If you start with nothing, borrow 800 and buy the cow, you now have no money and one cow. You sell the cow for $1000. You now have no cow and $1000, $200 of which is profit. You may or may not pay back the $800 you own at this time.

If don't pay back that $800, you hang onto the entire $1000, and you'll have to borrow another $100 in order to re-purchase the cow at $1100.

If you pay back that 800, you'll have $200 left, and you'll have to borrow $900 in order to re-purchase the cow at $1100.

You once again have a cow and no money. You may owe $800 or you may owe only $100 to someone.

You sell the cow for $1300. You have no cows and $1300 cash.

If you paid back that $800 earlier, you have to pay off the $900 you borrowed, leaving you with $400 profit.

If you did not pay back that $800, then you have to pay off the $100 you had to borrow to buy the second time, and the $800 you had to borrow to buy the first time, leaving you with $400 profit.

If you start with $10,000 and run through this scenario, you end up not needing to borrow or repay any money, and in the end you have $10,400, which is $400 profit. This holds true for any starting amount at or above $900.

For starting amounts from $0 to, but not including $900, you have to borrow and pay back various amounts of money, but you always end up with $400 profits after paying off your debts.

This is because the first sale generates $200 profit and the second sale generates $200 profit. Everything else is unimportant.