## Pages

### Tweaking The ROI Model

Our ROI calculations before took complex career situations of two different individuals over a 30-year period and brought everything down to a number.   But are such models accurate?

The old adage of “Garbage In Garbage Out” is relevant here.  The model itself isn’t smart enough to know the difference between right and wrong.  But it does accurately calculate the ROI based on the numbers given to it.

Reasonable people can disagree about the various inputs to the model, such as the starting salaries of the two individuals or their 3% and 5% raises, respectively.  Critics may question if the raises are as certain as the rising sun.  People get laid off, others get promoted, what happens to raises then?  What if the college attendee worked while he studied and made some payments towards his loan - lowering his “in the hole” amount?

These are all valid situations that can be modeled just as effectively as our original model.  But adding complexity doesn’t mean that our original model is inaccurate.  In fact, it is pretty good for what we are trying to determine: “Does college pay off, and if so, under what circumstances?”

## Sensitivity Analysis:  Does a difference in starting salaries matter?

This is why financial analysts and economists test their models by tweaking the inputs a bit to reflect true world situations - and seeing how the outputs vary.  They use a fancy name - Sensitivity Analysis - to describe the effort but the idea is the same.

Let us consider several different real-world scenarios.  In our original model, the two individuals had a \$15,000 starting salary difference.  What happens if the HS grad actually had a higher starting salary of \$30K bringing the difference in compensation down to just \$11,000?  It is important to keep all other variables the same.

In the adjoining table, the ROI of the TAMU grad drops to 18.54%, but is still higher than the Fed estimate.  Note that he has to wait until Year 19 to overtake the HS grad, a slip of 4 additional years compared with the previous model.   Clearly, the model is sensitive to the starting salary difference - something our gut tells us.

## Sensitivity Analysis:  How impactful is the graduation rate?

Let us now look at additional scenarios.  Everyone talks about how important graduation rates are, but what does our model say?   To do this, we will go back to our ROI calculations before and delay the TAMU grad’s graduation date by two years.

The ROI for the TAMU grad drops to just 9%, nearly by three quarters compared to the first model of graduating in 4 years.   This can be explained by the very late inflection point, in Year 22, the first time that the college grad does better than the HS grad - see Column E.   Also, the college grad carries the loan for a longer period and is not done paying off his loan until Year 26.

If one must graduate late, what should be his starting compensation at which he will have an ROI of 15%, the Fed estimate?  The table below shows that our 6-year graduate needs to negotiate a \$43,000 starting salary to get to this goal.

The last two tables show how impactful delayed graduation can be, so impactful that it in some cases it may not be worth going to college at all.  Students at elite institutions know this because the Department of Education says that graduation rates are the highest at post-secondary degree-granting institutions that are the most selective (i.e., had the lowest admissions acceptance rates).  For example, at 4-year institutions where the acceptance rate was less than 25 percent of applicants, the 6-year graduation rate was 89 percent; at 4-year institutions with open admissions policies, only 34 percent of students completed a bachelor's degree within 6 years.

UCLA’s Higher Education Research Institute has published an online Graduation Rate Calculator which can be used to predict expected degree completion figures for a single student or an entire cohort of students at a college or university based upon ethnicity, gender, SAT scores and GPA.  It is a good tool to estimate how likely you are to graduate from college in 4 years.