FM for Actuaries

Bonds and Bond Pricing 195
Table 6.1:
A bond premium amortization schedule
Half- Coupon Effective Amortized amount Book
year payment interest earned of premium value
0 1,028.01 a
1 25.00 b 20.56 c 4.44 d 1,023.57 e
2 25.00 20.47 4.53 1,019.04
3 25.00 20.38 4.62 1,014.42
4 25.00 20.29 4.71 1,009.71
5 25.00 20.19 4.81 1,004.90
6 25.00 20.10 4.90 1,000.00
Total 150.00 121.99 28.01
The details of the computation are as follows:
a The purchase price is the beginning balance of the book value.
b The coupon payment is 1,000 × 0.05
2
=$25.00.
c Effective interest earned in the first half-year is 1,028.01 × 0.04
2
=$20.56.
d Amortized amount of premium in the first half-year is 25.00 − 20.56 =$4.44.
e The book value after amortization is 1,028.01 – 4.44 = $1,023.57.
The rest of the computations follow similarly.
The bond amortization schedule is useful to bondholders for accounting and
taxation purposes. In some countries the bond interest income is taxable. In the
above example, however, the $25 coupon payment received each period should not
be fully taxable. The actual (taxable) amount of interest earned in each period is
computed in the schedule (the third column in Table 6.1). Furthermore, the book
values, which should be entered into the bondholder’s balance sheet at the end of
each period, can also be obtained from the amortization table.
In the bond discount situation the bondholder purchases the bond for less than
the face value. The discount represents an amount that must be paid by the issuer
to the investor at the time of maturity. The discount (a form of pre-paid interest)
will be amortized periodically from the coupon payments over the life of the bond.
We re-visit the illustrative example. For the $1,000 face value 3-year bond with
semiannual coupons at the rate of 5% per annum, we now assume that the required
rate of return is 6% convertible semiannually. The purchase price of this bond is
$972.91, and the discount is $27.09. We construct a bond discount amortization
schedule in Table 6.2. The computational steps follow closely those of Table 6.1.