If you're interested in Venture Capital (VC) or Private Equity (PE), you've likely heard the term IRR. IRR is often used to judge the performance of a fund. Compared to the simple return multiple, IRR takes into account the time value of money in investment activities, i.e., investment efficiency, and has thus become the "internationally accepted performance indicator for VC/PE institutions."
The Internal Rate of Return (IRR) is the discount rate that makes the Net Present Value (NPV) equal to zero. This is the standard textbook explanation. To understand it, we first need to understand NPV.
Net Present Value (NPV)
Net Present Value is the method of converting future expected income into its present-day value. For example, if you expect to earn $110 next year and the discount rate is 10%, its present value is 110/(1+10%) = $100. This means that the $110 you'll earn next year has the same purchasing power as $100 today (conversely, if you have $100 now with a 10% interest rate, you'll have $110 next year). The same logic applies to subsequent years. Then, you sum up the present value of each year's net cash flow and subtract the initial investment cost to get the cumulative net present value. The higher the cumulative NPV, the better. Theoretically, if the NPV > 0, the project is feasible, indicating it's profitable.
For example, let's assume two projects, A and B, both with an initial investment of $100,000 and a discount rate of 10%. The expected income and NPV are as follows (assuming a 5-year project cycle, unit: $10k).
| Investment: 100k | Project A Expected Income | Project A Present Value | Project B Expected Income | Project B Present Value |
|---|---|---|---|---|
| Year 0 | -10 | -10 | -10 | -10 |
| Year 1 | 1.1 | 1.1/(1+10%)=1 | 2.2 | 2.2/(1+10%)=2 |
| Year 2 | 2.42 | 2.42/(1+10%)^2=2 | 4.84 | 4.84/(1+10%)^2=4 |
| Year 3 | 3 | 3/(1+10%)^3=2.25 | 4.48 | 4.48/(1+10%)^3=3.37 |
| Year 4 | 5 | 5/(1+10%)^4=3.42 | 4 | 4/(1+10%)^4=2.73 |
| Year 5 | 7 | 7/(1+10%)^5=4.35 | 3 | 3/(1+10%)^5=1.86 |
| Cumulative NPV | 1+2+2.25+3.42+4.35-10=3.02 | 2+4+3.37+2.73+1.86-10=3.96 |
As you can see, Project B has a higher NPV and is a better investment. This is because although the total income of A and B over 5 years is the same ($185.2k) without considering the time value of money, Project B's income arrives earlier, resulting in a higher NPV. This shows that NPV mainly calculates how much money you can make after accounting for the impact of currency depreciation.
Internal Rate of Return (IRR)
The Internal Rate of Return is the discount rate at which the cumulative NPV is zero. It represents the maximum rate of currency depreciation a project can withstand (i.e., its profit margin and risk tolerance). Using the same example, if the discount rate changes to 20%, the NPVs of Project A and B are as follows:
| Investment: 100k | Project A Expected Income | Project A Present Value | Project B Expected Income | Project B Present Value |
|---|---|---|---|---|
| Year 0 | -10 | -10 | -10 | -10 |
| Year 1 | 1.1 | 1.1/(1+20%)^1 | 2.2 | 2.2/(1+20%)^1 |
| Year 2 | 2.42 | 2.42/(1+20%)^2 | 4.84 | 4.84/(1+20%)^2 |
| Year 3 | 3 | 3/(1+20%)^3 | 4.48 | 4.48/(1+20%)^3 |
| Year 4 | 5 | 5/(1+20%)^4 | 4 | 4/(1+20%)^4 |
| Year 5 | 7 | 7/(1+20%)^5 | 3 | 3/(1+20%)^5 |
| Cumulative NPV | -0.44 | 0.92 |
Here, Project A's NPV is negative, while Project B's is still positive. This indicates that Project A's IRR is less than 20%, while Project B's IRR is greater than 20%. After calculation, we find that when the discount rate is 18.45%, Project A's NPV is exactly 0.
| Investment: 100k | Project A Expected Income | Project A Present Value | Project B Expected Income | Project B Present Value |
|---|---|---|---|---|
| Year 0 | -10 | -10 | -10 | -10 |
| Year 1 | 1.1 | 1.1/(1+18.45%) | 2.2 | 2.2/(1+18.45%) |
| Year 2 | 2.42 | 2.42/(1+18.45%)^2 | 4.84 | 4.84/(1+18.45%)^2 |
| Year 3 | 3 | 3/(1+18.45%)^3 | 4.48 | 4.48/(1+18.45%)^3 |
| Year 4 | 5 | 5/(1+18.45%)^4 | 4 | 4/(1+18.45%)^4 |
| Year 5 | 7 | 7/(1+18.45%)^5 | 3 | 3/(1+18.45%)^5 |
| Cumulative NPV | 0 | 1.32 |
At this point, we say Project A's IRR is 18.45%.
Similarly, when the discount rate is 23.94%, Project B's NPV is 0.
| Investment: 100k | Project A Expected Income | Project A Present Value | Project B Expected Income | Project B Present Value |
|---|---|---|---|---|
| Year 0 | -10 | -10 | -10 | -10 |
| Year 1 | 1.1 | 1.1/(1+23.94%) | 2.2 | 2.2/(1+23.94%) |
| Year 2 | 2.42 | 2.42/(1+23.94%)^2 | 4.84 | 4.84/(1+23.94%)^2 |
| Year 3 | 3 | 3/(1+23.94%)^3 | 4.48 | 4.48/(1+23.94%)^3 |
| Year 4 | 5 | 5/(1+23.94%)^4 | 4 | 4/(1+23.94%)^4 |
| Year 5 | 7 | 7/(1+23.94%)^5 | 3 | 3/(1+23.94%)^5 |
| Cumulative NPV | -1.45 | Cumulative NPV |
At this point, we say Project B's IRR is 23.94%.
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Summary
NPV tells us how much money we can make within a project's lifecycle, considering the time value of money. IRR tells us the maximum rate of depreciation the project can withstand. More colloquially, if we were to take out a loan to invest in this project, IRR is the maximum annual interest rate we could bear. For instance, if a project's IRR is 20%, it means the project can withstand a 20% annual currency depreciation. If we take a loan, the maximum bearable annual interest rate is 20%; at this rate, the project just breaks even. If the actual depreciation rate is only 5% (or the loan interest rate is 5%), the remaining 15% becomes our profit. Although it seems to represent a margin for error (how much can I mess up and still break even), or risk tolerance, it can also be seen as profit margin and earning potential. It's like an exam where 60 is a passing grade. If your actual skill level is 90, you have a 30-point margin for error. Even if you lose 30 points, you'll still pass. This 30-point margin, converted to a rate, is your IRR. If your skill level is only 65, your margin for error is just 5 points. A small mistake will cause you to fail. In this case, your IRR is only 5 points. Although we calculate the IRR, it also reflects your true level (whether it's 90 or 65).
In actual project investment, NPV is a specific value, while IRR is a ratio. For comparison, IRR is better because it's a relative value. NPV alone is an absolute value and doesn't consider the investment size. Only by considering the investment amount simultaneously can the project's profitability be fully reflected. After all, an NPV of $50k from a $100k investment is different from an NPV of $50k from a $1M investment in terms of profitability.