It’s difficult for ordinary people to understand a policy document, and traditional financial planning is based on understanding annualized returns. However, the calculation method of an increasing term life insurance policy is Internal Rate of Return (IRR), and there’s a difference between these two – what’s the difference and why does it exist?
When funds are invested in one go, Internal Rate of Return (IRR) and Annualized Return (Annualized Return) produce the same results.
Layman’s Explanation
Imagine you planted a tree.
- Lump Sum Investment: You invested the money to buy the sapling and the fertilizer for the first year all at once.
- Annualized Return: This is like measuring how much your tree grows each year, then calculating the average percentage it grows by per year. It measures how much your money grew on average over one year.
- IRR (Internal Rate of Return): The IRR concept is broader and can handle situations with multiple cash inflows and outflows. However, in a simple scenario where you have a single investment and a single return, IRR also seeks to find an “average annual growth rate” that makes the money grow at this percentage over time, exactly equaling the amount you finally receive back. Because in a single investment, single return scenario, there are no intermediate cash flows (like regular dividends or additional investments), the calculation of IRR is simplified into finding a compound annual growth rate, which is exactly what the annualized return expresses.
An Example
Let’s assume you:
- Initial Investment: On January 1st, 2024, you invested 10,000 yuan.
- Investment Term: 3 years.
- Final Return: On January 1st, 2027, you received back 13,310 yuan.
1. Annualized Return:
The formula for calculating annualized return is:
$$\text{Annualized Return} = \left( \frac{\text{Ending Value}}{\text{Beginning Value}} \right)^{\frac{1}{\text{Investment Period}}} - 1$$Substituting the data:
$$\text{Annualized Return} = \left( \frac{13310}{10000} \right)^{\frac{1}{3}} - 1$$ $$\text{Annualized Return} = (1.331)^{0.3333} - 1$$ $$\text{Annualized Return} = 1.1 - 1 = 0.1 = 10\%$$Therefore, the annualized return on this investment is 10%. This means your money grew an average of 10% per year.
2. Internal Rate of Return (IRR):
IRR is the discount rate that makes the net present value (NPV) of all cash flows zero. In this example, the cash flows include:
- January 1, 2024: -10,000 (Cash outflow – investment)
- January 1, 2027: +13,310 (Investment recovery) We need to find a discount rate r such that: $$-10000 + \frac{13310}{(1+r)^3} = 0$$ $$\frac{13310}{(1+r)^3} = 10000$$ $$(1+r)^3 = \frac{13310}{10000} = 1.331$$ $$1+r = (1.331)^{\frac{1}{3}}$$ $$1+r = 1.1$$ $$r = 1.1 - 1 = 0.1 = 10\%$$ Therefore, the internal rate of return (IRR) for this investment is 10%.
Summary
In this simple example of a one-time investment and one-time recovery, you will find that the results of calculating the annualized yield and internal rate of return are identical. This is because in this specific case, the IRR calculation logic is equivalent to the compound interest calculation logic used to determine the annualized yield.
IRR truly comes into play when an investment involves multiple cash flows, such as investing in a fund where you contribute money each month, or investing in a project that pays dividends at different points in time and ultimately recovers a final sum of money. In this complex cash flow pattern, the annualized yield may not accurately measure the true return on investment, while IRR can better reflect the time value of money and the overall rate of return for the investment.