We clarify the foundations of project evaluation under multiple risk sources and we show that the way the NPV method is typically applied in most firms and organizations violates some fundamental principles of value creation such as the additivity and absence of arbitrage principles. Project evaluation must be done through (i) decomposing the project cash flows into components corresponding to the different sources of risk and (ii) obtaining the present value of each component with a specific risk-adjusted discount rate. The value of the project is obtained as the sum of the present values so obtained. Alternatively, the different components can be corrected for their respective risk to obtain their certainty equivalents. The value of the project is then obtained as the sum of those certainty equivalents discounted at the unique, observable, identical, risk free rate.