I make the case that colocating pays off at just about any scale, assuming you have $10k in the bank, have a use for at least 40 cores and are able to pay upfront to handle anticipated scale.
Hurricane Electric has prices online of $300/mo for a rack. On AWS, a single full c4 machine (36 threads) costs $1.591 per Hour x 24 x 30 = 1145/mo -- this is more than the cost of running a whole rack with 40 machines. Decent internet can be gotten for hundreds per month.
Ok, so how about buying your own machines? E5-2630 with 20 threads is $700 x 2 = $1400 + motherboard + disk + ssd brings it to several thousand, so it will pay off in at most 6 months, and we're not even talking bandwidth or storage costs. Depending on the application you could be looking at a payoff after 2-3 months.
Worried about installing or remote management? IPMI, iDRAC, etc included with basically every server make this a piece of cake.
The only good case for cloud are if you may suddenly scale 10x and can't predict it; don't have $10k in the bank; or don't have 1-2 months to order machines and sign a contract for rack space.
Sure for a few instances, its likely to be true because there is a certain amount of fixed overhead for dedicated hardware, but it remains a relatively low constant, but in reality there isnt much difference in terms of labour between wrangling hundreds of AWS instances, and hundreds of servers, and the servers will be many times cheaper to run.