You need the value of debt and equity to arrive at WACC. If a company’s equity is publicly traded, the value of the equity can be computed using the market price of equity. But how do you get the market value of equity if a company’s equity is privately held (not publicly traded)?
A generally accepted valuation method is to use earnings multiples derived from comparable firms. However, remember that the industry/comparable multiples valuation was also arrived at using DCF valuation and so there is a circularity question. Any errors in those valuations are being carried onto your DCF valuation.
A possible solution is to iterate a few times – first, start with a multiples valuation to arrive at your weights for WACC. Then, you value your equity and debt by discounting cashflows with the WACC. Redo the weights for WACC using your values. Iterating a few times in this manner will get you to a better valuation estimate in a privately help business.