Question

In southern California a photovoltaic (PV) system for a certain home costs $20,250 for parts and installation. This 6.2 kW system requires 300 ft- of rooftop space and has an estimated life of 22 years. a. If this PV system saves $150 each month in electricity expenses, what is the simple payback period in months? b. If the market value of the PV system is negligible, what is the system's IRR? a. The simple payback period for the PV system is months. (Round to the nearest whole number.)

Answer 1

a. Simple payback period = initial cost / savings per month = 20250 / 150 = 135 months

b. Let monthly IRR be i%

Total months = 12 * 22 = 264 months

then 150 * (P/A, i%,264) = 20250

(P/A, i%,264) = 20250 / 150 = 135

using trail and error method

When i = 1%, (P/A, i%,264) = 92.769683

When i = 0.5%, (P/A, i%,264) = 146.396927

When i = 0.75%, (P/A, i%,264) = 114.787589

Using interpolation

i = 0.5% + (146.396927 - 135) / (146.396927 - 114.787589) *(0.75% - 0.5%)

i = 0.5% + 0.09%

i = 0.59% per month

Nominal return = 0.59% * 12 = 7.08%