Question

A bond with a face value of Rs. 1000 matures in 10 years. if the market rate (YTM) is at 12% and the price of the bond is 990, what is the annual coupon rate for the bond?

Answer 1

Formula for price of bond can be used to compute coupon amount and coupon rate as:

Price of bond = C x [1-{1/ (1+r) ⁿ}/r] +M/ (1+r) ⁿ

Price of bond - M/ (1+r) ⁿ = C x [1-{1/ (1+r) ⁿ}/r]

C = [Price of bond - M/ (1+r) ⁿ]/ [1-{1/ (1+r) ⁿ}/r]

M = Face Value = $ 1,000

C = Coupon amount = (Face Value x Coupon rate) / No. of coupon payments annually

r = Rate of interest = 12 % or 0.12 p.a.

n = No of periods = 10

C = [$ 990 - $ 1,000/ (1+0.12)¹⁰]/ [1-{1/ (1+0.12)¹⁰}/0.12 ]

    = [$ 990 - $ 1,000/ (1.12)¹⁰]/ [1-{1/ (1.12)¹⁰}/0.12 ]

   = [$ 990 - $ 1,000/ 3.10584820834421]/ [1-(1/ 3.10584820834421)/0.12]

     = [$ 990 - $ 321.973236590696]/ [(1-0.321973236590696)/0.12]

     = $ 668.026763409304/ (0.678026763409304/0.12)

     = $ 668.026763409304/5.65022302841087

     = $ 118.230158358402

$ 118.230158358402 = ($ 1,000 x Coupon rate) / 1

Coupon rate = $ 118.230158358402/$ 1,000 = 0.118230158358402 or 11.82 %

Annual coupon rate for the bond is 11.82 %