Question

Question: Barton Simpson, the chief financial officer of Broadband Inc. could hardly believe the change in interest rates that had taken place over the last few months. The interest rate on A2 rated bonds was now 6 percent. The \(30 million, 15-year bond issue that his firm has outstanding was initially issued at 9 percent five years ago. Because interest rates had gone down so much, he was considering refunding the bond issue. The old issue had a call premium of 8 percent. The underwriting cost on the old issue had been 3 percent of par, and on the new issue it would be 5 percent of par. The tax rate would be 30 percent and a 4 percent discount rate would be applied for the refunding decision. The new bond would have a 10-year life. Before Barton used the 8 percent call provision to reacquire the old bonds, he wanted to make sure he could not buy them back cheaper in the open market.

a. First compute the price of the old bonds in the open market. Use the valuation procedures for a bond that were discussed in Chapter 10 (use annual analysis). Determine the price of a single \)1,000 par value bond.

Short answer

The present value of old bonds in open market is $1,405.

Step-by-step solution

Information provided in question

Interest rate on A2 rated bonds = 6%

Outstanding bond value = $30,000,000

Remaining bond period = 10 years

Interest rate on bonds at the time of issue = 9%

Call premium = 8%

Tax rate = 30%

Discount rate =4%

Single price of par value bond =$1,000

Calculation of present value of interest payments

The present value of interest payments is $730.

$\begin{array}{rcl}\mathbf{\text{Interest payments}}& \mathbf{=}& \mathbf{\text{Interest rate}}\mathbf{\times }\mathbf{\text{Bond value}}\\ & \mathbf{=}& \mathbf{9}\mathbf{\%}\mathbf{\times }\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{000}\\ & \mathbf{=}& \mathbf{\$}\mathbf{90}\\ & & \end{array}$

$\begin{array}{rcl}\mathbf{\text{PV of interest}}& \mathbf{=}& \mathbf{\text{Interest payment}}\mathbf{\times }\frac{\mathbf{1}\mathbf{-}\frac{\mathbf{1}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{i}\mathbf{)}}^{\mathbf{n}}}}{\mathbf{i}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{90}\mathbf{\times }\frac{\mathbf{1}\mathbf{-}\frac{\mathbf{1}}{{\mathbf{(}\mathbf{1}\mathbf{.}\mathbf{04}\mathbf{)}}^{\mathbf{10}}}}{\mathbf{0}\mathbf{.}\mathbf{04}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{730}\\ & & \end{array}$

Step 3:Calculation of present value of the future principal payment

The present value of the future principal payment is $675.

$\begin{array}{rcl}\mathbf{\text{PVof principal payment}}& \mathbf{=}& \mathbf{\text{FV}}\mathbf{\times }\frac{\mathbf{1}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{i}\mathbf{)}}^{\mathbf{n}}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{000}\mathbf{\times }\frac{\mathbf{1}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{04}\mathbf{)}}^{\mathbf{10}}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{675}\end{array}$

Calculation of total present value

The total present value is $1,405.

$\begin{array}{rcl}\mathbf{\text{Total PV}}& \mathbf{=}& \mathbf{\text{PV of prinicpal payment}}\mathbf{+}\mathbf{\text{PV of interest payments}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{675}\mathbf{+}\mathbf{\$}\mathbf{730}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{405}\end{array}$