Question

KIC, Inc., plans to issue $8 million of bonds with a coupon rate of 11 percent and 20 years to maturity. The current market interest rates on these bonds are 10 percent. In one year, the interest rate on the bonds will be either 12 percent or 8 percent with equal probability. Assume investors are risk-neutral.

  

a.	If the bonds are noncallable, what is the price of the bonds today? Assume a par value of $1,000 and semiannual payments. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

     

Price of the bonds

$

    

b.

If the bonds are callable one year from today at $1,150, will their price be greater or less than the price you computed in part a?

X	Less than
	Greater than

Answer 1

Coupon rate = 11%

Par value = $1000

Coupon = $1000*0.11 = $110

Semi Annual Coupon = 110/2 = $55

Maturity = 20 years

a. We calculate the present value of the bond’s payments for the

both interest rates scenarios.

i) 12% interest rate scenario:

If the interest rate in one year will be 12%, then the value of the bond in

one year will be:

= 55 + (55/0.06)[1-(1/(1.06)³⁸)] +1000/(1.06)³⁸

= $980.77

Now to find the current price of the bond for the 12% rate scenario

just discount the value of the bond in one year by the current

interest rate of 10%:

= 55/(1.05) + 980.77/(1.05)²

= $941.96

ii) 8% interest rate scenario:

In the case that the interest rate in one year will be 8%, then the value

of the bond will be:

= $55 + $(55/0.04)[1-(1/(1.04)³⁸)] + 1000/(1.04)³⁸

= $1345.51

Now to find the current price of the bond for the 8% rate scenario

just discount the value of the bond in one year by the current

interest rate of 10%::

= 55/1.05 +1345.51/(1.05)²

= $1272.80

Since Investors are risk-neutral and the probability of occurrence of both scenarios is 50%

So,

Price of bonds = 0.5*941.46 + 0.5*1272.80

= $1107.13

So, If the bonds are noncallable, the current price of the bonds is $1107.13

b. Again calculating the various scenarios under callable option

i) 12% interest rate scenario:

If the interest rate in one year will be 12%, then the value of the callable bond in

one year will be:

= 55 + (55/0.06)[1-(1/(1.06)³⁸)] +1000/(1.06)³⁸

= $980.77

Now to find the current price of the bond for the 12% rate scenario

just discount the value of the bond in one year by the current

interest rate of 10%:

= 55/(1.05) + 980.77/(1.05)²

= $941.96

ii) 8% interest rate scenario:

In the case that the interest rate in one year will be 8%, then the value

of the callable bond in one year will be:

= $55 + $(55/0.04)[1-(1/(1.04)³⁸)] + 1000/(1.04)³⁸

= $1345.51

Here since the price of the bond is higher, the company is better off calling the bond at a lower price. So the price of the bond under the 8% scenario will not go beyond $1150 the amount at which the bond would be bought back.

Discounting this amount by the current interest rate of 10% gives the

current price of the callable bond for the 8% rate case:

= 55/1.05 + 1150/(1.05)²

= $1095.46

Since investors are risk-neutral the value of the bonds

Price of bonds  = 0.5*$941.96 + 0.5*$1095.46

Price of bonds = $1018.71

The current price of the callable bonds is $1018.71 , this is less

than the price of the same but non-callable bonds ($1107.13).

Answer is Less than