## Explain It

The College Risk Report brings up many concepts that you may not be familiar with, but that will be indispensable to you in making an informed financial decision about your education and career path. On this page, we aim to explain these important concepts in-depth. You may need to spend some time to become comfortable with these concepts, but we believe that it will be well worth your while in the face of having to make a lifetime of student loan payments.

## Concepts

## Net Present Value

Because money changes value over time, when comparing costs and payoffs it is necessary to make the comparison at a common time point. Although one may compare costs at any time point, either the present value, or at some future value (e.g. 20 years in the future) we stick with the present value comparison on this site because it is more intuitive. It is a lot easier to grasp what it means to have $1 million at present than to imagine what it will be like to have $1 million 20 years in the future.

A good example of why making cost comparisons at a common time point is necessary is to consider the price your grandparents paid for a candy bar at your age vs. the price you might pay for a candy bar today. They might have paid $0.10 for a candy bar that you would have to pay $1 for today. Now say that your grandparents had an allowance of $0.10 per week, and you have an allowance of $0.50 per week today. At first glance it might seem like your allowance is 5 times as much as your grandparents', but this doesn't take into account how the value of money has changed over time. Clearly, something has changed. Your grandparents could buy one candy bar per week on their smaller allowances, however you will only be able to afford one candy bar every two weeks on your allowance. In order assess who gets a better allowance - you or your grandparents - we need to bring both allowances to a common time point. To do this "transformation" we need to assume a discount rate.

### The Discount Rate

The discount rate is, in general, a way to account for how money changes over time; this is often also equivalently called "the time value of money."

To motivate this, imagine that someone offered you either $100 today, or $100 a year from now. Which would you take? You would take the $100 today! Why? Because you could take the $100 today, invest it, and it would be worth more than $100 a year from now. What you just intuitively understood is called "the opportunity cost of capital" where in this example capital is money and the opportunity cost is your ability to invest money that you get sooner for longer so that it is worth more. In general, IT IS BETTER TO HAVE MONEY SOONER RATHER THAN LATER due to this opportunity cost.

So where does the discount rate factor into all this? In the example above, say you took the $100 today, invested it for one year, and at the end of that year had $105. The annual discount rate would be 5% (or 0.05). It means that, in order for someone to give you an amount of money one year from now equivalent to $100 today, they would, at the end of the year, have to give you 5% more money, or $105.

Strongly related to paying for college, is that a similar example can be considered, but with debt. Say you must take out $1,000 in loans to pay for college, and those loans have a 6% interest rate (roughly typical). Then, in one year from now, you would need $1060 to pay off your loan. In this case, a 6% annual discount rate might be a better choice for the discount rate.

This highlights the fact that choosing a reasonable discount rate is challenging and probably more of an art than a science. For example, you might have loans that charge different rates, or the interest rate paid by banks for a savings account changes over time. With all of these different rates at play, how does one choose a reasonable discount rate?

There is no straightforward answer, but the key thing to remember is that - since money does tend to lose value over time - it is better to have money now rather than later, and the discount rate measures our belief of HOW MUCH better it is to have money now rather than later. If you believe that money does not lose value that much over time, you should choose a lower discount rate. If you believe that money loses quite a bit of value over time, then you should choose a larger discount rate. For this site, we use a 5% discount rate, which is probably on the low side. The long-term average interest rate for a US Government 10-year Treasury Bond is about 6.6%. The US Post office uses 4.9% for budgeting its pension plans. Note that the US government is able to borrow at incredibly low interest rates because it is perceived as extremely low-risk. You will almost certainly NOT be able to borrow at rates as low as the US Government.

### Back to Present Value

Before we took a brief detour to discuss the discount rate, we had mentioned that we needed to do a "transformation" on the amount of money at some time point to bring it to another time point - preferably the present time, since it is more intuitive for us to understand what a dollar amount in "today's dollars" can buy today. As alluded to, we must assume a discount rate which describes how the value of money changes over time to make this transformation. Once we have a discount rate, the transformation between a present value is given by an equation - that although it might look complicated at first glance - is rather simple, and we will break it down.

...where N is the number of years between Present and Future Values. Let's look at what this means. Since we will always have a Future Value that we are trying to turn into a Present Value, let's look at the denominator (bottom) of the fraction on the right-hand side of the equation. The larger the bottom/denominator of the fraction is, the smaller our Present Value will be for a fixed Future Value. We might ask ourselves: How does the denominator get bigger? And how QUICKLY does the denominator get bigger?

Well, one thing that makes the denominator bigger is a larger Discount Rate. This is easy to see since the Discount Rate is a small, positive number that gets added to 1. Another thing that makes the denominator bigger is a large N - the number of years between the Present Value we seek and the Future Value. And not only that, but the rate at which an increasing N makes the denominator bigger is exponential - meaning, for our purposes, that it grows much faster than you would expect. It's important to note that this exponential growth of the denominator also compounds the effect of a larger Discount Rate because the Discount Rate also is taken to that exponential power.

So, to summarize, the Present Value is small when the denominator is large. The denominator is large when both the Discount Rate and the number of years between Present and Future values is large. Furthermore, the denominator gets large quite quickly as the number of years term goes up due to its presence as an exponential in the equation. In short, this means that earnings in the near future are more valuable at Present Value because the denominator is smaller when N is small. Conversely, it means that earnings in the far future are much less valuable at Present Value because N is large and the decrease is exponential (rapid). This mathematically confirms what we stated earlier: IT IS BETTER TO HAVE MONEY SOONER RATHER THAN LATER. This is important to keep in mind as we go to the next section, because college will require a lot of money up front (which is worth more at Present Value) in exchange for payouts (salary) later that is generally worth less at Present Value.

### ...And Back to Net Present Value

So let's bring this all back to Net Present Value. We've discussed what it means to make a comparison at Present Value. The "Net" part simply means "net of expenses" or even more explicitly: Earnings minus Expenses, at Present Value. As we saw in the paragraph just before, it matters substantially when these expenses and Earnings occur because earnings/expenses are discounted more heavily the further in the future they are realized.

This is where the great "risk" of going to college comes from: it requires substantial early expense for earnings that are delayed by several years. This is what the Net Present Value attempts to convey. It's not to say that college isn't always worth it. In several cases it is, particularly when the college is relatively inexpensive (public school, in-state tuition), or when the future payments are high (engineering degree). However, you need to consider your options carefully. When a 2-year degree is less expensive than college - typically by one or two orders of magnitude - and often pays as well as better than a lot of college degrees, plus starts earning money 2 years earlier, it is something you should at least consider.

Back to top## Annual Rate of Return

The annual Rate of Return or "ROR" is a way of viewing how much your chosen degree returns, in terms of salary, on a yearly basis as a percentage of the investment you put into it (tuition). The ROR is calculated at Present Value. The reason for this is that it accounts for your return AFTER the declining value of money has been taken into account. For example, say we did not do the calculation at Present Value and, in this way, determined that your annual rate of return was 3%. Now consider that the Discount Rate during that time period was 5%. Despite having a 3% rate of return, you are actually losing money because this does not exceed the rate at which money is losing value. Thus, we perform the ROR calculation at present value to automatically account for our best estimate of how quickly money is losing value (the Discount Rate).

You will probably notice that 2-year degrees tend to return an incredibly high ROR compared to college degrees, although they might not necessarily have a higher Net Present Value (NPV) than college. The reason for this is that, ALTHOUGH 2-YEAR DEGREES DON'T ALWAYS EARN AS MUCH AS A COLLEGE DEGREE, THEY REQUIRE SUCH A SMALL UP-FRONT INVESTMENT THAT THE RETURN ON THAT INVESTMENT IS EXCEPTIONAL. This is something to carefully consider, particularly if you (or your parents) don't have a lot of money to put down for an education up-front, or if you are very wary about taking on large amounts of student debt (which cannot be discharged in bankruptcy) to fund your education.

Back to top## Break-even Time

The Break-even Time (BET) is probably the most intuitive metric to understand of all of the metrics presented in your custom report. It is simply the amount of time that it will take you, after finishing your degree, to earn back, from your chosen profession, the amount of money it cost to obtain your degree, all calculated at Present Value (since future dollars are worth less than the near-future dollars you will have to use to pay for your degree). Sometime it is easier for a person to grasp the cost of something if it is presented as years of their life rather than number of dollars.

Back to top## Executive Summary Plot

In the Executive Summary of your report, you received a plot that looks similar to the one below. Here we go in-depth to explain that plot.

This plot is contained in the Executive Summary because it visually represents all of the results that come out of the report. That is, all the key results of this report are contained in this plot if you know how to read it. Since this plot is so important, we will take some time to explain what it means. Please note that this entire graph is plotted in dollars at PRESENT VALUE.

First, the example plot above is for an engineering degree from a public school paying in-state tuition, therefore the college path provides quite a nice return. Your plot will not look exactly like this one, but will be similar. The curve of your college path may or may not grow higher than the other two paths as this one does, depending on what college and career path you chose.

With that out of the way, let's start at the left hand side of the graph where the y-axis shows "$0" and the x-axis is at 0 years from high school graduation and begin to follow each path to the right. All paths start out at $0, because at this point your cumulative (running total) expenses/earning are $0. Both the college and 2-year curves will first dip down below the $0 line representing the fact that you will first be paying money for a degree before you can start earning money. In contrast, the high school path goes from zero and starts heading up as time progresses, representing the fact that you will have no up-front educational expenses to put you in the negative dollar territory in the first few years.

Both the 2-year and college curves go downwards for a bit before they eventually turn back and start heading for positive territory. The lowest point on these curves before they switch direction and start heading up represents the Present Value of your expenses for that degree path. This is labeled for the college path in the plot above. The number of years (on the x-axis) that it takes for your college and 2-year paths to get back to the $0 line and cross into positive-money territory is the Break-even Time (BET) for that degree. This is, again, labeled for the college path.

As we continue to follow the curve for each career path to the right, they keep growing in value and the running sum of your earnings (net of expenses) continues to increase until all curves finally end on the right-hand side of the graph, at which point in time it is assumed that you retire. Where these curves hit the right-hand vertical line represents the Net Present Value (NPV) of each respective career path. This is labeled for all curves on the example plot above.

This plot can also be quite useful for non-traditional students - those students who are starting either a college degree or two year degree later in life and not right after high school. If you are a non-traditional student and want to know what your Net Present Value of either a college or 2-year degree is, then simply do the following: (1) Figure out how many years from when you START your degree you will work until (ex. 30 years). (2) Now go to that number on the x-axis and draw a line straight up so that it intersects the curves. (3) Look at where this vertical line that you drew intersects the curves and follow it to see where that intersection coincides with on the y-axis. This should give you a dollar amount which is the NPV of whichever curve you were considering, for the amount of years you plan to work.

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