Forgive my flat tone in this post, I’ve been exhausted for weeks and weeks.

There is one basic housing decision: Rental versus Ownership. I disregard homelessness as a degenerate case (EV $0, but high social cost). Below I will show that a mixed rental-ownership strategy dominates the expected value of straight ownership.

Case 1: Renting Only

Let’s say you rent a place for $1,000 per month for 25 years and rent increases at 5% per year. To simplify, let’s peg prevailing interest rates at 7%.

The present value of this decision is given by (A / (i – g))[1 - ((1 + g)/(1 + i))^n], where A is the rental payment, i is the prevailing interest rate, g is the growth in the payment, and n is 25 years * 12 months.

PV = (A / (i – g))[1 - ((1 + g)/(1 + i))^n = (-1000 / (7% - 5%))[1 - (1.05 / 1.07)^300] ~= $49,825.97

The cost to you today of the “I will rent for 25 years” decision is, let’s call it $49,850.

Case 2: Owning Only

This is a more complicated decision. Let’s pick some numbers:

Home value: $375,000
25% down: $93,750
Mortgage life: 25 years

Let’s say that your home grows in value 5% per year and prevailing interest rates are 7%. Let’s make a further simplifying assumption (because I want to go to bed soon) that you’re the LeBron James of mortgage negotiations and you’ve locked that interest rate down for the whole 25 year period.

You’ve saved $93,750 and put that down so your mortgage is for $281,250. Whipping out the RBC mortgage calculatrix on these naughty numbers you can see that your mortgage payment is $1,969.92 per month — call it $2,000.

Because mortgages are basically just present value calculations we’re almost there. The last component of the calculation is something accountants call “salvage value” — what you get for the asset at the end of its life. Let’s assume you never make repairs and sell it as soon as you pay off the mortgage.

If the house grows in value 5% per year for 25 years it is worth:

$375,000 * 1.05^25 = $1,269,883.10

(Aside: Yes, by the time you’re in your mid-50s that’s what condos and similar will cost. This is why you need to save early and often. See why I’ve been studying wealth management since high school?)

The present value of $1,269,883.10 in twenty-five years at 7% interest today is, similarly:

$1,269,883.10 / (1.07)^25 = $233,975 (approx.)

So the total cost of the “ownership only” strategy is $233,975 in future salvage value which accrues to you today less an outlay of $375,000, for a net present value of -$141,025.

Since we’d like to compare that to case one’s rental flows we should double the rental rate from $1,000 to $2,000 to closer approximate the mortgage payment of about $2,000. For the sake of simplicity, again, let’s leave aside the costs of obtaining the down payment. So the present value of renting is then about -$99,700 and the present value of ownership is about -$141,025.

Both cases are hugely negative value sinks. They’re not really comparable because these are made up numbers — the purchase and salvage value in particular are big variables given fixed growth and interest rates — but I think we’re basically being reasonable here.

Clearly owning a house costs more than renting. The excess comes from the difference between upfront costs and salvage value, which in reality can more than cancel making rental more expensive. But luckily that’s not my point: The same dynamic applies equally in the case below, for which all of this is but groundwork.

Case 3: Mixed Rental and Ownership

Let’s recap our adjusted rough comparables:

Rent: $2,000 per month.
Own: $2,000 per month plus $93,750 down plus $288,250 mortgage less $233,975 salvage.

Now let’s assume that, instead of renting or owning, you both rented and owned. Specifically that you rented a place to live, bought the house, and then rented it out to a third party. Again, for simplicity’s sake, let’s just say they pay the same as you in rent. The new net present value calculation looks like this:

PV(rent & own) = PV(rent) + PV(own) + PV(rental income)

We know all those numbers though as PV(rental income) is just -PV(rent) (per our simplifying assumption) so it becomes:

PV(rent & own) = PV(own)

Innnnteresting: Renting while owning is the same as just owning, assuming you rent your house for what you pay! However, it’s probably more reasonable to assume that you rent a smaller place than the one you own, which you let out to a family. Let’s assume that you rent the house out for $100 more than you yourself pay in rent. From above (this is easy because it’s just 10% of our original rental estimate):

PV(extra) = (A / (i – g))[1 - ((1 + g)/(1 + i))^n = (100 / (7% - 5%))[1 - (1.05 / 1.07)^300] ~= $4,985.

PV(rent & own) = PV(own) + PV(extra)

If everything goes according to plan PV(extra) is going to be positive so the net result is that renting and owning is always cheaper than just owning. This wouldn’t be true, for example, if you let out a condo while leasing a mansion, but that’s degenerate bone-headery. More likely you’d have trouble finding tenants but as long as you’d make any positive amount per month on average over 25 years you’ll be in the clear.

Wealth is all about accepting calculated risks.

Anyway, this is all pretty hand-wavey, but I think I’ve described the basic theory. The trick is finding real places that fit into the numbers of this framework, but, and this is the neat part: That is always possible given a big enough down payment.

Further, if you pick a down payment size that forces your monthly mortgage payment to be lower than what you can rent the place for, including all other costs, then not only does the above nice result hold but you get another. You could, in theory, keep doing it again and again until your accumulated PV(extras) move the entire calculation positive. Then you’d actually be making money from accommodation instead of spending money on it, net, all while renting.

Then you can buy however many single family dwellings you need to make your spouse happy without pushing your net accommodation present value into the negative

This, in broad strokes, is my own wealth management plan.