We design and implement a dynamic program (DP) for valuing corporate securities, seen as derivatives on a firm's assets, and computing the term structure of yield spreads and default probabilities. Our setting accommodates arbitrary corporate debts, multiple seniority classes, payouts, tax benefits, bankruptcy costs, and a reorganization process. This flexibility comes at the expense of a minor loss of efficiency; the analytical approach proposed in the literature is exchanged here for a quasi-analytical approach based on dynamic programming coupled with finite elements. We provide several theoretical properties of the debt- and equity-value functions. Finally, to assess our construction, we carry out a numerical investigation along with a complete sensitivity analysis. DP shows flexibility and efficiency.