Nereo, I appreciate you helping me to break this down (although I'm still not quite sure how to set up the equation myself).

I have another question though, related to the 15 year vs 30 year refinance. From an expense perspective, if I'm forecasting spending 30K in ER, and currently 650 a month for the next 20 years is going to that, then in 20 years my expenses should drop by 7800, so instead of 30k I only need 22.2K a year. That means in 20 years my stash doesn't have to be nearly as big right? (Not that it wouldn't be, just trying to understand.)

In the other scenarios (15 year vs 30 year), the expenses drop differently. In 15 years, (with the 15 year refinance), my expenses drop to 22.2, so that's 5 years sooner that my stash can be "smaller".

For the 30 year, my immediate expenses go down today to 28.6K, (and I add 12K to my stash before FIRE) but expense doesn't drop off to 22.2K for 30 years. That "delta" could affect how much money I actually need to accumulate in my stash right now.

How do I set up the equation to evaluate all these variables so I can put actual numbers to them? (Hopefully that makes sense!)

Sure.

There's two things going on here that will affect your calculations. #1) your debt will be held in 2016 dollars while #2) your WR will be adjusted upward for inflation each year.

Above, you've said that your mortgage costs $7,800/yr ($650/mo) and concluded that in 20 years your necessary expenses will drop down to $22.2k (you subtracted $7800 from $30,000 to get $22,200). However, the math doesn't work out that way because of inflation. We can't predict what inflation will be, but for the moment let's assume that it's 2% per year. Following a normal 4% WR you will adjust your withdraws each year to match inflation.

HEre's what it what that will look like in non-adjusted terms:

Year 01: $30.0k - $7800. Mortgage = 26.0% of expenses

Year 02: $30.6k - $7800. Mortgage = 25.5% of expenses

Year 05: $32.5k - $7800. Mortgage = 24.0% of expenses

Year 10: $35.9k - $7800. Mortgage = 21.8% of expenses

Year 15: $39.6k - $7800. Mortgage = 19.7% of expenses

Year 20: $43.7k - $7800. Mortgage = 17.8% of expenses

Year 21: $44.6k - $0000. Mortgage paid off. Note: in real adjusted terms this is exactly the same as having $30,000 in 2016.

Now this is a pretty rosy picture where inflation never rises its ugly head. Historically, the mean inflation rate has been closer to 3%, with occasional multi-year sorties into 5%+. If we create a scenario where inflation is higher things are even more dramatic. Your ability to pay off debt becomes easier each year, because it's a lower percentage of your total budget. If you take the 30 year term with moderate inflation estimates (~3%) the portion of your mortgage will be just ~11% of your budget towards the end of your term.

To get to your other question - you are correct that once that debt is gone, you can survive on a smaller stache. However, there's no good formula for calculating this because the returns over 20 years will be far from uniform. A much better idea is to use FireSim to see how your success rate would change after x# of years when your debt goes away.

I haven't touched on the added $12,000 in your portfolio from increasing your savings over hte next four years because of the refinance (and since I'm on a tablet I'm not likely to do it right now). But suffice to say it adds a healthy chunk to your overall bottom line.

A single caveat: Having a mortgage assumes we don't suffer the economy-crushing deflation. I haven't tried to model this because I honestly don't know how market returns would fare over such a period (there's little historical evidence to go by for an extended period of deflation).