(Adds estimates in paragraph 2, copper context in paragraph 3-5, investment plan in paragraph 6, background in paragraphs 8-11)

MEXICO CITY, July 27 (Reuters) - Mining and rail conglomerate Grupo Mexico, one of the world's largest copper producers, reported on Thursday a 38% rise in second-quarter net profit on higher copper sales and solid results from its transportation unit.

Earnings hit 11 cents per share, beating the Refinitiv estimate of 9 cents a share.

Sales of copper, which account for the majority of the mining division's operations, rose nearly 13% from the year-ago quarter, with production up 9.2% in part because of higher ore grades at its Toquepala mine in Peru.

The rise in revenue came despite copper prices dipping 11% from the same time last year to an average of $4.34 a pound, said Grupo Mexico, which is controlled by Mexico's second-richest person, billionaire German Larrea.

The company said it aimed produce 1.048 million metric tons of copper this year, slightly above the 1.007 million metric tons produced last year.

Grupo Mexico also bumped its investment plan for the year up to $1.83 billion from the $1.76 billion previously estimated, saying the funds would go to various improvement and expansion projects.

The firm's overall revenue during the April-to-June period rose almost 8% to $3.45 billion, it said, also propped up by increased volumes moved by its transportation division, Grupo Mexico Transportes.

The company operates two major freight rail companies in Mexico.

In June, Mexico's president announced a deal with Grupo Mexico to compensate it after the government expropriated a section of railway it operates in southeastern Mexico.

President Andres Manuel Lopez Obreador, who has often clashed with Larrea, ordered the takeover of the rail line because it is located where he aims to create a trade and freight corridor between the country's Pacific and Gulf coasts.

As part of the accord, Grupo Mexico's concession in the area was extended by eight years. (Reporting by Carolina Pulice and Noe Torres; Editing by Kylie Madry, Isabel Woodford and Jamie Freed)