I can't point you at a study, but I can tell you a bit about my costs.
First, server cost varies wildly. seriously. I build something from parts, and I'll pay 1/3rd what dell charges, especially if you want more than 16GiB ram. Hell, even if you go with dell, often small, poor companies will pay 75% or less what larger, richer companies will pay.
Second, unless you are huge (or a weirdo) and own the data center, your cooling cost is rolled into your power cost. I buy by the rack, and every co-lo has a per-rack (well, per-squarfoot, but we can think of it as per-rack if you are renting per-rack) limit on the number of circuits they sell you. But every watt you use in power becomes a watt of heat, no? so they charge you not only for the watt you pump into your server, but the two or three watts it will take to pump out. But as the person renting racks, you really only need to think about power, and the allowed power density.
Maintenance of the cooling and power systems are included in the power/rack rental costs.
so, let's use my co-lo: A full rack with 2x20A circuits is somewhere around $1100 a month (I mean, varies based on negotiation, how many racks, etc... but about.)
Now, you really should only use 75% of a circuit's rated capacity, so this gives us 30A of 120v power. One of my 8-core low-power opterons, with 32GiB ram and 2 disks eats about two amps, so you can put 15 in a rack. That is $73/month/server for rack/power/cooling.
A rack is around 40 rack units... so as you can see, you don't need to buy 1u servers. 2u and 3u servers stay cooler, and often you can pick up 2u and 3u server chassis on the cheap.
(note, the he.net data centers sound cheap in comparison, as you can get a full rack for $600 a month, but they only give you 1 15a circuit, which is 11.25a, or 5 of my servers, a cost of $120 per server month.)
Now, the servers set me back around $1500 each to build. (I'll build you one for $500, if you buy the parts. Pester me and I'll post my parts list sometime. But remember your ESD protection very important. pay the dell or HP tax if you are unable/unwilling to use paranoid ESD precautions.)
If you use good parts and you don't fuck up the installation (I.E. you are careful with the wriststrap) the server will be very reliable for three years. (get rid of it after 3 years. you will be able to buy something twice as powerful that eats half the power.)
But I'm getting sidetracked. Uh, yeah. so if you didn't fuck up, you shouldn't have to touch your servers for 3 years, except the hard drives. Hard drives fail. Always mirror. But still, if you mirror (and especially if you add a 3 disk mirror or a hot spare, disk is cheap) you don't need to actually touch the servers often.
so, uh, not counting my knowledge costs, (which is a lot to set the thing up, but almost nothing ongoing, unless you fuck up the setup.) for a low-power, 8 core, 32GiB ram opteron with 2 disks, I've spent $1500 on hardware and $2628 on power/cooling/rackspace after 3 years. Now, you gotta figure labor. It's knowledge, really, more than labor you are paying for. If you have someone on staff who does this, that one person can handle a whole lot of hardware, especially if you get him or her a few lackies.
But, uh, yeah. if you don't have that knowledge, well, yeah, you are better off overpaying to outsource your hardware to someone else.