A new Forth crossing is to get the go-ahead at Holyrood this afternoon, as John Swinney announces plans for the vast construction project and sets out his plans to pay the billions of pounds it will cost.

The Finance and Sustainable Growth Secretary is to tell MSPs the decision reached last night by the Scottish Cabinet. It is thought a strong likelihood that he will announce a bridge will be built to the west of the current Forth Road bridge, rather than a tunnel under the firth.

The higher cost and uncertainty of boring a tunnel or immersing a tube under the river makes the options of a bridge more attractive to ministers. According to Transport Scotland's estimates, the options for a tunnel would take at least five-and-a-half years to construct and would cost between £2.1bn and £2.3bn.

Bridge options could take less time, with a cable-stay bridge costed at £1.5bn and a suspension bridge, similar in design to the current road crossing at Queensferry at £1.7bn.

Those were the costs when design options were presented in a public exhibition in the Lothians and Fife during August and September. But the full cost, with road links and at the 2016 prices when the crossing is scheduled for completion, looks far bigger: £2.5bn to £3.5bn for a bridge, or £3.6bn to £4.7bn for a tunnel.

That raises awkward questions for Mr Swinney about how the costs should be met. If it is to be paid fully by the Scottish Government, the money will have to be found during the years the crossing is under construction, dwarfing the current transport budget. Other options include borrowing against the projection of future tolls or the use of private finance, but the Scottish government has been against the use of both.

The current road crossing was opened in 1964 and is suffering from corrosion. Unless the suspension cable can be repaired, engineers estimate it will have to be closed to heavy vehicles by 2013 and to all vehicles five years later.