Chapter 19, Problem 32P

1.

To determine

Calculate the after-tax cash flows for the manual and robotic systems by preparing a schedule.

Explanation of Solution

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 after-tax cash flows for the manual and robotic systems by preparing a schedule:

For manual systems:

Year	Revenue	Expenses	Depreciation after tax	Cash flow
	(1) (a)	(2) (b)	(3) (c)	$\begin{array}{c}\left(d=a+b+c\right)\end{array}$
1	$240,000	($180,000)	$8,000	$68,000
2	$240,000	($180,000)	$8,000	$68,000
3	$240,000	($180,000)	$8,000	$68,000
4	$240,000	($180,000)	$8,000	$68,000
5	$240,000	($180,000)	$8,000	$68,000
6	$240,000	($180,000)	$8,000	$68,000
7	$240,000	($180,000)	$8,000	$68,000
8	$240,000	($180,000)	$8,000	$68,000
9	$240,000	($180,000)	$8,000	$68,000
10	$240,000	($180,000)	$8,000	$68,000

Table (1)

Working note (1):

Compute the amount of annual revenue:

$\begin{array}{c}\text{Revenue}=\left[\left(\text{Total sales}\right)\times \left(\text{1}-\text{Tax rate}\right)\right]\\ =\$400,000\times \left(\text{1}-\frac{40}{100}\right)\\ =\$240,000\end{array}$

Working note (2):

Compute the amount of expense:

$\begin{array}{c}\text{Expenses}=\left[\begin{array}{l}\left(\begin{array}{l}\text{Variable expenses}+\text{Fixed }\\ \text{expenses}-\text{Depreciation expenses}\end{array}\right)\\ \times \left(\text{1}-\text{Tax rate}\right)\end{array}\right]\\ =\left[\$228,000+\$92,000-\$20,000\times \left(\text{1}-\frac{40}{100}\right)\right]\\ =\$180,000\end{array}$

Working note (3):

Compute the amount of after tax depreciation expense:

$\begin{array}{c}\text{Depreciation Expenses}=\left[\text{Depreciation Expenses (Given)}\times \text{Tax rate}\right]\\ =\left[\$20,000\times \frac{40}{100}\right]\\ =\$8,000\end{array}$

For robotic systems:

Year	Revenue	Expenses	Depreciation after tax	Other expenses (9)	Cash flow
	(4) (a)	(7) (b)	(8) (c)		$\begin{array}{c}\left(d=a+b+c\right)\end{array}$
			$64,000	$(480,000)	$(416,000)
1	$240,000	($124,320)	$29,723	-	$145,403
2	$270,000	($132,960)	$50,939	-	$187,979
3	$300,000	($141,600)	$36,379	-	$194,779
4	$360,000	($158,880)	$25,979	-	$227,099
5	$360,000	($158,880)	$18,574	-	$219,694
6	$360,000	($158,880)	$18,554	-	$219,694
7	$360,000	($158,880)	$18,554	-	$219,694
8	$360,000	($158,880)	$9,277	-	$210,397
9	$360,000	($158,880)	-	-	$201,120
10	$372,000	($158,880)	-	-	$213,120

Table (2)

Working Note (4):

Compute the amount of revenue:

Year	Sales	$\left(\text{1}-\text{Tax rate}\right)$	Revenue
	(a)	(b)	$\begin{array}{c}\left(c=a\times b\right)\end{array}$
1	$400,000	60%	$240,000
2	$450,000	60%	$270,000
3	$500,000	60%	$300,000
4	$600,000	60%	$360,000
5	$600,000	60%	$360,000
6	$600,000	60%	$360,000
7	$600,000	60%	$360,000
8	$600,000	60%	$360,000
9	$600,000	60%	$360,000
10	$620,000 $\left(\text{\$600,000}+\$\text{20,000}\right)$	60%	$372,000

Table (3)

Working Note (5):

Compute the fixed expense:

$\begin{array}{c}\text{Fixed Expenses}=\left[\left(\begin{array}{l}\text{Direct labor}+\text{other}\\ \text{fixed expenses}\end{array}\right)\times \left(\text{Tax rate}\right)\right]\\ =\left[\$20,000+\$92,000-\$20,000\times \left(\frac{40}{100}\right)\right]\\ =\$55,200\end{array}$

Working Note (6):

Compute the total variable expense percentage:

Particulars	Cost as a % of sales	$\left[\begin{array}{l}100\%–Costof\%\\ reduceddueto\\ improvedquality\end{array}\right]$	$\left(\text{1}-\text{Tax rate}\right)$
	(a)	(b)	$\begin{array}{c}\left(c=a\times b\right)\end{array}$
Direct materials	$16\%\times \text{sales}$	75%	60%	$0.0720\times \text{sales}$
Variable overhead	$9\%\times \text{sales}$	66.67%	60%	$0.0360\times \text{sales}$
Variable selling	$12\%\times \text{sales}$	90%	60%	$0.0648\times \text{sales}$
Total				$0.1728\times \text{sales}$

Table (4)

Working Note (7):

Compute the amount of expense:

Year	Sales units	Variable cost % (6)	Fixed cost (5)	Expense
	(a)	(b)	(c)	$\begin{array}{c}\left(a\times b+c\right)\end{array}$
1	$400,000	0.1728	55,200	($124,320)
2	$450,000	0.1728	55,200	($132,960)
3	$500,000	0.1728	55,200	($141,600)
4	$600,000	0.1728	55,200	($158,880)
5	$600,000	0.1728	55,200	($158,880)
6	$600,000	0.1728	55,200	($158,880)
7	$600,000	0.1728	55,200	($158,880)
8	$600,000	0.1728	55,200	($158,880)
9	$600,000	0.1728	55,200	($158,880)
10	$620,000	0.1728	55,200	($158,880)

Table (5)

Working note (8):

Step 1: Compute the depreciation expenses after tax:

$\begin{array}{c}\text{Depreciation Expenses}=\left[\left(\begin{array}{l}\text{Book value}\\ -\text{Sales value}\end{array}\right)\times \left(\text{Tax rate}\right)\right]\\ =\left[\$200,000-\$40,000\times \left(\frac{40}{100}\right)\right]\\ =\$64,000\end{array}$

Calculate the amount of depreciation expenses under MARCS:

Year	Initial investments	Deprecation rate	MACRS for 7 years	Depreciation
	(a)	(b)	(c)	$\left(a\times b\times c\right)$
1	$520,000	40%	0.1429	$29,723
2	$520,000	40%	0.2449	$50,939
3	$520,000	40%	0.1749	$36,379
4	$520,000	40%	0.1249	$25,979
5	$520,000	40%	0.893	$18,574
6	$520,000	40%	0.892	$18,554
7	$520,000	40%	0.893	$18,554
8	$520,000	40%	0.446	$9,277

Table (6)

Compute the amount of net investment:

$\begin{array}{c}\text{Net investment}=\left[\left(\text{Purchase costs}-\text{Recovery of capital}\right)\right]\\ =\left[\$520,000-\$40,000\right]\\ =\$480,000\end{array}$

2.

To determine

Ascertain the net present value for each system and describe whether it is advisable for the company to invest in the robotic system or manual systems.

Explanation of Solution

Ascertain the net present value for each system and describe whether it is advisable for the company to invest in the robotic system as follows:

For manual systems:

Year	Cash flow	Discount factor @ 12%	Cash flow
	(a)	(b)	$\begin{array}{c}\left(a\times b\right)\end{array}$
0	0	1.000	0
1	$68,000	0.893	$60,724
2	$68,000	0.797	$54,196
3	$68,000	0.712	$48,416
4	$68,000	0.636	$43,248
5	$68,000	0.567	$38,556
6	$68,000	0.507	$34,476
7	$68,000	0.452	$30,736
8	$68,000	0.404	$27,472
9	$68,000	0.361	$24,480
10	$68,000	0.322	$21,896
Net present value			$384,200

Table (7)

For robotic systems:

Year	Cash flow	Discount factor @ 12%	Cash flow
	(a)	(b)	$\begin{array}{c}\left(a\times b\right)\end{array}$
0	$(416,000)	1.000	$(416,000)
1	$145,403	0.893	$129,845
2	$187,979	0.797	$149,819
3	$194,779	0.712	$138,683
4	$227,099	0.636	$144,435
5	$219,694	0.567	$124,566
6	$219,694	0.507	$111,385
7	$219,694	0.452	$99,302
8	$210,397	0.404	$85,000
9	$201,120	0.361	$72,604
10	$213,120	0.322	$68,625
Net present value			$708,255

Table (8)

From the above calculation it is clear that the net present value of robotic systems is higher than the net present value of manual systems. Hence, the company should invest in the robotic system.

3.

To determine

Ascertain the net present value for the given situation using 12 % and 20 % discount factors, and describe whether the robotic system would be acquired if 20% is used. State whether this conservative approach could have a negative impact on a firm’s ability.

Explanation of Solution

Under 12%:

Year	Cash flow	Discount factor @ 12%	Cash flow
	(a)	(b)	$\begin{array}{c}\left(a\times b\right)\end{array}$
0	$(340,000)	1.000	$(340,000)
1	$80,000	0.893	$71,440
2	$80,000	0.797	$63,760
3	$80,000	0.712	$56,960
4	$80,000	0.636	$50,880
5	$80,000	0.567	$45,360
6	$80,000	0.507	$40,560
7	$80,000	0.452	$36,160
8	$80,000	0.404	$32,320
9	$80,000	0.361	$28,880
10	$80,000	0.322	$25,760
Net present value			$112,000

Table (9)

Under 20%:

Year	Cash flow	Discount factor @ 20%	Cash flow
	(a)	(b)	$\begin{array}{c}\left(a\times b\right)\end{array}$
0	$(340,000)	1.000	$(340,000)
1	$80,000	0.833	$66,640
2	$80,000	0.694	$55,520
3	$80,000	0.579	$46,320
4	$80,000	0.482	$38,560
5	$80,000	0.402	$32,160
6	$80,000	0.335	$26,800
7	$80,000	0.279	$22,320
8	$80,000	0.233	$18,640
9	$80,000	0.194	$15,440
10	$80,000	0.162	$12,960
Net present value			$(4,640)

Table (10)

From the above calculation it is clear that the company would not acquire the robotic system, if it uses 20% discount rate.

In this case, using an excessive discount rate could damage the ability of the firm to stay competitive. Because the usage of excessive discount rate may lead a firm to reject new technology (which would increase the quality and productivity). Whereas, the other firms would invest in the new technology, as a result their products will be priced lower and would have a higher quality. Thus, these features would probable cause severe difficulty for the more conservative firm.