Forest carbon sink (FCS) is essential for achieving carbon neutrality and supporting sustainable development in ecologically fragile, resource-based cities such as those on the Loess Plateau. Despite the success of national afforestation programs, economic valuations of FCS at the city level remain limited. This study develops an integrated framework combining carbon stock estimation, regional carbon pricing, and net present value (NPV)-based valuation. Using Shenmu City in Shaanxi Province as a case study, forest carbon stocks from 2010 to 2023 are estimated based on the 2006 IPCC Guidelines. Future stocks (2024-2060) are projected using the GM (1,1) model. A dynamic pricing mechanism with a government-guaranteed floor price is applied under three offset scenarios (5%, 10%, 15%). The results show that Shenmu's forest carbon stock could reach 20.67 million tonnes of CO2 by 2060, and under a 15% offset scenario, the peak NPV reaches CNY 4.02 billion. Higher offset ratios increase FCS value by 18-22%, reflecting the growing scarcity of carbon credits. The pricing model improves market stability and investor confidence. This study provides a replicable approach for carbon sink valuation in semi-arid areas and offers policy insights aligned with SDG 13 (Climate Action) and SDG 15 (Life on Land).