We develop a perturbation-based solution method to study a model of sovereign default. We consider a canonical real business cycle small open economy model with sovereign default, where the default choice is driven by fundamentals and a stochastic utility cost of default. We show that the model is isomorphic to an endogenous regime-switching model. Our solution method is both fast and accurate. We estimate the model using likelihood methods and time-series data for Argentina to decompose the main drivers of the interest rate spread in normal times and around a sovereign debt crisis. Our fully micro-founded approach also allows us to conduct policy counterfactuals.