The Present Value of a project's cash flows when its cost of capital equals its internal rate of return :
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A. B. C. D.B
The IRR is by definition the discount rate at which the NPV = 0. Therefore, at this point, the PV is greater than zero, since the initial outlay is always non-zero and
NPV = PV - cash outlay.
The correct answer to this question is D. "could be all of these answers."
To understand why, let's first define some key terms:
Present Value (PV): It represents the current value of a future stream of cash flows, discounted at a specific rate of return, which is often the project's cost of capital.
Internal Rate of Return (IRR): It is the discount rate that makes the net present value (NPV) of a project equal to zero. In other words, it is the rate at which the project's cash inflows equal its cash outflows.
Cost of Capital: It is the rate of return required by investors to provide funds for a project. It represents the opportunity cost of investing in the project, taking into account the risk associated with it.
Now, let's consider the relationship between the present value of cash flows and the cost of capital when it equals the internal rate of return.
If the cost of capital equals the internal rate of return, it means that the discount rate used to calculate the present value of cash flows is equal to the rate at which the project's cash inflows equal its outflows. In this case, the net present value (NPV) of the project is zero.
If the NPV is zero, it means that the present value of cash inflows is equal to the present value of cash outflows. Therefore, the Present Value of the project's cash flows is equal to zero, which corresponds to option A.
However, it is also possible that the cash inflows exceed the cash outflows, resulting in a positive NPV. In this case, the Present Value of the project's cash flows will be positive because the present value of cash inflows exceeds the present value of cash outflows. This corresponds to option B.
On the other hand, if the cash outflows exceed the cash inflows, the NPV will be negative. In this scenario, the Present Value of the project's cash flows will be negative because the present value of cash outflows exceeds the present value of cash inflows. This corresponds to option C.
Therefore, depending on the specific characteristics of the project and the relationship between cash inflows and outflows, the Present Value of a project's cash flows when its cost of capital equals its internal rate of return could be any of the three possibilities: zero (option A), positive (option B), or negative (option C). Thus, the correct answer is D. "could be all of these answers."