 10 to 15 percent during the first year after issue
rather than fallen from 10 to 5 percent, then you would enter N14, I15,
PMT100, and FV1000, and then press the PV key to find the value of the
bond, $713.78. In this case, the bond would sell at adiscountof $286.22 below its
par value:
The total expected future return on the bond would again consist of a current yield
and a capital gains yield, but now the capital gains yield would be positive.The total
$286.22.
DiscountPricePar value$713.78$1,000.00
$1,494.93.
$989.86$505.07
$100(9.89864)$1,000(0.50507)
VB$100(PVIFA5%,14)$1,000(PVIF5%,14)
160 CHAPTER 4 Bonds and Their Valuation
156 Bonds and Their Valuation
