Question

AB Builders, Inc., has 22-year bonds outstanding with a par value of $2,000 and a quoted price of 106.657. The bonds pay interest semiannually and have a yield to maturity of 6.74 percent. What is the coupon rate

Answer 1

Answer:

7.32%

Explanation:

The price of a bond is the present of its interest payment and the present value of redemption value (RV

Present value of the Redemption Value (RV) =

FV× (1+r/2)^(-2×n)

FV- 2000, r- yield rate, r/2= 6.74%/2 = 3.37%, n-22

=2000× (1.0337)^(-2×22)

= 465.233

Present Value of the coupon payment =Price of bond - PV of RV

                          = (106.657% × 2000) - 465.233

                         =    $1667.90

PV of coupon payment= A × (1-(1+r)^(-2×n)

A- semiannual coupon payment, r -yield

   1667.90 = A × (1-(1.0337)^(-2*22))/0.0337

    1,667.90   = A × 22.7710

A = 1,667.90/22.7710

A= 73.246

Annual coupon payment = 2× 73.246=  146.493

Annual coupon rate = coupon payment/ face value

                                = (146.493/2,000 )× 100

                                = 7.32%

Answer 2

Answer:

Coupon rate is 7.32%

Explanation:

In calculating the coupon rate on the bond,we first of all need to determine the amount of interest payable by the bond on semi-annual basis using the pmt formula in excel:

=pmt(rate,nper,-pv,fv)

rate is the yield to maturity divided by 2 since it is a semi-annual interest paying bond i.e 6.74%/2

nper is the time to maturity of the bond multiplied by 2=22*2=44

the present value is the current price of the bond:$2000*106.657%=$2133.14

The fv is the face value of $2000

=pmt(6.74%/2,44,-2133.14 ,2000)

pmt= 73.25  

annual pmt= 73.25*2= 146.49  

coupon rate=pmt/face value= 146.49/2000

                                              =7.32%