Question

Company X needs to sell new bonds for financing purpose. Company X’s currently
outstanding bonds have a $ 1000 par value, a 10 % coupon rate, and pay interest semiannually.
The outstanding bonds have 25 years remaining to maturity, are callable after 5 years at a price of
$ 1,090, and currently sell at a price of $ 700. The yield curve is expected to remain flat. On the
basis of these data, what is the best estimate of company’s nominal interest rate on the new bonds
it plans to sell ?

Answer 1

Semiannual Coupon =$1000 *10%/2 = $50

No of Coupons till maturity = 25*2 = 50

No of Coupons till 1st call period = 5*2 = 10

So,

Current Semiannual Yield to maturity (y) is given by

50/y*(1-1/(1+y)^50)+1000/(1+y)^50 = 700

Solving y =0.0723998

So, YTM = 0.0723998 *2 = 0.1448 or 14.48% p.a. compounded semiannually

Current Semiannual Yield to Call (r) is given by

50/r*(1-1/(1+r)^10)+1090/(1+r)^10 = 700

Solving r =0.10547915

So, YTM = 0.10547915 *2 = 0.210958 or 21.10% p.a. compounded semiannually

Based in the data, the company will not call the bonds and hence the company’s nominal interest rate on the new bonds it plans to sell is the same as YTM i.e. 14.48% p.a.