The question implies that you are considering refinancing into a loan that may have higher monthly payments than your current loan, but has a lower interest rate and/or a shorter term than your current loan. It also implies that there is no need for cash-out during the refinance. Start with the following steps:
Here is a sample scenario. Assume the current loan is a 30 year fixed at 7%. If the original loan amount was $200,000, the minimum principal and interest payment would be approximately $1,330.60. If you've made 5 years of minimum payments, the current principal balance would be approximately $188,262.83. Assuming that with closing costs the loan amount for the new loan would be $192,000 and the rate was 6% on a 15 year fixed, the minimum payment on the new loan would be approximately $1,620.21. What if, instead of refinancing, you took that extra $289.61 and made extra payments on your current loan?
15 years from now the new loan would be paid off, but you would still owe $22,802.13 on your current loan if you made the extra payments. Clearly, refinancing would save you money if you were going to be in the home 15 years or more. What if you don't expect to be in the home so long? When would you break even on closing costs? After two years and 3 months, the principal balance on the new loan would be $172,956.92 while it would be approximately $173,045.64 if you made extra payments on the current loan. After that the difference only gets more compelling. So, in this example, if you plan to be in the home less than 27 months you should not refinance, but you can make a compelling case for it if you plan to be in the home longer.