How to convince the banker in terms of coherence, viability and the sustainability of the activity?

A banker always based his/her opinion on some documents. If you are applying for financing for some activity you have to have:

A viable Financial Projection, ensure this projections is in line with your business experties and that can generate enough profit and cash flow to pay off their liability within a specified period. 

Any sustainable business model is more valuable than short term focused ventures. Value of any venture depends on expected returns and risk associated with returns. Sustainable businesses have lesser risks associated with their future earnings. Triple bottom line reduces uncertainty in availability of factors of production and also accessibility to potential customers. Hence in long term, a sustainable business would always comes out as a winner.