After research, I found an answer on Businessweek. The conclusion is that the Olympics are a boon to cities that are "upcoming"- cities such as Seoul- because these places can be helped by the tourism and the exposure. For established cities that already draw tourists, however, hosting the Olympics may not make sense.
So what about London? London is definitely an established city, so it is speculated that the city will not fully recover all its expenses within a reasonable time frame (essentially, there is a high opportunity cost. London could have invested the money into more worthwhile investments)
Of course, there are strong arguments on both sides. Some sources say that no matter what, "hosting the olympics is a huge money suck". One person from reason.com made the following argument:
These days the summer Games might generate $5-to-6 billion in total revenue (nearly half of which goes to the International Olympic Committee). In contrast, the costs of the games rose to an estimated $16 billion in Athens, $40 billion in Beijing, and reportedly nearly $20 billion in London. Only some of this investment is tied up in infrastructure projects that may be useful going forward...."
Then, of course, there are others who adamantly argue the opposite. One person from nationmultimedia.com made the following argument:
While almost everything has a price, there are some things in life - such as reputation and soft power - which remain priceless.
As you can see, there is no clear answer to the value of hosting the olympics; there are too many factors and too many different pieces of the puzzle to consider.
Personally, I think businessweek made a solid argument- upcoming cities should host the olympics.
If you do happen to come upon an interesting opinion piece on the olympics, please make sure you weigh in under the comments! It is interesting to read the different thoughts on the event.