Europe is heading for what could be the last stand in its two-year-old sovereign debt crisis. By the time the Group of 20 nations holds its summit in Cannes, France, on Nov. 3-4, the European Union aims to have a rescue plan sound enough to ensure the financial troubles of struggling governments don’t bring down the banking system.

If Europe wants to avert a financial and economic disaster worse than that of 2008 and 2009, it had better apply overwhelming firepower.

Achieving credibility will require three things Europe’s leaders have so far failed to do. They must discard the illusion that certain euro-area governments, particularly Greece, can afford to pay their debts. They must provide a realistic accounting of how much Europe’s banks will lose when those governments default. And they must offer financial guarantees large enough to convince markets that the defaults and the losses will be final.

Anything short of a full and honest reckoning will only make the situation worse. Repeated efforts to avoid a Greek default have added to the country’s debt burden, deepened its economic pain and allowed the malaise to spread to otherwise solvent countries such as Spain, Italy and France. Uncertainty about the health of the banking system is beginning to paralyze the entire euro-area economy, to the extent that some economists believe it’s already entering a new recession.

How much, then, will it cost to stop the rot? To provide a rough answer, the editors at Bloomberg View did some number-crunching.

The first key question is which European governments need to default on their debts. The calculation has a lot of moving parts: The slower a country’s economy is growing, and the higher its borrowing costs, the less affordable its obligations.

Greece is by far in the worst shape. At current interest rates, and given growth forecasts from the International Monetary Fund, the government would have to implement severe austerity measures to keep its debt burden merely stable. Specifically, Greece would have to run a primary budget surplus (not counting debt-service payments) of more than 5 percent of gross domestic product indefinitely. Portugal, too, would struggle: It can’t afford to pay market interest rates, and would probably need many years to get its debt down to a level low enough to restore investor confidence. Other euro-area countries ― including Ireland, Italy, Spain, Belgium and France ― can stabilize their debt burdens with primary surpluses of less than 2 percent of GDP, assuming jittery markets don’t push up their interest costs. Such surpluses are well within the historical range, suggesting the bloodletting could end at Greece and Portugal.

The next question is how much debt insolvent governments can actually afford to pay. If we assume that a primary budget surplus of about 1 percent of GDP is sustainable, and that European guarantees would allow the governments to borrow at reasonable rates after defaulting, Greece would need a 70 percent writedown, after which holders of its bonds would be left with securities worth only 30 percent of face value. The required writedown for Portugal would be 40 percent. The market seems to recognize this: The countries’ 10-year bonds are trading at discounts of about 60 percent and 40 percent, respectively.

The two defaults would wipe out about 300 billion euros ($416 billion) in Greek and Portuguese debt, a large share of which is held by banks that are pretending it’s worth full face value. Hence, current estimates of the fresh capital needed to prop up the banking system ― such as the International Monetary Fund’s 300 billion euros ― seem reasonable. Governments will have to be prepared to provide that capital, though banks might ultimately raise a large portion themselves, and some financial institutions might be allowed to fail.

The final, and perhaps most crucial, question is how big a war chest would be needed to support bank recapitalizations and protect solvent governments from speculative attacks. The European Financial Stability Facility and the European Central Bank, with the collective backing of euro-area governments and possibly the IMF, would have to guarantee all new bonds issued by Greece, Portugal, Ireland, Spain, Italy, France and Belgium for at least several years, or until a more permanent fix, such as jointly issued euro bonds, can be arranged. Data compiled by Bloomberg, and separately by the IMF, suggest those countries’ financing needs add up to about 2.5 trillion euros through 2015.

In all, then, and adding in some buffer for error, 3 trillion euros would be the minimum amount that European governments must pledge to stop the crisis. Given the potential global repercussions of failure, it would be in the interests of countries beyond Europe to contribute to an even larger fund. Official guarantees are like nuclear deterrence: If they’re big enough, you don’t need to use them. Ideally, speculators would be daunted, markets would provide funding to banks and governments on their own, and the guarantees would never be exercised.

Money alone won’t solve the euro area’s problems. If the euro is to survive, European leaders must find the political will to deal with fundamental issues, such as the lack of a unified fiscal authority to match the currency union, and deeply flawed bank-capital rules. A show of overwhelming force, though, is the only way they can get from here to there.

(Editorial, Bloomberg)