The issue of valuing tax loss-carryforwards (TCLFs) and carrybacks (TLCBs) arises frequently in theory and practice. While there have been a number of empirical papers that have shown TLCFs (TLCBs) are value relevant, there is little guidance on how to actually value these. The few analytical papers that have attempted to provide valuation formulas are stylized and inadequate. Incorporating the institutional aspects of the tax code, we construct a general algorithmic discrete time framework for valuing TLCFs (TLCBs). We provide explicit formulas with practical applications, and discuss it's implications for dynamic portfolio selection decisions.