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corporate finance - capital budgeting

In corporate finance,
why in capital budgeting that net present value (NPV) of an investment propject
uses the cost of the capital to discount the cash flows from the project;
Rather than using required rate of return, discount rate, or opportunity cost
of the cash flows from the project to discount the cash flows?

My thought is that using cost of capital to discount the cash flows is
unreasonable since the cost of the capital is required by its capital lenders
while the cash flows earned from the project are used by project manager
(or company). The interest rate--the required rate of return, discount
rate, or opportunity cost of the cash flows from the project, may be
differing from the cost of the capital since the manager can require different
rate of return for her or his use of these cash flows.
Thus, how can we reasonably use the cost of the capital to discount the
cash flows?

The curriculum also mentions that financing cost is reflected
in reuqired rate of return, but how? By defining the discount rate equal to
the cost of the capital? If so, does it mean that this NPV calculation
method is very rough way to value a project by using cost of capital to
discount cash flows, thereby, at least the financing cost is covered
when discounting?


Or maybe I have mixed up the project with others?

Many thanks! indeed!

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