Synthetic cash flow model with singularity functions. I: Theory for periodic phenomena and time value of money

Precisely and efficiently calculating balances of cash flows is crucial for successful engineering economics analysis within construction project management. However, such balance calculation is challenged by mercurial conditions; e.g., individual cash flows may occur periodically, profit markups may be distributed evenly or unevenly, and the balance must consider the time value of money. These intricate phenomena can be modeled with singularity functions. Singularity functions perform customized case distinctions, which yield enormous modeling flexibility. Contributions to the body of knowledge are threefold: A new signal function is introduced to express the periodicity of incremental payments and compound interest in detail for both integer and noninteger periods. Outflows and inflows both explicitly consider the time value of money for accurate direct calculation of variable balances, which can identify breakeven points. All formulas are validated with worked examples. Future research can extend the new approach toward analyzing other phenomena, such as prompt payment discounts.