Question

NB Power wants to assess the potential for a photovoltaic system to produce electricity from solar energy at a lower cost than electricity production from a thermal plant (such as coal). Unit cost of electricity, currently produced by the thermal power plant, is $0.07 per kilowatt-hour. The photovoltaic system is characterized by the following:

Item	Value
Equipment and tools: solar cell batteries wiring power control	$3,000 $1,000 $800 $100
Operating costs	$100/year

Batteries must be replaced every 5 years while power control - every 10 years. Assuming service life of 20 years, annual interest rate of 10%, capacity of the photovoltaic system of 35 kilowatt-hours per day and ignoring the installation cost, should NB Power implement the system?

Answer 1

Working notes:

(1) Annual saving = $0.07 x 35 x 365** = $894.25

(2) Net annual benefit, NAB ($) = Annual saving - Annual cost

(3) Annual cost, year 5 and year 15 = $(100 + 1,000) = $1,100 (replacement of battery)

(4) Annual cost, year 10 and year 20 = $(100 + 1,000 + 100) = $1,200 (replacement of battery & power control)

(3) First cost ($) = 3,000 + 1,000 + 800 + 100 = 4,900

Present Worth (PW) of NAB is computed as follows.

Year	Saving ($)	Cost ($)	NAB ($)	PV Factor @10%	Discounted NAB ($)
	(A)	(B)	(C)=(A)-(B)	(D)	(C)x(D)
0		4,900	-4,900.00	1.0000	-4,900.00
1	894.25	100	794.25	0.9091	722.05
2	894.25	100	794.25	0.8264	656.40
3	894.25	100	794.25	0.7513	596.73
4	894.25	100	794.25	0.6830	542.48
5	894.25	1,100	-205.75	0.6209	-127.75
6	894.25	100	794.25	0.5645	448.33
7	894.25	100	794.25	0.5132	407.58
8	894.25	100	794.25	0.4665	370.52
9	894.25	100	794.25	0.4241	336.84
10	894.25	1,200	-305.75	0.3855	-117.88
11	894.25	100	794.25	0.3505	278.38
12	894.25	100	794.25	0.3186	253.07
13	894.25	100	794.25	0.2897	230.07
14	894.25	100	794.25	0.2633	209.15
15	894.25	1,100	-205.75	0.2394	-49.25
16	894.25	100	794.25	0.2176	172.85
17	894.25	100	794.25	0.1978	157.14
18	894.25	100	794.25	0.1799	142.85
19	894.25	100	794.25	0.1635	129.87
20	894.25	1,200	-305.75	0.1486	-45.45
				PW of NAB ($) =	413.98

Since PW > 0, NB should implement the system.