This is about common law again with lesson number 11 earnings table and ROI modeling. Let's go back a few lessons when we did the ROI formula for college total earnings over say 30 years, divided by the total cost of college attendance. Until now, we have been focusing on lowering the denominator because we know this will improve our ROI. In this lesson, we will examine what happens to the ratio if we increase the numerator. We know from our middle school math classes that the ratio will increase, but we will learn about how impactful it is To do this, we will build a few simple financial models. At first, it might seem premature to discuss post college earnings in a college financial planning course.

But please bear with us. The decisions we make during college and immediately afterwards can have a profound impact on finances. In this lesson, we will build a simple model in Excel where we can simulate real life decisions in college. We will revisit our previous question of whether or not it is a good idea to pursue college. But we will do this with real numbers, no guesswork or gut feeling anymore. You will see this for yourself.

Suppose that your starting salary after graduation in your first job is $41,000 and you earn a 5% raise for the rest of your career. How much money will you earn over a lifetime of 30 years? That's easy, we can simply construct an earnings table in a spreadsheet. Notice that we have no earnings while you're in college. And then the first year earnings are 41,000. in year five, the second year is 41,000 times 1.05. The 5% raise and the third year is 40,050 times 1.05.

And so the total earnings in this model after 30 years $1.95 million. Our earnings table shows income earned over a long period. But there's one problem. Everyone knows that $1 earned 30 years now is just not as valuable as $1 today. To understand this, just ask an adult friend or a family member, what they paid for their first car for the same model and make chances are that they paid a lot less than what the same car sells for today. But simply there is a time value to money.

Here's a good example. On April 30 18 03, the US agreed to pay France $15 million for what is known as the Louisiana Purchase, which was about 820,000 square miles and it nearly doubled the size of the US. How much would it cost us to buy this much land today? So let us go back to the earnings table. Again, we said that over 30 years, this college grad will earn $1.95 million. But if you look at the timeline value of money.

What is 1.95 million worth in today's dollars? That is called the net present value, which is a calculation that compares the amount invested today to the present value of the future cash proceeds from the investment. This technical definition seems to be a lot of gobbledygook. So let's try and understand what it's saying. What amount invested in a bank today at say 4% interest would have given you an income stream identical to that of the college grad over 30 years that is 41,000 in year 540 $3,000, in year six and so on. Such an amount would represent the net present value of the college grads earnings.

In other words, mathematically at least, it would not matter if we had an earnings stream over 30 years or this NPV amount today. Both would be identical. NPV is a simple but powerful approach to bring forward a series of Cash Flows each year to a single number a valued today's dollars eliminating the time component for our NPV calculators are available online and as a function in most spreadsheets. An important quantity needed to calculate NPV is the discount rate the interest that takes into account not just the time value of money but also the risk or uncertainty of future cash flows. This we assumed to be 4% in the bank example, it's also called the internal rate of return. So let us calculate the NPV for our college grad.

Over 30 years, we can bring it down to a single number and that number is 1.02 million. If you were to place this amount in a bank At a 4% annual interest rate for 30 years, the bank would give you an annuity income identical to the earnings table that you see here of this college graduate. The 1.95 million over 30 years is mathematically equivalent to 1.02 million today. This is why this amount is called net present value. But how do we know if it's worth it to go to college? The truth is we don't know yet.

One thing we could do is to compare a college grads earnings over 30 years with a high school grads earnings over 30 years. And then if we could bring both of these earnings amounts to today's dollars, that is if we were to compare the NPV of the college grad with the NPV of the high school grads, we would be technically comparing apples to apples. Let's try this exercise. We already have the NPV of the college grad we need to calculate the NPV of the high school grad and if the NPV of the college grad is higher, we could conclude that the ROI of the college grad is better. Let's go back to what we did for for the high school friend, we said that he will get a job as a technician for a company and he makes $13 an hour and gets a 3% raise each year.

So he would have made $26,000 during year 120 6007 80 during year two and so on until he earns $108,000 over the four years that you will be at college. So we will use these values in the high school grad at DVC. Now you see that it is $654,000. Now we can compare the two. We already know that the NPV of the college grad is 1.02 million and clearly the NPV of the college grad is higher than that of High school grads. So now can we conclude that it is worth it to go to college?

Not really. We are missing something very important here in calculating the college grads in TV, we completely forgot the college grads costs that our borrowing costs and monthly loan payments for a long time 15 years. So we need to subtract these costs from the college grads earnings to calculate net earnings. Those surprise that is why the calculation is called net present value where net indicates earnings minus the costs. So let us recalculate the college grads NPV after taking into account loan costs. Let's go back to our example before it costs $109,000 to go to Texas a&m There is free cash of 13 plus 16 about $29,000.

And this student takes $80,000 of loan that you agreed to repay. Our loan costs are $7 per month for 15 years and we will assume that we will begin repaying this after the student graduates in four years that is starting EFI. assumed a $16,000 interest free loan is first paid off through working on campus and the summer. Now, let's construct the table. The loan payments are $700 times 12 $8,400 a year and this will happen every year for 15 years. So if you look at the first year's earnings for the student, he earns $41,000 but he has to pay $8,400 in loan payments and therefore the only gets to keep $32,600 for the first year.

So, we do this for all the 15 years. Now, if you calculate the net present value, you will see that it is $894,000. Much less than the 1.02 million that we said when we did not account for the costs. We had already agreed to ignore other costs eating out. Now if we were to calculate the ROI, we see that it is 36.78%. If your starting salary in your first job after college is $41,000, and you earn a 5% raise for the rest of your career.

And you have a college loan where you pay $700 a month for 15 years over a 30 year career. Your total ROI is nearly 37%. Much better than the 15% ROI standard of the Federal Reserve Bank. So when will the college grad pass the high school grad in net earnings? Look at the yellow bar. This is year 15.

That is when the total college grads earnings exceed the high school grads salary for the first time after you account for the costs from then onwards, the college grad is better off year 19 is when he makes his last payment to the bank. So what did we do just now? We took complex situations of two different individuals over a 30 year period and brought everything down to a number or a set of numbers. But are such models accurate? Well, yes and no. The math is perfectly accurate.

No question. What may be inaccurate are our assumptions such as starting pay of the two raise each year On in real life, these numbers could be off. People could lose their jobs or obtain promotions. What are the college attendee work while he studied and made some payments towards is known, lowering his in the whole amount. These are all valid situations that can be modeled just as effectively as original model. But adding complexity doesn't mean that our original model is inaccurate.

The larger point holes, the truer we can model real life situations, the more accurate our results will be. We just learned how powerful financial models can be rather than make important life decisions on gut feel. Models help us use simple math to predict outcome based on a set of inputs and rules. Models are powerful, we use sophisticated models every day. We just don't think about them too much. Just look at the weather forecast.

There is an additional benefit of modeling the ability to change inputs one at a time and see how outputs change. Financial Analysts and economists use the fancy name sensitivity analysis to describe this effort. But the idea is the same reflect true world situations. In most situations doing so that is financial modeling confirms directionally, at least what we already intuitively know the models give us more details about the magnitude of the change. That is how much outputs change when inputs change. In the next lesson, we will try and simulate a few different real life conditions to appreciate how they will affect our financial plans to go to college.

If you have any questions, please let us know. Thank you.