Suppose Kraus Intercable Company intends to issue perpetual bonds of $$1,000$ face value at a $10-$percent interest rate. Annual coupons have been set at $$100.$ There is an equal chance that by the end of the year interest rates will do one of the following:

$$ Fall to $62/3$ percent. If so$,$ the bond price will increase to $$1,500$

$$ Increase to $20$ percent. If so$,$ the bond price will fall to $$500$

$1.$What is the bond price if the bond is not callable?

Value of noncallable bond $=$ PV $($First$-$year coupon $+$ Expected price at the end of year$).$ Answer is$\_\_\_\_\_$

$2.$What will be the value of the call provision to the firm?

If interest drops, $\_\_\_\_\_\_$

The firm will call the bonds for $$1,100.$

And it will issue new bonds with $10\%$ coupon rate, which will generate $$1,500$ at the $62/3$ percent interest rate.

It will allow the firm to pay out an extra dividend of $$400($$$1,500-$$$1,100)$ to its shareholders.

If interest rises, $\_\_\_\_\_\_$

The firm will not exercise the call.

Thus, the value of the call provision to the firm or shareholders is $\_\_\_\_\_$

$3.$ Suppose the followings.

Call premium $=$ $$100$ over par value $($Call price $=$ $$1,100)$

The bonds can be called only at the end of the first year.

How high must the coupon on the callable bond be so that it can be issued at the par value of $$1,000?$

Step $1$: Determine end$-$of$-$year value if interest rates drop Let$$s suppose the annual coupon payment in question is C$.$ Then at the end of year, the bondholder gets: $\_\_\_\_\_\_$

Step $2$: Determine end$-$of$-$year value if interest rates rise The bondholder gets at the end of year: $\_\_\_\_$

Step $3$: Solving for C Since interest rates are equally likely to rise or to drop, the expected value of the bondholder$$s end$-$of$-$year position is: $\_\_\_\_\_\_\_$

Using the current interest rate of $10$ percent, Then C $=$ $$157\mathrm{.}14.$ Therefore, callable bonds can sell at par only if their coupon rate is $15\mathrm{.}714\%.$

Can you fill the blank? Thanks