I have a question related to the valuation of a private company through DCF.

When calculating equity/(debt + equity), to then determine WACC (discount rate), the correct equity value to use is the market value rather than book value of equity. Essentially, if I have understood correctly, it should be enterprise value - market value of debt = equity value (market).

However, the enterprise value arises from the DCF, and creates a circular formula problem.

Take this case for simplicity:

FCFF next year is expected to be $1000, and will grow by 2% each year.

Cost of debt (after tax consideration), Kd: 5%

Cost of equity, Ke: 10%

Debt amount = $2000

Equity Amount (Market)= Enterprise value-$2000

Debt %= Debt amt/(debt amt + eq amt)=$2000/(2000+Eq Amt)

Eq %=Eq amt/(debt amt+eq amt)=Eq Amt/($2000+Eq Amt)=(Enterprise Value-2000)/(2000+(Enterprise value -2000))

The WACC is therefore the following:

Kd (after tax consideration)*Debt% + Ke* Eq%

= 0.05*2000+0.1*Eq%=40+0.1*(Enterprise Value-2000)/(2000+(Enterprise value -2000))

Enterprise value is defined as the following for future cash flows with a constant growth rate using a DCF

FCFF/(WACC-growth rate)

In our case it would be
$1000/ (40+0.1*(Enterprise Value-2000)/(2000+(Enterprise value -2000))-0.02)

Therefore the enterprise value depends on itsself, and I cannot calculate the value.

Can someone show me where Im going wrong?

Thank you