The first thing that comes to mind – because it’s the big number – is the profit we were lucky enough to get when we sold the condo. The profit was 20 median salaries2² This entire article is written in terms of median salaries. By median I mean median for the general area of the city we live in. By salary I mean monthly. Although for much of the article, it doesn’t matter whether you read it as monthly or annual salaries, in some cases it does matter., after deducting all fees and taxes. One might think that corresponds to a hypothetical post-tax monthly income of

\[\frac{20}{12 \times 5} = 0.33\]

median salaries, but that fails to account for compounding. The way to calculate this properly is to whip up an hp-12c. Surely you have one of those? Oh, no. Poor thing. But don’t worry. Here, you can have this online hp-12c.

Now it’s time for a brief hp-12c tutorial, because everyone needs a little miracle in their toolbox. Just to be safe, first clear all registers by pressing f and then CLx, which corresponds to the orange CLEAR REG function.

The question we want answered is “how much would we have had to make in monthly income to end up with a lump sum of 20 median salaries after five years, when we include the effect of compounding interest on investments?” Here are the steps to the answer:

1. From the perspective of this question, the 20 median salaries is a future value. For reasons3³ This gets a bit complicated and I’d rather not get into it now. The manual has a few tricks for remembering which numbers need to be of which sign under which circumstances. The gist of it is that the payments are transactions in the opposite direction of the future value, so to get positive payments for this example, we need a negative future value., this number needs to be negative, so we store −20 in the future value register by pressing 2 0 CHS FV.
2. Then we assume a conservative investment return of 4 % annually, and insert that into the calculator as a monthly interest by pressing 4 and then the 12÷ function. The 12÷ function is a shortcut that takes a number, divides it by 12, and puts it in the interest register. We find it, logically, by first pressing g and then the interest key i.
3. We enter 5×12 months with 5, then 12×. The 12× function is a similar shortcut but stores a number of periods, thus we find it by first pressing g and then the n key.
4. At last, we ask the calculator to solve the corresponding monthly payment by pressing PMT. It solves the equation iteratively, and comes back with 0.30 median salaries.

Thus, the sales profit of 20 median salaries after five years corresponds to an additional income of 0.3 median salaries4⁴ This is one of those cases where I mean it as 0.3 median monthly salaries per month, but you can also think of it as 0.3 median annual salaries per year, if that’s easier for you.. It makes sense that this is slightly lower than the naïve guess of 0.33, since our hypothetical income of 0.3 median salaries would accrue some interest over these five years.

Of course, the condo arrangement is not free. We had to pay both a monthly homeowners association fee, and interest on a mortgage. These together averaged out to −0.31 median salaries.5⁵ I think it’s technically incorrect to account for variable costs using averages because if the high costs happen early in the period, that’s worse for compounding interest than if they happen later in the period. But give me a break, I’m already treating this with way too much intensity. Techncially we would also count renovations and other improvement work here, since e.g. in a rental agreement the landlord would do that for us, but the few such things we had to do will disappear into rounding errors at the end so we won’t bother here.

This seems like a satisfying result: we’d expect the total to be negative, since living somewhere ought to cost something. An in this case, the additional 0.30 monthly income from the sales result are very nearly cancelled out by the monthly costs of −0.31 we incurred, leaving a small residual negative cost.

Unfortunately, that’s not the full story.

If we didn’t buy a condo, we would have been able to invest our down payment.6⁶ Well, technically we did invest our down payment, but we would have been able to do it in something with greater risk-adjusted return than a single property. This down payment was as large as 32 median salaries. We also used 0.25 median salaries to pay off the principal of the mortgage every month.7⁷ Around 0.15 median salaries were required by law. We decided to pay off slightly more for risk management reasons. Both of these expenditures use money we could otherwise have invested.

This is sort of the inverse of the previous hp-12c calculation we did, because now we’re starting with a present value and recurring payments, and we want to figure out what the hypothetical future value would have been had we been able to invest them.

Since we will reuse some of the numbers from the previous calculation, we do not need to clear our registers.8⁸ If you have played around with the calculator since the previous computation, you may want to CLEAR REG and then enter the interest rate and period count again instead: 4 12÷ 5 12×.

1. We enter −32 as the present value, by pressing 3 2 CHS PV.
2. We enter −0.25 as the PMT, since this was how many median salaries we chose to pay off on the loan.
3. We press FV to compute the future value.
4. Now we want to extract the part of this that is pure interest missed. We do that by subtracting the payments we made from the future value. First we enter 32 and press − to subtract the down payment.
5. Then we want to subtract the product of 0.25 and the number of months. We can do that by pressing 0.25, then RCL followed by n, and multiply with ×. Finally, subtract this by pressing −.

This comes out to 8.65, and then we do the operation backwards to get the monthly income this would correspond to, i.e.

1. Set 8.65 as the future value by pressing FV.
2. Enter 0 into the PV.
3. Press PMT to compute corresponding monthly income.

The calculator responds with −0.13, which was the opportunity cost in median salaries of (a) using the down payment for a condo, and (b) paying off some of the mortgage, compared to investing that money into a portfolio with a 4 % return.9⁹ I realise now it’s a little sloppy to say just “return”, but what I mean is cost-adjusted compound annual growth rate.

But wait there’s more! We need to live somewhere. The only real alternative to the condo arrangement for us would be renting somewhere. The rent for a corresponding apartment is around 0.36 median salaries. This is money we would have had to pay if we rented, but thanks to the condo arrangement we could pocket it instead.

Thus, bringing it all together:

• The sales result corresponds to 0.30 median salaries.
• The direct costs (mortgage interest and homeowners association) correspond to −0.31 median salaries.
• The opportunity costs of the mortgage (down payment and recurring principal reductions) correspond to −0.13 median salaries.
• The opportunity gain of not paying rent corresponds to 0.36 median salaries.

Summing up, this is comes out to 0.22. In other words, the condo arrangement, in the end, earned us 0.22 median salaries that we otherwise would not have. This is crazy. We had a beautiful home to live in for five years, and the cost of this was … well, nothing. We earned money on it.

It’s as if someone would say, “Sure, you can live in this very nice apartment. But I’ll have you know there are consequences. I’ll insert money into your bank account every month for as long as you live here, so think twice about it!”

There are some reasons this happens, of course. One is that condo ownership is a financial risk, and – in emsemble average – one gets paid for taking financial risks. Another reason is that by showing up with the capital for the down payment, one unlocks more capital from the banks, who also stand to profit from the deal. A third, perhaps more subtle reason, is that the actual earnings from this (compared to renting) only materialised during the sale. If we remove the sales result, the sum would be −0.08 median salaries, i.e. slightly worse economically than renting.

All of these can be traced back to the same principle: money unlocks more money. We needed to be able to afford taking a financial risk, we needed to show the bank that they could profit from a mortgage, and we needed to afford to defer income by five years. All of that takes money.

But it also seems slightly unfair that those with a lot of money can effectively be given more money for living somewhere, whereas those with little must pay for their privilege of living somewhere.

The situation is actually slightly better than indicated in the above calculations, because in Sweden, one is, under certain circumstances, allowed to defer property sales tax. In our case, we expect to be able to do this for at least a couple of decades, but let’s be conservative and say that we can only do it for ten years.

The deferred tax amounts to 5 median salaries. During ten years, this will accrue an interest of

1. Enter 4 then 12÷
2. Enter 1 0 then 12×
3. Enter 5 PV
4. Enter 0 PMT
5. Request FV
6. Enter 5 + FV
7. Enter 0 PV
8. Request PMT

i.e. 0.02 median salaries monthly. This is not a large effect, but it does improve the earnings from the condo arrangement (instead of renting) to 0.24 median salaries.

This was all assuming a fairly conservative 4 % return on investments outside of condo ownership. I think that’s a reasonable assumption, but it does affect the result so it’s worth looking at how changing that assumption affects the result.

It makes sense that the more savvy investors we are outside of condo ownership, the less attractive condo ownership is economically compared to the alternative. But it would take a whopping 10 % cagr to make condo ownership (in our case) economically unsound.10¹⁰ Fair enough – the S&P 500 had a 12 % cagr during that time, but betting on that happening at the start of those five years would not have been sound strategy. You must make choices using your best forecast of the future, not the lucky draw that just was.

If we assume the same price development of the condo as during these past five years, we can also see how the time spent owning the condo affects its economic sensibility.

Rather unsurprisingly, this also decreases over time, because the longer one stays there, the longer the compounding time available for the slightly-better return from other investments.

Now comes an interesting observation: this timer does not really reset when one moves from one condo to another. So technically, then, if one plans to live in condos for the rest of their lives we should extend this table to greater numbers of years.

Turns out one can live in condos for all of one’s life and still have it be a net positive.

However, I’d be wary about putting too much faith into this because it’s using price appreciation numbers from the past five years, which is something like 3.7 % per year. It seems like longer-term trends in my area suggest closer to 7.5 % per year. With appreciation at that scale, it beats the investment return and the net result increases the longer one stays in condos.

But again, I know nothing about this so I wouldn’t put any faith in it. I do know what happened in the past five years, and that remains true. You’ll figure out on your own what’ll happen in the future.

I don’t know. If it affects this analysis, it would probably mainly come in as reduced cagr on investments, which I’ve already somewhat accounted for by opting for a conservative 4 %. It also ties into other things such as how rents probably started out lower and increased during this period, but I’ve just picked a representative maybe–average out of my ass looking at what listings I could find.

I think these effects, and others like them, are small enough over a five year period that we can just ignore it.