Sorry to disagree with you ... especially in your own market.... Now agreed I don't do programming but ...
Standard rates in T.O. for a headhunter/contracting company is $130-150/hr with the sub getting between $40 & $70 of that depending on how bad they want you. (More if they realize you know the calculations).
20 years ago I would have said the markups you suggest are about right but about 15 years ago the market changed here ... the big boys want more of the rate and are taking it.
The key bit in your discussion is that you need to know the market. And recognize that there may be multiple markets at work. There are "sweet spots" or markets where you can maximize your income (as an independent) as well as markets where the entrance cost is beyond your means.
The rates you are quoting are for direct to subs (meaning you are dealing with people who are used to working as subs) and with 2nd stringers (small shops who don't know their costs/market).
In short they represent your hiring practices rather than the market. (Gee -- a manager who does their job despite HR -- how refreshing).
Interesting that there are some standard calculations that every other service industry uses but IT seems blissfully unaware of.
Looking at it from a cost standpoint, you can calculate your billable cost easily. Take the yearly salary you feel is fair for the job and divide by 1000. So $40K/year gives $40/hr. To calculate what you would expect to be billing for that (if you were reselling) take the yearly salary ($40K) and divide by 2000 then multiply by 3
($60) and then add salesman's commission (10-20%). The result is $72/hr for a junior earning $40K/year. Below that it probably isn't worth your while to be a contractor.
Note that $40/hr represents the cost per billable hour including employment taxes and basic benefits (i.e. Corp-to-Corp sub-contract in US parlance). NOT what you are paying an employee per hour (equivalent is $20/hr wage).
However, in this market you're not going to get a fully qualified programmer for $40K.
There are several ways to check the market. www.realrates.com is a good way to start. But the best method is to check everyone you know in the industry. Be part of the local associations .... ask managers what they pay and what they are willing to pay. If worse comes to worse -- call around. Make up a (typical) project then call around. Say that you are just at the budgeting stage, you know that you are going to use contractors but aren't in a position of making it official. Ask them what they charge for that type of work -- just for budgeting purposes.
Best of luck.