If you’ve done the research and have found that it will cost you more to outsource than to do the work in house then you’ve uncovered a real problem. If, on the other hand, you’re just assuming it would cost more, this is a presenting problem. You’re actually just afraid of delegating the authority.
If you’ve done your research this is a rational problem. After all, one reason for outsourcing is to save money. If, however, you’re just making an assumption, this is an emotional problem. Get some specifics. How much will it cost? How much more is that than what you’re paying now?
Double-check your numbers. Make sure you’ve accurately estimated your current costs. If necessary, have your accountant do the calculations. Next, look for more outsourcing firms. Perhaps you’ve only gotten bids from the most expensive players in the market. Leave no stone unturned. At this point your goal is simply to find out what the market rate is for the service.
If it appears that no outsourcing firm will offer direct cost savings, determine whether the firm’s more efficient operations will offer indirect savings, not just in dollars but in freeing up personnel schedules.
It’s the outsourcing firm’s job to get you to trust them. If you’ve thoroughly investigated the issue and have found that no outsourcing firm can do the work for the same as or less than you’re currently paying, or create any cost savings or labor savings through efficiency, keep the function in house. Don’t outsource a function simply because it’s the trendy thing to do.
If you find that the firm you’d like to take on the task is charging more than you’re paying now, and that their fee is above the market value, ask them to reconsider their bid. Offer up your research and note that you’d love for them to do the work, but you can’t justify their retention in light of the facts you’ve uncovered.