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IRR Calculator Tutorial - Internal Rate of Return Guide

Find the rate of return that makes NPV equal zero

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Calculate internal rate of return (IRR) for investments. Free IRR calculator for cash flow analysis, project evaluation, and investment decision-making.

How to Use the IRR Calculator

  1. Enter Initial Investment: Input the initial cost as a negative value
  2. Add Cash Flows: Enter all expected future cash flows
  3. Calculate IRR: Click Calculate to find the internal rate of return
  4. Compare to Hurdle Rate: If IRR exceeds your required return, consider accepting

Understanding Internal Rate of Return

Internal Rate of Return (IRR) is the discount rate at which the NPV of all cash flows equals zero. It represents the investment's actual rate of return. When IRR exceeds the required return rate (hurdle rate), the investment is considered attractive.

IRR is the expected compound annual rate of return on an investment, assuming all intermediate cash flows are reinvested at the IRR rate.

IRR Decision Rule & Considerations

  • IRR > Required Return: Accept the investment
  • IRR = Required Return: NPV = 0 (breakeven)
  • IRR < Required Return: Reject the investment
  • Multiple Sign Changes: May have multiple IRRs or no solution
  • IRR vs NPV: NPV is generally preferred for mutually exclusive projects

Limitations

IRR assumes reinvestment at the IRR rate and may give multiple or no solutions for unconventional cash flows. Consider using Modified IRR (MIRR) for more realistic assumptions.

Formula & Variables

0 = Σ[CFt / (1+IRR)^t] - Initial Investment
  • CFt: Cash flow at time t
  • IRR: Internal rate of return (to be solved)
  • t: Time period

Example Calculations

Machine Investment IRR Analysis

Scenario: A company pays $7,000 for a new machine and expects these annual cash flows over the next 6 years:
Year 1: $3,000 | Years 2-5: $5,000 each | Year 6: $4,000
What actual rate of return does this investment generate? How does it compare to the 20% required return?

Step 1: Enter Cash Flows

Step Input Display Description
1 CF CF0= 0.00 Access Cash Flow worksheet
2 7000 +/- ENTER CF0= -7,000.00 Enter initial investment (negative = outflow)
3 ↓ C01= 0.00 Move to first cash flow
4 3000 ENTER C01= 3,000.00 Year 1 cash inflow
5 ↓ F01= 1.00 Frequency (occurs once)
6 ↓ C02= 0.00 Move to second cash flow
7 5000 ENTER C02= 5,000.00 Years 2-5 cash inflow
8 ↓ F02= 1.00 Move to frequency
9 4 ENTER F02= 4.00 Occurs 4 times (years 2-5)
10 ↓ C03= 0.00 Move to third cash flow
11 4000 ENTER C03= 4,000.00 Year 6 cash inflow

Step 2: Calculate IRR

Step Input Display Description
12 IRR IRR= 0.00 Access IRR calculation
13 CPT IRR= 55.63 Calculate internal rate of return
Answer: IRR = 55.63%

The IRR of 55.63% far exceeds the 20% required return, confirming this is an excellent investment. The machine generates a 55.63% annual return on the initial $7,000 investment.

Machine Investment Summary
  • Initial Investment: -$7,000
  • Total Cash Inflows: $27,000 (over 6 years)
  • IRR: 55.63% ✅ (exceeds 20% hurdle rate)
  • NPV @ 20%: $7,625.99 ✅ (positive = profitable)
  • Decision: Strong accept - investment adds significant value

Frequently Asked Questions

IRR is the discount rate that makes the net present value (NPV) of all cash flows equal to zero. It represents the expected annual rate of return on an investment, assuming all cash flows are reinvested at the IRR rate.

Use NPV when you want to know the dollar value added by an investment. Use IRR when you need to compare returns across different-sized investments or communicate returns as a percentage. NPV is generally preferred for capital budgeting decisions.

MIRR addresses IRR's unrealistic reinvestment assumption by assuming positive cash flows are reinvested at the cost of capital rather than the IRR. This provides a more realistic expected return.

When cash flows change sign multiple times (unconventional cash flows), there may be multiple IRRs or no IRR at all. In such cases, use NPV or MIRR for decision-making.

IRR calculations use iterative methods to find the solution. Our calculator uses advanced algorithms to ensure accuracy to several decimal places, suitable for professional financial analysis.

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Disclaimer

This Financial Calculator is an independent, third-party tool provided by ryanoconnellfinance.com. It is not affiliated with, endorsed by, or connected in any way to Texas Instruments Incorporated or any of its products. All trademarks, including "BA II Plus," are the property of their respective owners. This tool is provided for educational and informational purposes only and should not be used for official examinations where specific hardware calculators are required. The accuracy of calculations is not guaranteed; verify all results.

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