Apple (AAPL) claims to run the App Store at or near break even, and apparently that’s not terribly far from the truth.

In a report to clients issued Wednesday, Piper Jaffray’s Gene Munster uses two data points Steve Jobs delivered in his keynote two weeks ago — 5 billion apps downloaded, $1 billion to developers — to build the first independent model of the App Store as a line of business. His key findings:

• $1 billion generated for developers since the store launched on 7/10/08 suggests gross app store revenue of $1.4 billion, $429 million of which Apple keeps after paying the developers’ 70% cut.
• App pricing data suggest that 81% of apps are free and 19% are paid, with an ASP (average selling price) of $1.49.
• Apple’s gross margin on the App Store is about 44%, according to Munster, assuming 70% goes to the developer, $0.20 plus 2% of the ASP to the credit card company, and 1% for storage and delivery.
• Apple has generated a total of $33.7 billion in gross profit since the App Store launched, to which the App Store has contributed $189 million, or 1%.
• Over the same time period (Q4 2008 to Q2 2010), the entire iTunes store has generated $3.6 billion in revenue, to which the App Store has contributed $429 million, or 12%.

Of course, the purpose of the App Store is to drive sales of Apple hardware, and in that it is succeeding admirably.

Fun factoid: Munster’s numbers suggest that iPhone, iPad, and iPod touch users download more than 16.6 million apps per day, nearly double the 8.9 million daily rate of iTunes tracks downloaded.

[Follow Philip Elmer-DeWitt on Twitter @philiped]