It is feasible to go for a refinance when you have built up at least 10% equity in your home (For Fannie Mae owned mortgages, the value is 5%). It is also possible for you to choose the option if your equity is less than 5%, but you may have to pay a certain amount of cash in order to make up for the difference in equity.
Refinancing is not the only way to decrease the term of your mortgage. By paying a little extra on principal each month, you will pay off the loan sooner and reduce the term of your loan. For example, adding $50 each month to your principal payment on the 30-year loan above reduces the term by 3 years and saves you more than $27,000 in interest costs.
If your property value reduces and you refinance up to 80% of the reappraised value, your original mortgage amount may be higher than this amount. Thus, the new loan will not be sufficient enough to help you pay down the existing one.
It's better to follow the 2% Rule which suggests that you can enjoy the benefits of a home refinance if your mortgage refinance rate is 2% lower than that on your current loan. The interest savings will help you recoup the costs you've paid for the new loan provided you stay in the property for a certain period of time (break-even period). However, there are no-cost as well as low-cost refinance loans wherein the costs are included into the loan. But you can expect comparatively higher rates on such loans. Moreover, these loans are limited when the market is in a credit crunch.