@Scott Leezer, absolutely there is a way to structure such a deal. First of all, toss the word "fair". Fair is whatever all parties agree to. In fact, trying to split a deal you found right down the middle with a money partner is really not "fair" at all to you.
OK, so how do you do it? There isn't A way to do this deal, there are MANY ways. The choice depends on you, your partner and the specifics of the deal. Lacking clarification on these points, allow me to take a shot in the dark.
First, I'd like to ask you to take a deeper look at your numbers on the deal. Did you make sure you've taken into account every expense? Have you factored in vacancy? If the tenants are paying below market rents, why weren't the rents raised before now? Are you sure you can raise the rents without increasing vacancy? How long will the rehab take and what will that do the revenues?
Frankly, I'm kind of doubting your $28k/year cash flow on a 4 unit plex with $400k in debt service. What sort of rents are you expecting to get on this property. I'm assuming that you'd be looking at about $1200/month per unit. If there were no vacancies for a year and your other expenses amounted to about 1/2 of gross income. You would end up with a Net Operating Income (NOI) of somewhere around $28k, but that is NOT cash flow.
Assuming you got bank financing at a really great terms and had mortgage payments of, say, $1800/mo, which would add up to $21600. That amount would come out of the NOI, leaving only $6400/year in cash flow. Of course, maybe all my assumptions are wrong. I just don't have enough information.
OK, so let's assume I've gotten pretty close and that you split the cash flow with your investor who put up the entire $196k (because he has the money and you have little to no capital to invest.) Your investor would get $3200/yr, which amounts to an ROI (return on investment) of only 1.6%.
So, let's assume you're correct about generating a cash flow of $28k and that you split it 50/50 with your investor. In that case he would have an ROI of about 7.2%. Better, but still pretty sucky. So what does your investor want to make on his capital outlay?
Let's say your equity partner wants nothing less than a 10% return and you really do have $28k to play with. He'll need $19600 of the cash flow. That will leave $8400 for you. My for you in this case is this: Is this enough compensation to justify the time and effort it takes to generate it? If so, then this could be a good deal, but make sure your number include everything that's real today. Future appreciation and other hopeful thinking should NOT be included just to make the deal look better.
If, after all diligence, the deal doesn't produce what you thought it would, then be willing to renegotiate with the seller or back out of the deal. Don't fall in love with what "should" happen nor what you hope will happen.
I had to make A LOT of assumptions to work out these calculations. My results could be highly skewed. If you'd be willing to share more details about this particular details, I'll help you dial in the valuation. Let me know. I hope this helps.
Cheers!!