The rise to a five-year high added £1.3 billion to the com-pany's stock market worth which now stands at £20.9bn.
The update was published a day after BT revealed it had hired Clare Balding as a sports presenter as it seeks to persuade more customers to subscribe to its television products.
Mr Livingston, who is also a director of Celtic Football Club, said: "We have made progress in a number of areas and delivered solid financial results."
Richard Hunter, head of equities at Hargreaves Lansdown Stockbrokers, said: "As it sprawls out into becoming something of a media company, BT continues to show its strength in its more traditional markets."
BT said its underlying pre-tax profit in the three months to December 31 rose 7% to £675 mil-lion, ahead of what the market had expected. Revenues were down 6% at £4.5bn but the business was helped by continued cost cutting. It was also boosted by demand for broadband which it sells directly to consumers and as a whole-saling service to rivals.
The group said it now has the biggest fibre broadband network in Britain, after overtaking Virgin Media.
"Our fibre plans are helping to make the UK a broadband leader in Europe. More than 13 million premises can access our fibre broadband and we are passing around 100,000 additional premises every week. Take-up is growing strongly with around 1.25 million homes and businesses now enjoying the benefits of faster speeds. This gives us an excellent platform for our push into TV and sport," Mr Livingston said.
BT recruited 21,000 more customers to its BT Vision tele-vision service in the quarter and now has more than 60,000 customers with a YouView box that gives access to catch-up television.
It hopes the launch of its BT Vision sports channels with football and rugby will encourage others to upgrade to the faster and more expensive product.
Last year, BT paid £738m to show 38 English Premier League football matches.
Earlier this week the company revealed it had signed up Olympics broadcaster Balding to present a weekly sports show.
With £1.9bn of new orders – a 17% increase, BT Global Services, the group's division which deals with multinational corporations, also looked to be performing strongly after problems with unprofitable contracts.
Among its deal wins was a mandate to update technology at Edinburgh city council's education service.
At BT's retail business, revenues fell 3%, in line with the previous quarter as customers made fewer calls and line revenue fell although this was partially offset by growth in broadband.
It took on another 122,000 retail broadband customers, accounting for 44% of the market.