The seller discounted the price of house a bit but asked us to transfer the lease to us (they wouldn't take it with them).

If you buy properties at a discount like I do, you can use your purchase prices to significantly reduce those assessed values, thus reducing your property tax bill and increasing cashflow. 

(No I'm not pitching myself.)This is likely more involved than a turnkey but also gives more control and more margin.

Most banks are not set up to own homes, and are often motivated to sell you the home at a discounted price."

You can drastically increase your margin by selling a finished product.  

It would effect your investment returns and profit margins because you did not account for those expenses to start with.I have only been doing this for a couple of years and still consider myself new to the game.  

I already expect all my expenses to be subjected to the 40% discount.

You then build a projection for your cash flow for however long your hold period is and then do a discounted cash flow analysis.

Determine your approximate Rehab costs and subtract it from the ARV to get your offer price.Use all the negative things (Vacancies, poor condition, Rehab/Pending CapEx, lack of data) to justify your discounting the price.  

Remember, you make your $ on the buy... you need to have enough of a margin in there to hang if/when the market dips.