nt value (with 1cent rounding error) is derived by summing the three separate multipliers from Table 1.Con-
Ie computations are avoided by using annuity tables.
d
Valuation
that a bond agreement specifies a pattern of future cash flows-usually
a series of interest payments and a
_ e payment of the face amount at maturity, and bonds are priced using the prevailing market rate on the day the
i
sold. This is the case for the original bond issuance and for subsequent open-market sales. The market rate
e date of the sale is the rate we use to determine the bond's market value (its price). That rate is the bond's
o
The selling price of a bond is determined as follows:
Use Table) to compute the present value of the future principal payment at the prevailing market rate.
Use Table 2 to compute the present value of the future series of interest payments (the annuity) at the
prevailing market rate.
Add the present values from steps 1 and 2.
~
~
-~-
~
~
EXHIBIT 7A.1
Calculation
of Bond
Price Using Present Value Tables
Multiplier
(Table 1)
Multiplier
(Table 2)
Future Cash Flows
Present Values
at 4% Semiannually
(1)
$100,000
of 8%, 4-year
bonds
with interest
payable
semiannually
priced
to yield 8%.
Principal
payment,
$100,000
(a single amount
received
after
8 semiannual
periods).
. . . . . . . . . . . . . . . ..
0.73069
Interest
payments,
$4,000
at end
of each of 8 semiannual
periods.
. . . . . . . . .
6.73274
Present value (issue price) of bonds
.
$
73,069
26,931
$100,000
Calculator
N=8
l/Yr
=
4
PMT = 4,000
FV = 100,000
= 100,000
Future Cash Flows
Multiplie
(Table 1)
(2)
$100,000
of 8%, 4-year
bonds
with interest
payable
semiannually
priced
to yield 10%.
Principal
payment,
$100,000
(a single amount
received
after
8 semiannual
periods).
. . . . . . . . . . . . . . . ..
0.67684
Interest
payments,
$4,000
at end
of each of 8 semiannual
periods
0
•
•
•
•
•
•
6.46321
Present value (issue price) of bonds
.
$
67,684
25,853
$
93,537
Calculator
N=8
IlYr
=
5
PMT
=
4,000
FV
=
100,000
I
PV = 93,536.79
Multiplier
(Table 1)
Multiplier
(Table 2)
Future Cash Flows
Present Values
at 3% Semiannually
(3) $100,000
of 8%, 4-year
bonds
with interest
payable
semiannually
priced
to yield 6%.
Principal
repayment,
$100,000
(a single amount
received
after
8 semiannual
periods).
. . . . . . . . . . . . . . . ..
0.78941
Interest
payments,
$4,000
at end
of each of 8 semiannual
periods
0
•
•
•
•
7.01969
Present value (issue price) of bonds
.
$ 78,941
28,079
$107,020
Calculator
N=8
IlYr = 3
PMT = 4,000
FV = 100,000
PV = 107,019.69