* Increase is second time cost of project has risen
* Cost C$800 million above initial expectation
* First trains expected summer 2021, previous target 2020 (Adds details on value of contracts; SNC Lavalin shares)
TORONTO, Feb 8 (Reuters) - Quebec's public pension fund on Thursday said the expected cost of building one of the world's biggest light rail systems in Montreal had risen for a second time and was now C$800 million ($635 million) above its initial forecast.
The Caisse de depot et placement du Quebec also said a consortium led by SNC Lavalin had won a contract worth around C$5 billion to provide engineering, procurement and construction on the project. A consortium led by Alstom and including SNC Lavalin will provide rolling stock and systems through a contract worth more than C$1 billion.
The Caisse said the project was now expected to cost C$6.3 billion and would not be completed until the summer of 2021, a year later than originally planned. It had said in November 2016 the project would cost C$5.9 billion, of which it would provide C$3.1 billion with the remainder coming from Quebec's provincial government and Canada's federal government. That was an increase of C$400 million from when the project was first announced.
The Caisse is both financing and overseeing the construction of the 67 km (42 miles) public transit system in Montreal. The project breaks with a tradition of pension funds preferring to invest in infrastructure which is already built and is seen as a test case by other funds mulling whether to develop skills to manage the building of new infrastructure.
The Caisse will own and operate the track which will link several Montreal suburbs to downtown and Montreal's Trudeau International Airport once it has been built.
Shares in SNC Lavalin were up 1.1 percent at 1110 EST (1610 GMT). Alstom shares were down 2.1 percent.
Bombardier, the plane and train manufacturer based in Quebec, was not selected in the process which was overseen by an independent committee having tendered to supply the rail cars. The Caisse is one of SNC-Lavalin's largest shareholders and holds a 30 percent stake in Bombardier's rail business.
Shares in Bombardier were down 1.2 percent.
The Caisse said that construction will begin in April with initial testing of the track to be conducted at the end of 2020.
($1 = 1.2546 Canadian dollars) (Reporting by Matt Scuffham; Editing by Susan Thomas and James Dalgleish)