Question

Consider a 2.0 MW wind turbine that operates with a capacity factor of 30% (i.e. it produces 5,300 MWh/y). The initial cost is $3.5 million. The project life is 30 years and the salvage value is negligible. Maintenance costs are $50,000/y. The minimum attractive rate of return is 7%. For each of the following cases, determine the present value of the project and whether the cost is justified.

a. Power can be sold to the grid at $0.055/kWh. (ans. -503200, not justified)

b. Power can be sold to the grid at $0.10/kWh. (ans. 2456000 justified)

Answer 1

Initial cost = 3500000 $

Project life = 30 years

IRR = 7 %

Maintenance cost = 50000 $/year

(A)

Power produces = 5300 MWh/y = 5300000 kWh/y

Power sold = 0.055 $ / kWh

So, total power sold per year = 5300000 kWh/y x 0.055 $/kWh = 291500 $

Present Value = (power sold + Maintainence cost)*rate of return

YEAR	CAPITAL COST	POWER SOLD	RATE OF RETURN	MAINTENANCE COST	PRESENT VALUE
0	3500000		1		3500000
1		291500	0.934	50000	225561
2		291500	0.873	50000	210829.5
3		291500	0.816	50000	197064
4		291500	0.763	50000	184264.5
5		291500	0.713	50000	172189.5
6		291500	0.666	50000	160839
7		291500	0.623	50000	150454.5
8		291500	0.582	50000	140553
9		291500	0.544	50000	131376
10		291500	0.508	50000	122682
11		291500	0.475	50000	114712.5
12		291500	0.444	50000	107226
13		291500	0.415	50000	100222.5
14		291500	0.388	50000	93702
15		291500	0.362	50000	87423
16		291500	0.339	50000	81868.5
17		291500	0.316	50000	76314
18		291500	0.296	50000	71484
19		291500	0.276	50000	66654
20		291500	0.258	50000	62307
21		291500	0.242	50000	58443
22		291500	0.226	50000	54579
23		291500	0.21	50000	50715
24		291500	0.197	50000	47575.5
25		291500	0.184	50000	44436
26		291500	0.172	50000	41538
27		291500	0.161	50000	38881.5
28		291500	0.15	50000	36225
29		291500	0.14	50000	33810
30		291500	0.131	50000	31636.5
		Total	12.404

NPV = (291500 - 50000) * 12.404 - 3500000 = - 504435 $

which is negetive, so its cost is not justified

(B)

Power produces = 5300 MWh/y = 5300000 kWh/y

Power sold = 0.1 $/kWh

So, total power sold per year = 5300000 kWh/y x 0.1 $/kWh = 530000 $

NPV = (530000 - 50000) * 12.404 - 3500000 = 2453920 $

which is positive, so its cost is justified