Question

Consider a PV solar power project with the following parameters:

• Initial cost: $18M for hardware + $14M for installation.

• The yearly energy produced is 24 millions kWh which will bring an income of $2.9M per year

• $0.5M per year is used for operation and maintenance.

• At the end of the 25 year time horizon, a net expenditure of $1M will be required for removal and site cleaning.

• The MARR is 7%.

a) Calculate the NPV for this investment.

b) Recalculate the NPV, this time assuming that an investment tax credit of 20% for hardware and 10% for installation costs are available.

c) Calculate the IRR for this investment (with tax incentive).

d) Calculate the levelized cost of energy (with tax incentive)

Answer 1

Answer a.

Calculation of NPV-

= PV of net cash inflow - PV of net cash outflow

= 27.97 - 32.18

= $ -4.21 M

Cash flow = Income per year - Operating cost

= 2.9 - 0.5 = 2.4 per year

PV factor for 25 years = (1/1+r)^n1 + (1/1+r)^n2 + ......

= 11.6534

PV factor for 25th year = (1/1+r)^n25

= (1/1+0.07)^25 = 0.1842

PV of net cash inflow = 2.4*11.6534

= $27.97 M

PV of Cash outflow = PV of Initial investment + PV of Expenditure at 25th year

= 32 + 1*0.1842

= $32.18

Answer b.

Present value of tax credit will be included in the present value of cash flow-

Calculation of PV of cash credit-

= (18*20% + 14*10%)

= $5M

PV factor for 1st year = 0.9346

PV of tax credit = 5*0.9346

= $4.67 M

NPV = (27.97+4.67) - 32.18

= $0.46 M

Answer c.

Year	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25
Cash Flow	-32	7.4	2.4	2.4	2.4	2.4	2.4	2.4	2.4	2.4	2.4	2.4	2.4	2.4	2.4	2.4	2.4	2.4	2.4	2.4	2.4	2.4	2.4	2.4	2.4	2.4

Applying the IRR formula in excel on above table the IRR will be 7.25%

Answer d.

Levelized cost of energy = PV of total cost over the year / PV of electricity produced over the year

= 32+(0.5*11.6534) / 24*11.6534

= 37.83 / 279.68

= $0.13 M