After a sharp run-up in its share price, Apple has won the title of most valuable company of all time. The tech company started the work week up about 2 percent, continuing a rally that was driven last week by rumors about redesigns in the works for both the iPhone and iPad, the Wall Street Journal reported. The company was valued at about $621 billion or $662 a share during late afternoon trading, a valuation that tops the 1999 record of $616.3 billion held by Microsoft, the Journal reported. Microsoft's market cap comparison doesn't account for inflation, which means that Apple is now worth 53 percent more than Exxon Mobil -- the world's second-most valuable company. Some analysts have predicted Apple could go even higher, with several firms boosting its price target to over $900. The iPhone, one of Apple's hallmark products, is undergoing a design overhaul that's been generating buzz and driving the stock price higher. The new design, which will hit the market in September, is expected to be a vast improvement from the current version.