Is cost of equity the same as WACC?

No. Cost of equity is the return stock investors require. WACC, the weighted average cost of capital, blends that with the after-tax cost of debt. A firm funded 60% by equity at 11% and 40% by debt at 6% pre-tax, with a 21% tax rate, has a WACC of about 8.5%.

Use the rate that matches the cash flows. When you value the whole business, discount free cash flow to the firm at WACC, because that cash goes to lenders and owners. When you value only the shares, or cash left after debt payments, use cost of equity. Banks are usually valued on equity alone.

Cost of equity is one input to WACC, usually the largest. The cost of equity and WACC guide shows the full math, and the WACC glossary entry explains the weights. You can also read whether cost of equity can be lower than WACC.