Chapter 12, Problem 43E

1.

To determine

Determine the cash flow after-tax at the time of purchase of new machine.

Explanation of Solution

Compute the cash flow after-tax at the time of purchase of new machine:

Particulars	Amount	Amount
Incremental net working capital	$10,000
Net purchase price of new machine	$190,000
Total cost (A)		$200,000
Current disposal	$68,000
Tax shield from deductibility of loss	$13,300
After-tax cash inflow from sale (B)		$81,300
Net cash flow after-tax (A-B)		$118,700

Working notes

Determine the amount of tax from deduction of loss:

$\begin{array}{c}\text{After tax cash flow}\}\text{ = }\left(\begin{array}{l}\text{Estimated loss }\\ \text{on disposal of machine}\times \text{40\%}\end{array}\right)\\ =\$33,250\times 40\%\\ =\$13,300\end{array}$

Determine the estimated loss on disposal of machine:

$\begin{array}{c}\begin{array}{l}\text{Estimated loss }\\ \text{on disposal of machine}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Original cost}-\text{Accumulated depreciation}\\ -\text{Selling price}\end{array}\right)\\ =\$150,000-\$48,750-\$68,000\\ =\$33,250\end{array}$

2.

To determine

Determine the after-tax cash inflow for each year.

Explanation of Solution

Compute the after-tax cash inflow for each year:

$\begin{array}{c}\begin{array}{l}\text{Net difference }\\ \text{After tax cash flow}\end{array}\}\text{ = }\left[\begin{array}{l}\text{Difference in annual tax (Variable cost)}\\ \text{+Difference in}\\ \text{ annual tax (Fixed cost)+Annual difference}\\ \text{ in depreciation}\end{array}\right]\\ =\$18,000+\$600+\$6,700\\ =\$25,300\end{array}$

Working notes:

Determine the difference in annual after tax variable cost:

$\begin{array}{c}\begin{array}{l}\text{Net difference }\\ \text{After tax cash flow}\end{array}\}\text{ = }\left[\begin{array}{l}\text{Machine per unit × Units per year}\\ \text{ × (1}-\text{Tax rate}\end{array}\right]\\ \text{=}\left[\begin{array}{l}\left(\text{\$0}\text{.25 - \$0}\text{.19}\right)\\ \times \text{500,000 units}\\ \times \left(\text{1 - 0}\text{.40}\right)\end{array}\right]\\ \text{=\$0}\text{.06}\times \text{500,000}\times 0.6\\ =\$18,000\end{array}$

Determine the difference in annual after tax fixed cost:

$\begin{array}{c}\begin{array}{l}\text{Annual After tax }\\ \text{cash flow (Fixed cost)}\end{array}\}\text{ = }\left[\begin{array}{l}\text{New Machine}\\ \text{ × (1}-\text{Tax rate}\end{array}\right]\\ \text{=}\left[\begin{array}{l}\left(\text{\$25,000}-\text{\$24,000}\right)\\ \times \left(\text{1}-\text{0}\text{.40}\right)\end{array}\right]\\ \text{=\$}1\text{,000}\times 0.6\\ =\$600\end{array}$

3.

To determine

Determine the relevant cash flow at the end of the project.

Explanation of Solution

Compute the relevant cash flow at the end of the project:

$\begin{array}{c}\begin{array}{l}\text{Relevant tax cash flow }\\ \text{at the end of the project}\end{array}\}\text{ = }\left[\begin{array}{l}\text{Recovery of net working capital (new)}\\ -\text{Recovery of net working capital (old)}\\ \text{+Difference in after-tax cash flow}\\ \end{array}\right]\\ =\left(\$40,000-\$30,000\right)+\$8,000\\ =\$10,000+\$8,000\\ =\$18,000\end{array}$

Working notes:

Determine the after tax cash flow from disposal of machines:

Particulars	Old Machine	New Machine
Original cost	$150,000	$190,000
Total depreciation over 5 years	$130,000	$165,000
Book value of machines	$20,000	$25,000
Terminal value of machines	$12,000	$22,000
Gain (Loss) on disposal of machines	-$8,000	$3,000
Tax savings on loss (@ 40%)	$3,200	$1,200
Terminal value of machines on Dec. 31, 2023	$12,000	$22,000
After-tax cash flow from disposal of machines	$15,200	$23,200

4.

To determine

Identify and indicate the relevant cost and revenue data related with asset-replacement decision:

Explanation of Solution

The original cost ($150,000) of the old machine and the accumulated depreciation are considered as sunk cost. Thus, both the information are required to determine the NBV of the old machine. The NBV affects the estimated amount of gain and loss from the disposal of the machine and cash flow after tax.

5.

To determine

Determine the undiscounted net cash flow for new machine.

Explanation of Solution

Particulars	Amount
Net cash flow after-tax	-$118,700
Cumulative cash flow after-tax	$126,500
After-tax cash flow end of the project	$18,000
Undiscounted net cash flow	$25,800

Working notes

Determine the cumulative cash flow tax:

$\begin{array}{c}\text{Cumulative cash flow}\}\text{ = }\left(\begin{array}{l}\text{Net difference in annual after-tax}\\ \times \text{Number of years}\end{array}\right)\\ =\$25,300\times 5\\ =\$25,800\end{array}$