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.

b. Calculate the present value of total inflows.

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 present value of interest savings is $1,177,619.

$$\begin{gathered} \mathbf{\text{Interest savings}}\mathbf{=}\mathbf{(}\mathbf{\text{Interest on old bonds}}\mathbf{-}\mathbf{\text{Interest on new bonds}}\mathbf{)}\mathbf{(}\mathbf{1}\mathbf{-}\mathbf{\text{Tax rate}}\mathbf{)} \\ \mathbf{=}\mathbf{(}\left(\$18,000,000\times 10\%\right)\mathbf{-}\left(\$18,000,000\times 8.5\%\right)\mathbf{)}\mathbf{\times }\mathbf{(}\mathbf{1}\mathbf{-}\mathbf{35}\mathbf{\%}\mathbf{)} \\ \mathbf{=}\mathbf{(}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{800}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{530}\mathbf{,}\mathbf{000}\mathbf{)}\mathbf{\times }\mathbf{(}\mathbf{1}\mathbf{-}\mathbf{35}\mathbf{\%}\mathbf{)} \\ \mathbf{=}\mathbf{\$}\mathbf{175}\mathbf{,}\mathbf{500} \end{gathered}$$

$$\begin{gathered} \mathbf{\text{Present value of interest savings}}\mathbf{=}\mathbf{\text{Interest savings}}\mathbf{\times }{\mathbf{\text{PVAF}}}_{\left(i=8\%,n=10years\right)} \\ \mathbf{=}\mathbf{\$}\mathbf{175}\mathbf{,}\mathbf{500}\mathbf{\times }\mathbf{6}\mathbf{.}\mathbf{71008} \\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{177}\mathbf{,}\mathbf{619} \end{gathered}$$

The present value of gain on the underwriting cost is $21,878.

$$\begin{gathered} \mathbf{\text{Unamortized underwriting cost}}\mathbf{=}\mathbf{\text{Original amount}}\mathbf{-}\mathbf{\text{Amount written off}} \\ \mathbf{=}\mathbf{\$}\mathbf{380}\mathbf{,}\mathbf{000}\mathbf{-}\frac{\mathbf{\$}\mathbf{380}\mathbf{,}\mathbf{000}}{\mathbf{20}}\mathbf{\times }\mathbf{10} \\ \mathbf{=}\mathbf{\$}\mathbf{190}\mathbf{,}\mathbf{000} \end{gathered}$$

role="math" localid="1649771203961" $$\begin{gathered} \mathbf{\text{PV of deferred future underwriting cost}}\mathbf{=}\frac{\mathbf{\text{Future underwriting cost}}}{\mathbf{\text{Time remaining}}}\mathbf{\times }{\mathbf{\text{PVAF}}}_{(i=8\%,n=10years)} \\ \mathbf{=}\frac{\mathbf{\$}\mathbf{190}\mathbf{,}\mathbf{000}}{\mathbf{10}}\mathbf{\times }\mathbf{6}\mathbf{.}\mathbf{71008} \\ \mathbf{=}\mathbf{\$}\mathbf{19}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{6}\mathbf{.}\mathbf{71008} \\ \mathbf{=}\mathbf{\$}\mathbf{127}\mathbf{,}\mathbf{492} \end{gathered}$$

role="math" localid="1649771258403" $$\begin{gathered} \mathbf{\text{Gain in old underwriting cost}}\mathbf{=} \\ \mathbf{\text{Unamortized amount}}\mathbf{-}\mathbf{\text{PV of deferred future underwriting}} \\ \mathbf{=}\mathbf{\$}\mathbf{190}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{127}\mathbf{,}\mathbf{492} \\ \mathbf{=}\mathbf{\$}\mathbf{62}\mathbf{,}\mathbf{508} \end{gathered}$$

$$\begin{gathered} \mathbf{\text{After tax value of old underwriting cost}}\mathbf{=} \\ \mathbf{\text{Gain in old underwriting cost}}\mathbf{\times }\mathbf{\text{Tax rate}} \\ \mathbf{=}\mathbf{\$}\mathbf{62}\mathbf{,}\mathbf{508}\mathbf{\times }\mathbf{35}\mathbf{\%} \\ \mathbf{=}\mathbf{\$}\mathbf{21}\mathbf{,}\mathbf{878} \end{gathered}$$

The present value of inflows is $1,199,497.

$$\begin{gathered} \mathbf{\text{Present value of inflows}}\mathbf{=} \\ \mathbf{\text{PV of interest savings}}\mathbf{+}\mathbf{\text{Present value of gain in old underwriting cost}} \\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{177}\mathbf{,}\mathbf{619}\mathbf{+}\mathbf{\$}\mathbf{21}\mathbf{,}\mathbf{878} \\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{199}\mathbf{,}\mathbf{497} \end{gathered}$$