It should be long enough to show how everyone will make money over the time period. On the other hand, a plan should not be too heavy to lift. Plan ahead and have a scenario to show the potential success of the project in terms of audience approval and financial projections. You will score more points than the person who does not do this. Too many filmmakers assume that profits are not important.
Investors are gamblers and risk-takers.
By no stretch of the imagination is film a rational investment. But investors are also entrepreneurs. As such, they expect to make their money back, at the very least, and have a mega hit, at the very best. Even though financing movies is a risk, investors do not set out to throw away money. Never underestimate the influence of a good tale.