Chapter 19, Problem 31P

1.

To determine

Calculate the cash flow and net present value (NVP) for make alternative of Company J.

Explanation of Solution

Cash inflows: The amount of cash received by a company from the operating, investing, and financing activities of the business during a certain period is referred to as cash inflow.

Cash outflows: The amount of cash paid by a company for the operating, investing, and financing activities of the business during a certain period is referred to as cash outflow.

Net present value method (NVP): Net present value method is the method which is used to compare the initial cash outflow of investment with the present value of its cash inflows. In the net present value, the interest rate is desired by the business based on the net income from the investment, and it is also called as the discounted cash flow method.

Calculate the cash flow and net present value (NVP) for make alternative of Company J as follows:

Year	Cash inflow (9) (A)	Present value factor @12% (B)	Present value $\left(A\times B\right)$
2015	$ -499,013	0.893	-$ 445,619
2016	$ -456,312	0.797	-$ 363,681
2017	$ -594,130	0.712	-$ 423,021
2018	$ -658,546	0.636	-$ 418,835
2019	$ -679,800	0.567	-$ 385,447
Total present value			-$ 2,036,602
Less: Cash outflow for investment (7)			$ 956,600
Net present value			($ 2,993,202)

Table (1)

Working note (1):

Calculate the variable cost per unit.

$\begin{array}{c}\text{Variable cost per unit}=\left[\begin{array}{l}\text{Direct material cost per unit}+\text{Direct labor}\\ \text{cost per unit}+\text{Variable overhead}\end{array}\right]\\ =\left(\text{\$10}\times \text{0}\text{.75}\right)+\left(\$8\times 1.00\right)+\left(\$6\times 0.75\right)\\ =\$7.50+\$8.00+\$4.50\\ =\$20\end{array}$

Working note (2):

Calculate the variable cost after tax for each year.

Year 2015:

$\begin{array}{c}\text{Variable cost = }\left(\begin{array}{l}\text{Number of wates continers}\times \\ \text{Variable cost per continer (1)}\end{array}\right)\times \left(1-\text{Tax rate}\right)\\ =\left(50,000\times \$20\right)\times \left(1-40\%\right)\\ =\$600,000\end{array}$

Year 2016:

$\begin{array}{c}\text{Variable cost = }\left(\begin{array}{l}\text{Number of wates continers}\times \\ \text{Variable cost per continer (1)}\end{array}\right)\times \left(1-\text{Tax rate}\right)\\ =\left(50,000\times \$20\right)\times \left(1-40\%\right)\\ =\$600,000\end{array}$

Year 2017:

$\begin{array}{c}\text{Variable cost = }\left(\begin{array}{l}\text{Number of wates continers}\times \\ \text{Variable cost per continer (1)}\end{array}\right)\times \left(1-\text{Tax rate}\right)\\ =\left(52,000\times \$20\right)\times \left(1-40\%\right)\\ =\$624,000\end{array}$

Year 2018:

$\begin{array}{c}\text{Variable cost = }\left(\begin{array}{l}\text{Number of wates continers}\times \\ \text{Variable cost per continer (1)}\end{array}\right)\times \left(1-\text{Tax rate}\right)\\ =\left(55,000\times \$20\right)\times \left(1-40\%\right)\\ =\$660,000\end{array}$

Year 2019:

$\begin{array}{c}\text{Variable cost = }\left(\begin{array}{l}\text{Number of wates continers}\times \\ \text{Variable cost per continer (1)}\end{array}\right)\times \left(1-\text{Tax rate}\right)\\ =\left(55,000\times \$20\right)\times \left(1-40\%\right)\\ =\$660,000\end{array}$

Working note (3):

Calculate the fixed cost after tax for each year.

$\begin{array}{c}\text{Fixed cost after tax = Fixed cost }\times \left(1-\text{Tax rate}\right)\\ =\$45,000\times \left(1-40\%\right)\\ =\$27,000\end{array}$

Working note (4):

Calculate the operating expense for each year.

Year	Variable cost (2) (E)	Fixed cost (3) (F)	Total operating expense $\left(E+F\right)$
2015	$600,000	$27,000	$627,000
2016	$600,000	$27,000	$627,000
2017	$624,000	$27,000	$651,000
2018	$660,000	$27,000	$687,000
2019	$660,000	$27,000	$687,000

Table (2)

Working note (5):

Calculate the initial investment.

$\begin{array}{c}\text{Initial investment = }\left[\begin{array}{l}\left(\text{Purchase price }-\text{Discount}\right)+\\ \text{Frieght expense+Installation cost}\end{array}\right]\\ =\left[\left(\$945,000-\left(\$945,000\times \frac{2}{100}\right)\right)+\$11,000+\$22,900\right]\\ =\$945,0000-\$18,900+\$11,000+\$22,900\\ =\$960,000\end{array}$

Working note (6):

Calculate the depreciation expense after tax for each year.

Depreciation Schedule
Year	MACRS Percentage (W)	Depreciation $X=\left(W\times \$960,000(5)\right)$	Tax Rate (Y)	Depreciation Tax Shield $\left(X\times Y\right)$
2015	33.33%	$319,968	40%	$127,987
2016	44.45%	$426,720	40%	$170,688
2017	14.81%	$142,176	40%	$56,870
2018	7.41%	$71,136	40%	$28,454
Total		$960,000

Table (3)

Working note (7):

Calculate the cash outflow for new equipment.

$\begin{array}{c}\text{Cash outflow = }\left[\begin{array}{l}\text{Initial investment + }\\ \text{Salvage value after tax+}\\ \text{Working capital reduction}\end{array}\right]\\ =\$960,000+\left(\$1,500\times \left(1-40\%\right)\right)+\$2,500\\ =\$956,600\end{array}$

Working note (8):

Calculate the salvage value after tax.

$\begin{array}{c}\text{Salvage value after tax = }\left(\begin{array}{l}\text{Salvage value of }\\ \text{new equipment}\end{array}\right)\times \left(1-\text{Tax rate}\right)\\ =\$12,000\times \left(1-\frac{40}{100}\right)\\ =\$7,200\end{array}$

Working note (9):

Calculate the cash inflow of new equipment each year.

Year	Operating expense after tax (P)(4)	Depreciation expenses after tax (Q) (6)	Salvage value after tax (R) (8)	Net cash inflow $\left(P-Q-R\right)$
2015	($627,000)	$127,987		($499,013)
2016	($627,000)	$170,688		($456,312)
2017	($651,000)	$56,870		($594,130)
2018	($687,000)	$28,454		($658,546)
2019	($687,000)		$7,200	($679,800)

Table (4)

2.

To determine

Calculate the cash flow and net present value (NVP) for buy alternative of Company J.

Explanation of Solution

Calculate the cash flow and net present value (NVP) for buy alternative of Company J as follows:

Year	Cash inflow (10) (A)	Present value factor @12% (B) (11)	Present value $\left(A\times B\right)$
2015	$ -810,000	0.893	-$ 723,330
2016	$ -810,000	0.797	-$ 645,570
2017	$ -842,400	0.712	-$ 599,789
2018	$ -891,000	0.636	-$ 566,676
2019	$ -891,000	0.567	-$ 505,197
Total present value			-$ 3,040,562
Less: Salvage value (11)			-$ 600
Net present value			-$ 3,039,962

Table (5)

Working note (10):

Calculate the cash inflow for each year.

Year 2015:

$\begin{array}{c}\text{Cash inflow = }\left(\begin{array}{l}\text{Number of wates continers}\times \\ \text{Quoted price per continer (1)}\end{array}\right)\times \left(1-\text{Tax rate}\right)\\ =\left(50,000\times \$27\right)\times \left(1-40\%\right)\\ =\$810,000\end{array}$

Year 2016:

$\begin{array}{c}\text{Cash inflow = }\left(\begin{array}{l}\text{Number of wates continers}\times \\ \text{Quoted price}\text{per continer (1)}\end{array}\right)\times \left(1-\text{Tax rate}\right)\\ =\left(50,000\times \$27\right)\times \left(1-40\%\right)\\ =\$810,000\end{array}$

Year 2017:

$\begin{array}{c}\text{Cash inflow = }\left(\begin{array}{l}\text{Number of wates continers}\times \\ \text{Quoted price per continer (1)}\end{array}\right)\times \left(1-\text{Tax rate}\right)\\ =\left(52,000\times \$27\right)\times \left(1-40\%\right)\\ =\$842,400\end{array}$

Year 2018:

$\begin{array}{c}\text{Cash inflow = }\left(\begin{array}{l}\text{Number of wates continers}\times \\ \text{Quoted price per continer (1)}\end{array}\right)\times \left(1-\text{Tax rate}\right)\\ =\left(55,000\times \$27\right)\times \left(1-40\%\right)\\ =\$891,000\end{array}$

Year 2019:

$\begin{array}{c}\text{Cash inflow = }\left(\begin{array}{l}\text{Number of wates continers}\times \\ \text{Quoted price per continer (1)}\end{array}\right)\times \left(1-\text{Tax rate}\right)\\ =\left(55,000\times \$27\right)\times \left(1-40\%\right)\\ =\$891,000\end{array}$

Working note (11):

Calculate the salvage value after tax for year 2014.

$\begin{array}{c}\text{Salvage value after tax = Salvage value }\times \left(1-\text{Tax rate}\right)\\ =\$1,500\times \left(1-40\%\right)\\ =\$900\end{array}$

3.

To determine

Indicate whether company J should make the containers or buy the containers, and explain the quantitative factors that should be considered for the capital investment analysis.

Explanation of Solution

Indicate whether company J should make the containers or buy the containers, and explain the quantitative factors that should be considered for the capital investment analysis as follows:

In this case, company J should make the containers because make decision ($2,993,203) has less cost than the buy decision ($3,039,662). Qualitative factors of capital investment analysis are,

• Reliability of supplier,
• Quality of the product,
• Stability of purchasing price,
• Labor relations, and
• Community relation.