how does the irr change if the cost of capital increases
The IRR is that specific cost of capital/discount rate of a particular project which equalizes the total present value of the project cash flows to the project's initial investment. In other words, the IRR is that discount rate which makes the project's NPV equal to zero. Hence, the cost of capital does not have any relationship with the project's IRR. The IRR is solely determined by the project's initial investment value and subsequent cash flows. Therefore, an increase in the cost of capital would keep the IRR unchanged.
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