When Yahoo Inc. (NASDAQ:YHOO), the No. 3 search engine, reports fourth-quarter results late Monday, investors expect an improvement from last year. The question may be whether new CEO Marissa Mayer is moving fast enough.

The Sunnyvale, Calif., search, media and advertising company is expected to report net income rose 13 percent to $335.6 million, or 28 cents a share, from the year-earlier’s $295.6 million, or 24 cents a share. Revenue is expected to gain about 4 percent to $1.21 billion, according to a Thomson Reuters survey of 30 analysts.

Mayer, 37, has only been in office seven months after leaving rival Google Inc. (NASDAQ:GOOG), the No. 1 search engine, where she’d been a senior VP. She gave birth to a son, Macallister Bogue, on Sept. 30 but barely took maternity leave.

Meanwhile, Google already reported record results, followed by those of Microsoft Corp. (NASDAQ:MSFT), the No. 1 software company, which performs many mechanical tasks for Yahoo search even as its Bing search engine is No. 2.  Facebook (NASDAQ:FB), the No. 1 social networking website, has just launched its own graph search service.

Last year, Third Point Capital, the New York hedge fund managed by Daniel S. Loeb, which owns a 6.1 stake in Yahoo, knocked out prior management and won effective control of the board because it saw untapped value in the company, especially investment in offshore sites including China’s private Alibaba Group as well as Yahoo Japan (TYO:4689).

That investment was valued at $15.4 billion, or $13.25 a share, when the third quarter ended, which may account for Yahoo’s stellar share performance: Over the past 52 weeks, they’ve gained nearly 29 percent, trading Monday at $20.32, down 5 cents.

Analyst Collin Gillis of BGC Financial sees that as a barometer for future gains, rating the shares a “buy,” with a $21 price target.

The value of the offshore investments was one reason for the Third Point investment in Yahoo. The other was Loeb’s belief that it had not properly managed its Yahoo News, Yahoo Sports and Yahoo Finance websites, among other properties. Now Mayer and her team, including a number of other Google veterans, must show they’ve attracted more eyeballs and advertisers.

Yahoo has tweaked its Yahoo Mail service and tapped some new partnerships for news with Walt Disney Co.’s (NYSE:DIS) ABC News division. But the company hasn’t spelled out much for mobile search yet, so the service still depends mainly on PCs and laptops. Sales of PCs fell an estimated 3.5 percent last year, Gartner (NYSE:IT) said.

Google, meanwhile, acquired the former Motorola Mobility to get directly into smartphones. More recently, it launched a new iOS-compatible version of Google Maps for the iPhone 5 from Apple Inc. (NASDAQ:AAPL), the most valuable technology company, after the product was shipped with a buggy Apple Maps.

Yahoo might have countered with its Yahoo Maps, long well-regarded by mobile users.

Other top items to consider will be forecasts by Mayer and new CFO Ken Goldman for the company’s first-quarter performance, full-year guidance, as well as plans for rewarding shareholders with the cash Yahoo has from its offshore investments.

Third-quarter cash and investments were $9.4 billion, which Mayer said would start to be returned to shareholders via share buybacks, which have helped boost the share price.

Meanwhile, analysts expect Yahoo to report full-year net income to jump 38 percent to $1.13 a share from 82 cents in 2011, as revenue inches up less than 2 percent to $4.45 billion. For 2013, analysts estimate Yahoo earnings of at least $1.15 a share on revenue of $4.59 billion.