Companies make investments according to the future cash flows these investments will generate. Since money sooner is more valuable than money later — $100 today is better than $100 in ten years — they discount these cash flows back to the present. In order to find the value of the project, a company will add all of the discounted cash flows associated with the project, minus the initial investment amount, to get the Net Present Value (NPV). If the NPV is positive, the investment is a good one.

Say I want to buy a kebab stand for $100,000 and it will generate profits of $25,000 for 5 years whilst I have the right to operate on a street corner in New York City. Let’s say my bank likes me and I can borrow the money at 5% interest.

Is this a good investment? Here are the discounted cash flows:

Year 0, -$100,000 investmentYear 1, $25,000/(1.05^1) = 23,809.50 Year 2, $25,000/(1.05^2) = 22,675.70Year 3, $25,000/(1.05^3) = 21,595.90Year 4, $25,000/(1.05^4) = 20,567.50Year 5, $25,000/(1.05^5) = 19,588.10

If we sum year 0 through 5 we get $8,236.90, a positive net present value. Corporate Finance 101 says we’re buying the kebab stand if no other opportunities are available.

Wait! What about the interest and principal payments on the debt? That’s already factored into each cash flow via the discount rate (the 5%). Since we’re netting out the original investment as well, we don’t need to factor principal payments either.

What if instead of buying a kebab stand we are thinking of going to college at Pretty Campus University (PCU)?

Since PCU is expensive — $75,000 per year — the admissions counselor shares with us data for average college graduate earnings versus average high school graduate earnings from the Hamilton Project’s Career Earnings by Major.

Each year in the table below is a year since starting work and goes for 42 years (until we’re about 65). The earnings numbers are annual. The “Improvement” column is the amount a college graduate earns (averaged of all majors) in excess of high school graduates.

Those with college degrees in the table earn a lot more than high school graduates each year. We will use this annual difference as our cash flows to evaluate the investment. (This difference, of course, is not necessarily “caused” by college since it could be that high IQ individuals are the ones that go to college in the first place and would have higher earnings regardless, but that is a separate paper.)

Since we are a cash-strapped 18-year old, we choose to borrow the entire $300,000 tuition. Luckily, our credit is good and our bank offers loans at 7.5% interest to fund the entire amount.

Is PCU a good investment?

For the sake of simplicity, we will assume we pay all of the tuition up front ($75,000 x 4 years = $300,000).

In the above table we include the present values of the wage improvements. Just like we did for the kebab stand, we add all of the present values of the wage improvements, $320,163.39, and then subtract our original investment of $300,000. We get a net present value of $20,163.39. Not bad!

Unfortunately, we still need to pick a major. The data above is the average of all majors. What if we ran the NPV calculation for each major separately?

Perfect! We have several majors to choose from. Tuition could cost $300,000 and, on a pure investment basis, many majors would still produce a solidly positive net present value.

Of course, this assumes no marginal tax cliffs, debt payments are manageable, our cost of capital (generally, our borrowing cost) is 7.5% , we don’t experience prolonged unemployment, our school falls within the national averages, inflation will remain constant, and the next 42 years will look like the 42 years in our data.

We aren’t satisfied though. Even if the NPV is positive, will we be able to afford our loan payments without impacting our living standards?

Technically speaking, the NPV calculation already factors in the financing costs (ie our interest and principal payments) so including those again would be double-counting. Nonetheless, the loan payments for borrowing our entire tuition are high. The monthly payment on a $300,000 loan at 7.5% interest to be paid off in 42 working years (our whole working life in the data) is $1959.81, or $23,517.72 a year.

For some majors, like Criminology, this high loan payment would make the early and later years of a career worse off than high school earnings (debt payments are larger than the total wage improvement) and this intuition doesn’t show in the NPV calculation explicitly (Criminology had positive NPV). Specifically, if our earnings improvement for a year is less than $23,517.72 then the high school graduate is better off for that year. While the potential shortfall can be “smoothed” by additional borrowing (like on a credit card), it’s likely at a materially worse rate than 7.5%.

What if we remove majors that (after loan payments) ever do worse than high school graduates?

These majors always do better than high school graduates, on average, even after they make (big!) loan payments. All other majors have at least one year where they pay $23,517.72 in debt expenses but earn less than $23,517.72 more than high school grads. That is, the high school grads would be making more money (net) than them.

So, is it smart to borrow 100% of a $300,000 tuition to attend college?

Possibly, but only for four subjects: Nursing, Accounting, Computer Science, and Engineering.

The point here is that debt isn’t bad per se, but it can be terrible on a financial basis if a student picks the wrong major. Our current system that relies on student loans forces students to make this large financial decision before they are reasonably equipped to calculate it. Indeed, pre-university students, who have yet to take classes that cover these topics, don’t know how to evaluate this decision by definition.