If a private equity firm triples its investment in five years, what is the estimated IRR?

To determine the estimated internal rate of return (IRR) when a private equity firm triples its investment over five years, we can use the formula for compounding returns. The basic premise is that if an investment grows to a certain multiple over a specific period, we can find the IRR by solving for the rate in the following formula:

Final Value = Initial Investment * (1 + IRR) ^ Years

In this case, the Final Value is three times the Initial Investment and the investment period is five years. This can be framed as:

3 = (1 + IRR) ^ 5

To solve for IRR, we can take the fifth root of 3 and then subtract 1:

1 + IRR = 3^(1/5)

Calculating the fifth root gives us approximately 1.2457. So, subtracting one and converting it to a percentage, we find:

IRR ≈ 1.2457 - 1 = 0.2457 or 24.57%

Thus, rounding to one decimal place gives us an estimated IRR of approximately 24.6%. This calculation inherently reflects the definition of IRR as the rate at which the present value of future cash flows equals