## Rent or own?

This is a question that I’ve seen come up a fair amount recently. It is, of course, far too narrow and reductionist in its base form: all things being equal, is is better to rent or buy your primary dwelling?

The first thing to remember is that all else is never equal. Renting gives you the freedom to move out easily, but gives up the freedom to alter the inside of your house at will. Owning frees you from worries of rent increases, but exposes you to property tax hikes. But the big issue is properties are discrete, and have their own individual characteristics; you can’t go out and buy the average house of n-thousand square feet for n hundred thousand dollars if all of the houses on the market are either .5*N or 2*N, catering to two very distinct markets in your area.

But, given all that, is one a better plan than the other? Let’s do math and find out!

The first factor we need to consider is opportunity cost. Let’s imagine that you are Richie Rich, and that you want to maximize your long-term income. Right now, you have a lot of money in the stock market, earning a comfortable 7% after taxes, fees, and so on. Your previous dwelling vanished in a comic-book-related mishap. How should you proceed?

Well, as above, it depends strongly on the actual properties available where you want to live. Let’s say that you want to live in a handsome townhome very similar to my own, in a neighborhood very similar to my own, bought under…hell, we’re using my house as an example.

Now, my neighborhood is neat; the townhomes are nigh-identical, and there are several houses available for both rent and several more for ownership, so we can compare like with like. In this case, purchase price is about $130,000, and rent is about $1,200 per month.

If Richie buys outright, he ties up $130,000 of his wealth, as a one and done. If he rents, he’s drawing less than a hundredth of that amount down each month. But how many months will that be?

Richie is a kid, remember. He’s got the bulk of his threescore-and-ten ahead of him. Let’s say that he’s ten, and has 60 years ahead of him that he wants to plan for. So, over his lifetime, if Richie rents, he will incur $14,400 in rent costs a year, or $864,000.

Of course, we need to consider that opportunity cost again. Let’s set aside the money Richie won’t be touching for this transaction set. Let’s just say he has a million to play with. If he were willing to be homeless, he’d just be earning 7% on that million annually, so $1,070,000 in year 2, $1,0155,000 in year 3, and so on.

Now, we’ve got two really simple models. In one, we pull $130,000 right off the top, and do the interest for the remainder for those 60 years. In the other, we pull off the yearly rent price every year. So, what happens then?

The short version is that house-buying Richie makes up the losses in net worth by 25, and the gains just grow from there. Not hugely, mind you; it’s a difference of $51 million vs. $45 million; significant, but very much close enough that you need to do the math.

Of course, this doesn’t stop here. Richie Rich didn’t get that way because he managed his money poorly. What if Richie went to the bank and asked for a 30-year mortgage?

“Of course!” they’d say; Richie is the living embodiment of the safe lending prospect. He’d get a nice, middle-of-the-road 3.75% mortgage. (There would also be closing costs and down payment minimums and such, but we’re waiving them for simplicity here.) Essentially, Richie is taking out a $120,000 loan when he already has a million in the bank. Why?

Because 7 > 3.75. The opportunity cost of dropping $120,000 immediately is significant, as we have shown previously. In this case, Richie is paying about $556 a month, or $6700 a year, to pay back that mortgage. By doing this, Richie is maximizing the amount of money that’s earning the full 7% interest in the markets. That pushes his expected gains from $51 million to $53 million.

Now, all of these examples contain many assumptions. I neglect the cost of maintenance of the house, as well as the ability of the homeowner to optimize their own maintenance to limit their own costs. (How many apartment complexes that don’t pay for tenant water put in low-flow showers and toilets?) I assume that houses can sell fungibly, and that Richie can either live in his one new house indefinitely, or sell it for market value and move into another painlessly. But most of all, I ignore the downside risk. Downsizing your apartment in an economic crunch period is painful, but having to do so for a house you can no longer afford the mortgage payments on can be catastrophic if you can’t safely discharge the mortgage debt. Richie was never at risk of a property downturn wiping out his savings, because his house was such a small percentage of that million-dollar hunk of savings he had allocated. If his finances were tighter, and he had to worry about that downside risk, he might well have elected to rent for a few years, save up a buffer, and only then go for the purchase. How many years? How much a buffer? That depends entirely on Richie’s individual tolerance for risk.

So, is there a lesson here? Well, one lesson is that there is not a huge amount of difference between renting and owning if you live in my neighborhood. But the other lesson is that you can solve thorny and seemingly opened-ended questions with a little research and a little math.