M&I, 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 M&I bonds are non-callable, 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 (a)? Why?

"The price of a perpetual bond is therefore the fixed interest
payment, or coupon amount, divided by some constant discount rate,
which represents the speed at which money loses value over time
(partly because of inflation)."  "Perpetual Bond" Investopedia.com
(2005) http://www.investopedia.com/terms/p/perpetualbond.asp

The bond pays $120 each year (0.12 * $1000).  The expected value of
long-term interest rates is the average of the 14 percent and the 7
percent, which amounts to 10.5%.  Risk neutral investors price on the
basis of expected value.  Therefore, the value of the payments as of
next year is $120/0.105.  This value must be discounted back to the
present time using the one-year bond interest rate of 11%, to obtain
the current price.

So, $120/0.105/(1.11) = $1029.60.

"Callable bonds are more risky for investors than non-callable bonds
because an investor whose bond has been called is often faced with
reinvesting the money at a lower, less attractive rate."  "Callable or
Redeemable Bonds" US Securities and Exchange Commission
http://www.sec.gov/answers/callablebonds.htm.  Because of the risk of
the bond being called, it would be priced lower.

Sincerely,

Wonko