re: What is the purpose of swaps?

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Interest rate hedging

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So one company thinks the fixed interest rate will be more favorable in the future than the floating rate and this will minimize their exposure to risk?

I understand hedging but I'm having trouble understanding why the two parties make payments to each other. My first thought of hedging is something like an oil company locking in a price of $100 per barrel because they think the future price will drop to $98 per barrel. No simultaneous payments are being made here.