Question

Flora​ Co.'s bonds, maturing in 19 years, pay 12 percent interest on a $1,000 face value.​ However, interest is paid semiannually. If your required rate of return is 11 percent, what is the value of the​ bond? How would your answer change if the interest were paid​ annually?

Answer 1

Solution

First the calculation if the intrest paid semiannualy

Value of bond=Present value of coupon payments+Present value of face value

Value of bond=Coupon payment*((1-(1/(1+r)^n))/r)+Face value/(1+r)^n

where

n=number of periods=19*2=38

r-rate of return per period=11/2=5.5%

Face value =1000

Coupon payment=Coupon rate*face value/2=12%*1000/2=60

Putting values in formula

Value of bond=60*((1-(1/(1+.055)^38))/.055)+1000/(1+.055)^38

=$1079.024

calculation if the intrest paid annualy

Value of bond=Present value of coupon payments+Present value of face value

Value of bond=Coupon payment*((1-(1/(1+r)^n))/r)+Face value/(1+r)^n

where

n=number of periods=19

r-rate of return per period=11%

Face value =1000

Coupon payment=Coupon rate*face value=12%*1000/2=120

Putting values in formula

Value of bond=120*((1-(1/(1+.11)^19))/.11)+1000/(1+.11)^19

=$1078.39

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