What is Internal Rate of Return (IRR)?

Calculating the internal rate of return is like eyeballing whether you should try to jump over a stream...

You’re making some guesses about how far your jump — your potential investment in your project — will take you. If it takes you far enough, you’ll soar through the air to the other side (lots of profit); if it falls short, you’ll get all wet (i.e., lose money by making a suboptimal investment).

The internal rate of return shows you a percentage representation of how fast an investment generates funds and offsets costs. This rate allows you to find the break-even point (the point where costs are equal to money returned) of an investment by comparing the rate of increase (how fast the investment generates money) to time and costs. Because IRR only deals with generated cash, time, and cost, it can be used to analyze almost any type of project or investment. While no one method can tell you everything about an investment or project, IRR gives one possible way to compare apples to apples when the investments themselves may be very different types of projects.

Like any formula dealing with future events, the accuracy of your data guesses is a limit for IRR. If you use the wrong figures for future cash generated, the resulting percentage will be incorrect. Another restriction of IRR is the project scale. The strength of IRR in focusing only on cash flow is also its weakness. IRR tells you at what rate cash is returned. An extensive project with a high initial cost may look bad when compared with a smaller project if the small project gains cash to offset costs faster –- Even if the larger project will make more cash over the long run. Continuing investment costs are also not considered in IRR. IRR ignores things like maintenance on new equipment, taxes, energy for new buildings, and fuel for vehicles. IRR also assumes that cash flows from the project are reinvested elsewhere at the same rate of growth as the project itself.

Where the internal rate of return takes future cash flows and length of time into consideration, modified internal rate of return (MIRR) is a more complicated calculation almost always done with a financial calculator or software. This is not because of the formula, but because of the number of items to be calculated before the formula can be used.

The formula for MIRR is:

FVCF represents the future value of positive cash flows (discounted for their reinvestment rate). PVCF represents the current (present) value of any negative cash flows (discounted for their financing rate). N represents the number of periods (usually the time of the investment in years).

MIRR looks at:

• the future value of cash flows discounted by a reinvestment percentage rate
• the current value of negative cash flow adjusted by the percentage cost of financing
• the number of periods involved (how long the investment or project lasts)

Future value of cash flows attempts to figure out how much cash is worth based on when the money is received. For example, your paycheck today may be worth more than your paycheck next week if you can invest the current paycheck at a high interest rate. Current value of negative cash flows is similar to future value of cash flows, but it compares money based on cost of financing rather than growth of reinvestment. The number of periods used in MIRR is just how long the project is expected to last.

MIRR addresses IRR's assumption of the reinvestment rate and recognizes the possibility of negative cash flow. This means that with MIRR, you can get a feel for how reinvesting cash flows will add (hopefully) to the project's total cash production. Further, the effects of any periods of negative cash flow and their rippling impacts on reinvestment results.

Where the IRR metric looks forward to how fast an investment with return cash, net present value (NPV) accounts for positive and negative cash flow while also accounting for a more realistic view of the reinvestment of cash received from the project — This results in a clearer picture of the true returns generated by an investment. Return on investment (ROI) is a simplified measure of whether or not investment results are positive, and it is a much more straightforward calculation than IRR.

NPV is complicated (in concept of the variables involved rather than the actual math) so that it is often done by a financial calculator program rather than by hand by non-accountants. The actual NPV formula is: NPV(sub)XYZ=((Z(sub)1)/(1+r))+(Z(sub)2)/(1+r)^2)-X0 with Z(sub)1 and Z(sub)2 representing cash flows for time periods 1 and 2, r is the discount rate (the investment percentage rate), and X0shows the cost or initial amount invested.

NPV is often used with IRR because it addresses the time value of money that IRR does not. NPV modifies the expected future income by considering when each cash set is received. This modification means a better picture of reinvestment of cash flow can be achieved than with IRR, which takes all future cash flows as one lump sum. NPV and IRR are often used together to give a fuller picture of the possible profitability of a project or investment, especially comparing it to alternative investments. Where IRR shows speed, NPV shows a value of the investment or project.

Return on investment simplifies the idea of investment returns to the total return for the life of the investment or project. To find ROI (((Ending value - Cost)/Cost)x100), subtract the starting value (cost) of an investment from the expected end value of an investment. Divide that number by the starting value. Finally, multiply that result by 100 to get an ROI percentage. ROI does not take into account periods of negative cash flow, reinvestment of cash results, costs of financing, or any other variables. ROI results are purely a comparison of investment value at the beginning vs. the value at the end of the investment to see if it made a profit and how much.

IRR is not a simple calculation without a financial calculator, and it uses NPV calculations as part of the formula. An NPV of zero is the starting point of the IRR formula. This does not mean that the NPV of the project is zero, just that it must be set as zero when used in the IRR formula. A full NPV calculation result without limits can still be used to compare to the final IRR result. This manipulation of the NPV value is one reason that IRR calculations are almost always done with the help of a program. The IRR calculations are, in many ways, a bit like doing gymnastics with math.

The formula for IRR is: 0 = NPV = nΣn=0 (CF(sub)n)/(1+IRR)^n

CF(sub)n=Cash flows n = Periods N = The holding period NPV = Net present value IRR = Internal rate of return

The complexity of the formula can easily lead to mistakes when calculated by hand. The length of calculation complexities, like multiple guesstimates required, means that it is almost always handled using a financial calculator or spreadsheet. Many financial calculators are available online, and are usually more powerful than spreadsheets. Both Excel and Google sheets have built-in IRR functions (XIRR for periodic cash flows in Excel). The built-in function reduces programming required so that you can enter your initial information, and the programs do the calculation. However, setting up the data input can be tricky. Downloadable Excel templates remove this uncertainty. Because of inherent spreadsheet limitations, guesstimates of growth rates must be entered over and over until the correct one is guessed by the user. These guessing steps lead most to stick to more powerful financial calculators to skip the rate guess steps.