91Ó°ÊÓ

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.

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

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

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

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

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

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

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