I have been contacted because mortgage rate dropped recently. But to what extent it will be beneficial to me to do re-finance.
When evaluating a refinance, you need to figure out the payback time. Refinancing costs money in closing costs. The payback time is the time it takes to recover the closing costs with the amount of money you are saving in interest.
For example, if the closing costs are $2,000, your payback time is 2 years if it takes 2 years to save that amount in interest with the new interest rate vs. the old one.
To estimate this, look at the difference in interest rate between your mortgage and the new one, and your mortgage balance. For example, let's say that you have $100,000 left on your mortgage, and the new rate is 1% lower than your current rate. In one year, you will save roughly $1,000 in interest. If your closing costs are $2,000, then your payback time is somewhere around 2 years. If you plan on staying in this house longer than the payback time, then it is beneficial to refinance.
There are mortgage refinance calculators online that will calculate payback time more precisely.
One thing to watch out for: when you refinance, if you expand the term of your mortgage, you might end up paying more interest over the long term, even though your rate is less and your monthly payment is less. For example, let's say you currently have 8 years left on a 15-year mortgage. If you refinance to a new 15-year mortgage, your monthly payment will go down, but if you only pay the new minimum payment for the next 15 years, you could end up paying more in interest than if you had just continued with your old mortgage for the next 8 years. To avoid this, refinance to a new mortgage with a term close to what you have left on your current mortgage. If you can't do that, continue paying whatever your current monthly payment is after you refinance, and you'll pay your new mortgage early and save on interest.
It would help if we had numbers to walk you through the analysis. Current balance, rate, remaining term, and the new mortgage details.
To echo and elaborate on part of Ben's response, the most important thing is to not confuse cash flow with savings. If you have 15 years to go, and refinance to 30 years, at the rate rate, your payment drops by 1/3. Yet your rate is identical in this example.
The correct method is to take the new rate, plug it into a mortgage calculator or spreadsheet using the remaining months on the current mortgage, and see the change in payment. This savings is what you should divide into closing costs to calculate the breakeven. It's up to you whether to adjust your payments to keep the term the same after you close.
With respect to keshlam, rules of thumb often fail. There are mortgages that build the closing costs into the rate. Not the amount loaned, the rate. This means that as rates dropped, moving from 5.25% to 5% made sense even though with closing costs there were 4.5% mortgages out there. Because rates were still falling, and I finally moved to a 3.5% loan. At the time I was serial refinancing, the bank said I could return to them after a year if rates were still lower. In my opinion, we are at a bottom, and the biggest question you need to answer is whether you'll remain in the house past your own breakeven time.
Last - with personal finance focusing on personal, the analysis shouldn't ignore the rest of your balance sheet. Say you are paying $1500/mo with 15 years to go. Your budget is tight enough that you've chosen not to deposit to your 401(k). (assuming you are in the US or country with pretax retirement account options) In this case, holding rates constant, a shift to 30 years frees up about $500/mo. In a matched 401(k), your $6000/yr is doubled to $12K/year.
Of course, if the money would just go in the market unmatched, members here would correctly admonish me for suggesting a dangerous game, in effect borrowing via mortgage to invest in the market. The matched funds, however are tough to argue against.
The proper answer is that you run the numbers and see whether what you'll save in interest exceeds the closing costs by enough to be interesting. Most lenders these days have calculations that can help with this on their websites and/or would be glad to help if asked.
Rule of thumb: if you can reduce interest rate by 1% or more it's worth investing.