Nationwide Health Properties Inc., a real estate investment company, said that its profit for the third quarter increased 53% to $8.7 million, or 53 cents a share, from $5.7 million, or 43 cents a share, for the same period a year earlier. Revenue rose 46% to $13.9 million from $9.5 million. For the latest nine months, the company, which invests in health care facilities, recorded a profit of $20.6 million, or $1.44 a share, on revenue of $35.7 million. That compares to a profit of $12.4 million, or 98 cents a share, on revenue of $25.9 million for the same period a year earlier. The 1991 earnings figure included a first-quarter charge of $3.5 million related to prepayment of a substantial portion of the company's secured debt.