IRR- abit more

IRR -

The Internal Rate of Return (IRR) is defined as the discount rate that makes the project have a zero Net Present Value (NPV). IRR is an alternative method of evaluating software investments without estimating the discount rate. IRR takes into account the time value of money by considering the cash flows over the lifetime of a project. The IRR and NPV concepts are related but they are not equivalent.

The IRR uses the NPV equation as its starting point:

Definition of Terms

Initial investment: The investment at the beginning of the project.

Cash Flow: Measure of the actual cash generated by a company or the amount of cash earned after paying all expenses and taxes.

IRR: Internal Rate of Return.

n: Last year of the lifetime of the project.

Calculating the IRR is done through a trial-and-error process that looks for the Discount Rate that yields an NPV equal to zero. The trial-and-error calculation can by accomplished by using the IRR function in a spreadsheet program or with a programmable calculator. The graph below was plotted for a wide range of rates until the IRR was found that yields an NPV equal to zero (at the intercept with the x-axis).

As in the example above, a project that has a discount rate less than the IRR will yield a positive NPV. The higher the discount rate the more the cash flows will be reduced, resulting in a lower NPV of the project. The company will approve any project or investment where the IRR is higher than the cost of capital as the NPV will be greater than zero.

For example, the IRR for a particular project is 20%, and the cost of capital to the company is only 12%. The company can approve the project because the maximum value for the company to make money would be 8% more than the cost of capital. If the company had a cost of capital for this particular project of 21%, then there would be a negative NPV and the project would not be considered a profitable one.

The IRR is therefore the maximum allowable discount rate that would yield value considering the cost of capital and risk of the project. For this reason, the IRR is sometimes referred to as a break-even rate of return. It is the rate at which the value of cash outflow equals the value of cash inflow.

There are some special situations where the IRR concept can be misinterpreted. This is usually the case when periods of negative cash flow affect the value of IRR without accurately reflecting the underlying performance of the investment. Managers may misinterpret the IRR as the annual equivalent return on a given investment. This is not the case, as the IRR is the breakeven rate and does not provide an absolute view on the project return.

Equations:

The Internal Rate of Return (IRR) equation is a unique case of the Net Present Value (NPV) equation. The IRR is found by solving the NPV equation for the rate that will yield a NPV equal to zero:

Internal Rate of Return (IRR) Equation

Definition of Terms

NPV: Net Present Value

initial investment: The investment made at the beginning of the project.

Cash Flow Year n: Measure of the actual cash generated by a company or the amount of cash earned after paying all expenses and taxes.

IRR: Internal Rate of Return. n: Last year of the lifetime of the project.

Modified Internal Rate of Return (MIRR) Equation

Other variations of the IRR equation are sometimes used in an attempt to fix some of its shortcomings. The most popular modification of the IRR concept is, not surprisingly, called the Modified Internal Rate of Return (MIRR).

The goal of the concept is to correct for the intermediate cash flows that are reinvested at the IRR, not at the cost of capital to the company. This correction does not accurately represent the risk of the investment or the cost of capital to the company for the particular project. IRR calculations are based on the assumption that returns earn the IRR for the entire duration of the investment.

In the MIRR equation, the intermediate cash flows are invested at the cost of capital of the company, thus compensating for the reinvestment assumption.

Definition of Terms

NPV: Net Present Value

FV (Cash flow at Year N): Cash flow for a particular year.

MIRR: Modified Internal Rate of Return. N: Total number of years for the project

Consider the example below for an implementation of a Human Resources software application during a four year period:

HR Application Example Initial Year 1 Year 2 Year 3 Year 4 cost: $150K benefit: $60K benefit: $60K benefit: $40K benefit: $20K Cost of capital = 10%

The MIRR equation will invest the benefits or cash flows generated by the project at the cost of capital to the company rather than the IRR. The future value of the benefits at the end of the investment is calculated by using the cost of capital and then the equation is solved to find the IRR:

Establish the future value at Year 4 from the following cash flows: $60,000 (1+ 10%)^3 +$60,000 (1+ 10%)^2+ $40,000 (1+ 10%) + $20,000. The total future value is equal to $200,000. Then, the IRR is determined by solving the equation below:

0=Costs + Future Value/(1+IRR)^4
0=-$150K + $212K/(1+IRR)^4
MIRR = 9.11%

The standard IRR would have given a value of 9.22%. Therefore, the standard IRR equation tends to overestimate the return of the project.

Benefits:

The Internal Rate of Return (IRR) concept has been widely adopted by companies as they compare their cost of capital against the IRR for a particular project or investment. The main benefits of IRR are its simplicity and intuitive appeal. Companies can easily compare the rate of their cost of capital against the IRR of the project or investment. If the IRR is higher, then the project can be approved.

In addition, the IRR method does not require establishing the discount rate, as is necessary in a Net Present Value (NPV) calculation. Finding the appropriate discount rate can be a difficult task when including the unique risks of the project. Therefore, using IRR simplifies the process of estimating the value derived from a project. The IRR concept can also be complementary to NPV analyses.

The IRR graph can be plotted to understand the dynamics of the discount rates considering the cash flows. The graph can provide information on the discount rates that would yield a negative NPV. This information in itself will create a limit on the maximum allowable discount rate or risk for the project. A company can then restructure the project to lower the project risk to a level that will yield a positive NPV.

Problems:

The Internal Rate of Return (IRR) concept has several limitations and although the concept is relatively simple, it can be easily misinterpreted and confused with the actual project rate of return. These limitations are listed below.

Timing of Costs and Benefits

Projects that require investments at a later stage may yield IRRs that are not representative of the value of the project. These later expenditures may turn a project's net benefits negative in a particular year. From the equation standpoint, these negative net benefits or cash flows are treated the same as borrowing money, resulting in misleading IRRs. When dealing with negative net benefits, the IRR concept can generate multiple IRR values for the same project, making it difficult to compare which IRR is the true value. To avoid these scenarios, it is best to apply the IRR concept only to projects or investments having positive cash flows throughout their lifetimes.

Relative vs. Absolute Values

The IRR does not indicate the magnitude of the value of the project. This presents a problem when comparing the IRR values from different projects. For example, a project with a high IRR may appear more appealing than a project with a lower IRR, even if the project with the lower IRR has a greater Net Present Value (NPV).

In summary, the IRR model is a good first approximation as to the value of a project. In fact, the IRR model is somewhat better than a Return on Investment (ROI) model to perform this initial evaluation because the IRR considers a project's risk and the time value of money. But given the limitations presented above, it is better to combine the IRR analysis with more comprehensive financial evaluation tools, such as Net Present Value (NPV) or Real Options.