91Ó°ÊÓ

Bond obligation = 40,000,000

Interest rate at the time of issue = 12 7/8%

Interest rate after decline = 12%

Time remaining of bonds = 18 years

Call premium on old issue =8%

Tax rate = 36%

Underwriting cost on old issue = 2.5% of total bond value

Underwriting cost on new issue = 1.8% of total bond value

The discount rate is 7.68% and this rate is rounded to 8%.

$\begin{array}{rcl}\text{Discount rate}& =& \text{Decreased interest rate}×\left(1-\text{Tax rate}\right)\\ & =& 12\%×\left(1-36\%\right)\\ & =& 7.68\%\end{array}$

The call premium payment is $1,920,000.

$\begin{array}{rcl}\text{Call premium payment}& =& \left(\text{Bond obligations}×\left[\text{Premium rate}-\text{Decline in premium rate}\right]\right)\\ & & ×\left(1-\text{Tax rate}\right)\\ & =& \left(\$40,000,000×\left[8\%-0.5\%\right]\right)×\left(1-36\%\right)\\ & =& \left(\$40,000,000×7.5\%\right)×\left(1-36\%\right)\\ & =& \$1,920,000\end{array}$

The present value of the underwriting cost is $585,043.

$\begin{array}{rcl}\text{Amortization of cost}& =& \frac{\text{Actual cost}}{\text{Years remaining}}×\text{Tax rate}\\ & =& \frac{1.8\%×\$40,000,000}{18}×36\%\\ & =& \frac{720,000}{18}×36\%\\ & =& \$40,000×36\%\\ & =& \$14,400\end{array}$

$\begin{array}{rcl}\text{Present value of future tax savings}& =& \text{Amortized cost}×{\text{PVAF}}_{\left(i=8\%,n=18years\right)}\\ & =& \$14.400×9.372\\ & =& \$134,957\end{array}$

$\begin{array}{rcl}\text{Net underwriting cost}& =& \text{Actual cost}-\text{PV of future tax savings}\\ & =& \left(1.8\%×\$40,000,000\right)-\$117,674\\ & =& \$720,000-\$134,957\\ & =& \$585,043\end{array}$

The present value of outflows is $2,505,043.

$\begin{array}{rcl}\text{Present value of outflows}& =& \text{Call premium payment}+\text{Present value of underwriting cost}\\ & =& \$1,920,000+\$585,043\\ & =& \$2,505,043\end{array}$

The present value of interest savings is $2,099,328.

$\begin{array}{rcl}\text{Present value of interest savings}& =& \text{Interest savings}×{\text{PVAF}}_{\left(i=8\%,n=18years\right)}\\ & =& \$224,000×9.372\\ & =& \$2,099,328\end{array}$

The present value of gain on the underwriting cost is $124,243.

$\begin{array}{rcl}\text{Unamortized underwriting cost}& =& \text{Original amount}-\text{Amount written off}\\ & =& 2.5\%×\$40,000,000-\frac{\$40,000,000×2.5\%}{25}×7\\ & =& \$1,000,000-\$280,000\\ & =& \$720,000\end{array}$

$\begin{array}{rcl}\text{PV of deferred future underwriting cost}& =& \frac{\text{Future underwriting cost}}{\text{Time remaining}}×{\text{PVAF}}_{\left(i=8\%,n=17years\right)}\\ & =& \frac{\$720,000}{18}×9.372\\ & =& \$40,000×9.372\\ & =& \$374,880\end{array}$

$\begin{array}{rcl}\text{Gain in old underwriting cost}& =& \text{Unamortized amount}-\text{PV of deferred future underwriting}\\ & =& \$720,000-\$374,880\\ & =& \$345,120\\ & & \end{array}$

$\begin{array}{rcl}\text{After tax value of old underwriting cost}& =& \text{Gain in old underwriting cost}×\text{Tax rate}\\ & =& \$345,120×36\%\\ & =& \$124,243\\ & & \end{array}$

The present value of inflows is $2,223,571.

$\begin{array}{rcl}\text{Present value of inflows}& =& \text{PV of interest savings}+\text{Present value of gain in old underwriting cost}\\ & =& \$2,099,328+\$124,243\\ & =& \$2,223,571\end{array}$

The net present value is -$281,472.

$\begin{array}{rcl}\text{Net present value}& =& \text{Present value of inflows}-\text{Present value of outflows}\\ & =& \$2,223,571-\$2,505043\\ & =& -\$281,472\end{array}$

As per our calculations, the company will have a negative cash flow if they refund the old issue with a new issue of bonds. Therefore, the company should not use refunding for retiring old bonds.