Getting money out of improvements without refinancing

[Seth McGathey]

Hello, I am somewhat confident that there is no way to do what I want, but figured I would at least ask. 
My wife and I are possibly looking to make some major improvements to our house. Possibly build an additional bedroom, build a 4 season room to attach the garage to the house, and expand the 1 car garage to a 2 car garage. This all would obviously add some serious value to our house. I would likely be using a HELOC to pay for most of it. The issue is, after all of that, it would obviously be nice to pay off the HELOC by cash-out refinancing. The only problem is we have a 3% interest rate on a 15 year mortgage with only 10 years left to pay it off. I would hate to double our interest rate. So I am wondering if there is some way to pay off the HELOC with the equity we would add without refinancing our loan.
Any creative thoughts? 

[Matt Devincenzo]

Quote from @Seth McGathey:

@Ned Carey what would be the benefit of a second mortgage over the HELOC besides more time to pay it down?

You said 'get the equity out', but you keep talking not about getting equity out but lowering the borrowing costs on the new improvements. The cost of the build itself isn't equity, it's borrowed funds which it sounds like you want to lower the cost of paying that back not get more money out of the increased value of the home. Is that right? 

The benefit of a fixed second is/can be two things 1) you can get a fixed rate vs. the HELOC floating rate...though often HELOCs will include an ability to fix rate the balance as of a specific date if you request it 2) the rate on a fixed product is often just a little lower, so you can save a bit of your borrowing costs.

Another thought on the refi, 'ignore' the 3%, that's a tail wagging the dog analysis. It's cheap money so you want to irrationally keep it. You need to do a weighted average on both the rate and the term. If you owe $200K at 3% for 10 more years, and your HELOC payback is $200K at 9% for 20 years, then you (simple math here) have an effective $400K at 6% for 15 years. This ignores the time value of money on the different amortization schedules, but I think you can see the concept. 

Once you know that info, now the analysis is, can you refi at a new 15 year for 6% or better? If so then dig more into the benefits of a refi vs. keeping the low rate 1st and getting the guaranteed return of paying the higher rate second off aggressively. If not then focus on options to get the best rate/terms on the second that you possibly can.