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IRR – Meaning, Formula, Comparison with CAGR and ROI

Internal Rate of Return (IRR)

Introduction

Internal Rate of Return (IRR) is a financial metric that considers the cash flows from an investment to evaluate its profitability. In other words, it evaluates investment returns by considering both positive and negative cash flows. It is called the internal rate of return as it doesn’t consider external factors to evaluate a business opportunity.It is the discounting rate at which the total inflows from a project is equal to the total outflows, where Net Present Value (NPV) is equal to zero.

What is the internal rate of return?

Internal Rate of Return (IRR) is a financial metric that helps estimate the profitability of a potential investment. It is the discount rate which makes the net present value of the cash flows equal to zero. In other words, NPV equals zero. It is widely used in discounted cash flow analysis. It is ideal for analyzing capital budgeting projects. Also, it helps in comparing the potential annual rate of return over time.

While calculating the IRR, the present value of future cash flows equals zero. Upon determining the internal rate of return, it is often compared to the cost of capital or the hurdle rate. For example, for a company, if the IRR is greater than or equal to its cost of capital, then the project is a profitable option for it. On the other hand, if the IRR is lower than the hurdle rate, then the project isn’t a profitable option. However, IRR isn’t the sole decision making factor for a business or investment. Other qualitative and quantitative factors play a role in making an investment decision.

To calculate IRR, one can rely on the NPV formula itself. However, in the case of IRR, NPV equals zero.

Internal rate of return is the expected annual growth rate of an investment. It is also the rate of interest where the sum of all cash flows is zero. Moreover, IRR is useful to compare investments.

How is IRR calculated?

IRR calculation uses the same formula of the Net Present Value (NPV).

NPV = (Cash flows /(1+r)^n) – Initial investment

Where,

Cash flows = All the cash flows during the time period of investment.

r = IRR

n = time period.

Initial investment is the first investment made into the project.

IRR will be the rate at which the present values of all future cash flows match the cost of investment. IRR is the ideal rate at which the investors would be profitable. Hence, all the cash inflows will be equal to cash outflows.

To calculate IRR, the NPV is set to zero. However, solving IRR manually can be done only through a trial and error basis. One can also use software like Microsoft Excel to solve for IRR. While calculating IRR in Excel, the IRR function is used.

IRR can’t be used as a standalone measure for one project. One can use IRR to compare two projects. A project with higher IRR will be more desirable.

Let’s understand IRR with an example.

There are two projects which require an investment of INR 5,00,000. A company has to choose between the two projects to invest. The cash flows of project 1 for the next four years are INR 1 lakh, INR 3 lakh, INR 1 lakh and INR 2 lakhs. The cash flows of project 2 for the next four years are INR 3 lakh, INR 2 lakh, INR 1 lakh and INR 1 lakh. One can calculate IRR in Excel using the IRR function.

The IRR formula in MS Excel is = IRR(cash flows)

The IRR for project 1 is

Project 1Cashflows
Year 0-500000
Year 1100000
Year 2300000
Year 3100000
Year 4200000
IRR14%

The IRR for project 2 is

Project 2Cashflows
Year 0-500000
Year 1300000
Year 2200000
Year 3100000
Year 4100000
IRR19%

If the company were to choose based on the Internal Rate of Return, then it would choose project 2. This is because the return on project 2 (19%) is higher than project 1 (14%).

What does it tell you?

Internal Rate of Return (IRR) is used by businesses to determine which projects are more profitable to invest. In other words, it evaluates investment returns. Since IRR is in the form of a percentage, it becomes easier to compare it with the company’s financing cost. And if the financing cost is lesser than the potential rate of return, the project is worth investing.

IRR is often used along with the Weighted Average Cost of Capital (WACC) and Net Present Value (NPV).  As mentioned above, it is computed by equating NPV to zero. This means, at NPV of zero, the value of IRR will be high. Additionally, companies also ensure that the IRR is higher than the Weighted Average Cost of Capital (WACC)

Usually, in theory, any project with high IRR is considered for investment. However, companies usually determine the required rate of return (RRR) from a project. RRR will be the minimum acceptable rate of return that the company is expecting from a project. A project’s internal rate of return will be compared to its RRR. Projects with IRR greater than RRR will be considered for investing.

In case there are multiple projects, then the project with the highest difference between IRR and RRR (required rate of return) will be chosen.

Along with IRR, companies also use the payback period and investment indicator. The payback period is the time in which the businesses will get back their investment.

CAGR vs IRR

Compounded Annual Growth Rate (CAGR) determines the annual return from an investment. CAGR considers only the investment’s beginning value, ending value and the duration of the investment (time period). CAGR doesn’t consider the periodic investments made. On the other hand, IRR also determines the return from an investment. However, it takes into account all the cash flows (positive and negative), while computing the return.

CAGR is easy to compute in comparison to IRR. However, IRR gives a more realistic picture as it takes into account all the cash inflows and outflows. Therefore, IRR is preferable in case there are multiple cash flows to a project or investment.

CAGR is the annualized rate of return of an investment. At the same time, IRR is the total return of an investment over a period of time.

ROI vs IRR

Return on Investment (ROI) tells the total growth or return from an investment. ROI is not an annual rate of return. On the other hand, IRR depicts the annual growth rate from an investment. Both ROI and IRR will be the same for a year; however, for longer investment durations, they differ. This is the major difference between IRR and ROI.

ROI is the percentage increase or decrease of an investment from the start to end. ROI is the percentage of the difference between the current or future value of an investment and the original value of an investment divided by the original value of the investment. Furthermore, ROI is not very helpful while calculating for long term investments. Also, ROI doesn’t consider the periodic cash flows and returns. Hence ROI has its own limitations.

How is IRR used for capital budgeting?

Internal Rate of Return is a measure of determining the profitability of an investment or project. Capital budgeting is the process a business carries out to evaluate different business opportunities. Payback period, IRR and NPV are few capital budgeting techniques. Often multiple options are available for companies to invest in. It can be investing in new machinery for an existing product or entering a line of business altogether. Having multiple opportunities puts the business in a dilemma. Hence businesses use capital budgeting techniques to evaluate these options.

If a business has to choose between two projects involving similar costs, then it would choose the one with the highest IRR. This process involves ranking the projects based on the highest return and then selecting the one with the highest difference between the costs and return.

Internal Rate of Return is never used as a standalone measure or metric. It is used in tandem with NPV and payback period. NPV and payback period are other capital budgeting techniques that help in selecting the best investment opportunity.

Example

Let’s take an example of a company which has an option to expand production by buying new machinery or a new investment or project involving a new product.

The cash outflow (investment amount) of buying the new machinery is INR 10 lakhs. The expected series of cash flows (inflows) for the next five years is INR 1 lakh, INR 2 lakhs, INR 4 lakhs, INR 4 lakhs and INR 5 lakhs.

The cash outflow (investment amount) for investing in a new product is INR 10 lakhs. The expected series of cash flows (inflows) for the next five years is INR 5 lakhs, INR 5 lakhs, INR 1 lakh, INR 1 lakh and INR 1 lakh.

 New machinery Cash FlowsNew Product Cash Flows
Year 0-1000000-1000000
Year 1100000500000
Year 2200000500000
Year 3400000100000
Year 4400000100000
Year 5500000100000
IRR14%14%
Payback period3 years 9 months2 years
The following has been solved using the IRR function in MS Excel.

The IRR for buying the new machinery is 14%, and the for investing in a new product is also 14%. Since the return from both the projects is the same, the payback period can be used. The payback period for the first project is 3 years 9 months. For the second project, it is two years. Since the payback period for the second project is lower, the business will choose this.

Apart from these two, the business also considers the cost of capital. Let’s assume the company’s cost of capital of buying new machinery is 8% and for investing in a new product is 10%. In this case, the business will be more profitable if it goes with new machinery as the cost of capital is less.

Hence the business will choose to invest in new machinery instead of investing in a new product as the cost of capital for this is less.

If investing in market securities is giving a return higher than the above projects, then the business will rather invest in financial securities and earn a higher return.

IRR in mutual funds

Internal Rate of Return is not just popular among businesses to evaluate opportunities. Individual investors can also use IRR as a metric to calculate the return on their investments. Investors investing in mutual funds through SIPs can calculate their actual SIP returns by using IRR. While calculating IRR in Excel for SIP mutual fund investments, XIRR function can be used.

Limitations

IRR is widely in use by many investors and companies in determining the returns. Also, companies couple IRR value with other techniques for capital budgeting. However, the following are some of the limitations of IRR:

Duration

IRR doesn’t take into consideration the investment horizon or duration of a project or investment. For example, a company has to choose between two projects Project Alpha and Project Beta with IRR 20% and 25% respectively. The duration of project alpha is one year, while the duration of project beta is three years. The company’s cost of capital is 15%. Here both the projects are profitable. If the company chooses project beta based on IRR, then the decision might not be favourable. Though the IRR is higher, the duration of the project is higher too.

Reinvestment rate

IRR assumes that the cash flows are reinvested. It assumes that the reinvestments are done at the same rate as that of the project rather than at the cost of capital. Therefore, it might not give the right picture of profitability.

It assumes cash flows are reinvested; however, it doesn’t consider the reinvestment rate. Hence it isn’t a true indicator of the profitability. One can also use the modified internal rate of return to estimate the investment returns. Modified internal rate of return considers the reinvestment rate as the cost of capital of a company.

Published on September 25, 2020