Chapter 16, Problem 18P

a.

Summary Introduction

To calculate: The discount rate of Robinson Corporation.

Introduction:

Discount Rate:

A rate that is used for the calculation of the present value of the cash flows is termed as the discount rate.

Answer to Problem 18P

The discount rate of Robinson Corporation is 7.53% and after rounding off to a whole number, the discount rate is 8%.

Explanation of Solution

Computation of the discount rate:

$\begin{array}{c}\text{Discount rate}=\text{Interest rate}\times \left(1-\text{Tax rate}\right)\\ =10.75\%\times \left(1-0.30\right)\\ =10.75\%\times \left(0.70\right)\\ =7.53\%\end{array}$

b.

Summary Introduction

To calculate: The PV of total outflows of Robinson Corporation.

Introduction:

Present value (PV):

The current value of an investment or an asset is termed as its present value. It is calculated by discounting the future value of the investment or asset.

Answer to Problem 18P

The PV of total outflows of Robinson Corporation is $3,171,831.

Explanation of Solution

Computation of PV of total outflows:

$\begin{array}{c}\text{Present value of total outflow}=\text{After tax cost}+\text{Net cost of underwriting expense on new issue}\\ =\$2,558,500+\$613,331\\ =\$3,171,831\end{array}$

Working Notes:

Calculation of net cost of underwriting expense on new issue:

$\begin{array}{c}\text{Net cost of underwriting expense of new issue}=\text{Actual expenditure}-\\ \text{Present value of tax savings}\\ =\left(1.7\%\times \$43,000,000\right)-\$117,669\\ =\$731,000-\$117,669\\ =\$631,331\end{array}$

Calculation of after-tax cost:

$\begin{array}{c}\text{After tax cost}=\text{Call premium percentage in 7th Year}\times \text{Outstanding bonds}\times \left(1-\text{Tax rate}\right)\\ =8.5\%\times \$43,000,000\times \left(1-0.30\right)\\ =\$2,558,500\end{array}$

The calculation of the tax savings per year is as follows:

$\begin{array}{c}\text{Tax savings per year}=\left(\frac{\text{Underwriting cost}\times \text{Bonds outstanding}}{\text{Time to maturity}}\right)\times \text{Tax Rate}\\ =\left(\frac{1.7\%\times \$43,000,000}{17}\right)\times 30\%\\ =\$43,000\times 30\%\\ =\$12,900\end{array}$

The calculation of current price of bond, that is, PV of future tax savings is shown below.

The formula used for the calculation of current price of bond, that is, PV of future tax savings is shown below.

c.

Summary Introduction

To calculate: The PV of total inflows of Robinson Corporation.

Introduction:

Present value:

The current value of an investment or an asset is termed as its present value. It is calculated by discounting the future value of the investment or asset.

Answer to Problem 18P

The present value of total inflow of Robinson Corporation is $2,847,244.

Explanation of Solution

Calculation of the present value of total inflow:

$\begin{array}{c}\text{Present value of total inflow}=\text{Present value of savings}+\\ \text{Present value of deferred future write off}\\ =\$2,745,613+\$101,631\\ =\$2,847,244\end{array}$

Working Notes:

The calculation of the savings per year is as follows:

$\begin{array}{c}\text{Savings per year}=\left(\left({\text{Interest Rate}}_{\text{Old Bond}}-{\text{Interest Rate}}_{\text{New Bond}}\right)\times \text{Bonds Outstanding}\right)\times \\ \left(\text{100\%}-\text{Tax Rate}\right)\\ =\left(\left(11\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.\%-10\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.\%\right)\times \$43,000,000\right)\times \left(100\%-30\%\right)\\ =\left(\left(11.75\%-10.75\%\right)\times \$43,000,000\right)\times 70\%\\ =\left(1\%\times \$43,000,000\right)\times 70\%\end{array}$

$\begin{array}{c}\text{Savings per year}=\$430,000\times 70\%\\ =\$301,000\end{array}$

The calculation of PV of savings is shown below.

The formula used for the calculation of PV of savings is shown below.

Calculation of underwriting cost write off:

$\begin{array}{c}\text{Underwriting cost write off}=\text{Immediate gain in old underwriting write off}\times \text{tax rate}\\ =\$338,770\times \$0.30\\ =\$101,631\end{array}$

Calculation of PV of deferred future write off:

$\begin{array}{c}\text{Immediate gain in old underwriting write off}=\text{Unamortized old underwriting cost}-\\ \text{Present value of deferred future write off}\\ =\$731,000-\$392,230\\ =\$338,770\end{array}$

The calculation of current price of bond is shown below.

The formula used for the calculation of current price of bond is shown below.

d.

Summary Introduction

To calculate: The NPV of Robinson Corporation.

Introduction:

Net present value (NPV):

It is the difference between the PV (present value) of cash inflows and cash outflows. It is used in capital budgeting and planning of investment to assess the benefits and losses of any project or investment.

Answer to Problem 18P

The NPV of Robinson Corporation is ($324,478).

Explanation of Solution

Calculation of NPV:

$\begin{array}{c}\text{Net Present Value}=\text{Present Value of inflow}-\text{Present value of outflow}\\ =\$2,847,348-\$3,171,826\\ =\left(\$324,478\right)\end{array}$