what is the discount rate really? How is it different from the cost of capital (eg if cost of capital is 10%)
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Cost of capital is one type of discount rate.
Essentially, the discount rate is saying “what could we earn on this money if we spent it elsewhere”? That's literally why the NPV equation exists…to compare our investment to alternatives!
As such, the discount rate is determined by the company/case. It could be set based on the cost of capital, the cost of equity, the interest rate, the hurdle rate, etc. etc!
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