Cash Out Refinance Tax Implications

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We've just completed our second out-of-state rental purchase and with the recent rate cut our lender suggested a re-finance on our primary residence (he's hustling for money, good for him I guess. lol). That should be fine and would theoretically make sense at face value, however I started to wonder if we could pull out enough equity to pay off the most recent mortgage we just did and have that property start funding the next investment. But then I started to wonder if this would have implications on the tax deduction of our primary residence mortgage?

Here's the details:

Primary Residence: Bay Area - $1mil

Mortgage: $630k @ 3.9%
Cash-out Re-fincance: $730k @ 3.625%

So we're staying under the $750k cap for new mortgages, which I believe means we're in the clear? The principle of the re-fi is just a bit over the initial loan amt. so I'm assuming we don't get grandfathered in, but again if I'm reading things right that really doesn't matter? The thing that makes me question is that HELOCs have a limitation that the cash must be used for substantial renovations, which in this case we wouldn't qualify, but since this is a cash-out re-finance those limits don't apply?

The long-term goal here is that if we get 4 of these units free and clear then we've got this primary mortgage covered and I'd feel safe turning to investing as our only income, so the faster I can get these paid off the closer we are to that goal.

@Scott B. taking out a loan is not a taxable event. You owe someone money, that's not income. This is one of the most attractive things with RE - after you have paid off a mortgage and you take out a new one, there is no income tax and you can brun the money in Vegas as far as the IRS is concerned. You still have a new loan to pay back. Different if you sell the property you own free and clear: the funds your receive ar subject to long term capital gains and also you have to recaputure your depreciation write off's (because it actually did not depreciate). A HELOC is different, typically you can also do with the money as you please. Also not taxable, because it's a lone. But of course you have to pay it back. Often you have a ten year draw period with interest only and you can move money in and out as you please. Then it converts into a regular loan and with a pay off period. Find a few great local banks and ask them to quote you both!