The biggest proxy fight in history, pitting activist investor Nelson Peltz against Procter & Gamble Co., will also be one of the most expensive.

The two sides expect to spend a combined $60 million on the contest for a board seat at the Cincinnati-based company, according to separate regulatory filings this week by P&G and Peltz's Trian Fund Management. Peltz estimated his firm will deploy $25 million to gain access to the consumer-products company's boardroom, while P&G said it budgeted an extra $35 million to keep him out.

The driving force behind the high spending will be reaching the millions of individual investors who own P&G shares, said Tom Ball, a managing director at Morrow Sodali, a proxy-solicitation firm. Peltz, 75, suffered his first-ever loss in an activist campaign in 2015, when he tried to get on the board at DuPont Co., another old-line company that is widely held by mom-and-pop investors.