Apple loses over $1 billion a year on Apple TV. The part almost nobody knows is that the losses were budgeted. The original business plan projected $15 to 20 billion of red ink over the first decade, approved before a single show aired. Six years in, they're losing money slower than planned. The per-subscriber math shows how strange this business is. Apple spends around $4.5 billion a year on content for 45 million subscribers. That works out to $100 per subscriber. Netflix spends about $18…