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

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

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

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

The net present value is -$259,031.

$$\begin{gathered} \mathbf{\text{Net present value}}\mathbf{=} \\ \mathbf{\text{Present value of inflows}}\mathbf{-}\mathbf{\text{Present value of outflows}} \\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{199}\mathbf{,}\mathbf{497}\mathbf{-}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{458}\mathbf{,}\mathbf{528} \\ \mathbf{=}\mathbf{-}\mathbf{\$}\mathbf{259}\mathbf{,}\mathbf{031} \end{gathered}$$