OK. Private equity companies such as Merlin and Blackstone (Merlin's owners) generally fund all their huge purchases with huge loans. They aim to increase profit of the property they bought (theme parks) in order to pay for the loan and get a return on their investment.
Take this scenario, very much borrowed and adapted from here
Merlin want to buy Lightwater Valley, which has assets of/is worth £100. Merlin pay £125 to secure the deal. Merlin get a mortgage on their assets and take a loan of £100. They then have to pay £25 of their own money to complete the deal. The repayment of the loan and interest is taken care of by the cash flows generated from the business. In theory.
So why would Merlin pay more than the price Lightwater Valley is worth? Well, the price at which you purchase a company depends not only on the value of its lands and buildings, but also on many other factors. There are many intangible things, such as the value of the goodwill enjoyed by the company in the market, the future earning prospects of the company, and so on.
So what do Merlin do with Lightwater Valley when they've bought it? They try to turn the fortunes of the company around by providing better management and technical inputs. They are famous—or should I say infamous?— for stripping costs and streamlining operations through hard decisions such as retrenchment of the workforce. Once the company is successful, they float the shares to other investors, mostly through initial public offerings (IPOs). In this manner, they earn handsome returns on their investments.
Merlin are financing their debts by taking on new parks and trying to increase profit. As seen they are doing this with very limited investment - investment in things that will make the most return from the minimum expenditure: car parking charges, selling more fasttracks, poor sponsorship etc. The coasters cost a lot (although much less than their European counterparts pay for decent coasters) but they are the best at improving/maintaining strong guest figures, not to mention increasingly large parts of the budget are spent on marketing as it could be argued this has a greater effect, rather than the actual quality of the coaster itself.
Edit: Crofty got there first!