# How to Calculate the IRR of an Investment?

by Adarsh Raj Bhatt in July 28th, 2021

Image credit: Pexels

## Key Takeaways

• Internal Rate of Return or IRR is a technique used within capital budgeting that helps in better decision-making. It is a method used to measure the total profitability of your potential investments.
• IRR can be useful in many aspects of building a startup. In capital allocation and planning, IRR is commonly used to compare the profitability of establishing new operations and the profitability of expanding existing operations.
• An investment cannot be considered a success or a failure based on a single calculated value. There are a few factors that the IRR must consider to meaningfully evaluate an investment.
• As a rule of thumb, if all of your investment options show large gaps between discount rates and IRR, choose the one which has the most significant lead.
• To find the IRR of an investment or project, you must use the formula for NPV (Net Present Value). If you equate the value of NPV to zero and solve the equation, you will solve the only variable in the equation, which is IRR.
• Four different methods can help you determine MIRR (Modified Internal Rate of Return). Two of these methods use a spreadsheet package, while the other two are more manual in their approach.
• Making an investment or starting a project requires intensive research into many factors - and IRRs will help give you a mathematical perspective by highlighting the returns that a potential project or investment will make for your startup.

## What is the Internal Rate of Return in Finance?

Internal Rate of Return or IRR is a technique used within capital budgeting that helps in better decision-making. It is a method used to measure the total profitability of your potential investments.

Essentially, IRR is a discounting cash flow technique that gives you the rate of return earned by a project. This means that IRR is a discount rate, which refers to the interest rate used in discounted cash flow (DCF) analysis that helps determine the current value of future cash flow. However, in the case of IRR, the net present value (NPV) of all cash flows is considered to be zero in DCF analysis.

IRR can be useful in many aspects of building a startup. In capital allocation and planning, IRR is commonly used for comparing the profitability of establishing new operations with the profitability of expanding existing operations. For example, energy companies can use IRR to decide whether opening a new power plant is a better option than renovating and expanding the existing facility. While both options will add value in their way, IRR will help decide what the more logical option is. Early-stage startups with limited finances can use the Internal Rate of Return to better understand where (and how) to allocate their capital for better future results.

Another use of IRR is for the evaluation of stock buyback programs. If a startup decides to repurchase its stock, then critical analysis for this decision should show a higher IRR. In case it doesn’t, the decision-makers at the startup (or the founders) should consider using the funds to create new outlets or perhaps even acquire other startups.

The goal for calculating IRR is often to identify the rate of discount. The best way to look at IRR is as the rate of growth that an investment is expected to generate annually. This look at IRR makes it somewhat identical to Compound Annual Growth Rate (CAGR). While CAGR uses beginning and ending values to estimate the annual rate of return, the IRR uses values from multiple periodic cash flows. The other difference between CAGR and IRR is that CAGR is simpler to calculate.

## What is a good IRR for an investment?

One of the main purposes of the Internal Rate of Return is to ascertain whether one should pursue an investment or not. It functions as a reliable guideline (or gauge) for startups to identify the project or investment which would be more profitable.

There is a standard IRR rule followed by established startups. This rule states that if the IRR of the concerned project or investment is higher than the minimum IRR, which is considered to be the cost of capital, then the startup can go forward with the project or investment.

On the other hand, if the IRR of a particular investment is lower than the cost of capital, then it would be better to put the allocated funds in another direction. Since there are a couple of limitations to IRR, there is little solidity to the term “good IRR.” One must keep in mind that IRR calculations are biased toward investment timeline and cash flow timing within said timeline. Since IRR is calculated based on annual value, you might not be able to gain a distinct insight into your investment choices.

While IRR gives a broader idea of the right investment choice(s), there is a more numbers-oriented approach. Following is a list of IRRs to monitor based on the type of investment that you plan on making:

• Acquisition of a stabilized asset - 10% IRR
• Acquisition and repositioning of an ailing asset - 15% IRR
• Development in an established area - 20% IRR
• Development in an unproven area - 35% IRR

While they are approximations, if any of the above-mentioned IRR values are achieved by the specific investment, then your startup can probably consider it a good investment and go forward with further investigation.

An investment cannot be considered a success or a failure based on a single calculated value. There are a few factors that the IRR must consider to meaningfully evaluate an investment. An IRR must be considered in tandem with the following factors:

• The going in and coming out cap rates of the investment. Remember, while the going-in cap rate can be calculated, the coming-out rate can be assumed (or estimated) at best.
• The Net Present Value (the difference between the present value of cash inflows and the present value of cash outflows over a period of time) at the end of the investment timeline.
• The number of times you get returns on your cash investment at the end of the investment timeline.

Having identified all the factors that must be considered along with your IRR, you can make a far more informed decision for your future investments. Though you must keep an eye out for investments with an IRR higher than the discount rate, there is no fixed value as to how high the IRR must be. As a rule of thumb, if all of your investment options show large gaps between discount rates and IRR, choose the one which has the most significant lead.

## How to calculate an internal rate of return?

To find the IRR of an investment or project, you must use the formula for NPV (Net Present Value). If you equate the value of NPV to zero and solve the equation, you will solve the only variable in the equation, which is IRR.

Source

In the above equation

Ct = Net cash inflow during the period "t"

C0 = total initial investment costs

IRR = the initial rate of return

t = the number of periods

Another way to directly solve IRR is given as follows:

Source

Where

Cash flow = cash flows in the time period

r = discount rate

i = time period

There are a few things that need to be kept in consideration when calculating IRR. One must remember that the initial investment is always a negative value as it is going to represent an outflow.

Afterward, every cash flow can be considered positive or negative based on how the investment delivers or what it requires as a capital inflow in the foreseeable future.

## How to calculate the modified internal rate of return?

Modified Internal Rate of Return is (mostly) the same as standard Internal Rate of Return. The only difference between the two is that Modified Internal Rate of Return (MIRR) is IRR for a project with identical investment and NPV to the one being considered but with only a single terminal payment.

Four different methods can help you determine MIRR. Two of these methods use a spreadsheet package, while the other two are more manual in their approach.

#1: Method 1

The first way will help you better understand the definition of MIRR. Create two rows, one named “Project Cash Flow” and the other as “Discounted Cash Flow.” The rows will represent the number of years starting from zero and going up to the final year of the investment timeline. The last two columns should represent NPV and IRR.

Using the ‘Goal Seek’ function in Excel (under ‘’data > what-if’’ for the 2007 version and ‘tool’ in the 2003 version), you can find the IRR for the Discounted Cash Flow.

#2: Method 2

In spreadsheet-based software like MS Excel, there is a MIRR function included in the following form:

=MIRR(value_range, finance_rate, reinvestment_rate)

In the above function, the finance rate represents the startup’s cost of capital, and the reinvestment rate is any chosen rate preferred by the startup.

#3: Calculator

The next method involves using your calculator and hands to do basic mathematics. This is a more tedious method of finding the modified internal rate of return, and founders frequently make mistakes with this method. To use this method with minimum error, we will divide it into two parts.

In the first stage, we take the project cash flows from the return phase and compound each of them forward to the end of the project. This will be done using the startup’s cost of capital. In stage two, we take the total of the cash flow extended to the final year of the project timeline and calculate the discount rate required to set this value when discounted equally to the outlay.

This can be done as follows:

Source

The only downside is that this method is very time-consuming. For this reason, it is best suited for small projects and/or examinations.

This is a straightforward approach to calculating MIRR. MIRR can be calculated as follows:

Source

The above-mentioned formula is the mathematical representation of calculating the modified internal rate of return. Founders can take the future value of positive cash flow at reinvesting rate and divide it by the present value of the negative cash flow at the finance rate. Find the ‘nth’ root of this value, ‘n’ being the number of periods. Subtract the final number by one, and the final value will represent your Modified Internal Rate of Return.

## How to calculate initial investment from IRR in Excel?

Calculating the Internal Rate of Return is important as it helps startups make important assessments regarding future projects and investments. As IRR is an approximation considering many factors, it is necessary for the decision-makers that this value is as accurate as possible.

To make things easier, many developers have included specific functions and tools in software like Excel and other spreadsheets to calculate IRR. The goal is to find an investment where initial outflow and inflow from the investment are equal to zero.

So, Excel will do all the heavy lifting and help you arrive at the discount rate that you are seeking for a specific project. Open a spreadsheet and combine your cash flows which include the initial outlay and subsequent inflows using the IRR function. This function can be found in the Formulas Insert (fx) icon in Excel.

As mentioned above, Excel also offers you the option to calculate Modified Internal Rate of Returns (MIRR). However, there is another function that can be found in Excel and can help in calculating the Extended Internal Rate of Return (XIRR). The XIRR function is used when the cash flow model doesn’t have a fixed annual periodic cash flow.

## Summary

As a startup, one of the most important crossroads that founders may find themselves at is comparing the respective values of expansion vs. investment. Since startups don’t tend to have particularly overflowing war chests in their early years, an extremely well-informed decision must be made when using funds for starting with new projects or investing in untested waters.

Internal Rate of Return will help you better understand the next path that your startup must take as a fledgling business. Making an investment or starting a project requires intensive research into many factors - and IRRs will help give you a mathematical perspective by highlighting the returns that a potential project or investment will make for your startup. With that said, IRRs should not be considered stand-alone proofs and must be compared with other factors for a better picture.

There is a standard mathematical representation of calculating IRR, as shown above with the 4 methods. However, calculating it by hand can become tedious, complex, and error-prone, especially if the investment timeline expands over several years. Under such circumstances, the tools provided by Excel spreadsheets can help you better assess IRR over long periods and arrive at accurate values.

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Reference

Modified Internal Rate of Return – MIRR Definition

Internal Rate of Return (IRR) Definition & Formula