Here’s the story: Back in October, the Danish government agreed to sell 26% of the state-owned utility DONG Energy to a group of investors, including two Danish pension funds.

Initially, the deal was greeted as good news. DONG needed money to go forward with an ambitious wind project, and the deal would provide the capital to do it without having to go to the government for help. More clean energy. Victory.

Then someone got wind of the fact that the largest investor in the deal was going to be Goldman Sachs, that Goldman Sachs. Since then, all heck has broken loose in Copenhagen. There has been a public outcry against the deal, mostly because of Goldman’s (GS) involvement. One protestor called the investment bank “completely criminal.” And Danes seemed to have found all types of evidence to back that up. Articles in the Danish press have accused Goldman of causing the financial crisis and “profiting from cluster bombs,” which a MarketWatch article says are unpopular in Denmark, but I guess popular somewhere else. About 200,000 people signed a petition to stop the deal. And a national poll found that 68% of Danes were against it.

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On Thursday, the government voted to approve the deal. But that hasn’t eased the political turmoil. Six ministers have resigned from the Danish prime minister’s cabinet and ruling coalition over the deal. And more protests are planned.

So, was it really such a bad deal, or does Denmark just hate Goldman Sachs that much?

Goldman and its partners are investing $2 billion, with roughly $1.5 billion coming from Goldman, mainly from its infrastructure fund. Based on that price, Goldman is paying 0.8 times book value for its 19% stake of the Danish utility. But the deal is a bit better than that.

Along with its shares, the Danish government granted Goldman, and the other investors, the right to essentially return some of those shares. If DONG doesn’t go public sometime in the next four years, DONG will repurchase 60% of Goldman’s stake, giving Goldman its money back plus about 3% interest a year for its trouble.

On Wall Street, this is called an in-the-money put, because Goldman is guaranteed to make some money on the investment. In-the-money puts, like all insurance plans, usually come at a cost. But in this case, Goldman is getting it for free, because the strike price is equal to what Goldman paid in the first place. You can figure out what Goldman should be paying for that put option, but that would require a bunch of math, creating a Black-Scholes option pricing model, and probably one of those Wall Street HP calculators, and I don’t have those. But, luckily, two economics professors have done the math and have come to the conclusion that it is worth a lot — roughly $330 million. That brings the price the Goldman group is paying down to about 0.6 of DONG’s book value.

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Is that cheap? I don’t know. It sounds cheap. Many European utilities trade for one times book value or more. Electricite de France (ECIFY) trades for 1.8 times book. But DONG recently announced a big loss, after losing money for all of 2012. And it has an ambitious expansion plan that will hold down profits for some time. What’s more, it has a lot of debt rated at BBB+, which is pretty close to junk. So that means the company’s shares should be cheap.

Here’s another way to look at the deal: If the stock gets up to 1.8 times book, then yes, Goldman will make a killing, especially if the book value rises as well. But so will the two Danish pension funds that are investing alongside Goldman, and so will the Danish government which, after all, will still own about 60% of DONG after the Goldman deal.

Lets say, instead, DONG’s stock over the four-year period drops by 10%. Goldman would get 60% of its money back, or $900 million plus 3% annual interest ($81 million). But it would lose $60 million on the 40% of its shares. A net gain of $21 million.

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But that’s only compared to Goldman sticking its money in the ground for four years, and it assumes that Goldman will come by this money at no cost. If Goldman had just put that money in a five-year U.S. Treasury bond, it would have made $90 million over the time period. Based on that comparison, Goldman would lose $69 million.

If DONG’s stock goes nowhere (wind projects take a while to pay dividends), the utility will end up paying Goldman $81 million, which translates to a 1.4% interest rate. That would be a great deal. Last year, DONG paid 4.88%-a-year interest in a bond deal to borrow $650 million for five years. At that rate, DONG would have to pay Goldman nearly $300 million in interest over the next four years. So Goldman is effectively lending money to DONG at a huge discount, and they still don’t want the investment bank’s money.

The Danes must really hate Goldman Sachs.