When the costs of the thing are so low that you can live free off the rent that the other unit is generating, it adds to your life.I would recommend reading Set for Life by @Scott Trench and looking at his data about living in duplexes.

The seller is giving me a one year home warranty.As someone who has never bought a house a 20k renovation right off the bat feels very scary.

This affords the opportunity for a homeowner to sell the property if it is not under water for market value and pay off the loan before they are foreclosed upon, or more commonly, short sale the property with the bank's approval. 

I have no credit debt and $12,000 of student loan debt I'm looking to pay off within the year.

High yield savings, pay off debt, 401K, etc.?

This duplex was purchased off-market, bundled with another duplex for below market value (off-market).

No leads so far.This is summer where most of the students are either off on holidays or have an apartment.It is a 1 bed, 1 bath.

Because the market is difficult right now, it may take much longer to buy your next property, but you will be better off saving and investing from a position of strength rather than borrowing money to borrow more money.

Would be too far off to assume a a rehab cost of $40k?

. - 6% cap rate reflects a nice safe part of Los Angeles, California, a prudent investment, not one that will make anyone rich overnight, but a place that higher net worth individuals park wealth to preserve it (imagine the depreciation write-off). 6% cap rate also tells us, right off the bat, that we're going to be in the ballpark of 60% LTV.- We will stipulate that this is hypothetical.