Question

A coupon bond that pays interest semiannually has a par value of $1,000, matures in 8 years, and has a yield to maturity of 6%. If the coupon rate is 8%, the intrinsic value of the bond today will be $1,125.61 $1,000 $1,062.81 $1,081.82

Could i get the solution without using excel? by hand please.

Answer 1

A.$1,125.61..

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

here,

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

here,

r = 6% per year =>6%*6/12 =>3% =>0.03.

n =8 years * 2

=>16.

[1-(1.03)^(-16)]/0.03

=>0.3768331/0.03

=>12.561103.

interest payment = $1000*8%*6/12 =>$40.

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

=>1/(1.03)^16

=>0.62316694.

face value = 1000

value of the bond = [12.561103*40]+[0.62316694*1000]

=>$1,125.61.