The Net Present Value (NPV) and the Internal Rate of Return (IRR) are the golden standards in evaluating the potential profitability of an investment. This paper points out several properties of the solutions of the equation determining the IRR, which includes the equivalence of this equation with an algebraic equation whose degree is less than or equal to n, the existence of solutions, the number of real solutions, the relative position of real roots with -1 and 0 and some illustrations for that. Mokhtari et al. calculated the economic probability of the project in the case when the cash flow has exactly one random component with a normal, exponential, or uniform distribution by using the moment-generating function. We show that we can obtain their results by much simpler probabilistic transformations. At the same time, we generalize the problem to the case when the cash flow is a sequence of independent and normally distributed random variables. Simulation studies confirm the given results.