On paper, he would be able to make $50,000-$100,000 annually on increase in value of the property he had debt on. in that timeframe, the amount he was making on paper was significantly higher than what people were making on annual salary.With that thought in mind, I would lean towards the content of leverage is King.

I really thought I would be asked to increase my offer if their were other offers.

I wouldn't trade my life for a corporate job even with a 30% pay increase. 

This of course assumes that this property was not acquired in a 1031 exchange.However, any costs incurred to acquire your mortgage (if you have one, which it sounds like you do since you got an appraisal) should be amortized over the term of your mortgage.Also, there are some costs on your closing statement that you may be able to expense immediately.Also, it's possible that you incurred some additional costs that increase your basis in the property post-acquisition or possibly even pre-acquisition.You may also have start-up costs that you may deduct up to $5,000 (assuming you don't have in excess of $50,000 of these costs), the excess being amortized over 180 months.Check with your tax professional.

Its value has increased by at least $100k since we bought it, but if we were to sell it and not do a 1031, we'd only get something like $80k back after taxes and commission.  

How much would you increase the rent by?

By day I work in the oil and gas sector as an accountant, but I'm looking to increase my knowledge related to real estate and hopefully invest in some buy and hold multi-family units for some additional long-term cash flow.

This would allow me to increase my portfolio by a home every few years if I put my rental income and additional income into more real-estate. 

I followed up and mentioned that I wanted to increase rent about $50 (~3%) minimum.

Just talk to some local lenders about what their refinancing policies are.As I see it, if you want to be able to pull all ypur money out when refinancing you either have to buy below appraisal value, do renovations that increase the appraisal value more than the reno cost, or both.You can buy properties in good condition that cash flow well, but you probably won't be able to pull all your money back out unless you are buying them well below market price.