KIC, Inc., plans to issue $5 million of perpetual bonds. The face
value of each bond is
$1,000. The annual coupon on the bonds is 12 percent. Market interest
rates on one-year
bonds are 11 percent. With equal probability, the long-term market
interest rate will be
either 14 percent or 7 percent next year. Assume investors are risk-neutral.
a. If the KIC bonds are noncallable, what is the price of the bonds?
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?

Hi pbc141!! 


a. If the KIC bonds are noncallable, what is the price of the bonds?

In this case, the present value of the bond?s payments is the price of the bond.
The bond pays an annual coupon equal to its face value multiplied by
its coupon rate:
$1000*0.12 = $120 

We must calculate the present value of the bond?s payments for the
both possible rates scenarios.
If the interest rate in one year will be 14%, the value of the bond in
one year will be:
$120 + $120/0.14 = $977.14

Discount this amount by the current interest rate of 11% to find the
current price of the bond for the 14% rate scenario:

P(14%) = $977.14/1.11 = $880.31


In the case that the interest rate in one year will be 7%, the value
of the bond will be:
$120 + $120/0.07 = $1,834.29

Discount this amount by the current interest rate of 11% to get the
current price of the bond for the 7% rate scenario:

P(7%) = $1,834.29/1.11 = $1,652.51


Since investors are risk-neutral the value of the bond is the weighted
sum (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

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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 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.

To answer this question we must consider the two possible scenarios again.

· 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 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 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%), then 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


Again we don't know the interest rate of the next year, but we know
each interest rate's probability. Investors are risk-neutral, then the
value of the bond is the weighted sum (for probabilities) of the value
of the bond in each scenario:

P = 0.5*$880.31 + 0.5*$1,306.31 = $1,093.31

For the callable bonds the current price of the is $1,093.31 , less
than the price computed in the first question ($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.

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I hope that this helps you. Feel free to request for a clarification
if you need it.


Regards.
livioflores-ga

Answer was excellent.