KIC Inc. plans to issue $5 million of perpetual bonds. THe fave value of each bond is $1,000. The annual coupon bond is 12%. Market interest rates on one-year bonds are 11%. With eqaul probability, the long-term interest rates will be either 14% or 7% next year. Assume investors are risk-neutral. A. If the KIC bond are noncallable, what is the price of the bonds? b. if the bonds are callable one year from todayat $1,450, will their price be greater than or less than the price you computed in (A)? Why?
Please see the attached file. for a better formatted solution
Since investors are risk-neutral, the value of the bond should simply
be the expected present value of the payments of the bond. Let's see
how we calculate this.
The face value of the bond is $1,000 and the annual coupon on the
bonds is 12%. This means that the bond holder receives $120 (12% of
$1,000) each year, assuming annual payments. We're also told that the
current market interest rate is 11%, and next year it will change to
either 7% or 14% for the long term. So we will need to calculate what
would be the value of the bond if the interest rate turns out to go to 7%, and what would be its value if the interest rate goes to 14%.
Assume we are already in the "next year" (we will then discount the
results to get the present -today's- value). Let's also assume that
the interest rate is 7% for the long term. The present value of the
bond would then be:
$120 + $120/(1.07) + $120/(1.07)^2 + $120/(1.07)^3 + ...
until infinity, because this is an noncallable perpetual bond, so KIC
committed to pay $120 forever, without the option of redeeming it. The formula that solves ...
The solution is in a word document format that explains how to calculate the price of bonds.