Question

Williams Industries has decided to borrow money by issuing perpetual bonds with a coupon rate of 8 percent, payable annually. The one-year interest rate is 8 percent. Next year, there is a 30 percent probability that interest rates will increase to 10 percent, and there is a 70 percent probability that they will fall to 6 percent. Assume a par value of $1,000.

  

a.	What will the market value of these bonds be if they are noncallable? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Market value

$

  

b.

If the company decides instead to make the bonds callable in one year, what coupon rate will be demanded by the bondholders for the bonds to sell at par? Assume that the bonds will be called if interest rates fall and that the call premium is equal to the annual coupon. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

  

Coupon rate

%

  

c.	What will be the value of the call provision to the company? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Value of the call provision

$

Answer 1

a)

After one year we will find the expected value of the bond with the perpectuity formula.

As Value of bond will be if interest rate increases to 10% is =

= Coupon Payment / R

= 1000 * 0.08 / 0.1

= 80 / 0.1

= 800

Value of bond if interest rate decreases to 6% is =

= 80 / 0.06

= 1333.33

So expected value of bond will be =

= 800 * 0.3 + 0.7 * 1333.33

= 1173.33

b)

Here we know below things from question

1) Market interest rate has decreased to 6% (That is why company wants to have a callable bonds)

So for callable bonds

Price of the callable bonds = Present Value of Bond - Call Premium

Here

1000 = X - A

We assumed X = Present Value of Bond &

A = Call premium = 1000 * Coupon Rate (as per the question)

& we also know

= X = A / 0.06 (From perpectuity equation)

putting X value in first equation

A / 0.06 - A = 1000

A * 15.67 = 1000

1000 * R * 15.67 = 1000

R = 6.38%

c)

A call provision is a clause in a bond's indenture granting the issuer the right to call, or buy back, all or part of an issue prior to the maturity date.

as here we do not know the maturity date of the bond as well as a bond's indenture have multiple dates for calling the bonds like after 4 , 5 , 10 years of issue.

We assume that bond is called after one year when the price of the bond has increased. So the call premium is equal to one year's interest if the bond is called in the first year

= 1000 * 0.8

= $80

Thank You!!