## Internal Rate of Return (IRR) Tends to Overstate Education Return on Investment (ROI)

### Friday July 29, 2016

With dwindling government appropriations for higher education and elevated student loan default rates, more colleges and universities are conducting Return on Investment (ROI) analysis to demonstrate that higher education is a sound investment for students, taxpayers, and society at large. Those institutions include for-profit colleges, community colleges, and public and private not-for-profit four-year colleges.

Some of these studies borrowed a measure from finance, called Internal Rate of Return (IRR), as a measurement of return on investment for students and taxpayers. The origin of IRR can be traced to investment analysis, where the goal is to achieve a positive net present value (NPV) for an investment. Net present value depends on the discount rate chosen in the analysis and there is a need to see the break-even discount rate, which gives rise to IRR. IRR is defined as an annual percentage rate where the net present value of an investment (benefit minus the cost) is zero. So an IRR higher than the commonly used discount rate means the investment has a positive NPV, and vice versa. In a sense, a higher IRR points to a better return on the initial investment.

However, IRR is not the same as return on investment (ROI), which is defined as the benefit of an investment with respect to its cost. ROI can be expressed as benefit/cost ratio—the total benefit of an investment divided by the total cost. If an investment spans over multiple years, an average annual rate of return can be calculated based on the investment benefit and cost.

While IRR and ROI are related, and tend to move in the same direction, caution is needed when using IRR to represent the ROI of an investment.

A simple example can illustrate the difference. Let us assume that Al and Bob each place $10,000 in a savings account for 20 years with a 5% annual interest rate that is compounded once a year.

Al and Bob have different investment strategies. At the end of each year, Al takes that year’s interest income out ($500) and puts it under his mattress, while Bob keeps the interest in his account, which will generate interest for future years.[1] Bob’s strategy will generate a higher return over the 20 years. At the end of 20 years, the total amount of money for Al is $20,000 (including the initial $10,000), while that for Bob is $26,533—much higher than Al’s total.

The surprising part is that both Al and Bob’s investment strategies yield the same IRR at 5%. So, based only on IRR, the decision makers will think those two investments have the same return. But we have just seen that Bob’s investment results in an amount about 30% more than Al’s; and thus, has a higher ROI. More specifically, the benefit and cost ratio for Al is 2.0, which is equivalent to a 3.5% annual rate of return. Meanwhile, the benefit and cost ratio for Bob is 2.6, which is equivalent to a 5.0% annual rate of return.

Investing $10,000 at 5% Annual Interest |
|||

IRR | Annual Average ROI | Savings at Year 20 | |

Al (Spends Annual Interest) | 5% | 3.5% | $20,000 |

Bob (Leaves Annual Interest in Bank Account) | 5% | 5% | $26,533 |

In this case, using IRR will overestimate the rate of return for Al’s investment strategy. In fact, the IRR is equivalent to the annual rate of return on investment only if the annual benefit is reinvested at the same rate of the IRR.[2] That is the case in Bob’s strategy, where he invests interest income in the savings account that earns 5% interest. However, when the annual benefit is not reinvested (like Al), or is reinvested in something with less than a 5% annual interest rate, the actual annual rate of ROI is smaller than the IRR.

In ROI studies for higher education, the benefits are typically measured as the incremental income due to more education, and those are not universally reinvested. We rarely see college graduates save or invest all of that incremental income and maintain a lifestyle based on the income level of high school graduates. Some of the graduates may save a little more, but that amount is still only a small fraction of the incremental income. As a result, using IRR will overstate the actual rate of return for both students and taxpayers in ROI studies for higher education institutions.

Moreover, the longer the time horizon, the higher the degree of distortion with IRR. For example, in Al’s investment strategy, when the investment horizon is 20 years, IRR overstates Al’s ROI by 40% (5.0% IRR and 3.5% annual rate of ROI). If the investment horizon is 40 years or more (typical for education ROI studies because students typically will work more than 40 years after college), the actual annual rate of ROI is only about half of IRR.

When some reports claim that the IRR for higher education is 15% per year for community college students, the actual return on investment might only be half of that.

[1] This is called interest compounding—the interest income of prior years is treated as principal in future years and generates interest of its own.

[2] Source: Internal Rate of Return: A Cautionary Tale, The McKinsey Quarterly, 2004.

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