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.

c. Now do the standard bond refunding analysis as discussed in this chapter. Is the refunding financially feasible?

Interest rate on A2 rated bonds = 6%

Outstanding bond value = $30,000,000

Bond period = 15 years

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

Call premium = 8%

Underwriting on old issue = 3% on par

Underwriting on new issue = 5% on par

Tax rate = 30%

Discount rate =4%

Term on new bonds = 10 years

Single price of par value bond =$1,000

The call premium payment is $1,680,000.

$$\begin{gathered} \mathbf{\text{Call premium payment}}\mathbf{=} \\ \left(\text{Bond obligations}\times \text{Call premium}\right)\mathbf{\times }\left(1-\text{Tax rate}\right) \\ \mathbf{=}\left(\$30,000,000\times 8\%\right)\mathbf{\times }\left(1-30\%\right) \\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{680}\mathbf{,}\mathbf{000} \end{gathered}$$

The present value of the underwriting cost is $1,135,009.50.

$$\begin{gathered} \mathbf{\text{Amortization of cost}}\mathbf{=}\frac{\mathbf{\text{Actual cost}}}{\mathbf{\text{Years remaining}}}\mathbf{\times }\mathbf{\text{Tax rate}} \\ \mathbf{=}\frac{\mathbf{5}\mathbf{\%}\mathbf{\times }\mathbf{\$}\mathbf{30}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}}{\mathbf{10}}\mathbf{\times }\mathbf{30}\mathbf{\%} \\ \mathbf{=}\frac{\mathbf{1}\mathbf{,}\mathbf{500}\mathbf{,}\mathbf{000}}{\mathbf{10}}\mathbf{\times }\mathbf{30}\mathbf{\%} \\ \mathbf{=}\mathbf{\$}\mathbf{150}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{30}\mathbf{\%} \\ \mathbf{=}\mathbf{\$}\mathbf{45}\mathbf{,}\mathbf{000} \end{gathered}$$

role="math" localid="1649772657045" $$\begin{gathered} \mathbf{\text{Present value of future tax savings}}\mathbf{=} \\ \mathbf{\text{Amortized cost}}\mathbf{\times }{\mathbf{\text{PVAF}}}_{(i=4\%,n=10years)} \\ \mathbf{=}\mathbf{\$}\mathbf{45}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{8}\mathbf{.}\mathbf{1109} \\ \mathbf{=}\mathbf{\$}\mathbf{364}\mathbf{,}\mathbf{990}\mathbf{.}\mathbf{50} \end{gathered}$$

$$\begin{gathered} \mathbf{\text{Net underwriting cost}}\mathbf{=}\mathbf{\text{Actual cost}}\mathbf{-}\mathbf{\text{PV of future tax savings}} \\ \mathbf{=}\left(5\%\times \$30,000,000\right)\mathbf{-}\mathbf{\$}\mathbf{364}\mathbf{,}\mathbf{990}\mathbf{.}\mathbf{50} \\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{500}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{364}\mathbf{,}\mathbf{990}\mathbf{.}\mathbf{50} \\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{135}\mathbf{,}\mathbf{009}\mathbf{.}\mathbf{50} \end{gathered}$$

The present value of outflows is $2,815,009.50.

$$\begin{gathered} \mathbf{\text{Present value of outflows}}\mathbf{=} \\ \mathbf{\text{Call premium payment}}\mathbf{+}\mathbf{\text{Present value of underwriting cost}} \\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{680}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{135}\mathbf{,}\mathbf{009}\mathbf{.}\mathbf{50} \\ \mathbf{=}\mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{815}\mathbf{,}\mathbf{009}\mathbf{.}\mathbf{50} \end{gathered}$$

The present value of interest savings is $5,109,867.

$$\begin{gathered} \mathbf{\text{Interest savings}}\mathbf{=} \\ \left(\text{Interest on old bonds}-\text{Interest on new bonds}\right)\left(1-\text{Tax rate}\right) \\ \mathbf{=}\left(\left(\$30,000,000\times 9\%\right)-\left(\$30,000,000\times 6\%\right)\right)\mathbf{\times }\left(1-30\%\right) \\ \mathbf{=}\left(\$2,700,000-\$1,800,000\right)\mathbf{\times }\mathbf{(}\mathbf{1}\mathbf{-}\mathbf{30}\mathbf{\%}\mathbf{)} \\ \mathbf{=}\mathbf{\$}\mathbf{900}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{(}\mathbf{1}\mathbf{-}\mathbf{30}\mathbf{\%}\mathbf{)} \\ \mathbf{=}\mathbf{\$}\mathbf{630}\mathbf{,}\mathbf{000} \end{gathered}$$

$$\begin{gathered} \mathbf{\text{Present value of interest savings}}\mathbf{=} \\ \mathbf{\text{Interest savings}}\mathbf{\times }{\mathbf{\text{PVAF}}}_{\left(i=4\%,n=10years\right)} \\ \mathbf{=}\mathbf{\$}\mathbf{630}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{8}\mathbf{.}\mathbf{1109} \\ \mathbf{=}\mathbf{\$}\mathbf{5}\mathbf{,}\mathbf{109}\mathbf{,}\mathbf{867} \end{gathered}$$

The present value of gain on the underwriting cost is $34,004.

$$\begin{gathered} \mathbf{\text{Unamortized underwriting cost}}\mathbf{=}\mathbf{\text{Original amount}}\mathbf{-}\mathbf{\text{Amount written off}} \\ \mathbf{=}\mathbf{3}\mathbf{\%}\mathbf{\times }\mathbf{\$}\mathbf{30}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}\mathbf{-}\frac{\mathbf{\$}\mathbf{30}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{3}\mathbf{\%}}{\mathbf{15}}\mathbf{\times }\mathbf{5} \\ \mathbf{=}\mathbf{\$}\mathbf{900}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{300}\mathbf{,}\mathbf{000} \\ \mathbf{=}\mathbf{\$}\mathbf{600}\mathbf{,}\mathbf{000} \end{gathered}$$

$$\begin{gathered} \mathbf{\text{PV of deferred future underwriting cost}}\mathbf{=} \\ \frac{\mathbf{\text{Future underwriting cost}}}{\mathbf{\text{Time remaining}}}\mathbf{\times }{\mathbf{\text{PVAF}}}_{\left(i=4\%,n=10years\right)} \\ \mathbf{=}\frac{\mathbf{\$}\mathbf{600}\mathbf{,}\mathbf{000}}{\mathbf{10}}\mathbf{\times }\mathbf{8}\mathbf{.}\mathbf{1109} \\ \mathbf{=}\mathbf{\$}\mathbf{60}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{8}\mathbf{.}\mathbf{1109} \\ \mathbf{=}\mathbf{\$}\mathbf{486}\mathbf{,}\mathbf{654} \end{gathered}$$

$$\begin{gathered} \mathbf{\text{Gain in old underwriting cost}}\mathbf{=} \\ \mathbf{\text{Unamortized amount}}\mathbf{-}\mathbf{\text{PV of deferred future underwriting}} \\ \mathbf{=}\mathbf{\$}\mathbf{600}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{486}\mathbf{,}\mathbf{654} \\ \mathbf{=}\mathbf{\$}\mathbf{113}\mathbf{,}\mathbf{346} \end{gathered}$$

$$\begin{gathered} \mathbf{\text{After tax value of old underwriting cost}}\mathbf{=} \\ \mathbf{\text{Gain in old underwriting cost}}\mathbf{\times }\mathbf{\text{Tax rate}} \\ \mathbf{=}\mathbf{\$}\mathbf{113}\mathbf{,}\mathbf{346}\mathbf{\times }\mathbf{30}\mathbf{\%} \\ \mathbf{=}\mathbf{\$}\mathbf{34}\mathbf{,}\mathbf{004} \end{gathered}$$

The present value of inflows is $5,143,871.

$$\begin{gathered} \mathbf{\text{Present value of inflows}}\mathbf{=} \\ \mathbf{\text{PV of interest savings}}\mathbf{+}\mathbf{\text{Present value of gain in old underwriting cost}} \\ \mathbf{=}\mathbf{\$}\mathbf{5}\mathbf{,}\mathbf{109}\mathbf{,}\mathbf{867}\mathbf{+}\mathbf{\$}\mathbf{34}\mathbf{,}\mathbf{004} \\ \mathbf{=}\mathbf{\$}\mathbf{5}\mathbf{,}\mathbf{143}\mathbf{,}\mathbf{871} \end{gathered}$$

The net present value is $2,328,861.50.

$$\begin{gathered} \mathbf{\text{Net present value}}\mathbf{=} \\ \mathbf{\text{Present value of inflows}}\mathbf{-}\mathbf{\text{Present value of outflows}} \\ \mathbf{=}\mathbf{\$}\mathbf{5}\mathbf{,}\mathbf{143}\mathbf{,}\mathbf{871}\mathbf{-}\mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{815}\mathbf{,}\mathbf{009}\mathbf{.}\mathbf{50} \\ \mathbf{=}\mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{328}\mathbf{,}\mathbf{861}\mathbf{.}\mathbf{50} \end{gathered}$$

The refunding is a feasible option as the company will be able to generate high cash inflows and will not face any loss, so the company should use the refund option.