Question: The Bowman Corporation has a \(18 million bond obligation outstanding, which it is considering refunding. Though the bonds were initially issued at 10 percent, the interest rates on similar issues have declined to 8.5 percent. The bonds were originally issued for 20 years and have 10 years remaining. The new issue would be for 10 years. There is a 9 percent call premium on the old issue. The underwriting cost on the new \)18,000,000 issue is \(530,000, and the underwriting cost on the old issue was \)380,000. The company is in a 35 percent tax bracket, and it will use an 8 percent discount rate (rounded after-tax cost of debt) to analyze the refunding decision.

a. Calculate the present value of total outflows.

Bond obligation = 18,000,000

Interest rate at the time of issue = 10%

Interest rate after decline = 8.5%

Time = 20 years

Time remaining of bonds = 10 years

Call premium on old issue =9%

Underwriting cost of new issue =$530,000

Underwriting cost on old issue = $380,000

Discount rate = 8%

Tax rate = 35%

The call premium payment is $1,053,000.

$\begin{array}{rcl}\mathbf{\text{Call premium payment}}& \mathbf{=}& \mathbf{(}\mathbf{\text{Bond obligations}}\mathbf{\times }\mathbf{\text{Premium rate}}\mathbf{)}\mathbf{\times }\mathbf{(}\mathbf{1}\mathbf{-}\mathbf{\text{Tax rate}}\mathbf{)}\\ & \mathbf{=}& \mathbf{(}\mathbf{\$}\mathbf{18}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{9}\mathbf{\%}\mathbf{)}\mathbf{\times }\mathbf{(}\mathbf{1}\mathbf{-}\mathbf{35}\mathbf{\%}\mathbf{)}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{053}\mathbf{,}\mathbf{000}\\ & & \end{array}$

The present value of the underwriting cost is $405,528

$\begin{array}{rcl}\mathbf{\text{Amortization of cost}}& \mathbf{=}& \frac{\mathbf{\text{Actual cost}}}{\mathbf{\text{Years remaining}}}\mathbf{\times }\mathbf{\text{Tax rate}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{530}\mathbf{,}\mathbf{000}}{\mathbf{10}}\mathbf{\times }\mathbf{35}\mathbf{\%}\\ & \mathbf{=}& \mathbf{\$}\mathbf{53}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{35}\mathbf{\%}\\ & \mathbf{=}& \mathbf{\$}\mathbf{18}\mathbf{,}\mathbf{550}\\ & & \end{array}$

$\begin{array}{rcl}\mathbf{\text{Present value of future tax savings}}& \mathbf{=}& \mathbf{\text{Amortized cost}}\mathbf{\times }{\mathbf{\text{PVAF}}}_{(i=8\%,n=10)}\\ & \mathbf{=}& \mathbf{\$}\mathbf{18}\mathbf{,}\mathbf{550}\mathbf{\times }\mathbf{6}\mathbf{.}\mathbf{71008}\\ & \mathbf{=}& \mathbf{\$}\mathbf{124}\mathbf{,}\mathbf{472}\\ & & \end{array}$

$\begin{array}{rcl}\mathbf{\text{Net underwriting cost}}& \mathbf{=}& \mathbf{\text{Actual cost}}\mathbf{-}\mathbf{\text{PV of future tax savings}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{530}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{124}\mathbf{,}\mathbf{472}\\ & \mathbf{=}& \mathbf{\$}\mathbf{405}\mathbf{,}\mathbf{528}\\ & & \end{array}$

The present value of outflows is $1,458,528.

$\begin{array}{rcl}\mathbf{\text{Present value of outflows}}& \mathbf{=}& \mathbf{\text{Call premium payment}}\mathbf{+}\mathbf{\text{Present value of underwriting cost}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{053}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{405}\mathbf{,}\mathbf{528}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{458}\mathbf{,}\mathbf{528}\\ & & \end{array}$