German auto makers BMW AG, Audi AG, and Mercedes-Benz are racing pell-mell against each other for the industry's luxury-car sales crown, but the huge sums they are spending to get ahead are beginning to erode profits. In their quest for growth, the three German brands that dominate the global market for premium cars and sport-utility vehicles are spending tens of billions of euros to develop new technologies, build factories and churn out new models.