Input Assumptions and Logical Boundaries of the Constant Annual Cash Flow Model
The calculation engine of this tool is designed to accept only five basic parameters as input conditions: initial investment, annual revenue, annual expenses, project duration, and discount rate.
The most important implementation assumption here is the adoption of a static cash flow model in which the annual net cash flow (the amount obtained by subtracting annual expenses from annual revenue) remains constant every year during the project period.
In a real-world business environment, it is common for revenues and expenses to fluctuate from year to year, but this system eliminates complex multi-scenario branching and annually fluctuating parameters to provide a baseline for quickly grasping the broad profitability of an investment proposal while minimizing input effort.
Therefore, the results derived by this tool are merely mathematical estimates based on the assumption that the entered fixed values will continue throughout the period.
It does not guarantee actual future business revenues or investment outcomes, nor does it replace individual investment advice from financial institutions or experts.
Factors such as tax fluctuations, the decline in the value of money due to inflation, and the residual value at the end of the business are not incorporated into this model; it has a logical boundary that mechanically derives each indicator purely from the balance of the set initial cost and annual cash flow.
Calculation Structure and Interpretation of Total ROI and Annualized ROI
Return on Investment (ROI) is the most basic indicator showing how much profit can be obtained relative to the invested capital. This system adopts a structure that calculates this from two perspectives: "Total ROI" and "Annualized ROI".
Total ROI is calculated by taking the total profit—obtained by subtracting the initial investment amount from the total net cash flow for the entire period (which is the constant annual net cash flow multiplied by the project duration)—as the numerator, and dividing it by the initial investment amount as the denominator.
This value indicates the cumulative profitability of the entire project, representing what percentage of profit is added to the principal investment over the specified total period.
On the other hand, annualized ROI is an indicator calculated by directly dividing a single year's net cash flow by the initial investment amount.
This shows the simple percentage of profit earned per year relative to the initial investment, and is a concept distinct from the Compound Annual Growth Rate (CAGR), which considers compound interest, or the Return on Equity (ROE).
This tool does not calculate CAGR based on compound interest, but strictly presents a simple percentage based on a single-year constant cash flow.
This makes it possible to intuitively grasp the annual profit level generated by the project against the baseline of the initial investment.
Derivation of Simple Payback Period and Evaluation of Fund Liquidity
Evaluating how long it will take for invested funds to be returned to hand is extremely important for managing cash flow and liquidity risk in business operations.
This system implements an algorithm to calculate the "simple payback period" through the process of dividing the invested initial investment amount by the annual net cash flow.
This method is the most intuitive recovery model that does not account for the time value of money or discount rates, and the calculation result is output as the physical period of "how many years it takes to generate cash flows equal to the investment amount." For example, if the initial investment amount exceeds the constant annual net cash flow, the quotient directly becomes the number of recovery years.
If the annual net cash flow is positive, the tool displays the years from the formula, and the user compares whether those years fit within the entered project duration.
If the annual net cash flow is 0 or less, it displays that recovery is impossible. Because this indicator visualizes the fund lock-up period until the project begins generating profit, it functions as a guideline for investment decisions in projects requiring short-term funding or those with high risks of equipment obsolescence due to rapid technological innovation.
However, this tool strictly calculates a simple payback period; it is not intended for advanced capital recovery simulations that consider dynamic payback periods using discounted cash flows or recovery through asset sales after the investment ends.
Calculation Method for NPV (Net Present Value) Based on a Specified Discount Rate
Future cash flows have relatively lower value compared to the same amount of funds on hand today from the perspective of uncertainty and opportunity costs.
To incorporate this time value of money into the calculation model, this tool calculates the NPV (Net Present Value) using a "discount rate" (hurdle rate) specified by the user.
In the calculation process, each year's cash flow is first discounted to its present value by multiplying the constant annual net cash flow by a discount factor (1 / (1 + r)^n, where r is discountRate/100).
Then, the final NPV is derived by deducting the initial investment amount, which is a negative cash flow at the initial point in time, from the sum of these present values over the entire project period.
If the calculated NPV exceeds zero, it is mathematically interpreted that the project generates a return above the required hurdle rate and increases the value of the investing entity.
Conversely, if the NPV is negative, it means that the expected rate of return is not met. This system executes only direct discount calculations on the entered net cash flows, not including conversions to after-tax cash flows or the tax shield effects of depreciation expenses, to present the basic present value scale of the project itself.
Approximate Search for Positive IRR (Internal Rate of Return) Using the Bisection Method Algorithm
The Internal Rate of Return (IRR) refers to the discount rate at which a project's NPV becomes exactly zero, indicating the inherent yield of the investment project itself.
Calculating the IRR involves finding the roots of a higher-order equation, making it a non-linear process where deriving an analytical solution directly is difficult.
Therefore, the calculation engine of this tool adopts an approximate search algorithm using the "bisection method," which progressively narrows down a specific range.
The search target is limited to the range of positive return rates from 0 percent to 1000 percent. The algorithm calculates the NPV at the discount rate that is the median of the search range.
If the result is positive, it judges that the true IRR lies in the higher range; if negative, in the lower range. By repeating this process of halving the calculation range, it returns the approximate value when the absolute NPV is less than 0.00001 or after at most 100 iterations.
This approach is an implementation designed to avoid complex convergence calculations using calculus, such as Newton's method, and to search through a fixed procedure without using derivatives.
Furthermore, this calculation functions effectively only for simple investment scenarios where the annual net cash flow is positive and the total cash flow during the period exceeds the initial investment amount.
Complex projects with negative IRRs (deficit projects) or those where multiple IRRs could exist due to significant additional investments during the period causing multiple sign reversals in cash flows, are excluded from the calculation.
Graphing Undiscounted Cash Flows and Out-of-Scope Conditions for Simulation
In addition to the calculated numerical indicators, this tool is equipped with a graph display function for cumulative cash flows so that users can intuitively grasp the financial progression of an investment project over time.
This graph adopts a format that plots the accumulation of the constant net cash flow added each year, starting from the negative expenditure of the initial investment amount at Period 0 (initial point).
By visualizing the point where the graph's bars transition from the negative region to the positive region, the design allows users to confirm the arrival timing of the aforementioned simple payback period at a glance.
An important point to note here is that what this graph depicts is the progression of the "simple undiscounted cumulative cash flow," and it does not represent the progression of the present value factoring in the specified discount rate (the cumulative progression of NPV).
Also, it does not have a function to simultaneously display multiple trajectories when input parameters fluctuate, as in a sensitivity analysis.
This system is not a tool for conducting complex valuations during corporate acquisitions or calculating real value considering macroeconomic inflation rates; it is a lightweight mathematical interface for simultaneously estimating basic indicators of ROI, payback period, NPV, and IRR based solely on the input immutable numbers.
All calculation processes are completed on the user's terminal, enabling quick approximate simulations without sending data externally.
However, users are required to utilize the tool with a full understanding of these specification limits and out-of-scope conditions.