PositiveNPV

PositiveNPV refers to a project or investment whose net present value (NPV) is greater than zero. NPV measures the value created by an investment when future cash inflows and outflows are discounted back to their present value using a discount rate that reflects the cost of capital and project risk. In formula form, NPV = sum from t=1 to T of CF_t / (1 + r)^t minus C0, where CF_t are cash flows in period t, r is the discount rate, and C0 is the initial outlay.

Interpretation: A positive NPV indicates the project is expected to add value to the firm under the chosen discount rate, assuming cash flows and the rate accurately reflect reality. A negative NPV suggests the project would destroy value, while an NPV of zero implies neutrality with respect to value creation.

Discount rate and risk: The rate r embodies the opportunity cost of capital and the risk of the project. A higher discount rate reduces NPV, potentially flipping a positive project to negative. The method assumes that cash flows are estimated reasonably well and that the rate captures risk appropriately.

Limitations: NPV depends on forecast accuracy and the chosen discount rate, which can be uncertain. It may understate strategic or managerial flexibility, ignores non-financial factors, and can be sensitive to cash-flow timing. In practice, NPV analysis is often complemented by sensitivity or scenario analyses, real options considerations, and other metrics.

Example: With an initial outlay of 100, discount rate 10%, and inflows of 40, 50, and 60 in years 1–3, NPV ≈ 40/1.1 + 50/1.1^2 + 60/1.1^3 − 100 ≈ 22.8, a positive value.