LONDON -- I believe the shares of security group G4S (LSE:GFS) should continue their impressive ascent of recent months. The gigantic firm, which has more than 340,000 employees spread across more than 100 countries, is ready to rocket still higher on accelerating activity in new territories.

Indeed, broker Investec has hiked its price expectations for the firm to 330 pence from 280 pence in recent days, representing 16% upside from current levels.

Olympic struggle at an end
G4S announced last week that it had reached a financial settlement with the organizers of the London 2012 Olympic and Paralympic Games. The final sum -- owed as a result of the company's inability to adequately staff the events -- will cost some 70 million pounds, up from the previously estimated 50 million pounds.

Last year's sporting fiasco caused G4S' shares to shake frantically at times, exacerbated by the loss of a number of public-sector opportunities with the U.K. prison and police services. However, with the Olympics fiasco now at an end and possibilities in new geographies picking up pace, the company's valuation looks primed to shoot higher.

Developing markets are now responsible for more than a third of group revenues, and the company is aiming to hike this proportion to 50% in the medium term. In November, G4S reported organic growth of 9% in emerging markets in the nine months to September, powering the 5.5% rise across all markets. Further, the company has committed 200 million pounds for merger and acquisition activity from this year onward, which should supplement solid organic expansion.

Earnings ready for the high jump
City analysts expect G4S to bounce back after a difficult 2012, during which earnings per share are expected to have dipped 2% to 22 pence. Indeed, a double-digit comeback is anticipated for both 2013 and 2014.

The security specialist is also expected to offer increasing value for money: A P/E ratio of 12.7 is predicted to fall to 11.3 this year and 10.3 in 2014. This is reinforced by an inviting P/E-to-growth reading, which is forecast at 0.9 this year and 1.1 next year. A value below one is generally considered decent value for money.

The inside track to growth elsewhere
A peachy dividend yield strengthens the G4S investment case. Last year's 3.1% is expected to rise to 3.3% in 2013 and 3.6% in 2014, according to City estimates.

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Royston does not own shares in G4S. The Motley Fool has a disclosure policy. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. Try any of our Foolish newsletter services free for 30 days.