Williams Industries has decided to borrow money by issuing perpetual bonds with

Question

Williams Industries has decided to borrow money by issuing perpetual bonds with a coupon rate of 7 percent, payable annually. The one-year interest rate is 7 percent. Next year, there is a 35 percent probability that interest rates will increase to 9 percent, and there is a 65 percent probability that they will fall to 5 percent. Assume a par value of $1,000.

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.)

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.)

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.)

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.)

Explanation / Answer

Given -

Coupon rate = 7% annually

Next year,

i) 35 percent probability that interest rates will increase to 9 percent

ii) 65 percent probability that they will fall to 5 percent

Par value = $1,000

Coupon payment = $1,000*6% = $60

A) Market value of these bonds be if they are noncallable will be -

Today, the price of the bond = present value of the expected price in one year.

So, the price of the bond in one year (P1) if interest rates increase to 9% will be as under -

P1 = $60 + ($60 / 0.09)

= $60 + $666.67

P1 = $726.67

If interest rates fall to 5%, the price if the bond in one year will be -

P1 = $60 + ($60 / 0.05)

= $60 + $1,200

P1 = $1,260

Now, we will calculate price of the bond today (P0), which will be -

P0 = [0.35*$726.67 + 0.65*$1,260] / 1.07

= [$254.34 + $819] / 1.07

= $1,073.34 / 1.07

P0 = $1,003.12

Market value of these bonds be if they are noncallable will be $1,003.12

B) Coupon rate demanded by the bondholders for the bonds to sell at par will be -

If interest rates rise to 9%, the price of the bonds will fall, after which the company will not call them back.

Here, the bondholders will receive the coupon payment (C) + present value of the remaining payments.

So, if interest rates rise To 9%, the price of the bonds in one year will be:

P1 = C + C / .09

Assumption - If interest rates fall to 5%, the bonds will be called. Here, the bondholders will receive the call price + coupon payment, C. The call premium = coupon rate, so the price of the bonds if interest rates fall will be:

P1 = ($1,000 + C) + C

P1 = $1,000 + 2C

The selling price today, is the present value of the expected payoffs to the bondholders. The coupon rate will be calculated as, the desired issue price is = present value of the expected value at the end of year payoffs, and then we will find the value for C.

Calculation -

P0 = $1,000

$1,000 = [0.35(C + C / .09) + 0.65($1,000 + 2C)] / 1.07

$1,000 = [0.35(0.09C + C / 0.09) + $650 + 1.30C] /1.07

$1,000 = [0.35(1.09C / 0.09) + $650 + 1.30C] /1.07

$1,000 = [(0.3815C / 0.09) + $650 + 1.30C] /1.07

$1,000*1.07 = [(0.3815C / 0.09) + $650 + 1.30C]

$1,070 = [(0.3815C / 0.09) + $650 + 1.30C]

$1,070 - $650 = (0.3815C / 0.09) + 1.30C

$420 = (0.3815C / 0.09) + 1.30C

$420 = (0.3815C + 0.1170C) / 0.09

$420*0.09 = 0.3815C + 0.1170C

$37.80 = 0.4985C

C = $37.80 / 0.4985

C = $75.83

So, the coupon rate necessary to sell the bonds at par value will be:

Coupon rate = $75.83 / $1,000

Coupon rate = 0.07583 or 7.58%

Coupon rate demanded by the bondholders for the bonds to sell at par will be - 7.58%

C) Value of the call provision to the company

For the company, the value of the call provision = Value of an outstanding non-callable bond - Call provision.

So, let us fing the value of a non-callable bond with the same coupon rate as under -

Non-callable bond value = $75.83 / 0.05 = $1,516.60

Now let us find the value of the call provision to the company -

Value = 0.65[$1,516.60 – ($1,000 + 75.83)] / 1.07

= 0.65($1,516.60 – $1,075.83) / 1.07

= [0.65*($440.77)] / 1.07

= $286.50 /1.07

= $267.76

Value = $267.76

Value of the call provision to the company is $267.76

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