Chapter 4, Problem 56QP

a.

Summary Introduction

To discuss: The option that should be selected after comparing the present values

Explanation of Solution

The computation is as follows:

Option A: After tax cash flow

$\begin{array}{l}\text{Aftertax cash flows }=\text{ Pretax cash flows}\left(\text{1 – tax rate}\right)\hfill \\ =\$400,000\left(1–.36\right)\hfill \\ =\$256,000\hfill \\ \hfill \end{array}$ $\begin{array}{l}\text{Aftertax cash flows }=\text{ Pretax cash flows}\left(\text{1 – tax rate}\right)\hfill \\ =\$400,000\left(1–.36\right)\hfill \\ =\$256,000\hfill \\ \hfill \end{array}$

Option A: Present value of cash flow

$\begin{array}{l}{\text{PVA}}_{\text{due}}\text{= }\left(\text{1 +r}\right)\text{C}\left(\frac{\left\{\text{1 – }\left[{\frac{\text{1}}{\left(\text{1 +r}\right)}}^{\text{t}}\right]\right\}}{\text{r}}\right)\hfill \\ =\left(1+.045\right)\$256,000\left(\frac{\left\{1–{\left(\frac{1}{(1+.045)}\right)}^{31}\right\}}{.045}\right)\hfill \\ =\$4,425,955.47\hfill \\ \hfill \end{array}$

Hence the present value of cash flow is $4,425,955.47.

b.

Summary Introduction

To discuss: The option that should be selected after comparing the present values

Explanation of Solution

The computation is as follows:

Option b: After tax cash flow

$\begin{array}{l}\text{Aftertax cash flows = Pretax cash flows}\left(\text{1 – tax rate}\right)\hfill \\ =\$325,000\left(1–.36\right)\hfill \\ =\$208,000\hfill \\ \hfill \end{array}$

Option B: Present value of cash flow

$\begin{array}{l}\text{ PV}=\text{C}\left(\frac{\left\{\text{1 – }\left[{\frac{\text{1}}{\left(\text{1 +r}\right)}}^{\text{t}}\right]\right\}}{\text{r}}\right){\text{ + CF}}_{\text{0}}\hfill \\ \text{ = \$208,000}\left(\frac{\left\{\text{1 – }\left[{\frac{\text{1}}{\left(\text{1 + }\text{.045}\right)}}^{\text{30}}\right]\right\}}{\text{.045 }}\right)\text{ + \$1,000,000}\hfill \\ =\$4,388,088.82\hfill \end{array}$

Hence the present value of cash flow is $4,388,088.82.