Internal return (IRR) is a commonly noted measurement when talking about whole life and universal life insurance. This is because IRRs are well equipped to tell us what type of return we achieve on these types of life insurance policies. That answer, although very simple, satisfies most curiosity. <! – ->

But the exact reason for using IRR to achieve this goal is quite complex and an interesting discussion in financial mathematics. It has been quite a long time since I last went through a real discussion about mathematical technology. If you come to * The Insurance Pro Blog * for laughs (sarcasm) I'm afraid to say that this blog post may disappoint you a little. If, on the other hand, you are one of the three who enjoy a good numerical thriller (sarcasm … again) then you are looking for a treatment.

## What is internal return?

The core, internal return is a complex calculation of cash flows that is evaluated to achieve the effective return achieved by striving for an investment option. To understand IRR, you need to be in the right headspace, so you must first think about investing as costs. In other words, all investments have costs (ie what you pay to participate in them).

The majority of people look at investments linearly. What I mean is that they assume a fixed "investment" and calculate the return based on the dividend for that investment. This is an exact way to calculate returns insofar as we are only worried about the return for a very short period of time and / or we always have the same investment cost. Anything that dares outside these two necessary parameters forces us to either: <! – ->

- Attempt to flatten the variations in investment costs
- Aggregate the time periods as a long time period

In some cases both are necessary. In both cases, both approaches will lead to some (at best) or significantly (at worst and much more likely) erroneous conclusions. This is the case because our gross adjustments to the input data will generate output data that magnifies the effect of the adjustments.

So internal return is a method for accurately calculating the return based on both the reality with a varied investment cost and a longer period of time. The exact formula looks like this:

To calculate the actual IRR we would set the net present value (NPV) to zero and solve for r. Making this long form (by hand) is almost impossible because we usually use this formula by to connect a guess number for r and calculate NPV.

If the net present value comes out to a digit at or near zero, we determine our guess of the resulting IRR. Not too tricky when dealing with a short number of time periods, but quite the task when t increases. Thankfully, computer software will handle this task quickly and will work to reach a true NPV = 0 using non-integers.

## Difference between internal return and compound annual growth

For those who gain intermediate expertise in financial mathematics, we often see broad use of compound annual growth rate (CAGR) when discussing investment return. Some people may use the specific term ** compound annual growth rate ** and others may not. The specific CAGR calculation in itself only applies to the growth of something during a certain period of time without any control for ???

The compound annual growth rate tells about the effective return from an annual investment made by a single or fixed fee. over time. So CAGR can answer questions like:

- If Sam makes a $ 100,000 investment in 2010 worth $ 150,000 in 2019, what is his return over the entire ten-year period?
- If Lydia invests $ 5,000 per year from 2010 to 2019 and has $ 75,000 in 2019, what is her return over the ten-year period?

Using the calculation for compound annual growth rate, we can tell that Sam achieved a return of 4.14% over 10 years and Lydia achieved a return of 7.26% over 10 years

The easiest way to perform these calculations is with a calculator that is equipped to perform TVM (Time Value of Money) calculations. If you had to buy a TI-83 Plus calculator for high school math class, you own a calculator with the capacity to do this. If you do not happen to own one of these, there are several much cheaper options for financial calculator. Finally, everyone with Microsoft Excel also has the ability to easily perform TVM calculations.

The above examples are simply TVM solutions for "RATE" scenarios.

By the way, we cover a good introduction to Time Value of Money in * Predictable gains * so if you want a crash course that also contains examples of how to specifically include numbers in the calculations, you can check it out where. <! – ->

So this is fantastic, but what happens when circumstances become more complex. What if Sam invests $ 50,000 in year one and then another $ 50,000 in year five and ends up with $ 120,000 in 2019?

What if Lydia invests $ 5,000 for the first three years, nothing for the next two years, $ 3,000 the following year, and then $ 8,000 for the remaining years and ends instead of $ 61,000? Calculating the rate of return over the same time period only became much more complex.

This is where it's good to know how to use the IRR calculation. The internal return tells us that in these new scenarios, Sam achieves a return of 2.29% and Lydia 4.23%.

But IRR is more powerful than just telling about the effective return when someone varies the investment. It can also tell you what the effective return is when someone both deposits money * and * withdraws money. <! – ->

Suppose Sam invests $ 100,000 and takes $ 25,000 from his investment in year six, which resulted in a cash balance in year 10 of $ 110,000. This is another scenario where a simple CAGR calculation lacks the complexity to calculate his effective return. However, the IRR can easily handle this scenario, his return after year 10 is 3.39%.

Let's assume that Lydia invests $ 5,000 a year, but even in year six she withdraws $ 25,000 from the investment; by 2019, she has $ 30,000 left. What is her effective return or internal return? It is 6.14%.

## When we say "Effective return …"

When I use the term "effective return" I mean the year's interest rate equivalent result. So in the example above, the interest rate you see is the interest rate Sam and Lydia would need to earn each year on their investments to achieve the same result in year 10.

This is also what we normally call the geometric mean. <! – ->

## Difference Between Internal Return (IRR) and Return on Investment (ROI)

It sounds like IRR is focusing on return on investment, so why can we not just use a return on investment ? Is there any difference? It is certainly.

Return on investment is a simple calculation that measures the growth of a one-time investment. You use ROI when you need to answer the following questions:

Jim invested $ 50,000 in Amazon 2014 and sold his entire investment in 2018 for $ 65,000. What was Jim's total return on investment? The answer is 30%. Calculating return on investment is simply a calculation of percentage change:

The ROI calculation shows the percentage growth achieved by making the investment, but it does not take into account the time that elapsed between initial investment and exit. If we wanted to know what the effective return on investment was for Jim, we do not need IRR. We can simply use the RATE solution for TVM. His return year after year is 5.39%.

This calculation also lacks the ability to handle more complexity such as partial liquidation. What if Jim sold half of his 2018 investment for $ 25,000 and then the remaining investment in 2019 and received a total of $ 30,000 in 2019.

That question is too complex for the simple ROI calculation to answer. The IRR calculation, on the other hand, responds easily to that. His effective return year after year is 1.89%

## Why the internal return is important for life insurance

When we evaluate life insurance, we must evaluate against the other options we have to achieve the same goal. People often compare life insurance policies with investments of all kinds to determine if the values achieved through the life insurance contract are better, worse or the same as the expected results achieved elsewhere.

] The most accepted measure that compares financial vehicles is the year-on-year growth of its values. Life insurance can be a bit complex when it comes to inflows and outflows. While some people may pay a fixed premium for a number of years and simply want to know what the effective return on cash value and / or death benefit is, many more people do not follow a straight line to pay the premium. [19659016] For example, if you own a 10 Pay full life policy and want to know what the effective return achieved during year 25 is, you must have a mechanism to account for 10 years of inflow, followed by 15 years without inflows. If you decide to take out a loan against the insurance in 18, you also need a mechanism to report this.

The internal return is the only economic calculation that can do this with precision. Once you know the answer, you can compare it with the results you expect from other options and determine if life insurance is a good or bad option for you.

But note that this means that you must be careful with the way in which you evaluate your options. People often confuse returns. As you can see from the top, there are some ways to calculate a "return" on an investment. There are also a number of ways to approach the investment.

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