Chapter 19, Problem 30P

Mallette Manufacturing, Inc., produces washing machines, dryers, and dishwashers. Because of increasing competition, Mallette is considering investing in an automated manufacturing system. Since competition is most keen for dishwashers, the production process for this line has been selected for initial evaluation. The automated system for the dishwasher line would replace an existing system (purchased one year ago for $6 million). Although the existing system will be fully depreciated in nine years, it is expected to last another 10 years. The automated system would also have a useful life of 10 years.

The existing system is capable of producing 100,000 dishwashers per year. Sales and production data using the existing system are provided by the Accounting Department:

*All cash expenses with the exception of depreciation, which is $6 per unit. The existing equipment is being depreciated using straight-line with no salvage value considered.

The automated system will cost $34 million to purchase, plus an estimated $20 million in software and implementation. (Assume that all investment outlays occur at the beginning of the first year.) If the automated equipment is purchased, the old equipment can be sold for $3 million.

The automated system will require fewer parts for production and will produce with less waste. Because of this, the direct material cost per unit will be reduced by 25 percent. Automation will also require fewer support activities, and as a consequence, volume-related overhead will be reduced by $4 per unit and direct fixed overhead (other than depreciation) by $17 per unit. Direct labor is reduced by 60 percent. Assume, for simplicity, that the new investment will be depreciated on a pure straight-line basis for tax purposes with no salvage value. Ignore the half-life convention.

The firm’s cost of capital is 12 percent, but management chooses to use 20 percent as the required rate of return for evaluation of investments. The combined federal and state tax rate is 40 percent.

Required:

1. 1. Compute the net present value for the old system and the automated system. Which system would the company choose?
2. 2. Repeat the net present value analysis of Requirement 1, using 12 percent as the discount rate.
3. 3. Upon seeing the projected sales for the old system, the marketing manager commented: “Sales of 100,000 units per year cannot be maintained in the current competitive environment for more than one year unless we buy the automated system. The automated system will allow us to compete on the basis of quality and lead time. If we keep the old system, our sales will drop by 10,000 units per year.” Repeat the net present value analysis, using this new information and a 12 percent discount rate.
4. 4. An industrial engineer for Mallette noticed that salvage value for the automated equipment had not been included in the analysis. He estimated that the equipment could be sold for $4 million at the end of 10 years. He also estimated that the equipment of the old system would have no salvage value at the end of 10 years. Repeat the net present value analysis using this information, the information in Requirement 3, and a 12 percent discount rate.
5. 5. Given the outcomes of the previous four requirements, comment on the importance of providing accurate inputs for assessing investments in automated manufacturing systems.

To determine

Ascertain the net present value for both the old and automated system, and state the system that the company would choose.

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.

Ascertain the net present value for both the old and automated system, and state the system that the company would choose:

For Old system (in thousands):

Year	Revenue	Expenses	Depreciation after tax	Cash flow	Discount factor @ 20%	Present value
	(1) (a)	(2) (b)	(3) (c)	$\begin{array}{c}\left(d=a+b+c\right)\end{array}$	(e)	$\begin{array}{c}\left(d\times e\right)\end{array}$
1	$18,000	($13,440)	$240	4,800	0.833	3,998
2	$18,000	($13,440)	$240	4,800	0.694	3,331
3	$18,000	($13,440)	$240	4,800	0.579	2,779
4	$18,000	($13,440)	$240	4,800	0.482	2,314
5	$18,000	($13,440)	$240	4,800	0.402	1,930
6	$18,000	($13,440)	$240	4,800	0.335	1,608
7	$18,000	($13,440)	$240	4,800	0.279	1,339
8	$18,000	($13,440)	$240	4,800	0.233	1,118
9	$18,000	($13,440)	$240	4,800	0.194	931
10	$18,000	($13,440)	-	4,560	0.162	739
						20,088
Less: Initial investment						0
Net present value						20,088

Table (1)

Working note (1):

Compute the amount of revenue:

$\begin{array}{c}\text{Revenue}=\left[\begin{array}{l}\left(\text{Total sales}\times \text{selling price}\right)\\ \times \left(\text{1}-\text{Tax rate}\right)\end{array}\right]\\ =\$100,000\times \$300\times \left(\text{1}-\frac{40}{100}\right)\\ =\$18,000,000\end{array}$

Working note (2):

Compute the amount of expense:

$\begin{array}{c}\text{Expenses}=\left[\begin{array}{l}\left(\text{Total sales unit}\times \text{Total cost}\right)\\ \times \left(\text{1}-\text{Tax rate}\right)\end{array}\right]\\ =\left[\$100,000\times \left(\begin{array}{l}\$80+\$90\\ +\$20+\$34\end{array}\right)\times \left(\text{1}-\frac{40}{100}\right)\right]\\ =\$13,440,000\end{array}$

Working note (3):

Compute the amount of after tax depreciation expense:

$\begin{array}{c}\text{Depreciation Expenses}=\left[\frac{\text{Acquisition cost}-\text{Salvage value }}{\text{Estimated life}}\times \text{Tax rate}\right]\\ =\left[\frac{\$6,000,000-0}{10}\times \frac{40}{100}\right]\\ =\left[\$600,000\times 0.4\right]\\ =\$240,000\end{array}$

For New system (in thousands):

Year	Revenue	Expenses	Depreciation after tax	Cash flow	Discount factor	Present value
	(1) (a)	(4) (b)	(6) (c)	$\begin{array}{c}\left(d=a+b+c\right)\end{array}$	(e)	$\begin{array}{c}\left(d\times e\right)\end{array}$
0				(50,040) (7)	1.000	$(50,040)
1	$18,000	($7,740)	$2,160	12,420	0.833	3,998
2	$18,000	($7,740)	$2,160	12,420	0.694	3,331
3	$18,000	($7,740)	$2,160	12,420	0.579	2,779
4	$18,000	($7,740)	$2,160	12,420	0.482	2,314
5	$18,000	($7,740)	$2,160	12,420	0.402	1,930
6	$18,000	($7,740)	$2,160	12,420	0.335	1,608
7	$18,000	($7,740)	$2,160	12,420	0.279	1,339
8	$18,000	($7,740)	$2,160	12,420	0.233	1,118
9	$18,000	($7,740)	$2,160	12,420	0.194	931
10	$18,000	($7,740)	$2,160	12,420	0.162	739
Net present value						2,025

Table (2)

Working note (4):

Step 1: Compute the total cost:

Particulars	Total cost
Direct materials $\left(\left(100\%-25\%\right)\times \$80\right)$	$60
Direct labor $\left(\left(100\%-60\%\right)\times \$90\right)$	$36
Volume-related overhead $\left(\$20-\$4\right)$	$16
Direct fixed overhead $\left(\left(\$40-\$6\right)-\$17\right)$	$17
Unit cost	$129

Table (3)

Step 2: Compute the amount of expense:

$\begin{array}{c}\text{Expenses}=\left[\begin{array}{l}\left(\text{Total sales}\times \text{Total cost}\right)\\ \times \left(\text{1}-\text{Tax rate}\right)\end{array}\right]\\ =\left[\$100,000\times \$129\times \left(\text{1}-\frac{40}{100}\right)\right]\\ =\$7,740,000\end{array}$

Working note (5):

Compute the loss on sale of old machinery:

$\begin{array}{c}\begin{array}{l}\text{Loss from sale}\\ \text{of old machinery}\end{array}\}=\left[\begin{array}{l}\text{Acquisition cost}-\text{Depreciation }\\ \text{Expenses}-\text{Sales value}\times \text{Tax rate}\end{array}\right]\\ =\left[\$6,000,000-\left(\frac{\$6,000,000-0}{10}\right)-3,000,000\times \frac{40}{100}\right]\\ =\left[\$6,000,000-\$600,000-3,000,000\times \frac{40}{100}\right]\\ =\$960,000\end{array}$

Working note (6):

Compute the depreciation expense for cash outflow:

$\begin{array}{c}\text{Depreciation Expenses}=\left[\frac{\text{Acquisition cost}-\text{Salvage value }}{\text{Estimated life}}\times \text{Tax rate}\right]\\ =\left[\frac{\$34,000,000+20,000,000-0}{10}\times \frac{40}{100}\right]\\ =\left[\$5,400,000\times 0.4\right]\\ =\$2,160,000\end{array}$

Working note (7):

Compute the cash outflow:

$\begin{array}{c}\text{Cash outflow}=\left[\begin{array}{l}\text{Loss on sale of old machinery}-\\ \left(\begin{array}{l}\text{Acquisition cost of new }\\ \text{machinery}-\text{sale value}\end{array}\right)\end{array}\right]\\ =\left[\$960,000(5)-\left(\$54,000,000-\$3,000,000\right)\right]\\ =\$(50,040,000)\end{array}$

Description:

The company should choose the old system because it has the higher net present value.

To determine

Ascertain the net present value for both the old and automated system under 12% discount rate, and state the system that the company would choose.

Explanation of Solution

Ascertain the net present value for both the old and automated system under 12% discount rate, and state the system that the company would choose:

For Old system (in thousands):

Year	Revenue	Expenses	Depreciation after tax	Cash flow	Discount factor	Present value
	(1) (a)	(2) (b)	(3) (c)	$\begin{array}{c}\left(d=a+b+c\right)\end{array}$	(e)	$\begin{array}{c}\left(d\times e\right)\end{array}$
1	$18,000	($13,440)	$240	4,800	0.893	4,286
2	$18,000	($13,440)	$240	4,800	0.797	3,826
3	$18,000	($13,440)	$240	4,800	0.712	3,418
4	$18,000	($13,440)	$240	4,800	0.636	3,053
5	$18,000	($13,440)	$240	4,800	0.567	2,722
6	$18,000	($13,440)	$240	4,800	0.507	2,434
7	$18,000	($13,440)	$240	4,800	0.452	2,170
8	$18,000	($13,440)	$240	4,800	0.404	1,939
9	$18,000	($13,440)	$240	4,800	0.361	1,733
10	$18,000	($13,440)	-	4,560	0.322	1,468
						27,048
Less: Initial investment						0
Net present value						27,048

Table (4)

For New system (in thousands):

Year	Revenue	Expenses	Depreciation after tax	Cash flow	Discount factor	Present value
	(1) (a)	(4) (b)	(6) (c)	$\begin{array}{c}\left(d=a+b+c\right)\end{array}$	(e)	$\begin{array}{c}\left(d\times e\right)\end{array}$
0				(50,040) (7)	1.000	$(50,040)
1	$18,000	($7,740)	$2,160	12,420	0.893	11,091
2	$18,000	($7,740)	$2,160	12,420	0.797	9,899
3	$18,000	($7,740)	$2,160	12,420	0.712	8,843
4	$18,000	($7,740)	$2,160	12,420	0.636	7,899
5	$18,000	($7,740)	$2,160	12,420	0.567	7,042
6	$18,000	($7,740)	$2,160	12,420	0.507	6,297
7	$18,000	($7,740)	$2,160	12,420	0.452	5,614
8	$18,000	($7,740)	$2,160	12,420	0.404	5,018
9	$18,000	($7,740)	$2,160	12,420	0.361	4,484
10	$18,000	($7,740)	$2,160	12,420	0.322	3,999
Net present value						20,145

Table (5)

Description:

The company should choose the old system because it has the higher net present value. However when using 12% discount rate, the automated system becomes more attractive because under 10% discount rate the NPV was $ 2,025, whereas under 12% discount rate the NPV was $ 20,145.

To determine

Ascertain the net present value for the 12% discount rate using this given information.

Explanation of Solution

Ascertain the net present value for the 12% discount rate using this given information.

Year	Revenue	Expenses	Depreciation after tax	Cash flow	Discount factor	Present value
	(8) (a)	(9) (b)	(6) (c)	$\begin{array}{c}\left(d=a+b+c\right)\end{array}$	(e)	$\begin{array}{c}\left(d\times e\right)\end{array}$
0				$0	1.000	$0
1	$18,000	($13,440)	$240	4,800	0.893	4,286
2	$16,200	(12,300)	$240	4,140	0.797	3,300
3	$14,400	(11,160)	$240	3,480	0.712	2,478
4	$12,600	(10,020)	$240	2,820	0.636	1,794
5	$10,800	(8,880)	$240	2,160	0.567	1,225
6	$9,000	($7,740)	$240	1,500	0.507	761
7	$7,200	(6,600)	$240	840	0.452	380
8	$5,400	(5,460)	$240	180	0.404	73
9	$3,600	(4,320)	$240	(480)	0.361	(173)
10	$1,800	(3,180)	-	(1,380)	0.322	(444)
Net present value						$13,680

Table (6)

Working Note (8):

Compute the amount of revenue:

Year	Sales units	Selling price	$\left(\text{1}-\text{Tax rate}\right)$	Revenue
	(a)	(b)	(c)	$\begin{array}{c}\left(d=a\times b\times c\right)\end{array}$
1	$100,000	$300	60%	$18,000
2	$90,000	$300	60%	$16,200
3	$80,000	$300	60%	$14,400
4	$70,000	$300	60%	$12,600
5	$60,000	$300	60%	$10,800
6	$50,000	$300	60%	$9,000
7	$40,000	$300	60%	$7,200
8	$30,000	$300	60%	$5,400
9	$20,000	$300	60%	$3,600
10	$10,000	$300	60%	$1,800

Table (7)

Working Note (9):

Compute the amount of expense:

Year	Sales units	Total cost per unit	Purchase cost	$\left(\text{1}-\text{Tax rate}\right)$	Expense
	(a)	(b)	(c)	(c)
1	$100,000	$190	$3,400,000	60%	$(13,440,000)
2	$90,000	$190	$3,400,000	60%	$(12,300,000)
3	$80,000	$190	$3,400,000	60%	$(11,160,000)
4	$70,000	$190	$3,400,000	60%	$(10,020,000)
5	$60,000	$190	$3,400,000	60%	$(8,880,000)
6	$50,000	$190	$3,400,000	60%	$(7,740,000)
7	$40,000	$190	$3,400,000	60%	$(6,600,000)
8	$30,000	$190	$3,400,000	60%	$(5,460,000)
9	$20,000	$190	$3,400,000	60%	$(4,320,000)
10	$10,000	$190	$3,400,000	60%	$(3,180,000)

Table (8)

To determine

Ascertain the net present value for the given analysis; use the information in Requirement 3,

Explanation of Solution

Compute the salvage value for the new system:

$\begin{array}{c}\text{Salvage value}=\left[\left(\text{Sale value}\times \text{Estimated life}\right)\times 1-\text{Tax rate}\right]\\ =\left[\left(\$400,000\times 10\right)\times 1-\frac{40}{100}\right]\\ =\$2,400,000\end{array}$

Compute the net present value for the new system:

$\begin{array}{c}\text{Net present value}=\left[\begin{array}{l}\left(\text{NPV of new system existing}\right)+\\ \left(\begin{array}{l}\text{Salvage value}\times \text{Discount}\\ \text{factor @12\%}\end{array}\right)\end{array}\right]\\ =\left[\left(\$20,133,000\right)+\left(\$\text{2,400,000}\times \text{0}\text{.322}\right)\right]\\ =\$20,133,000+\$772,800\\ =\$20,905,800\end{array}$

Thereby, the salvage value of the new system would increase the after-tax cash flows by $2,400,000. On the other hand, the NPV of the new system has been increased by $772,800, whereas, the NPV analysis for the old system remains unchanged. Thus this makes the new investment more attractive.

To determine

Interpret the significance of providing accurate inputs for evaluating investments in automated manufacturing systems.

Explanation of Solution

Interpret the significance of providing accurate inputs for evaluating investments in automated manufacturing systems:

The key importance is that the usage of correct discount rate. Under requirement 2, the usage of 20% discount rate made the automated alternative system look entirely unappealing. Thus when using the correct discount rate (12%), the automated system results in a larger NPV, even though it was less than the NPV of the old system. However, the projections of future revenues for the old system were overly optimistic. On the other hand, the old system was not able to produce the same level of quality as the new system could produce. Thus, by considering the correct discount rate, the new system dominated the old. Moreover, the addition of salvage value simply increased this dominance.