Facebook know exactly how much Instagram is worth. They don't even have to ask the data from Instagram. They can just look at their own Facebook data to see how many of their users use the service. Also, every photo you see on the web has a Facebook Like button. They have all the data they need to make the decision.
Looking at their data, Facebook feared that not acquiring Instagram is a risk to their business, so they rather lose $1 Billion than giving advantage to other social networking sites such as Google+. Mark Elliot Zuckerberg is determined to stay on top.