Question

Bond-valuation Semiannual interest

Find the value of a bond maturing in 7 years, with a 1,000$ par value and a coupon interest rate of 14%(7% paid semiannually) if the required return on similar-risk bonds is 17%

annual interest (8.5% paid semiannually).

The present value of the bond is _____

(Round to the nearest cent.)

Answer 1

the present value of bond = [semi annual coupon payment * present value of annuity factor ] + [face value * present value factor]

here,

semi annual coupon payment = $1,000 * 7% =>$70

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

here,

r = 8.5% =>0.085

n = 7 years * 2 semi annual period =14

=> present value of annuity factor = [1 - (1.085)^(-14)] / 0.085

=> 0.6808582 / 0.085

=>8.01009647

face value = $1,000

present value factor = 1 / (1.085)^14

=>0.31914178

now,

the present value of bond = [8.01009647 * $70] + [0.31914178 * $1,000]

=>$879.85.............(rounded to nearest cent).

The present value of bond is $879.85.