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 which 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.