Question

Maggie Enterprises issued $110,000 of 6%, 5-year bonds with interest payable semiannually. Determine the issue price if the bonds are priced to yield (a) 6%, (b) 8%, and (c) 4%.

Answer 1

Answer-a)- The issue price of bonds is - $109989.

Explanation-Calculation of selling price of bond at issuance=

                B₀ =C/2 {1-(1+r/2)^-2t}/ r/2 +F/(1+r/2)^-2t

Where:-

Bo = Bond price

C= Coupon payment

r = Interest Rate

F= Face value

t = Years/Periods

Since the interest is paid semi-annually the bond interest rate per period is 3% (= 6%/ 2), the market interest rate is 3% (= 6%/ 2) and number of time periods are 10 (= 2*5). Hence, the price of the bond is calculated as the present value of all future cash flows as shown below:-

Price of Bond = 3%*$110000*{1-(1+3%)^-10/3%} +$110000/(1+3%)¹⁰

                         =($3300*8.530)+ ($110000*0.744)

                         = $28149+$81840

                         =$109989

Answer-b)- The issue price of bonds is = $101126.

Explanation-Calculation of selling price of bond at issuance=

                B₀ =C/2 {1-(1+r/2)^-2t}/ r/2 +F/(1+r/2)^-2t

Where:-

Bo = Bond price

C= Coupon payment

r = Interest Rate

F= Face value

t = Years/Periods

Since the interest is paid semi-annually the bond interest rate per period is 3% (= 6%/ 2), the market interest rate is 4% (= 8%/ 2) and number of time periods are 10 (= 2*5). Hence, the price of the bond is calculated as the present value of all future cash flows as shown below:-

Price of Bond = 3%*$110000*{1-(1+4%)^-10/4%} +$110000/(1+4%)¹⁰

                         =($3300*8.111)+ ($110000*0.676)

                         = $26766+$74360

                         =$101126

Answer-c)- The issue price of bonds is = $119844.

Explanation-Calculation of selling price of bond at issuance=

                B₀ =C/2 {1-(1+r/2)^-2t}/ r/2 +F/(1+r/2)^-2t

Where:-

Bo = Bond price

C= Coupon payment

r = Interest Rate

F= Face value

t = Years/Periods

Since the interest is paid semi-annually the bond interest rate per period is 3% (= 6%/ 2), the market interest rate is 2% (= 4%/ 2) and number of time periods are 10 (= 2*5). Hence, the price of the bond is calculated as the present value of all future cash flows as shown below:-

Price of Bond = 3%*$110000*{1-(1+2%)^-10/2%} +$110000/(1+2%)¹⁰

                         =($3300*8.983)+ ($110000*0.820)

                         = $29644+$90200

                         =$119844