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Boosted by sales of hot-weather merchandise and lower operating costs, profits at Sears, Roebuck and Co. grew 11.1 percent in the second quarter, the retailer reported Thursday.

Sears said net income in the quarter rose to $559 million, or $1.41 a share, from $503 million, or $1.27 a share, in the year-earlier period.

Meanwhile, Northbrook-based Allstate Corp., in its first report since separating from longtime parent Sears, said net income in the quarter increased 29.1 percent, to $519.1 million, or $1.15 a share, from $402 million, or 89 cents a share, in the year-earlier period.

The insurer’s operating income, however, dropped 2.9 percent, to $347.3 million from $357.5 million in the year-earlier period.

The auto and life insurance company attributed the lower operating income to a high number of catastrophes, including the Texas hailstorms that cost the firm $130 million.

The rise in net income reflected improvements in the life business and the sale of 70 percent of the PMI Group Inc., which led to an after-tax gain of $93.4 million.

The Sears figures include results from two discontinued operations: its 80.3 percent stake in Allstate, which was spun off to Sears shareholders June 30, and its commercial real estate subsidiary, Homart, which is expected to be sold in the current quarter.

Excluding Allstate and Homart, Sears’ second-quarter net income increased 14 percent, to $218 million, or 54 cents a share, from $191 million, or 47 cents a share, in the year-earlier period.

Revenues from the continuing operations rose 5 percent, to $8.2 billion from $7.8 billion. Merchandise sales and services climbed 4.7 percent, while credit revenues increased 7.1 percent.

The cost of operating its domestic stores improved, falling to 22.5 percent of sales from 23.6 percent.

Commenting on what could be his final quarterly report after a 38-year career with Sears, Chairman and chief executive officer Edward A. Brennan said he was “particularly pleased with the condition of the company.” Brennan has announced that he will retire from his posts after the complete divestiture of Sears’ subsidiaries and a transition period.

Sparked by a “very strong” July 4th weekend, along with blistering temperatures that ignited sales of air conditioners and hot-weather clothing, Sears’ retail performance “continued to be strong in a very difficult market,” Brennan said.

The rate of growth in same-store sales slowed in the second quarter to 3.2 percent from 9.7 percent in the year-earlier period. Same-store sales are sales at stores open at least a year.

While second-quarter losses in international operations doubled to $2 million from the year-earlier period, Brennan said he was “optimistic about international in the long run.” Citing the slowdown in the Mexican economy, Brennan said that “the next year or two could be rocky, but we’ve been doing a little better there and, long term, we expect business to be good.”

Brennan called Allstate’s second-quarter results “superb.”

For the six months, Allstate’s net income soared to $1.1 billion, or $2.36 per share, from $126.8 million, or 28 cents per share, in the 1994 half, when claims from the California earthquake cost the insurer $1.2 billion.

Operating income in the half totaled $803.1 million; in the year-earlier period, Allstate lost $9.9 million.

Sears’ net income for the first half of 1995, including the discontinued operations, was $1.12 billion, or $2.82 a share, up from $405 million, or $1.01 a share, in the 1994 half, which reflected Allstate’s losses due to the California earthquake.