NEW YORK ( TheStreet) - Yahoo ( YHOO) Mail, which is the second largest email provider behind Microsoft ( MSFT) Hotmail, has seen higher competition from Google ( GOOG) Gmail email service in the last few years.Although Yahoo does not face much competition from smaller players like AOL ( AOL), it certainly sees more competition from newer players like Facebook, which has recently entered into the email service. We estimate that Yahoo Mail users, a key metric for Yahoo, have shown declining growth over the last few years. If Yahoo does not innovate to cope up with increasing competition in email service, there may be downside to the $18.53 Trefis price estimate for Yahoo stock, which is about 12% higher than the current market price. Yahoo has faced higher competition from Microsoft Hotmail and Google Gmail email service. Microsoft showed 3% growth and Gmail grew at 22%, compared to the 7% decline for Yahoo mail users during the period from July 2009 to July 2010. Recently, Facebook unveiled an email service, which is expected to be tightly integrated with the existing Facebook features. For example, it will automatically sort communication into groups, giving priority to messages from a person one has already identified as a friend on the site. Facebook's unique visitors has increased at a fast pace in the past and recently overtook Yahoo, which means that its new email service could pose another major threat to Yahoo. Due to higher competition from Gmail, Yahoo's unique visitor number has declined from 302 million in July 2009 to 281 million in July 2010. Yahoo mail users' number are important to Yahoo's display advertising business, which constitutes around 22% of our estimate for Yahoo stock. We estimate that the average monthly unique visitors on Yahoo properties have increased from around 475 million in 2006 to around 620 million in 2010, and we expect this growth to continue to 702 million by 2013. As Yahoo mail users constitutes around 45% of the total users that visit Yahoo properties, which includes Yahoo News, Yahoo Finance, etc., it becomes important that Yahoo continues to innovate in the email market, otherwise it provides a risk to our estimate for Yahoo users forecast.