The value of your house is one of many parts of the refinance puzzle.

You're not necessarily subject to the mortgage interest rate that you've got, and your house could be a big factor in getting a better one. But did you know that shopping around could improve your terms even more?

While you're pinching pennies and planning out a budget for the coming year, stop and think about how a lower interest rate could help. With a strong home value and a choosy mindset about where you refinance, 2016 might be your best year yet.

You Can Shop for Your Own Mortgage

A home mortgage refinance serves as a vehicle for getting better loan terms. Not everyone can qualify, but those who do often walk away happier. If your home has increased in value, which is typical now that the market is improving again, your chances at a refinance are even better. And if you're picky about who gets your business, that's the best situation of all.

Surprised that you have a choice? Realty Times suggests that a lot of people are, or at least many think that choosing is only for the wealthy with perfect credit. You can talk with your bank, or you can work with a mortgage broker who does the searching for you exchange for a fee. But also have the right to shop around for the best rates.

Not only can you shop for the best lender, you can probably negotiate the best overall refinance plan for your situation. Most lenders have different programs and a range of interest rates to work within. Your credit is a factor in what you'll be offered, and so is the value of your home. You may also have the option of paying a fee in exchange for a lower rate.

A lot goes into determining the value of any house.

Your Home's Value Plays an Important Role

It's easy to think about a mortgage as your agreement with a lender to make payments every month. But those payments all circle back to your home. Except in usual situations, such as buying a home well below the market price, your home's value is what your original mortgage was based on. It's what any refinance deal will be based on, too.

The value of your home partly determines what interest rate you'll qualify for with any lender. If you have a lot of equity, Bankrate says you'll stand a better chance of getting a better rate. That's because less equity means a higher loan-to-value ratio, which carries a higher risk. A 100 percent loan-to-value ratio means the house is worth exactly the amount of the loan. That's rare. An 80 percent loan-to-value ratio means your house is worth about 20 percent more than the amount of the loan. That's more common.

You might qualify for a new loan with a higher loan-to-value, but you might also need mortgage insurance, which is an additional cost, and you'll probably get a higher rate than you want. A lower loan-to-value ratio means your home is worth considerably more than the amount being financed. That's a favorable situation for the lender, and it's favorable for you because you won't need mortgage insurance and you'll probably get a better rate.

You have a lot more say in who refinances your home and under which terms than you might have thought. There's nothing wrong, and a whole lot right, with talking to several lenders before making your decision. Your credit won't be negatively affected by shopping around, but your 2016 household budget might be a lot more comfortable.

The value of a home carries a lot of weight in any refinance. If you decide to move ahead, you'll likely have an appraisal before the process is complete. But a house valuation, which is what eppraisal does, is free and it can tell you in advance whether a refinance is worth pursuing.

Get a free property valuation today, and learn what your house is worth and how it compares to those around you. If the numbers are right, you could be on your way to a refinance that saves a lot of money.

Wondering whether refinancing is a good idea? Check out this mortgage article, 4 Top Reasons to Refinance Your Home.