Question

A bond has a par value of $1,000, a current yield of 7.13 percent, and semiannual coupon payments. The bond is quoted at 96.88. What is the coupon rate of the bond?

Harpeth Valley Water District has a bond outstanding with a coupon rate of 3.31 percent and semiannual payments. The bond matures in 19 years, with a yield to maturity of 3.93 percent, and a par value of $5,000. What is the market price of the bond?

Answer 1

coupon rate of the bond = quote * current yeild

=>96.88*7.13%=>6.91%.

2nd part:

price of the bond = [present value of annuity factor * interest payments] + [present value factor * face value]

here,

present value of annuity factor = [1 -(1+r)^(-n)]/r

here,

r =3.93% per annum => 3.93 *6/12 =>1.965% for 6 months =>0.01965......(since we have semi annual payments).

n =19 years * 2

=>38.

=>[1-(1.01965)^(-38)]/0.01965

=>26.5968244

interest payment = $5000*3.31%*6/12=>$82.75.

present value factor = 1/(1+r)^n

=>1/(1.01965)^38

=>0.4773724.

face value =5000

value of the bond = [26.5968244*82.75]+[5000*0.4773724]

=>$4,587.75.