Discount rates, WACC and their inputs

Explain what a discount rate is and how the weighted average cost of capital is built up, including how you estimate beta, the cost of equity, the market risk premium and the cost of debt.

WACC weights the costs of equity and after-tax debt. $\text{WACC}=\tfrac{E}{V}r_E+\tfrac{D}{V}r_D(1-t)$ with market-value weights. The cost of equity comes from CAPM, $r_E=r_f+\beta(\mathbb{E}[R_m]-r_f)$, where beta is estimated by regressing the stock's returns on the market's (or from unlevered peer betas relevered to the target structure) and the risk premium from long-run historical or implied estimates; the cost of debt is the yield on the firm's debt or its rating-based spread over risk-free.