Calculate the payback period for a PV system with $6000 cost after tax rebates, an output of 2000 kWh/year, $0.13/kWh cost of electricity, and MARR^{2} = 2%.
Chapter 10
Q. 10.5
Step-by-Step
Verified Solution
From above, the ratio P/A is 23.1 to the nearest tenth. Recalling P/A as a function of i and N:
P / A=\frac{\left[(1+i)^{N}-1\right]}{i(1+i)^{N}}=\frac{\left[(1.02)^{N}-1\right]}{0.02(1.02)^{N}}=23.1
Rearranging terms to solve for N gives
(1.02)^{N} = 1.859
Thus N = 31.3, or 31.3 years is the length of the payback period. Even with a relatively low MARR of 2% (i.e., the owner is willing to forego earning return on investment at market rates), the payback period has increased by over 8 years.
Note that the long payback for the system, whether simple payback or with MARR = 2%, is a function in part of the relatively low insolation in the region. As an illustration, in a sunnier region which averaged 125 kWh/kW/month downstream from the inverter, the simple payback is reduced to 14 years, all other things held constant.