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1As investment in residential photovoltaic systems is increasing at a rapid pace, it is important to 2 investigate whether delaying or otherwise timing these investments can maximize long term 3 investment gains. Conventional financial analysis methods for evaluating investment decisions in 4 solar-electric system are all based on a one-time installation of the PV systems and cannot be applied 5 to analyze the benefit of delayed and staged investment. Such benefits could be declining costs of PV 6 systems thus tempting investors to hold off and wait for a better moment to invest. This paper 7 proposes a decision making framework using the real option method to analyze the optimum time to 8 invest in a residential PV system in different scenarios. A reference residential house is used to test 9 the effect of different investment strategies. The results show the type of staged investment of 10 installing residential PV system that maximizes the long-term payoff. This reveals when the option to 11 delay investment is preferred. The supporting source code and data are available for download at 12 https://github.com/reisiga2/SolarPanelInvestment. 13 Programming 15 INTRODUCTION 16The U.S. building sector accounts for seven percent of world's total energy consumption, which 17 corresponds to 41% of the total energy usage and approximately half of the total greenhouse gas 18 (GHG) emission in the United States [1][2][3]. This high-level of energy usage suggests that investing in 19 building energy efficiency retrofits can effectively reduce a significant amount of energy 20 consumption and ozone depletion caused by GHG emission at relatively low cost. In particular, 21 investing in retrofitting residential buildings, which account for 54% of the building sector's 22 energy consumption [1], can make substantial contribution to the energy reduction. From the 23 3 individual homeowner perspective this will reduce the household's energy usage, environmental 24 footprint, as well as its energy bills. 25As one of the fast-growing emerging sustainable energy resources, solar energy has attracted 26 increasing attention worldwide. Recent decades have shown an increasing trend of implementing 27 photovoltaic (PV) systems in residential houses [4] as the PV system can partially or entirely fulfill 28 the household's electricity demand from a nonpolluting energy resource. However, effective 29 implementation of residential PV system requires the owner to make a large initial investment. The 30 return on this investment is affected by several uncertainties, such as future energy retail price and 31 technology costs, PV system performance, and house energy demand volatilities. These uncertainties 32 cause difficulties in the investment evaluation exacerbated by the limitation of traditional investment 33 techniques such as Net Present Value (NPV), Internal Rate of Return (ROR), and Discounted Cash 34 Flow (DCF) analysis [5-8]. These investment evaluation methods cannot provide an insightful 35analysis of the financial benefit because...

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