The hurdle rate is the company's required rate of return. The required rate of return may be the company's cost of capital, or it may be the company's cost of capital adjusted for various factors. It is not impossible for the hurdle rate to be the same as the interest rate at which the present value of the cash inflows equals the present value of the cash outflows, but there is no reason why it must be the same.
There is no such thing as the payback rate.
The internal rate of return of a project is the rate of return at which its NPV is zero. When the NPV is zero, it means the present value of the cash inflows equals the present value of the cash outflows. Therefore, the interest rate at which the present value of the cash inflows equals the present value of the cash outflows is the internal rate of return.
The cost of capital is what the company pays for the various sources of capital it accesses. It is not impossible for the cost of capital to be the same as the interest rate at which the present value of the cash inflows equals the present value of the cash outflows, but there is no reason why it must be the same.
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