Question

Henry is planning to purchase a Treasury bond with a coupon rate of 3.22% and face value of $100. The maturity date of the bond is 15 May 2033.

(b) If Henry purchased this bond on 5 May 2018, what is his purchase price (rounded to four decimal places)? Assume a yield rate of 1.09% p.a. compounded half-yearly. Henry needs to pay 23.2% on coupon payment as tax payment and tax are paid immediately.

Select one:

a. 119.7026

b. 120.2898

c. 120.2904

d. 119.0537

Answer 1

Solution:

Calculation of purchase price of bond:

Purchase price shall be equal to sum of present value of after tax coupons and present value of face value.

After tax coupon rate=3.22(1-0.232)

=2.47296%

Periodic coupon=($100*2.47296%)/2

=$1.23648

Periodic discount rate=1.09%/2

=0.545%

Periods to maturity=(2033-2018)*2

=30

Purchase price=Coupon*PVAF(0.545%,30)+Face value*PVIF(0.545%,30)

=$1.23648*27.606688+$100*0.849543

=$119.0894

Thus correct answer is option d.