Question

(Bond valuation​) Flora​ Co.'s bonds, maturing in 13 ​years, pay 6 percent interest on a $1,000 face value.​ However, interest is paid semiannually. If your required rate of return is 8 ​percent, what is the value of the​ bond? How would your answer change if the interest were paid​ annually?

a. If the interest is paid​ semiannually, the value of the bond is ​____. ​(Round to the nearest​ cent.)

b. If the interest is paid​ annually, the value of the bond is ____​. ​(Round to the nearest​ cent.)

Answer 1

a.price of bond = [present value of annuity*interest payment] +[present value factor * face value]

so,

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

here,

r=8% per annum=>4% for six months

=>0.04.

n=13 years* 2 semi annual periods

=>26

=> present value of annuity = [1 - (1.04)^(-26)]/0.04

=>[0.6393108/0.04]

=>15.98277.

interest payment = $1,000*6%*6/12=>$30.

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

=>1 /(1.04)^26

=>0.36068923

face value = $1,000.

now,

value of bond = [15.98277*$30] + [0.36068923*$1,000]

=>479.4831 + 360.68923

=>$840.17.

b.

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

so,

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

here,

r=8% per annum=>0.08

n=13 years

=> present value of annuity = [1 - (1.08)^(-13)]/0.08

=>7.90377625

interest payment = $1,000*6%=60

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

=>1 /(1.08)^13

=>0.36769792

face value = $1,000.

now,

value of bond = [7.90377625*$60]+[1,000*0.36769792]

=>474.226575+367.69792

=>$841.92