By Jacob Bunge And Chelsey Dulaney 

DuPont Co. projected declining sales across most of its divisions over the coming months as the chemical company jousts with an activist investor ahead of a key shareholder vote next month.

The strengthening U.S. dollar, slowing corn-seed sales and weakness in some chemical prices likely will remain challenges to DuPont's agriculture and chemical divisions, executives said on Tuesday as DuPont reported a 28% drop in first-quarter earnings.

DuPont's results, which topped analysts' expectations, came as Trian Fund Management LP prepared to host a town-hall meeting with investors in New York on Tuesday. The Nelson Peltz-led activist firm for months has sparred with DuPont over strategy and structure, arguing that the chemical giant's board of directors needs to push management to streamline operations and potentially break up the 212-year-old company. Shareholders will vote May 13 on director candidates nominated by Trian and DuPont's own slate.

Chief Executive Ellen Kullman said in an interview that DuPont's pipeline of new agricultural pesticides, improving sales volumes in safety products and stepped-up cost-cutting efforts reflected a bright future and would resonate with investors.

"I tend to think about the proxy as not just a short-term, one-quarter issue," Ms. Kullman said. "It's about where we are going, and how we create value for shareholders."

DuPont, which has a market value of about $66 billion, reported first-quarter profits of $1.03 billion, or $1.13 a share. That was down from $1.44 billion, or $1.54 a share, a year earlier.

Excluding pension costs and other items, operating earnings were $1.34 a share. Currency shifts trimmed 25 cents from per-share earnings, DuPont said.

DuPont's revenue slipped 7.6% to $9.37 billion. Analysts polled by Thomson Reuters had expected a profit of $1.31 a share and revenue of $9.41 billion.

DuPont shares were 3% lower at $70.65 in midday trading.

Ed Garden, Trian's co-founder and chief investment officer, told a gathering of investors and analysts Tuesday that DuPont's earnings were "simply not good enough" and showed why Trian needs to be on DuPont's board. The firm owns about 2.7% of DuPont shares.

The activist firm said DuPont has a history of beating analyst targets in its first quarter, which Mr. Garden called the most important period, but then failing to hit estimates for the rest of the year. Mr. Garden said Trian believes that DuPont will miss even the lower end of the company's guidance this year.

"It's all about earnings," Mr. Garden said. "That's why Trian and these board nominees are here."

The U.S. dollar's strength against other currencies has made DuPont's seeds, crop sprays and chemical products more expensive for overseas buyers and will remain a challenge in the second quarter, the company said.

The Wilmington, Del., company forecast operating earnings from its agricultural unit would decline by low- to mid-single digit percentage points in the second quarter after the division's earnings fell 21% in the first quarter, partly due to currency shifts and a further reduction in corn planting as North American farmers shift more fields toward soybeans. Corn generates the bulk of big seed companies' sales.

Second-quarter sales in DuPont's performance materials likely will be down by a "low-teens percent" due partly to lower ethylene prices and currency shifts, the company said, though earnings would increase in mid-single digit percentage points as sales volumes improved.

Ms. Kullman said DuPont is focusing on rolling out new and better products to help combat the foreign-exchange challenges, and hastening already-planned cost cuts. DuPont estimated Tuesday that expense reductions would improve its 2015 results by 40 cents a share, versus 35 cents projected in January.

"We look at every knob we have" to turn on expenses, she said.

Ms. Kullman and other senior DuPont officials have been canvassing shareholders in recent weeks ahead of the company's annual meeting, when shareholders will vote on the slate of 12 DuPont directors, including Ms. Kullman as chairman, along with four director candidates nominated by Trian, which include the firm's CEO, Mr. Peltz.

"To me, this is an opportunity," Ms. Kullman said. "I've been an underdog all my life, and I will continue to get out and represent the future of our company to shareholders."

Dave Benoit contributed to this article.

Write to Jacob Bunge at jacob.bunge@wsj.com and Chelsey Dulaney at Chelsey.Dulaney@wsj.com

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