et Present Value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows. NPV is used in capital budgeting to analyze the profitability of a projected investment or project.
NPV = Cash inflows / (1+r)^n – Cash outflows
Internal rate of return (IRR) is a metric used in capital budgeting to measure the profitability of potential investments. Internal rate of return is a discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero. the higher a project’s internal rate of return, the more desirable it is to undertake the project. IRR is uniform for investments of varying types and, as such, IRR can be used to rank multiple prospective projects a firm is considering on a relatively even basis.
Negative IRR indicates that the sum total of the post-investment cash flows is less than the initial investment; i.e., the non-discounted cash flows add up to a value that is less than the investment. Yes, both in theory and practice negative IRR exists, and it means that an investment loses money at the rate of the negative IRR. In such cases, the net present value (NPV) will always be negative unless the cost of capital is also negative, which may not be practically possible.
However, a negative NPV doesn’t always mean a negative IRR. Negative NPV simply means that the cost of capital or discount rate is more than the project IRR.
IRR is often defined as the theoretical discount rate at which the NPV of a cash flow stream becomes zero.