The cost of capital is a cornerstone of corporate finance, shaping investment decisions, valuation, and resource allocation. In the context of the climate crisis, understanding how climate change reshapes this core concept is essential. This chapter examines how climate risks affect the cost of equity, cost of debt, and weighted average cost of capital (WACC). Using the CAPM framework, we analyze how climate change drives shifts in systematic risk (beta) and equity risk premiums, with carbon-intensive sectors facing rising equity costs and green sectors perhaps benefiting from favorable financing conditions. The chapter also investigates the influence of climate risks on sovereign and corporate borrowing costs indicating that countries vulnerable to physical climate risk, especially the Global South will see heightened borrowing costs. At the firm level, climate risk can increase default risk premiums. Scenario analysis and case studies, including insights from the airline and energy sectors, illustrate the consequences for the cost of capital along different climate pathways.