CEOs’ who believe that selling off divisions will boost their stocks rating would do well to consider Cooper Tire & Rubber, whose recent sale of its auto parts unit has done nothing for its stock rating. Standard & Poor’s Ratings Services yesterday kept Cooper Tire & Rubber Co.’s credit rating at the lowest investment grade despite the Findlay, Ohio, tire maker’s recent $1.17 billion U.S. sale of its auto parts unit. Cooper Tire has about $936 million in debt, and its credit rating has been one step above junk-bond status since March 24, according to Standard & Poor’s. The company’s credit profile could be weakened depending on how it uses the sale’s proceeds to repurchase shares, reduce debt, reinvest in its tire business, and fund pension plans, the ratings firm said. Standard & Poor’s will meet with company management to discuss such issues, it said.