Internal rate of return (IRR) is an interest rate that investors use to compare your different investments. IRR is closely related to net present value (NPV), as both account for the time value of money (i.e., money is worth less if you must wait to receive it). Investors can calculate IRR to obtain the price of an investment precisely equal to the return, discounted for the passage of time.

## Background Information on IRR

The “internal” in IRR indicates the absence of external factors such as risk, inflation, the risk-free rate, etc. IRR measures the return not as a dollar amount but rather as a rate (i.e., dollars returned / dollars spent). Unlike the return on investment metric (ROI), the dollars returned are discounted by a given interest rate that measures the decay of value due to the passage of time. IRR is the interest rate (or discount rate) that sets the price of an investment equal to its return on future discounted cash flows.

Another way to define IRR is the interest rate that equates an investment’s present value of periodic cash flows with its price:

**P0 = PV**, or

**P0 = C1/(1 + r) ^1 + C2/(1 + r)^2 + C3/(1 + r)^3 + Cn/(1 + r)^n**

Where:

**PV** = present value

**P0** = Initial price

**n** = period number

**C1, C2, C3, Cn** _{} = cash flows for the designated period

**r** = discount rate, equal to the IRR when price equals present value.

As the Corporate Finance Institute explains, IRR is also expressed as the discount rate in which the net present value (NPV) is zero:

**NPV = PV – P0 = 0**

When calculating IRR for investments, the price is a negative number representing a cash outlay (i.e., a negative cash flow).

## Calculating the IRR of a Single Cash Inflow

As an example of an investment with a single cash inflow, suppose you are offered a bond for $10,000 that will pay you $25,000 in five years with no intervening interest payments.

Because this is a single cash inflow, the formula for IRR reduces to:

**IRR = (FV / P0)^(1/n) –1**

where **FV** = the future value of the investment.

Substituting, we have:

IRR = ($25,000 / $10,000)^(1/5) – 1 = 0.2011 = 20.11 percent

This IRR is the annual rate of return on the investment, equal to the interest rate that equates the future cash flows to the present value.

## Calculating IRR of Multiple Cash Inflows

The IRR for multiple cash inflows requires calculating each term in the NPV equation. Crucially, the cash flows per period are variables, but the period spacing must be fixed (usually yearly). For example, suppose a company invests in a project with the following cash flows:

The table (at bottom) indicates an initial outlay of $700,000 for the project, and the subsequent positive cash flows are the annual net income amounts.

To calculate IRR (i.e., the value of r when NPV = 0), substitute as follows:

NPV =[$120,000/(1 + r) + $150,000 /(1 + r)2 + $180,000 /(1 + r)3 + $210,000 /(1 + r)4 + $260,000/(1 + r)5 ^{} ] – $700,000 = 0

Solving for r gives a value of 8.67 percent, the IRR.

So, how exactly do you solve for r? If you’re doing it by hand, you start by guessing an r, plugging it in, seeing what you get, and trying again with an adjusted r. You repeat this iterative process until r equals 0.

It’s much easier to solve the IRR calculation using the Excel IRR formula: “=IRR(cell array).” According to Microsoft, you can supply a guessed starting valuation, but it’s optional.

## The Pros and Cons of Using IRR

IRR is a powerful tool for evaluating investments and making investment decisions. It has pros:

- It acknowledges the time value of money over any period of time.
- IRR is easy to understand and solve (with the Microsoft Excel IRR function).
- It doesn’t require you to provide the cost of capital you invest in a project, which is often imprecise.

On the downside:

- It ignores the dollar size of an investment return, which can cause you to prefer smaller investments with higher IRRs but smaller dollar returns.
- IRR doesn’t include any subsequent cash outflows that occur after the initial investment, cautions Iowa State University.
- It assumes the reinvestment rate of intermediate cash flows equals the IRR, which isn’t necessarily true.

## How to Analyze IRR for Decision-Making Purposes

Investors and businesses can use IRR to compare competing investments or projects. It will tell you which investment opportunity should have the biggest rate of return (i.e., the highest IRR) but not necessarily which returns the most money.

In corporate finance involving capital budgeting and financial modeling, businesses compare IRR to a hurdle rate, a required rate of return equal to the weighted average cost of capital (WACC, the company’s cost) invested in a project. The IRR must exceed the hurdle rate to earn a profit, allowing the business to eliminate unprofitable potential investments.

YEAR | AMOUNT |
---|---|

0 | $(700,000) |

1 | $120,000 |

2 | $150,000 |

3 | $180,000 |

4 | $210,000 |

5 | $260,000 |

References

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