Question

Gabriele Enterprises has bonds on the market making annual payments, with 6 years to maturity, a par value of $1,000, and selling for $920. At this price, the bonds yield 10 percent. What must the coupon rate be on the bonds?

Answer 1

Solution

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

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

Face value =1000

n=number of periods to maturity=6

r-intrest rate per period=YTM=10%

annual Coupon payment=?

Price of bond=920

Putting values in formula

920=Coupon payment*((1-(1/(1+10%)^6))/10%)+1000/(1+10%)^6

Solving we get

Coupon payment=$81.63

Thus coupon rate=Coupon payment/face value*100

Coupon rate=81.63/1000*100=8.163%

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