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 the present
value of the bond?s payments.
The bond's payments constitutes a perpetuity equal to its face value
multiplied by its coupon rate:
$1000*0.12 = $120
Recall that the PV of a perpetuity C with a discount rate r is:
PV(C,r) = C/r
See "Perpetuity":
http://www.investopedia.com/terms/p/perpetuity.asp
We must calculate the present value of the bond?s payments for the
both possible rates scenarios.
- 14% interest rate scenario:
If the interest rate in one year will be 14%, then the value of the bond in
one year will be:
$120 + $120/0.14 = $977.14
Now to find the current price of the bond for the 14% rate scenario
just discount the 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:
In the case that the interest rate in one year will be 7%, then the value
of the bond will be:
$120 + $120/0.07 = $1,834.29
Now to find the current price of the bond for the 7% rate scenario
just discount the value of the bond in one year by the current
interest rate of 11%::
P(7%) = $1,834.29/1.11 = $1,652.51
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*P(14%) + 0.5*P(7%) =
= 0.5*$880.31 + 0.5*$1,652.51 =
= $1,266.41
If the bonds are noncallable, the current price of the 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?
First we must take a look on what callable bonds are; callable bonds
can be redeemed at a stated price prior to its maturity date. When the
company calls the bonds, it must pays the stated price to the bond
holders and retire it before its original maturity date. Redeeming or
not the bonds is a decision of the company, and it does that only if
it is in its interests to do so.
- 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
The above result can be expressed in the following statement:
From the next year the company will pay to the bond holders infinite
payments that will have a present value of $977.14
The above situation is obviously PREFERABLE to pay $1,450 of bond
redemption in next year. Then KIC, Inc. will not redeem the bond in
this case (because actually it is financing its debt at a rate less
than 14%), then 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 the 14% rate case:
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 can be expressed in the following statement:
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 pay $1,450 of bond redemption. Now the
company will use its right to redeem the bond (because actually it is
financing its debt at a rate greater than 7%), 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. This is because the buyer of the bond is giving up something:
under certain conditions, the right to hold this bond until its
maturity is not exclusive of the bond holder, the company have the
right to redeeem the bonds if the market rate or other variables make
this option advantageous ofr its interests.
In this case if the market rate falls to 7%, the bond price rises
above $1,450 , and the company will call it. With this action wealth
will 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 |
,
0 Comments
)