Ford Motor Co. yesterday reported a fourth-quarter profit of $721 million, pushing fiscal 1984 earnings to a company record of $2.9 billion in a showing that will help push the 1984 profits of Detroit's Big Three car makers to nearly $10 billion for last year.

General Motors Corp. last week reported a record year-end profit of $4.5 billion. Chrysler Corp. is expected to report a record profit of about $2.4 billion when it releases its figures today.

Ford's fourth-quarter profit was down 8 percent from last year's $781 million. The No. 2 auto maker attributed that to a bigger tax bill, reflecting the general expiration of tax credits earned by the industry during the four-year sales slump that ended in 1983.

The previous record year for Ford was 1983, when it turned a $1.87 billion profit. The records being broken by GM and Chrysler also were set that year.

Like GM, Ford said it increased profits by selling more cars and trucks loaded with options such as air-conditioning.

Profits for the fourth quarter came to $3.89 a share compared with $4.29 a share the previous year. For the year, profits came to $15.79 a share compared with $10.29 a share a year earlier.

Sales for the quarter were $13.4 billion, up 8 percent from $12.4 billion in 1983. Sales for the year were $52.3 billion, up 18 percent from $44.4 billion.

In 1984, Ford gained two percentage points in car-market share, which is considered a significant amount. Increased sales of newer products, increased popularity of midsize and large cars and strikes against GM contributed to that.

* Hershey Foods Corp. said it had net income of $34.8 million ($1.11 per share) in the fourth quarter, up 15 percent from the $30.3 million (97 cents) earned a year ago.

Fourth-quarter sales rose to $523.5 million from $464.2 million.

Net income for 1984 totaled $108.7 million ($3.47), a 9 percent increase from the $100.2 million ($3.20) earned in the 1983 period. Sales rose to $1.9 billion from $1.7 billion in 1983.

Richard Zimmerman, president and chief executive, said the fourth-quarter results reflected "a strong finish" by the company's three major divisions, which are Hershey Chocolate Co., Friendly Ice Cream Corp. and Hershey Pasta Group.

He said Hershey Chocolate had strong Halloween and Christmas sales, while Friendly's sales were helped by favorable weather conditions and successful promotion efforts. Hershey Pasta's sales were aided by both selling price and volume increases.