# Internal Rate of Return(IRR)

The internal rate of return is one of the most fundamental analysis tools that can be used to inform financial investment decisions.  However, the internal rate of return is often confusing to many.  Despite popular belief, it's really not that confusing once one is able to understand how it's calculated.  And it's important one understands it...as we said already, the internal rate of return or IRR is one of the fundamental analysis tools available to investors.

So what is IRR?  Internal Rate of Return is the annualized rate of return that an investment is projected to receive or has received based upon future cash flows or cash flows that have already happened.

Why Is It Confusing?

So why is the Internal Rate of Return confusing? One reason the internal rate of return can be confusing is because it has some more common names that get used.  For example, the annualized rate of return, the IRR, and the discount rate can all be used in place of internal rate of return in certain situations.  But these are all just another anme for internal rate of return.

A second reason it can be confusing is because people can't wrap their mind around how IRR is calculated.  Let us try to help.

## How Is Internal Rate of Return Calculated

Point blank, the internal rate of return is calculated by figuring out the rate of return where the present value of future cash flows equals zero.  Yes, that is confusing so let us take you step by step and break it down.

### Understanding Present Value in Order to Understand IRR

First, let's figure out how the present value of future cash flows is calculated.

The present value of future cash flows is calculated by discounting future cash flows back to a present value.  Another way of saying the same thing is this, we're calculating what future money/value is worth today.  This is done by using a rate that is appropriately called the discount rate in order to discount future value to a present value.  The equation for present value is stated below.

Present Value = Future Cash Flow / (1 + r)n

r = Discount Rate

n = Number of periods to be discounted back

The present value of future cash flows, as represented by the formula above, will deliver as result that is either above or below zero.  if the present value is above zero, that means that the rate of return delivered is greater than the discount rate used to calculate the present value.  If the present value is less than zero, then that means that the rate of return delivered from the future cash flow is less than the discount rate used to calculate the present value.

Before going on, understanding that a typical present value calculation will involve many future cash flows to be discounted, including an initial investment of capital and a final sale of the investment where capital is recovered, with many cash flows in between.  That is what makes it possible for present value of future cash flows to be negative because the future cash flows need to be large enough in order to be larger than the initial negative cash flow...that is, the investment of capital.

So if the present value is positive, that means the rate of return is larger than the discount rate and if the present value is negative, that means the rate of return is smaller than the discount rate.  So what is the rate of return if my present value equals zero?  In this case, the rate of return equals the discount rate, and this is that rate of return that is called the internal rate of return or IRR.

### Internal Rate of Return Formula

The IRR formula is not simple as one could probably gather from the explanation.  Any time a person is solving for the rate of return in an equation with multiple cash flows, it gets complex.  That's why we recommend using our internal rate of return calculator.  But in order to help you understand the IRR calculation, here is the formula. ## Situations Where Internal Rate of Return Is Used

Industry and Manufacturing

The internal rate of return is often used inside of companies to measure the potential rate of return from a capital investment.  For example, if a company wants to purchase a new piece of machinery that will produce widgets, the company would create projections of the total cash flow after expenses the machinery would produce from selling widgets and try to determine if purchasing the machine would generate an acceptable internal rate of return on the capital invested.

Real Estate Investing

Real estate investors don't use internal rate of return nearly enough.  Real estate investors tend to want to rely on more simple calculations such as the cash on cash return or the capitalization rate.  That's because the internal rate of return is complicated when it comes to real estate, but we've created a rental property calculator that lets the user project cash flows as far out as 30 years and to calculate an internal rate of return from those cash flows.  Now real estate investors don't have an excuse for not using the IRR in their calculations.

In addition to calculating the IRR on a real estate investment, the institution lending you money is also required to make an IRR calculation as it relates to the interest rate they will charge on the loan.  This rate is called the "annual percentage rate" or APR for short and is an IRR calculation that factors in all expenses and fees associated with the loan to tell the borrower the rate of interest they are actually being charged.

Financial Planning

The financial planning industry is big on using the internal rate of return in order to determine an investment's rate of return.  You can see internal rate of return being calculated on things like stock and equity investments, annuities, life insurance contracts, and bond and debt instruments.  For example, for permanent life insurance contracts, the owner pays premiums and in return they get cash value savings and a dividend payment(depending on the contract) over time, in addition to the death benefit.  Each of these benefits/cash flows, can be measured and used to calculate the internal rate of return of the life insurance contract.

The same can be done with an annuity contract.  Similar to a life insurance contract, it is a contract with a series of cash flows in and cash flows out.  These cash flows can be used to calculate the IRR from the annuity.  In fact, that's exactly what our annuity rate of return calculator does.

Or if a person is trying to determine the rate of return they will get from investing in a bond if held until maturity, that is called the yield to maturity.  This is calculated by using the internal rate of return.  Our yield to maturity calculator can do that for you without hassle.

## Conclusion

As you can see from the examples above, the internal rate of return is used across many industries and in many different situations.  If you want a career in financial analysis or just want to make a more informed investment decision, then understanding internal rate of return is one of the first steps to take.  Because it is such a useful calculation and is common across many different use cases, you'll find the internal rate of return in a lot of our calculators.

We hope you found this article informative and useful.  IQ Calculators is the number one online financial calculator site on the web.