The key points from the Apple results

Apple released results for its fiscal fourth quarter after US markets closed last night, reporting lower prices for its smartphones and forecasting lower-than-expected profitability for the Christmas period. Here are the key points of the results from the world's most-valuable company:

-Apple sold 45.5 million iPhones in the quarter, more than expected, and the company said it had been unable to manufacture enough of the new iPhone 7 which was introduced in September