Netflix announced that it saw an increase in subscriptions in the fourth quarter, ending the year with 24.4 million members. The news helped the company’s stock jump more than 12 percent. But profits fell 13 percent as the company has continued to spend on building its library of streaming videos and expanding its business internationally. Netflix has been in need of some good news. The company has been battling to recover its footing since September, when it announced plans to spin off its DVD-by-mail service under the name Qwikster, an idea the company later scrapped.