Is this a good way to estimate Capex?

[Dave Meyer]

I am working on a project for BiggerPockets (stay tuned!) that is requiring me to estimate Capex (which for this exercise includes maintenance) across US cities. There is not too much data to go on, simply the median rent in that city. That's it! After talking it over with @Scott Trench we came up with a few thoughts. 

1. Using a simple percentage of rent won't work, because in our minds, Capex does not scale linearly. Let's use 10% as an example. If rent is $500/month and you estimated 10% of rent, you'd have only $50/month. That's only $600/year, which in my mind is far too little for estimate, no matter what the value of the home is. Even a $50,000 home needs a new boiler, roof, water hear, and to repair regular wear and tear. However, 10% might work perfectly fine for a property with $2500 of rent. That would amount to $3k/year. Might work great in some markets, and poorly in others.
2. If we did a higher %, say 30%, the opposite effect would likely happen. It would be accurate for lower-end rents ($150/month for $500/month in rent), and too high for higher rents ($750/month for $2500 in rent). 

These are just two random examples, but you get the point. So what I decided was that first, we needed to set a 'floor' for Capex. I came up with a number doing some back-of-the-envelope math of around $150/month (but I welcome input on that). Secondly, I decided that Capex should not scale linearly with increases in rent. Instead, the % of rent needed for capex should decrease as rent increases.

I won't get into the specific math here cause its nerdy and not necessary, but I spent some time 'fitting a curve' to our data and here is what I came up with: 

Here's what is going on in this graph: 

• The labels on the X-axis are the median rent for a given city (I am purposely omitting the city names here). 
• The orange bars show the estimated Capex
• The blue line shows the % of rent that I am using for that particular rent price. 

As you can see this is not a straight line, it's a curve. The left side of the graph starts around 23% of rent being used, and on the right side it decreases to about 13%. 

So what does everyone thing about this approach? Is $150 a good floor? Is my curve diminishing fast enough? Too fast? Would love to hear what everyone thinks. 

** and before everyone says that estimating capex at a city level is impossible, that certainly has merit. It's very difficult, but despite the challenges, that is still what I am trying to do so would appreciate feedback about this specific project.