Surf Extravaganza Inc. has two bonds outstanding. Bond A will return an interest

Question

Surf Extravaganza Inc. has two bonds outstanding. Bond A will return an interest payment every six months for 15 years, its yield to maturity is 15%, and it is currently priced at $850.00. Bond B pays interest annually, has 30 years left to maturity, has a yield to maturity of 13%, and is priced at $1,250.00. Both bonds have a face value of $1,000 payable upon maturity. Calculate each bond’s coupon rate.

Bond A 12.46% and Bond B 16.35%

Bond A 12.46% and Bond B 14.47%

Bond A 13.22% and Bond B 13.46%

Bond A 13.22% and Bond B 18.85%

Bond A 12.46% and Bond B 16.35%

Bond A 12.46% and Bond B 14.47%

Bond A 13.22% and Bond B 13.46%

Bond A 13.22% and Bond B 18.85%

Explanation / Answer

Bond A Coupon Payment Semi-annually Yield To maturity - Half yearly 7.50% 15/2 Current Price $850 Face Value $1,000 No of Payments 30 15*2 We would undertake trial and error to calculate the interest rates Value of Bond = Coupon payment*PV factor + Maturity amount*Discount factor Coupon payment*(1-(1/(1+r)^n))/r + Maturity amount*(1/(1+r)^n) Assuming the coupon rate is 12%, the value of bond is Coupon amount 1000*12*1/2 $60 60*(1-(1/(1+0.075)^30)/0.075 + 1000*(1/(1+0.075)^30) 60*11.81 + 1000*0.1142 708.60 + 114.20 822.8 Assuming the coupon rate is 12.50%, the value of bond is Coupon amount 1000*12.50%/2 62.5 62.50*11.81 + 1000*0.1142 852.325 Assuming the coupon rate is 12.46%, the value of bond is Coupon amount 1000*12.46%/2 62.3 62.30*11.81 + 1000*0.1142 850 Since, the value of bond is $ 850, the interest rate is 12.46% for Bond A Bond B Coupon Payment Semi-annually Yield To maturity - Half yearly 6.50% 13/2 Current Price $1,250 Face Value $1,000 No of Payments 60 30*2 We would undertake trial and error to calculate the interest rates Value of Bond = Coupon payment*PV factor + Maturity amount*Discount factor Coupon payment*(1-(1/(1+r)^n))/r + Maturity amount*(1/(1+r)^n) Assuming the coupon rate is 16%, the value of bond is Coupon amount 1000*16%*1/2 $80 80*(1-(1/(1+0.065)^60)/0.065 + 1000*(1/(1+0.065)^60) 60*15.0329 + 1000*0.0229 924.874 Assuming the coupon rate is 16.50%, the value of bond is Coupon amount 1000*16.50%/2 82.5 82.50*15.0329 + 1000*0.0229 1263.11425 Assuming the coupon rate is 16.35%, the value of bond is Coupon amount 1000*16.35%/2 81.75 81.75*15.0329 + 1000*0.0229 1250 Since, the value of bond is $ 1250, the interest rate is 16.35% for Bond A Therefore, Bond A has interest rate of 12.46% and Bond B has interest rate of 16.35%

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