Internal rate of return.

 The Internal Rate of Return (IRR) is the annualized effective compounded rate of return that makes the Net Present Value (NPV) of all cash flows (both positive and negative) exactly zero. It is the break-even interest rate used by investors to measure the profitability of potential investments. [1, 2]

How it Works

• The "If-Then" Test: If an investment's IRR is 15%, it means the project is expected to grow your invested capital at a compound annual rate of 15%.
• Comparison to Hurdle Rate: Investors compare the IRR to their "hurdle rate" or cost of capital. If the IRR exceeds this target, the project is generally accepted.
• Ranking Investments: When choosing between multiple projects, investors typically prefer the one with the highest IRR, assuming the risks are comparable. [1]

The Mathematical Formula

IRR is the discount rate (r) that satisfies the following formula, where $C_t$ represents the cash flow at time t, C₀ is the initial investment, and N is the total number of periods: [7, 8, 9]

$0 = \sum_{t=0}^{N} \frac{C_t}{(1 + \text{IRR})^t} = C_0 + \frac{C_1}{1 + \text{IRR}} + \frac{C_2}{(1 + \text{IRR})^2} + ... + \frac{C_N}{(1 + \text{IRR})^N}$ [8]

How to Calculate It

Calculating this manually involves trial and error, so most financial professionals rely on software.

• Excel / Google Sheets: Use the built-in formula , where is the range of your initial negative cash outflow and subsequent positive inflows.
• Calculators: Use the financial function on a standard calculator by inputting your cash flows chronologically. [1, 11, 12, 13]

Common Limitations

• Reinvestment Assumption: IRR assumes all interim cash flows are reinvested at the same calculated IRR, which may not be realistic for high-return projects.
• Multiple IRRs: If a project has alternating positive and negative cash flows throughout its lifecycle, the mathematical equation may yield multiple different IRR answers. [10]

For a deeper dive into evaluating capital projects and investment yields, read the Investopedia IRR Guide or check out the Corporate Finance Institute IRR Resource. [1, 3]

References:

[1] https://www.investopedia.com/terms/i/irr.asp

[2] https://en.wikipedia.org/wiki/Internal_rate_of_return

[3] https://corporatefinanceinstitute.com/resources/valuation/internal-rate-return-irr/

[4] https://www.youtube.com/watch?v=gBHKIyhkbTg

[5] https://www.accaglobal.com/gb/en/student/exam-support-resources/foundation-level-study-resources/ffm/ffm-technical-articles/the-internal-rate-of-return.html

[6] https://study.com/academy/lesson/video/internal-rate-of-return-method-definition-calculation.html

[7] https://www.canarahsbclife.com/blog/financial-planning/internal-rate-of-return

[8] https://www.bajajamc.com/knowledge-centre/internal-rate-of-return

[9] https://www.vedantu.com/maths/internal-rate-of-return

[10] https://www.youtube.com/watch?v=MCxqD6CE0cI

[11] https://www.studysmarter.co.uk/explanations/business-studies/corporate-finance/internal-rate-of-return/

[12] https://www.canarahsbclife.com/blog/financial-planning/internal-rate-of-return

[13] https://arrived.com/blog/internal-rate-of-return

[14] https://www.indiabonds.com/bonduni/blogs/internal-rate-of-return/

[15] https://www.indiabonds.com/kuchbhi/what-is-irr-internal-rate-of-return/