The time value of money $($TVM$)$ is a financial model. What are the various assumptions built into using it to evaluate projects? Do these assumptions lead to uncertainty in the real outcome of the projects? If assumptions are guesses, why do we use them for TVM decisions?

In reality, interest rates will change frequently. How can we incorporate interest rate changes when using TVM$?$ Do you think sensitivity analysis is important when calculating present values, especially when cash flows are complex?