Chapter 5, Problem 34P

To determine

Which of the two alternatives should be selected.

Answer to Problem 34P

The option to be implemented is the automated process, since it results in an overall lower cash outflow over a period of 15 years.

Explanation of Solution

Given information:

Initial Cost:

Labor Intensive Process $0

Automated Process $55,000

Installation Cost:

Labor Intensive Process $0

Automated Process $15,500

Operation and Maintenance costs:

Labor Intensive Process $1,500

Automated Process $4,800

Increase in Operation and Maintenance costs:

Labor Intensive Process $200

Automated Process $600

Labor Costs:

Labor Intensive Process $116,000

Automated Process $41,000

Increase in Labor Costs:

Labor Intensive Process 4%

Automated Process 4%

Salvage Value in year 15:

Labor Intensive Process $5,000

Automated Process $19,000

Rate of Interest for Calculation: 25%

Based on the above information, the following tables outlines the net present value calculation of the two options.

Labor Intensive Process:

Year	Particulars	Cash flow	Present value Factor @25%	Present value
0	Installation Cost	$-	1.0000	$-
1	Annual Operating costs	$ 1,500.00	0.8000	$ 1,200.00
2	Annual Operating costs	$ 1,700.00	0.6400	$ 1,088.00
3	Annual Operating costs	$ 1,900.00	0.5120	$ 972.80
4	Annual Operating costs	$ 2,100.00	0.4096	$ 860.16
5	Annual Operating costs	$ 2,300.00	0.3277	$ 753.71
6	Annual Operating costs	$ 2,500.00	0.2621	$ 655.25
7	Annual Operating costs	$ 2,700.00	0.2097	$ 566.19
8	Annual Operating costs	$ 2,900.00	0.1678	$ 486.62
9	Annual Operating costs	$ 3,100.00	0.1342	$ 416.02
10	Annual Operating costs	$ 3,300.00	0.1074	$ 354.42
11	Annual Operating costs	$ 3,500.00	0.0859	$ 300.65
12	Annual Operating costs	$ 3,700.00	0.0687	$ 254.19
13	Annual Operating costs	$ 3,900.00	0.0550	$ 214.50
14	Annual Operating costs	$ 4,100.00	0.0440	$ 180.40
15	Annual Operating costs	$ 4,100.00	0.0352	$ 144.32
1	Annual Labor costs	$116,000.00	0.8000	$92,800.00
2	Annual Labor costs	$120,640.00	0.6400	$77,209.60
3	Annual Labor costs	$125,465.60	0.5120	$64,238.39
4	Annual Labor costs	$130,484.22	0.4096	$53,446.34
5	Annual Labor costs	$135,703.59	0.3277	$44,470.07
6	Annual Labor costs	$141,131.74	0.2621	$36,990.63
7	Annual Labor costs	$146,777.01	0.2097	$30,779.14
8	Annual Labor costs	$152,648.09	0.1678	$25,614.35
9	Annual Labor costs	$158,754.01	0.1342	$21,304.79
10	Annual Labor costs	$165,104.17	0.1074	$17,732.19
11	Annual Labor costs	$171,708.34	0.0859	$14,749.75
12	Annual Labor costs	$178,576.67	0.0687	$12,268.22
13	Annual Labor costs	$185,719.74	0.0550	$10,214.59
14	Annual Labor costs	$193,148.53	0.0440	$ 8,498.54
15	Annual Labor costs	$200,874.47	0.0352	$ 7,070.78
15	Salvage Value	$ (5,000.00)	0.0352	$(176.00)
	Net Present value			$525,658.58

Automated Process:

Year	Particulars	Cash flow	Present value Factor @25%	Present value
0	Installation Cost	$70,500.00	1.0000	$70,500.00
1	Annual Operating costs	$4,800.00	0.8000	$3,840.00
2	Annual Operating costs	$5,400.00	0.6400	$3,456.00
3	Annual Operating costs	$6,000.00	0.5120	$3,072.00
4	Annual Operating costs	$6,600.00	0.4096	$2,703.36
5	Annual Operating costs	$7,200.00	0.3277	$2,359.44
6	Annual Operating costs	$7,800.00	0.2621	$2,044.38
7	Annual Operating costs	$8,400.00	0.2097	$1,761.48
8	Annual Operating costs	$9,000.00	0.1678	$1,510.20
9	Annual Operating costs	$9,600.00	0.1342	$1,288.32
10	Annual Operating costs	$10,200.00	0.1074	$1,095.48
11	Annual Operating costs	$10,800.00	0.0859	$927.72
12	Annual Operating costs	$11,400.00	0.0687	$783.18
13	Annual Operating costs	$12,000.00	0.0550	$660.00
14	Annual Operating costs	$12,600.00	0.0440	$554.40
15	Annual Operating costs	$13,200.00	0.0352	$464.64
1	Annual Labor costs	$41,000.00	0.8000	$32,800.00
2	Annual Labor costs	$42,640.00	0.6400	$27,289.60
3	Annual Labor costs	$44,345.60	0.5120	$22,704.95
4	Annual Labor costs	$46,119.42	0.4096	$18,890.51
5	Annual Labor costs	$47,964.20	0.3277	$15,717.87
6	Annual Labor costs	$49,882.77	0.2621	$13,074.27
7	Annual Labor costs	$51,878.08	0.2097	$10,878.83
8	Annual Labor costs	$53,953.20	0.1678	$9,053.35
9	Annual Labor costs	$56,111.33	0.1342	$7,530.14
10	Annual Labor costs	$58,355.78	0.1074	$6,267.41
11	Annual Labor costs	$60,690.02	0.0859	$5,213.27
12	Annual Labor costs	$63,117.62	0.0687	$4,336.18
13	Annual Labor costs	$65,642.32	0.0550	$3,610.33
14	Annual Labor costs	$68,268.01	0.0440	$3,003.79
15	Annual Labor costs	$70,998.73	0.0352	$2,499.16
15	Salvage Value	($19,000.00)	0.0352	($668.80)
	Net Present value			$279,221.46

Net present value is the difference of Sum of Present values of cash inflows and Sum of Present values of cash outflows. If the value is positive then the project may be accepted. While evaluation of two or more alternatives takes place, then the proposal with the higher net present value may be selected since it results in a greater cash inflow over the duration of the project.

In the given scenario, Present values are calculated by calculating the present values of cash inflows in the form of salvage value and cash outflows such as installation cost and operating cost.

In case of the labor intensive process theInstallation Cost is $0, Annual Operating costs are $1,500 with an increase of $200 each year.AnnualLabor costs is $116,000 with an increase of 4% each year. Salvage value at the end of year 15 is $5,000.

In case of the automated process the Installation Cost is $70,500 i.e. $55,000 for the Initial cost and $15,500 for the installation costs, Annual Operating costs are $4,800 with an increase of $600 each year. Annual Labor costs is $41,000 with an increase of 4% each year. Salvage value at the end of year 15 is $19,000.

Present value factor is calculated as 1/1.25 ^ N where N is the year of operation

Conclusion:

Hence the process to be implemented is the automated process since it results in lower overall cash flow for a period of 15 years.