One of the most important factors is the volume of graphic design projects or tasks you need every month. If your business depends heavily on fresh and new designs constantly, then hiring a graphic designer in-house is better. E-commerce stores and online businesses should consider investing in full or part-timers. 

But if your website is more about online presence and marketing tool, which may not require regular design work, then it's better to outsource to graphic design agencies or freelance graphic designers. However, each option has its own benefits and drawbacks, in terms of turnaround times, cost, etc. 

Great question! The answer is, it depends. 
Depending on your goals and the project, using an in-house designer may be a good option. You have control overtime allocation, they’re readily available, and they’re familiar with your organization. An added bonus to an in-house designer is that any skills they acquire will be applied to future projects. In-house may be the most budget-friendly option but they may not have the time for extra projects outside daily tasks. More importantly, they may not have the expertise for executing any number of other specialized jobs that may arise.

It really depends on your business. If you're a restaurant, it doesn't make sense, however if you're a branding agency - then perhaps! 

The question is how often are you going to be requiring graphic design work done? Agreed with Narine Poghosyan. Having an in-house designer can work out more cost-effective. There can be a lot of training involved with unfamiliar design agencies or contractors.