Hi!!
a. If the KIC bonds are noncallable, what is the price of the bonds?
If the KIC bonds are noncallable the price of the bond is simply the present
value of the bond?s payments. In this case the bond's payments
constitutes a perpetuity equal to its face value multiplied by its
coupon rate, that is:
Bonds' payments = $1000*0.12 = $120
The PV of a perpetuity P at a discount rate r is:
PV(P,r) = P/r
See for reference:
"Perpetuity":
http://www.investopedia.com/terms/p/perpetuity.asp
To answer this part of the question you need to calculate the present
value of the bond?s payments for each possible rate scenario.
- 14% interest rate scenario:
Bond price in one year = $120 + $120/0.14 = $977.14
Now to find the current price of the bond for this scenario discount
the future value of the bond in one year by the current interest rate
of 11%:
P(14%) = $977.14/1.11 = $880.31
- 7% interest rate scenario:
Bond price in one year = $120 + $120/0.07 = $1,834.29
Now to find the current price of the bond for this scenario discount
the future value of the bond in one year by the current interest rate
of 11%:
P(7%) = $1,834.29/1.11 = $1,652.51
Investors are risk-neutral, then the value of the bond is the weighted
average (for probabilities) of the value of the bond for each
scenario:
P = 0.5*P(14%) + 0.5*P(7%) =
= 0.5*$880.31 + 0.5*$1,652.51 =
= $1,266.41
The current price of the noncallable bonds is $1,266.41
-----------------------
b. If the bonds are callable one year from today at $1,450, will their
price be greater than or less than the price you computed in part (a)? Why?
Callable bonds can be redeemed by the issuer at a stated price prior
to its maturity date. Doing that is a company's decision, and it does
that only if it is in its interests to do so, i.e. only if it is the
better option.
- 14% interest rate scenario:
The bond pays an annual coupon equal to its coupon rate times its face
value:
$1000*0.12 = $120
With an interest rate in one year of 14%, the value of the bond in one
year will be:
$120 + $120/0.14 = $977.14
What does the above result mean?
It means that from the next year the company will pay to the bond
holders infinite payments that will have a present value of $977.14
This is obviously PREFERABLE to pay $1,450 of bond redemption in next
year. Then KIC, Inc. will not redeem the bond in this case and the
value of the bond will remain at $977.14 in one year.
Discounting this amount by the current market interest rate of 11%
gives us the current price of the callable bond for this scenario:
P(14%) = $977.14/1.11 = $880.31
- 7% interest rate scenario:
The bond pays an annual coupon equal to its coupon rate times its face
value:
$1000*0.12 = $120
With an interest rate in one year of 7%, the value of the bond in one year will be:
$120 + $120/0.07 = $1,834.29
The above result means that from the next year the company will pay to
the bond holders infinite payments that will have a present value of
$1,834.29
The above situation is NOT PREFERABLE to redeem the bonds by paying
$1,450 of bond redemption. The best option for the company is to use
its right to redeem the bond, therefore the value of the bond will be
equal to the redeeming price of $1,450.00 in one year.
Discounting this amount by the current interest rate of 11% gives the
current price of the callable bond for the 7% rate case:
P(7%) = $1,450.00/1.11 = $1,306.31
Since investors are risk-neutral the value of the bond is the weighted
average (for probabilities) of the value of the bond in each scenario:
P = 0.5*$880.31 + 0.5*$1,306.31 = $1,093.31
The current price of the callable bonds is $1,093.31 , this is less
than the price of the same but non-callable bonds ($1266.41).
Why?
A callable bond is sold for less than an otherwise identical ordinary
bond because the buyer of the bond is giving up something:
the right to hold this bond until its maturity is not exclusive of the
bond holder; under certain adverse conditions, the company have the
right to redeeem the bonds if the market rate or other variables make
this option advantageous to its interests.
In this case when the market rate falls to 7%, the bond price rises
above $1,450 , and the company prefer to use its redeem right. With
this action wealth is transferred from the bondholders to the
shareholders. Thus, the buyer is only willing to pay less for the
callable bonds.
------------------------------------------------------------------
I hope that this helps you. Feel free to request for a clarification
if you need it.
Regards.
livioflores-ga |
