Principal
payment
at maturity
.
$10,000,000
x
3%
=
$300,000
$10,000,000
$
6,000,U
10,000,00::
$16,000,
10 years
x
2
=
20
1
Specifically, the bond agreement dictates that the borrower must make 20 semiannual paymen
of $300,000 each, computed as $10,000,000
X
(6%/2). At maturity, the borrower must repay
$10,000,000 face amount. To price bonds, investors identify the
number
of interest payments
use that number when computing the present value of
both
the interest payments and the princi
(face) payment at maturity.
The bond price is the present value of the periodic interest payments (the annuity) plus the pres-
ent value of the principal payment (the lump sum). In our example, assuming that investors desire
3% semiannual market rate (yield), the bond sells for $10,000,000, which is computed as follow
Present
value
of a single
payment
in 20 periods
discounted
at 3%
per period.
d
Rounded.
Because the bond contract pays investors a 3% semiannual rate when investors demand a
.3
semiannual market rate, given the borrower's credit rating and the time to maturity, the inve
purchase those bonds at the par (face) value of $10 million.
DiscountBonds
As a second illustration, assume investors demand a 4% semiannual return for the 3%
semiza-
nual coupon bond, while all other details remain the same. The bond now sells for $8,640,
computed as follows:
Payment
Present
Value
Factor
Present
Value
Interest.
. . . . . . . . . . . . . . . .
$ 300,000
Principal.
. . . . . .. . . . . . . ..
$10,000,000
13.59033"
0.45639
b
$4,077,099
4,563,900
$8,640,999
a
Present
value
of an ordinary
annuity
for 20 periods
discounted
at 4% per period.
b
Present
value
of a single
payment
in 20 periods
discounted
at 4%
per period.
Because the bond carries a coupon rate
lower
than what investors demand, the bond is less
dI
able and sells at a discount. More generally, bonds sell at a discount whenever the coupon
is less than the market rate.