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

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%

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%