You own a bond that pays semiannual interest payments of $55. The bond is callable in 2 years at a premium of $100. What is the callable bond price if the yield-to-call is 12.2%?

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Quizplus · Accepted Answer

The price of a callable bond can be calculated using the present value of future cash flows, including the semiannual interest payments and the call premium, discounted at the yield-to-call rate. Here, the semiannual interest payment is $55, the bond is callable in 2 years (which equals 4 periods since it's semiannual), the call premium is $100, and the yield-to-call is 12.2% per annum (or 6.1% per period since it's semiannual). The formula to calculate the price of the bond is:$$ \text{Bond Price} = \frac{C}{r} \left(1 - \frac{1}{(1 + r)^n}\right) + \frac{F}{(1 + r)^n} $$Where:- $C$ is the semiannual interest payment ($55),- $r$ is the semiannual yield-to-call (12.2% / 2 = 6.1% or 0.061),- $n$ is the total number of periods until the call (4),- $F$ is the call price ($1,000 + $100 premium = $1,100).Plugging in the values:$$ \text{Bond Price} = \frac{55}{0.061} \left(1 - \frac{1}{(1 + 0.061)^4}\right) + \frac{1100}{(1 + 0.061)^4} $$$$ \text{Bond Price} \approx \$1,058.17 $$Therefore, the correct answer is E, $1,058.17.

You Own a Bond That Pays Semiannual Interest Payments of $55