Wednesday, September 14, 2022

Financing the Purchase of a Box Containing One Million Dollars

Suppose you have an opportunity to purchase a box containing a million dollars. It's not actually cash, but a series of IOUs that are only redeemable by you. Because the box is only valuable to you, the current owner has no other buyers. He's willing to sell for, say, $50k. 

A very confused onlooker observes this situation and says, "But, you don't have $50k. You can't afford to purchase this box!" I hope we can all agree that this is silly. Obviously you can finance the purchase of the box out based on your expected future windfall. You don't have $50k yet, but if you can credibly prove that you'll make good on your investment, you can borrow some money at a reasonable rate and pay back the loan out of your profits. (Most obviously, you can say, "Let me have the box and I'll immediately open it and give you $50k", and you and the current owner can then part ways.")

Change the example a little bit. Now it's not one big IOU for a million dollars. It's a series of IOUs that reach maturity at different times, stretching indefinitely into the future. The net present value, discounting future cash flows, is one million dollars. But really that's summing up your increased income over a lifetime. It would still be incredibly silly to say that you "can't afford" to purchase the box. It's worth just as much. The different maturities change the timing of your loan payback, but it's still overwhelmingly a good deal. 

Change the example a little more. Now it's not a series of IOUs, but rather a collection of extremely rare seeds that only you know how to cultivate. The resulting crop will be extremely valuable. The expected payoff is still a million dollars over the course of a lifetime, but making good on that requires some planting and nurturing. It's not something that will be your full-time job, but once you learn the craft it'll be a light hobby that pays off handsomely. Or maybe the box is full of a kind of cryptocurrency that requires solving some math or logic problems by hand. (Only solutions worked out by you will unlock the crypto, it somehow knows.) Given consistent effort, these math problems will definitely pay off. You will never get stuck on any one problem indefinitely. You can skip some of them if you truly get flummoxed, but there are enough such problems to solve that the expected net present value is still $1 million. All you have to do is put in the time. It's probably still worth purchasing this box. In this latest scenario, it would still be incredibly silly for someone to come along and say you "can't afford" to buy the box. It would be equally silly to take a look at your finances at some time before your loan was paid off and say you need financial help. It's still the case that you can finance the purchase of the box out of your expected future earnings, and still make an absurdly high rate of return on your purchase. 

This arrangement is starting to look more and more like a college education. The later examples change the timing and certainty of the payoff and the element of labor required to make the investment worthwhile. College isn't equivalent to a box full of ready cash, but it is a really good deal if you make good on it. It pays for itself several times over. You can finance a college education out of the expected increase in your future earnings. You can make those expected future earnings more certain by choosing a remunerative major (STEM or pre-professional) and working hard while in school (versus slacking off and getting bad grades, which I saw a lot of in my college days). 

Looking up some quick figures, a college degree pays off to the tune of around $1 million over a lifetime. (Obviously this is an average that glosses over several relevant variables, like choice of major.) The average cost of tuition is about $10k per year for in-state, $20k per year for out-of-state. (Once again, glossing over some relevant variables. A prospective student has a lot of choices s/he can make to lower or raise this figure.) The figures I used in the "magic box" example are roughly in the same ballpark. A student making the right decisions can make this a really good deal. They don't need help. It's true that some students overpay to go to fancy private schools or get worthless degrees. Some pay exorbitant tuition for elite private schools. They are essentially deciding to buy an overpriced status good, possibly seeing it as their key to elite positions in government. They don't really deserve our sympathy and they certainly don't need help. Some drift aimlessly in college and eventually decide they don't want to finish. That's unfortunate. I wish I could counsel some of these people before they made an impertinent life choice or talk them into sticking it out for a couple more years. But I don't think they deserve our help. This is someone who is declining to pick up a million dollar bill on the sidewalk. 

The recent chatter about the proposal to cancel student debt has been maddening. It's obvious that this is a middle-class and upper-class entitlement. The benefit of this debt forgiveness accrues to those people who are reaping that $1 million boost in lifetime earnings (on average). The cost, assuming the government eventually pays for it, is being spread to everyone. This means people who don't go to college are, on net, paying for the people who do. 

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