Chrysler Corp. yesterday reported first-quarter profits of $507.6 million, a 28.1 percent drop from the $705.8 million that it earned in the same period last year.

The auto maker's latest quarterly performance represents earnings of $4.18 a share compared with $5.64 in the first quarter of 1984.

New-product expenses and the assumption of a full tax load contributed to the earnings decline, Chrysler officials said yesterday. The company had been excused from tax payments since 1977, two years before drastically reduced car sales and rising operating costs drove it close to bankruptcy.

Chrysler became a taxpayer again in the fourth quarter of 1984 when, saved by a combination of federally guaranteed loans and financial concessions from unions, bankers and suppliers, it moved back into the high-profit columns.

The company paid $50 million in federal and state taxes in the fourth quarter last year. Comparable taxes for the first quarter of 1985 amounted to $217.5 million.

Chrysler reported record worldwide first-quarter sales of $5.4 billion, moving past the old record of $5.3 billion reached in the fourth quarter of 1984. Sales for the first quarter last year were $4.9 billion.

Chrysler is the nation's third-largest auto maker and the second of the Big Three so far to report its first-quarter earnings. Earlier this week, General Motors Corp., the largest of the three, said it made $1.07 billion ($3.26 a share).

GM's latest quarterly performance marked a 33.6 percent decline from $1.61 billion ($5.11 a share) made in the same period last year. Ford Motor Co. is scheduled to report its earnings today.

When all figures are in, analysts expect the Big Three to have finished the first quarter with combined profits of $2.5 billion, which is 21.8 percent less than the total $3.2 billion earned by the companies in the 1984 quarter.

But the Big Three will enjoy at least two more years of overall profitability, largely because of future products that will emerge from current, costly product-development programs, said David Eisenberg of New York-based Sanford C. Bernstein & Co. Inc.

"The current expansion in U.S. vehicle sales is now 11 quarters old" and "will last another 9 to 11 quarters," Eisenberg said in his latest report on the auto industry. Ford, Chrysler and GM plan to introduce 29 new cars from 1986 through 1990, according to Eisenberg.