The Green Building Fund (GBF) established in 2008 as part of the Clean Business Australia initiative is aimed at mitigating the risk of climate change by forming close partnerships between government, business and industry. It is specifically targeted to reduce the impact of the built environment on Australia's greenhouse gas (GHG) emissions by reducing energy consumption through the operation of commercial office buildings. As part of the selection process, projects are assessed against three merit criteria: the potential reduction in GHG emissions, demonstration of potential, and quality of project design and management. An alternative framework is proposed that contributes more rigour to the current selection process. In particular, it contends for the use of second-order moment and Markov chain to establish the present worth and feasibility of green investment where the underlying parameters of interest/discount rate and cash flows (in terms of savings) are uncertain. This framework will be useful not only to AusIndustry (the funding body of the GBF) and other government departments worldwide responsible for awarding green building funds but also to owners who are keen on strengthening their application by improving the demonstration of project feasibility.