I'm having some trouble understanding why if the rate of return were any less than the minimum rate of return that would make the PV (Present Value) of the cashflow stream 0, the cash flow stream would be non-negative.
The way I tried to understand it is that if you have a cash flow, a lower r would mean it gets discounted less. However, both positive and negative cash flows get discounted less, which is what confuses me. How can we conclude for certain that the PV of the cash flow stream with lower r than IRR(x) will be $\geq 0$?