A common structure is to give equity investors a preferred return on the project's cash flows, with the balance divided between LP and GP and then a split of the profits after investors then the sponsor's investments are returned upon disposition or refinance.
The preference (or pref) is the investor's first claim on the cash flow (NOI less debt service), usually stated as a percent of their investment for instance 7-1/2%. So an equity investor with a $1million investment would get the first $75k of cash flow, anything above that would be split at the agreed rate between the sponsor (GP) and the investor (LP).
If there isn't enough cash flow to cover the pref the portion not distributed is added to the investor's investment total to be paid at disposition. Depending on the terms these shortfalls can be compounding too so that the LP gets the first 7.5% on their initial investment plus any shortfalls from the previous year(s). This can get to be quite expensive for the GP who isn't hitting their projections.
At disposition or refinance the LP typically receives their investment plus any pref shortfall back, then the GP gets their investment back and finally the remainder is split. The split can be a fixed ratio, say 60/40 or it can have a waterfall structure where the ratio changes more in favor of the GP the higher the returns are. The waterfall thresholds can be set at certain LP IRR returns or multiples (2X, 3X, etc) and can be quite complicated to model so it is important to lay out clearly with dollar figures who gets what when with waterfall structures.
Note that the split of cash flow above any pref can also have a waterfall structure. These waterfalls can be great but they can also start with very low GP splits that really incentivize you to exceed your projections too.
What the terms including the pref, splits, compounding and thresholds are is subject to what you as the GP negotiate with your LPs. If the LPs are institutional investors such as a pension fund or private equity they'll typically demand better terms than you might negotiate with friends and family and it's really important to correctly model out the waterfalls so both parties know what to expect.
If no institutional equity is involved a simple structure is easier to explain, track and distribute. For instance Cash Flow: 7%pref non-compounding with anything above that split 50/50; Proceeds: LPs get 100% investment plus any pref shortfalls back, the GP gets 100% of their investment back then balance is distributed 60% LP - 40% GP.
Make sure to include enough of a asset management fee in the expenses so that you don't starve during the life of the project, neither you as GP or your LPs want you to go out of business midway.
I would definitely get professional help structuring and modeling your terms to make sure you don't box yourself into a corner where you make nothing or worse get sued by your investors. That's in addition to having an experienced securities attorney making sure you're good with the SEC and any state regulators where you, your investors and the property are located.
Good hunting-