Hey PF, have lurked on this sub for a while. I'm a practicing physician. When I went to medical school, I spent a lot of time thinking about the opportunity cost of medical school. Maybe ruminated on it too much, possibly. Recently, I have returned to this as I start thinking about saving for retirement. I figured I would share some of my thoughts, for anyone that is thinking about possibly going to graduate school. At the time, thinking about this stuff made me incredibly pessimistic about going to medical school, but fortunately, I now love what I do, and there are more important things that money at the end of the day.
To start, I decided to model retirement savings as a continuous function. This would be ignoring the volatility of investing, but greatly simplifies the model, and I wanted to keep it simple.
If you assume that the rate of savings over time is equal to income plus savings * interest, then ...
dS/dt = income + savings x interest x t
Solving this differential equation gives the following.
S[t] = (Exp[interestt]-1)(income/interest)
Now that we have an expression for compounded savings, we can solve for savings as a function of time, for a given interest rate, with a given rate of contributions.
For example, at the prevailing rate of return of the S&P 500 over the past 30 years has been approximately 8.5% annually. For example, investing 10000 USD / year over 15 years should yield approximately 300000 USD at the end of that period.
So with this we can calculate the opportunity cost of attending graduate school, by considering two scenarios. In one, the ORIGINAL scenario, you start working out of college (we'll assume debt free) and start saving at some rate. Because you are not going into debt, you immediately start accruing savings.
The ALTERNATIVE scenario, you decide to go to medical school (or some other expensive graduate school), requiring you to not just forgo income, but also possibly to incur debt for tuition. In this scenario, your net worth becomes initially negative, and you only achieve zero net some time after graduating from school.
To keep the model simple, I didn't bother to take into account the specifics of debt accrual or repayment. Again, too complicated. Rather, I decided to use the delay between starting saving between the two scenarios as an input to the model. For the ORIGINAL scenario, you would start saving right after college. For the ALTERNATIVE scenario, you would start effectively saving for retirement when the last of your loans were paid off. So a reasonable assumption would be a delay of 10 years - 4 years for medical school, 4 years of residency (presumably just paying small amounts on the loans), and then 2 years of being an attending, when the bulk of the loans would be paid.
Since we have a function that approximates savings as a function of time, we can solve for WHEN the savings of the alternative scenario, catches up with the ORIGINAL scenario.
So if we express the above function as Savings[time,interest,income] ... Then we can consider an example scenario.
Savings[10+t,0.085,10000]==Savings[t,0.085,30000]
Solving for t numerically yields approximately 13 years.
To summarize, this considers how long after reaching zero net worth, it would take for a medical school graduate to catch up to someone saving right out of college, assuming the physician started saving 3x as much after paying off the last of your loans. The term 10, is the delay between starting medical school (when the original scenario would start saving), and completing paying off loans (when the alternative scenario would start saving). As you can see, even by saving at a rate three times faster, it still takes almost 13 years to catch up. To contextualize this, assuming you start medical school at 21 (right after college), you wouldn't break even until age 44 years, 23 years later!
The above specific scenario involves several fairly aggressive assumptions. First of all, this assumes that after 4 years of medical school, and 4 years of residency, you are managing to pay off all of your loans (however large) in only a further 2 years of being an attending physician. Not necessarily impossible, but possibly difficult depending on how much debt is incurred. Intuitively, the longer that the higher income of the alternative scenario is differed, the larger the opportunity cost. Plugging in another set of values confirms this.
For example, if it took you 4 years of being an attending to fully pay off your loans (i.e. achieve zero net worth), then, assuming you're still saving 3x as much.
Savings[12+t,0.085,10000]==Savings[t,0.085,30000]
Where 12 represents 12 years consisting of 8 years of medical school and residency, and 4 years of being an attending.
Solving for t gives 25.6 years, which again assuming you go to medical school right out of college, would mean that you would catch up with the ORIGINAL scenario at age 58 years, approximately 37 years after starting medical school!
And again, this is assuming that you go immediately to medical school without any delays, and it's still assuming a somewhat aggressive strategy for paying off loans.
Alternatively, we can assume that we want to catch up after a certain delay, and solve for the multiple of income required to break even.
For example, let's say we plan on paying off loans 3 years after finishing residency, so a lag time of 11 years (4+4+3 years). If we were going to save 10k per year in the original scenario, and we want to catch up 20 years after achieving net worth, how much would we need to save in the ALTERNATIVE scenario, to catch up at age 52 (assuming we started medical school at age 21).
Savings[20+11,0.085,10000]=Savings[20,0.085,x]
Numerically solving for x gives us a value 28.9 k USD / year.
So, in other words, to break even by age 52, you would need to save almost three times as much as the original scenario.
Rather than numerically solving, it's also possible to solve for a symbolic expression that describes the multiple savings rate required, as a function of the delay to reaching zero net worth (the lag), prevailing interest rate, and the time from reaching zero net worth to catching up to the ORIGINAL scenario (the term).
I called the multiple required to catch up, alpha.
alpha = (Exp((Lag + Term) x interest)-1)/(Exp(Interest x term)-1)
Solving for the same values as the previous example shows consistent a consistent result.
alpha = 2.89
Notice that alpha grows exponentially the longer one takes to fully pay off loans.
It's worth considering the numbers if there is a large lag time until loans are paid off. For example, I heard of an attending where I did my residency who didn't pay off his loans until his 40s. Assuming he went to medical school in his mid 20s, and paid off his loans in his early 40s. Lets assume he wants to be done working by age 70.
Lag time = 42-25 = 17 years Term = 70-42 = 28 years Interest = 0.085
With these values, alpha is 4.6. Thus, he would need to save this multiple to catch up by age 70! Realistically, he may end up just saving at a lower multiple, and therefore never catching up with what he would have made if he had just started working out of college.
There are obviously several drawbacks to this model. The greatest of these is that it assumes continuous uninterrupted gains from investing. Obviously not true, especially recently. However, over the long run the stock market is a biased random process, so on average, this should be reasonably OK approximation for this model.
I guess the reason I felt like sharing this, was that I had only considered this after enrolling in medical school. It felt like that was too late to have considered this stuff. I was already committed at that point, mentally and financially. Honestly, when I finally considered this, it scared me. I felt like I was drowning in six-figure debt for over a decade. Even if you think about it, and you have a plan, it's scary to be that far in debt. And one of the things my model didn't cover was the fact that you might not like what do do as a physician when your done. Fortunately, I love what I do, but several of my classmates either dropped out, or switched into different fields after finishing medical school. They'll probably never recover from such a huge loss. I'm sure they'll make ends meet, but they'll most likely never catch up to where they would have been if they had just gotten a job out of college.
Anyways, if any of you are considering going to graduate school, I'd just suggest being extremely dispassionate about the costs, particularly the opportunity costs, both in time and money. The cost of tuition is only part of the picture. The other thing is, people everywhere assume that doctors make tons of money. While in general we're well paid, remember that that lag between making that salary can be significant. A physician making 200k per year, with an alpha of 3, is almost like someone making 66k per year, after considering the opportunity cost.
Just my two cents.
Submitted December 08, 2018 at 02:25PM by albinus1927 https://ift.tt/2rqnq5N
