That is the only way this loan or property would actually work mathematically. 

The best IRR mathematically ia a city that has a default cap rate ( lets say  8-9%) and within 5 years is decline into 6-7%. range That's the fastest declining cap rate possible from a historical standpoint.

The problem is that in a $150,000 purchase, $75 seems insignificant, and mathematically that is correct, too.

I have a degree in Mathematics.

If you read my first post - I may be only putting $2,000 down initially... so to use his calculations it would be 3600 (assuming 300/month cash flow per unit of the duplex I'm looking at) / 2,000 (total money down)= 180% Cash on Cash ROII'm a Mathematics major and teach Math...

If that is correct it would probably make more sense mathematically just to cash out refinance that property at a fixed rate and use the proceeds to fund other investments.Best of luck in the future.Cheers,

With regard to the numbers you posted, all other things being equal, it wouldn't make ANY sense mathematically to ever purchase a house that needs $60k worth of renovations when you could buy one that's already renovated for only $20k more.  

mathematically the cash for keys idea is a great financially.

Mathematically, in an appreciating market, you will likely be better off with a 30 year mortgage in almost every case.

I am currently a mathematics lecturer for a local college and a part time realtor.