Refi existing house at the same time as new loan for a new house?

[Lance Luvaul]

Hi all, just wondering if I could get some insight from those that have gone before.

I bought a rental 4 years ago, payments amortized over 30 years but the lender would only give me a 5 year term (I think they have the choice to either call the loan due or renew it for another 5 year term at whatever the going rate is at the time).  So I have one more year left.

I want buy another property but I don't have enough spare cash (which is approx 10k) to cover the full acquisition costs .  But there's about 42k in equity in the rental (bought it for 100k with 30% down, it's appreciated at 3% for 4 years, so is now worth 112k which agrees with recent tax assessors appraisal).

So I have 52k (10k+42k) to work with. If my credit is good enough to secure 20% down (80% LTV), 22.4k (112k*.2) secures the existing rental, meaning I have 29.6k (52k-22.4k) left over to play with. At 20% down, this means I could buy a 148k house.

[I don't know if it's relevant to my questions (see below) but I also own two other rentals, loans held by the same bank as the first, one at 20% down and the other at 25% down.]

Now for my questions:

1. is the math right, or am I overlooking some fundamental lending practice?
2. is it possible to combine a refi with a new loan for a new house?
3. (the tricky one) will a 740-780 range FICO score secure 20% down?  (credit summary: 2 accts; #1 is authorized user [AU] acct, 12 yrs old, 35k line, $4k balance; #2 is new credit acct, 2 mos old, 8k line, $0 balance)

If after reading #3 you think I'm building credit up from scratch in the US, you'd be right: got my dad to add me as AU to his 35k acct, then opened one of my own (the 8k line), and may open a third here in a month or so (AMEX transfer from Australia).  May even get dad to add me to another one of his mature lines to boost my AAoA.  I'm just not sure if the bank will see through the AU trick.

Any and all advice, comments, observations, tips, warnings, etc welcome!

Thanks, Lance