You'll want to consider full costs upfront and an architect + contractor team is helpful in that process.

Why not buy it with private money, borrow enough for the purchase/repairs/carrying costs, and then refinance once the repairs are done?

You should also set aside money as a reserve for vacancies, turnover costs, bad renters, or capital expenditures (roof, flooring, and other big expenses).

I realize the cost may fluctuate as time goes by. 

That'll require you to determine how much the rehab will cost and pay that up front.

There was a relatively low cost to purchase and rehad the property.

I designed a 2 bed 1 bath stacked triplex that fits on a 30' wide lot with 3' side yards and we can build it for $174 a sq ft hard cost. we do them where the land is 10% of after repaired asset value which in our market is 50k approx. we study multifamily trends and stay with it.

I showed them the whole business model and spreadsheet...We ordered the Feasibility study and appraisalThen they gave me a Term Letter that states everything even construction cost analysis by their 3rd partyThats where we are atwe have a GAP of $2.7MWe came up with the strategy last night.. that at the very least we need $1.5M cash to pay a balloon payment by June 27 or it forecloses... the lord will not let that happen.So I have the green light from the Lord to talk to all the interested investors as He is opening up the doors of Favor

It cost me 40k (20% down and 10k rehab).

This is called "costs of selling" and is added to your basis, reducing your capital gain.