Should companies charge the clients on the basis of number of bugs?

I came across an interesting software testing outsourcing technique here based on pay per bug approach. This testing consultancy is offering testing services and clients will be charged on the basis of number of bugs found in the application.Why outsourcing?
Many companies are outsourcing software testing work to concentrate on their core business competencies. The company will save time and money on testing processes that is tedious to perform in house.
Current offshore teams are working on per project deal means cost of software testing is decided according to the:

• Project size
• Time for testing
• Number of resources
• or Deliverables.

What if offshore teams start charging the clients on the basis of number of bugs?
Many companies don’t want to pay for documentation, as they might not require it in future. So such clients are more interested in getting the testing work done in less cost and within their budget. Pay per bug approach can work greatly for small projects where requirements are straightforward and clear. In this approach client have freedom to select the testing area as only UI or only Functional or only Security testing as per their requirements.
Will Pay per bug outsourcing technique work?
But I see many complexities in this model. It might not work for all kinds of projects. What if the tester is working to find only smaller and easy to find bugs to increase the bug count and not concentrating on the complex modules? One solution for this could be – Charge the client depending on fixed price per bug or can you can vary this amount according to the bug complexity and the type of testing.
Another problem with this module is – How to decide the severity of the bug? Tester will log bugs with high severity if they are earning high rate on the basis of bug complexity. Client will try to reduce the bug severity as to reduce the testing cost. It’s also difficult to decide whether it is a bug or not Or it is a feature itself? And what about the rejected or ‘won’t fix’ type bugs?
Worst case is if you are getting paid on the basis of number of bugs and you spent enough time to find the bugs, but if application is robust enough that you end up with very few or no bugs then how would you cover the testing recourses cost in this case?

There are lots many such areas of controversies but the concept is good and can be a good outsourcing solution if handled effectively.

http://www.softwaretestinghelp.com/charge-client-on-basis-of-number-of-bugs/