Hello candiria,
Here are the answers to your questions.
A)
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
commited to pay $120 forever, without the option of redeeming it. The
formula that solves this equation is:
A*(1+r)
-------
r
where A is the annual payment (A=$120) and r is the interest rate
(r=0.07). Therefore, the value of the bond next year if the long term
rate is 7% will be:
$120*1.07/0.07 = $1834.28
On the other hand, if the long term rate turns out to be 14%, applying
the same formula, we get that the value of the bond next year will be:
$120*1.14/0.14 = $977.14
Now, since the current one-year interest rate is 11%, we get that the
value of the bond today if next year the interest rate goes to 7% is:
$1834.28/1.11 = $1652.50
(I assumed here that the first payment happens next year). And if next
year the interest rate goes to 14%, then the value of the bond today
is:
$977.14/1.11 = $880.30
Finally, we don't know what will the interest rate be next year, but
we know that both scenarios have the same probability of happening.
Therefore, since investors are risk-neutral, the value of the bond
today is simply the average of the value of the bond in each scenario:
($1652.50 + $880.30)/2 = $1266.40
So if the bond is noncallable, it should be valued at $1266.40.
B)
What happens now if the bond is callable one year from today at $1450?
First of all, there's a good short description of a callable bond at
the following link:
Definition of a callable bond
http://www.investorwords.com/671/callable_bond.html
In order to evaluate what happens to the bond value when it's
callable, we must understand under what conditions will KIC choose to
excercise its right to redeem the bonds at $1450 in one year. This
will of course depend on the prevailing long term interest rate at
that time.
Let's first assume that the interest rate is 14%. We found previously
that in this case, the value of the bond next year is $977.14. In
other words, KIC will pay bondholders infinite payments that have a
present value of $977.14. Therefore, there's no reason for KIC to
redeem the bonds. KIC clearly will prefer to pay $977.14 (in present
value) rather than paying $1450. Therefore, the value of the bond next
year if the interest rate is 14% will still be $977.14. Intuitively,
you may think of this as a decision of the firm of whether to
refinance its debt or not. The bonds redemption is usually done in
order to reissue new bonds given new interest rate conditions. If the
market interest rate is 14%, and the firm has already managed to
finance its debt at 12%, it clearly has no incentive to redeem the
bonds and refinance its debt at a higher interest rate.
On the other hand, if the interest rate is 7% next year, the firm will
choose to redeem the bonds. We've already seen that the present value
of the firm's debt at 7% interest rate is $1834.28. Therefore, the
firm will be better off redeeming the bonds at $1450. The same
intuitive argument explained above applies here. So, in this case, if
the interest rate becomes 7%, then the value of the bond for the
bondholders will be $1450, because the company will choose to redeem
them.
Summing up, when the bonds are callable under the defined conditions,
in one year they will be worth the same as if they were noncallable
when interest rate is 14%, and they will be worth less than if they
were noncallable if the interest rate is 7%. Clearly, then, the price
of the bond today will be less than the price in part (a).
Specifically, the price will be:
($977.14/1.11 + $1450/1.11)
--------------------------- = $1093.30
2
which is less than $1266.40.
Google search terms
noncallable bond
://www.google.es/search?hl=es&q=noncallable+bond&meta=
callable bond
://www.google.es/search?hl=es&q=callable+bond&meta=
I hope this helps! If you have any doubt regarding my answer, please
don't hesitate to request clarification before rating it. Otherwise, I
await your rating and final comments.
Best wishes!
elmarto |
