Question 9.13: Financing a PV System. A 3-kWac PV system is predicted to de......
Financing a PV System. A 3-kWac PV system is predicted to deliver 6000 kWh/yr to a house that currently pays $0.12/kWh for electricity. The system, which costs $27,000, is eligible for a rebate of $4.50/Wac. If the balance is paid for with a 6%, 30-year loan and the owner is in the 37% tax bracket (combined state and federal), what is the cost of PV electricity in the first year and what would be the net economic benefit in the first year?
The net cost of the system after the rebate is
P \ = \ \$ 27,000 \ − \ {\$ 4.50}/{W} \ \times \ 3000 \ W \ = \ \$ 13,500From Example 9.11, CRF(0.06, 30 yr) is 0.07265/yr, so the annual loan payment is
\text{Loan} \ = \ {0.07265}/{yr} \ \times \ \$ 13,500 \ = \ \$ 980.78The reduction in income taxes on the first-year’s interest portion of the loan payment is
\text{Tax savings} \ = \ 0.06 \ \times \ \$ 13,500 \ \times \ 0.37 \ = \ \$ 299.70The first-year cost of electricity from the PV system is therefore
\text{Cost of electricity} \ = \ \frac{\$ 980.78 \ − \ {\$ 299.70}/{yr}}{6000 \ {kWh}/{yr}} \ = \ {\$ 0.1135}/{kWh}The net economic benefit in the first year is
\text{Benefit} \ = \ 6000 \ {kWh}/{yr} \ \times \ {\left(0.12 \ − \ 0.1135\right) \$}/{kWh} = {\$ 39}/{yr}