Chapter 5, Problem 100P

To determine

Which of the alternatives is preferable.

Answer to Problem 100P

The option to be selected is Solar Collector Field, since it results in a higher overall cash inflow over a period of 20 years.

Explanation of Solution

Given information:

Installation Cost:

Flat Solar Panels$87 Million

Mechanized Solar Panels $101 Million

Solar Collector Field $91 Million

Annual Operation and Maintenance costs (year 1):

Flat Solar Panels $2 Million

Mechanized Solar Panels $2.3 Million

Solar Collector Field $3 Million

Increase in Annual Operation and Maintenance costs (year 2 onwards):

Flat Solar Panels $250,000

Mechanized Solar Panels $300,000

Solar Collector Field $350,000

Annual Revenues in the form of Electricity

Flat Solar Panels $6.9 Million

Mechanized Solar Panels $8.8 Million

Solar Collector Field $9.7 Million

Annual Increase in Revenues:

Flat Solar Panels8%

Mechanized Solar Panels 8%

Solar Collector Field 8%

Useful Life: 20 Years

Rate of Interest for calculation: 10%.

Based on the above information, the following tables outlines the net present value calculation of the three options:

Flat Solar Panels:

Year	Cash Flows	Cash Inflows	Cash Flows	Cash Outflows	Net Cash Flows	P.V. @10%	Amount
0	Electricity Benefits	$ -	Initial Cost	$ 87,000,000.00	$ (87,000,000.00)	1	$ (87,000,000.00)
1	Electricity Benefits	$6,900,000.00	Operating Costs	$ 2,000,000.00	$ 4,900,000.00	0.9091	$ 4,454,590.00
2	Electricity Benefits (8% higher than last year)	$7,452,000.00	Operating Costs($250,000 higher than previous year)	$ 2,250,000.00	$ 5,202,000.00	0.8264	$ 4,298,932.80
3	Electricity Benefits (8% higher than last year)	$8,048,160.00	Operating Costs($250,000 higher than previous year)	$ 2,500,000.00	$ 5,548,160.00	0.7513	$ 4,168,332.61
4	Electricity Benefits (8% higher than last year)	$8,692,012.80	Operating Costs($250,000 higher than previous year)	$ 2,750,000.00	$ 5,942,012.80	0.683	$ 4,058,394.74
5	Electricity Benefits (8% higher than last year)	$9,387,373.82	Operating Costs($250,000 higher than previous year)	$ 3,000,000.00	$ 6,387,373.82	0.6209	$ 3,965,920.41
6	Electricity Benefits (8% higher than last year)	$ 10,138,363.73	Operating Costs($250,000 higher than previous year)	$ 3,250,000.00	$ 6,888,363.73	0.5645	$ 3,888,481.33
7	Electricity Benefits (8% higher than last year)	$ 10,949,432.83	Operating Costs($250,000 higher than previous year)	$ 3,500,000.00	$ 7,449,432.83	0.5132	$ 3,823,048.93
8	Electricity Benefits (8% higher than last year)	$ 11,825,387.45	Operating Costs($250,000 higher than previous year)	$ 3,750,000.00	$ 8,075,387.45	0.4665	$ 3,767,168.25
9	Electricity Benefits (8% higher than last year)	$ 12,771,418.45	Operating Costs($250,000 higher than previous year)	$ 4,000,000.00	$ 8,771,418.45	0.4241	$ 3,719,958.57
10	Electricity Benefits (8% higher than last year)	$ 13,793,131.93	Operating Costs($250,000 higher than previous year)	$ 4,250,000.00	$ 9,543,131.93	0.3855	$ 3,678,877.36
11	Electricity Benefits (8% higher than last year)	$ 14,896,582.48	Operating Costs($250,000 higher than previous year)	$ 4,500,000.00	$ 10,396,582.48	0.3505	$ 3,644,002.16
12	Electricity Benefits (8% higher than last year)	$ 16,088,309.08	Operating Costs($250,000 higher than previous year)	$ 4,750,000.00	$ 11,338,309.08	0.3186	$ 3,612,385.27
13	Electricity Benefits (8% higher than last year)	$ 17,375,373.81	Operating Costs($250,000 higher than previous year)	$ 5,000,000.00	$ 12,375,373.81	0.2897	$ 3,585,145.79
14	Electricity Benefits (8% higher than last year)	$ 18,765,403.71	Operating Costs($250,000 higher than previous year)	$ 5,250,000.00	$ 13,515,403.71	0.2633	$ 3,558,605.80
15	Electricity Benefits (8% higher than last year)	$ 20,266,636.01	Operating Costs($250,000 higher than previous year)	$ 5,500,000.00	$ 14,766,636.01	0.2394	$ 3,535,132.66
16	Electricity Benefits (8% higher than last year)	$ 21,887,966.89	Operating Costs($250,000 higher than previous year)	$ 5,750,000.00	$ 16,137,966.89	0.2176	$ 3,511,621.59
17	Electricity Benefits (8% higher than last year)	$ 23,639,004.24	Operating Costs($250,000 higher than previous year)	$ 6,000,000.00	$ 17,639,004.24	0.1978	$ 3,488,995.04
18	Electricity Benefits (8% higher than last year)	$ 25,530,124.58	Operating Costs($250,000 higher than previous year)	$ 6,250,000.00	$ 19,280,124.58	0.1799	$ 3,468,494.41
19	Electricity Benefits (8% higher than last year)	$ 27,572,534.54	Operating Costs($250,000 higher than previous year)	$ 6,500,000.00	$ 21,072,534.54	0.1635	$ 3,445,359.40
20	Electricity Benefits (8% higher than last year)	$ 29,778,337.31	Operating Costs($250,000 higher than previous year)	$ 6,750,000.00	$ 23,028,337.31	0.1486	$ 3,422,010.92
	Net Present Value						$ (11,904,541.97)

Mechanized Solar Panels:

Year	Cash Flows	Cash Inflows	Cash Flows	Cash Outflows	Net Cash Flows	P.V. @10%	Amount
0	Electricity Benefits	$ -	Initial Cost	$ 101,000,000.00	$ (101,000,000.00)	1	$ (101,000,000.00)
1	Electricity Benefits (8% higher than last year)	$ 8,800,000.00	Operating Costs	$ 2,300,000.00	$ 6,500,000.00	0.9091	$ 5,909,150.00
2	Electricity Benefits (8% higher than last year)	$ 9,504,000.00	Operating Costs($300,000 higher than previous year)	$ 2,600,000.00	$ 6,904,000.00	0.8264	$ 5,705,465.60
3	Electricity Benefits (8% higher than last year)	$ 10,264,320.00	Operating Costs($300,000 higher than previous year)	$ 2,900,000.00	$ 7,364,320.00	0.7513	$ 5,532,813.62
4	Electricity Benefits (8% higher than last year)	$ 11,085,465.60	Operating Costs($300,000 higher than previous year)	$ 3,200,000.00	$ 7,885,465.60	0.683	$ 5,385,773.00
5	Electricity Benefits (8% higher than last year)	$ 11,972,302.85	Operating Costs($300,000 higher than previous year)	$ 3,500,000.00	$ 8,472,302.85	0.6209	$ 5,260,452.84
6	Electricity Benefits (8% higher than last year)	$ 12,930,087.08	Operating Costs($300,000 higher than previous year)	$ 3,800,000.00	$ 9,130,087.08	0.5645	$ 5,153,934.15
7	Electricity Benefits (8% higher than last year)	$ 13,964,494.04	Operating Costs($300,000 higher than previous year)	$ 4,100,000.00	$ 9,864,494.04	0.5132	$ 5,062,458.34
8	Electricity Benefits (8% higher than last year)	$ 15,081,653.57	Operating Costs($300,000 higher than previous year)	$ 4,400,000.00	$ 10,681,653.57	0.4665	$ 4,982,991.39
9	Electricity Benefits (8% higher than last year)	$ 16,288,185.85	Operating Costs($300,000 higher than previous year)	$ 4,700,000.00	$ 11,588,185.85	0.4241	$ 4,914,549.62
10	Electricity Benefits (8% higher than last year)	$ 17,591,240.72	Operating Costs($300,000 higher than previous year)	$ 5,000,000.00	$ 12,591,240.72	0.3855	$ 4,853,923.30
11	Electricity Benefits (8% higher than last year)	$ 18,998,539.98	Operating Costs($300,000 higher than previous year)	$ 5,300,000.00	$ 13,698,539.98	0.3505	$ 4,801,338.26
12	Electricity Benefits (8% higher than last year)	$ 20,518,423.17	Operating Costs($300,000 higher than previous year)	$ 5,600,000.00	$ 14,918,423.17	0.3186	$ 4,753,009.62
13	Electricity Benefits (8% higher than last year)	$ 22,159,897.03	Operating Costs($300,000 higher than previous year)	$ 5,900,000.00	$ 16,259,897.03	0.2897	$ 4,710,492.17
14	Electricity Benefits (8% higher than last year)	$ 23,932,688.79	Operating Costs($300,000 higher than previous year)	$ 6,200,000.00	$ 17,732,688.79	0.2633	$ 4,669,016.96
15	Electricity Benefits (8% higher than last year)	$ 25,847,303.89	Operating Costs($300,000 higher than previous year)	$ 6,500,000.00	$ 19,347,303.89	0.2394	$ 4,631,744.55
16	Electricity Benefits (8% higher than last year)	$ 27,915,088.20	Operating Costs($300,000 higher than previous year)	$ 6,800,000.00	$ 21,115,088.20	0.2176	$ 4,594,643.19
17	Electricity Benefits (8% higher than last year)	$ 30,148,295.26	Operating Costs($300,000 higher than previous year)	$ 7,100,000.00	$ 23,048,295.26	0.1978	$ 4,558,952.80
18	Electricity Benefits (8% higher than last year)	$ 32,560,158.88	Operating Costs($300,000 higher than previous year)	$ 7,400,000.00	$ 25,160,158.88	0.1799	$ 4,526,312.58
19	Electricity Benefits (8% higher than last year)	$ 35,164,971.59	Operating Costs($300,000 higher than previous year)	$ 7,700,000.00	$ 27,464,971.59	0.1635	$ 4,490,522.86
20	Electricity Benefits (8% higher than last year)	$ 37,978,169.32	Operating Costs($300,000 higher than previous year)	$ 8,000,000.00	$ 29,978,169.32	0.1486	$ 4,454,755.96
	Net Present Value						$ (2,047,699.18)

Solar Collector Field:

Year	Cash Flows	Cash Inflows	Cash Flows	Cash Outflows	Net Cash Flows	P.V. @10%	Amount
0	Electricity Benefits	$ -	Initial Cost	$ 91,000,000.00	$ (91,000,000.00)	1	$ (91,000,000.00)
1	Electricity Benefits (8% higher than last year)	$ 9,700,000.00	Operating Costs	$ 3,000,000.00	$ 6,700,000.00	0.9091	$ 6,090,970.00
2	Electricity Benefits (8% higher than last year)	$ 10,476,000.00	Operating Costs($350,000 higher than previous year)	$ 3,350,000.00	$ 7,126,000.00	0.8264	$ 5,888,926.40
3	Electricity Benefits (8% higher than last year)	$ 11,314,080.00	Operating Costs($350,000 higher than previous year)	$ 3,700,000.00	$ 7,614,080.00	0.7513	$ 5,720,458.30
4	Electricity Benefits (8% higher than last year)	$ 12,219,206.40	Operating Costs($350,000 higher than previous year)	$ 4,050,000.00	$ 8,169,206.40	0.683	$ 5,579,567.97
5	Electricity Benefits (8% higher than last year)	$ 13,196,742.91	Operating Costs($350,000 higher than previous year)	$ 4,400,000.00	$ 8,796,742.91	0.6209	$ 5,461,897.67
6	Electricity Benefits (8% higher than last year)	$ 14,252,482.34	Operating Costs($350,000 higher than previous year)	$ 4,750,000.00	$ 9,502,482.34	0.5645	$ 5,364,151.28
7	Electricity Benefits (8% higher than last year)	$ 15,392,680.93	Operating Costs($350,000 higher than previous year)	$ 5,100,000.00	$ 10,292,680.93	0.5132	$ 5,282,203.85
8	Electricity Benefits (8% higher than last year)	$ 16,624,095.41	Operating Costs($350,000 higher than previous year)	$ 5,450,000.00	$ 11,174,095.41	0.4665	$ 5,212,715.51
9	Electricity Benefits (8% higher than last year)	$ 17,954,023.04	Operating Costs($350,000 higher than previous year)	$ 5,800,000.00	$ 12,154,023.04	0.4241	$ 5,154,521.17
10	Electricity Benefits (8% higher than last year)	$ 19,390,344.88	Operating Costs($350,000 higher than previous year)	$ 6,150,000.00	$ 13,240,344.88	0.3855	$ 5,104,152.95
11	Electricity Benefits (8% higher than last year)	$ 20,941,572.47	Operating Costs($350,000 higher than previous year)	$ 6,500,000.00	$ 14,441,572.47	0.3505	$ 5,061,771.15
12	Electricity Benefits (8% higher than last year)	$ 22,616,898.27	Operating Costs($350,000 higher than previous year)	$ 6,850,000.00	$ 15,766,898.27	0.3186	$ 5,023,333.79
13	Electricity Benefits (8% higher than last year)	$ 24,426,250.13	Operating Costs($350,000 higher than previous year)	$ 7,200,000.00	$ 17,226,250.13	0.2897	$ 4,990,444.66
14	Electricity Benefits (8% higher than last year)	$ 26,380,350.14	Operating Costs($350,000 higher than previous year)	$ 7,550,000.00	$ 18,830,350.14	0.2633	$ 4,958,031.19
15	Electricity Benefits (8% higher than last year)	$ 28,490,778.16	Operating Costs($350,000 higher than previous year)	$ 7,900,000.00	$ 20,590,778.16	0.2394	$ 4,929,432.29
16	Electricity Benefits (8% higher than last year)	$ 30,770,040.41	Operating Costs($350,000 higher than previous year)	$ 8,250,000.00	$ 22,520,040.41	0.2176	$ 4,900,360.79
17	Electricity Benefits (8% higher than last year)	$ 33,231,643.64	Operating Costs($350,000 higher than previous year)	$ 8,600,000.00	$ 24,631,643.64	0.1978	$ 4,872,139.11
18	Electricity Benefits (8% higher than last year)	$ 35,890,175.13	Operating Costs($350,000 higher than previous year)	$ 8,950,000.00	$ 26,940,175.13	0.1799	$ 4,846,537.51
19	Electricity Benefits (8% higher than last year)	$ 38,761,389.14	Operating Costs($350,000 higher than previous year)	$ 9,300,000.00	$ 29,461,389.14	0.1635	$ 4,816,937.12
20	Electricity Benefits (8% higher than last year)	$ 41,862,300.27	Operating Costs($350,000 higher than previous year)	$ 9,650,000.00	$ 32,212,300.27	0.1486	$ 4,786,747.82
	Net Present Value						$ 13,045,300.56

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 revenues in the form of electricity and cash outflows such as installation cost and operating cost.

Installation Costs in case of Flat Solar Panels are $87 Million, Mechanized Solar Panels + $101 Million and Solar Collector Field + $91 Million.

Annual Operation and Maintenance costs for year 1, in case of Flat Solar Panels+ $2 Million, Mechanized Solar Panels + $2.3 Million and Solar Collector Field + $3 Million.

Increase Annual Operation and Maintenance costs year 2 onwardsin case ofFlat Solar Panels+ $250,000, Mechanized Solar Panels + $300,000 and Solar Collector Field + $350,000.

Annual Revenues in the form of Electricity in case of Flat Solar Panels + $6.9Million, Mechanized Solar Panels + $8.8 Million and Solar Collector Field + $9.7 Million

Annual Increase in Revenues is 8% in case of all alternatives and the Useful Life is 20 Years. Rate of Interest for calculation is considered as 10%

Present value factor is calculated as 1/1.10 ^ N where N is the year of operation.

Conclusion:

Hence the option to be selected is Flat Solar Panels since it results in higher overall cash flow for a period of 20 years.