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24 March, 19:45

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

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  1. 24 March, 21:45
    0
    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%
  2. 24 March, 23:14
    0
    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%
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