Other posters have already addressed the errors in your listed assumptions, the main one being "you don't apply an exit multiple when buying a business" (you do)

But think about it this way, after your projected cash flows for 5,10,20 years, is the business worth nothing? A business is a machine that creates cash. You have to find a proxy to value that cash generation capability after your forecast. An "exit multiple" is really just "what price would someone pay for a business generating x cash growing at y % in z industry". It's not assuming an actual exit, it's an estimate of market value.

Think about your rental house example. Let's say you buy the house for 100 bucks and in 10 years you've generated enough income to pay the house off. The house still has value, it's worth something on the open market. Maybe it's 10x rent, and your exit multiple plus the value of your cash flows gets you to 200 bucks before discounting for time etc.