CAP rate is math calculation.

I'm here to start learning as much as I can about real estate investing in order to bolster my income with what I find to be a very interesting and enjoyable subject matter (you know us math nerds). 

Offer $780k and show the math for arriving at that price.  

Obviouslythe math is dependent on many factors but, the point is still there I believe.

The property is in Worcester, MA. The

Go find a LO that'll show you their math.

Do not cut any corners to make something look better.Always do the math analysis and try to look at the prospective properties before you make an offer or at least have a clause in the sales contract that will allow you the time (about15 days) to make a detailed inspection of the property and possibly back out of the deal without a penalty that will hurt you too much.  

If my math is right I am seeing 130k, you might see if you can refinance the current property and buy the out of market party out right and then use the remainder for down payment on the local property.  

I would like to "learn real estate math"... :) and would appreciate some advice regarding historical performance of the rental in terms of good metrics (cap rate, cash on cash, IRR et cetera, before and after tax).

Here's a few blog posts to get you started...An Introduction to Note InvestingElements of NPN Investment EvaluationEvaluating NPN Exit StrategiesDue Diligence for Notes - Tax and TitleDoing the Math on Mortgage Notes