The tax shield as present value of debt-related tax savings plays an important role in firm valuation. Driving the risk of future debt levels, the firm’s strategy to adjust the absolute debt level to future changes of the firm value, labeled as (re-) financing policy, affects the value of tax shields. Standard discounted cash flow (DCF) models offer two simplified (re-) financing policies originally introduced by Modigliani and Miller (MM) as well as Miles and Ezzell (ME). In this paper, we introduce a discontinuous financing policy that refers to the refinancing intervals, i.e., the maturity structure of the firm’s debt. By deriving APV valuation and beta unlevering equations that allow for this discontinuous financing policy, we show the MM and ME policies to be special cases of the proposed extension. While we document the effect of discontinuous refinancing to be economically significant when leverage is high and refinancing periods are extremely long, our results suggest that for low-levered firms with short refinancing periods, the traditional continuous refinancing-based models (like the Miles/Ezzell model) produce relatively robust value estimates. Combining capital structure and maturity structure choices, our model extends the set of feasible financing policies in DCF valuation models.