I would ask a few questions up front.

1. Is this a one time project?
2. Will this project need updating in the future?
3. Have you done any outsourcing before?
4. Are you sure you can manage the project within that 4 month period.

You can definitely get a firm to outsource your project for you at between 20-40 dollars an hour. However, if you just hire remote employees full time it will usually cost you half the price of the firm and you'll be able to manage the people yourself, won't be abandoned when the project is 'done' and can have them refine features as your needs change.