Net Present Value (NPV) (Multiple Cashflows) Calculator

Formula first

Overview

Net Present Value (NPV) is a capital budgeting tool that evaluates the profitability of an investment or project. It calculates the present value of all future cash flows generated by a project and subtracts the initial investment ($C{F}_0$). A positive NPV indicates that the project is expected to generate more value than its cost, making it a potentially desirable investment, while a negative NPV suggests the opposite. It's a cornerstone of financial decision-making.

Symbols

Variables

CF_t = Cash Flow at time t, r = Discount Rate, t = Time Period, n = Total Number of Periods, CF_0 = Initial Investment

Apply it well

When To Use

When to use: Apply NPV when evaluating potential investments, projects, or acquisitions to determine their financial viability. It's particularly useful for comparing mutually exclusive projects or when capital rationing decisions need to be made, as it directly measures the value added to the firm.

Why it matters: NPV is considered the most robust method for investment appraisal because it accounts for the time value of money and considers all cash flows over a project's life. It directly translates to shareholder wealth maximization, guiding firms to undertake projects that increase their value.

Avoid these traps

Common Mistakes

• Using an incorrect discount rate, which can significantly alter the NPV.
• Failing to include all relevant cash flows or including non-incremental cash flows.
• Incorrectly handling $C{F}_0$ (initial investment) as a positive cash inflow instead of an outflow.

One free problem

Practice Problem

A project requires an initial investment ($C{F}_0$) of $10,000.Itisexpectedtogeneratecashflowsof$4,000 in year 1, $5,000inyear2,and$6,000 in year 3. If the discount rate ($r$) is 10%, calculate the Net Present Value (NPV) of the project.

Solve for: result

Hint: Calculate the present value of each cash flow and sum them, then subtract the initial investment.

The full worked solution stays in the interactive walkthrough.

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Related Formulas

References

Sources

1. Brealey, Richard A., Myers, Stewart C., and Allen, Franklin. Principles of Corporate Finance. McGraw-Hill Education.
2. Ross, Stephen A., Westerfield, Randolph W., and Jordan, Bradford D. Fundamentals of Corporate Finance. McGraw-Hill Education.
3. Wikipedia: Net Present Value
4. Principles of Corporate Finance by Brealey, Myers, and Allen (13th ed.)
5. Fundamentals of Corporate Finance by Ross, Westerfield, and Jordan (12th ed.)
6. Net present value Wikipedia article
7. Brealey, Richard A., Myers, Stewart C., and Allen, Franklin. Principles of Corporate Finance. 13th ed. McGraw-Hill Education, 2020.
8. Ross, Stephen A., Westerfield, Randolph W., and Jaffe, Jeffrey F. Corporate Finance. 12th ed. McGraw-Hill Education, 2019.