Finding Cost of Capital when the market value of neither debt nor equity is known

When doing the valuation of a company we face the well-known circularity problem where one needs to know the cost of capital to find the value of a company and vice versa. In one of my past paper (available in ssrn.com), I discovered a simple method where one can simultaneously find the market value of equity and the cost of capital by using an iteration method. This assumes that one has access to all the other parameters required to value a company (other than the market value of equity).

These parameters include market value of debt, beta, debt yield, cash flows, growth rate, tax rate, etc. This is in a sense a practical approach because the theoretical problem of circularity still remains. That is how else we will know the beta if we do not know the market value of equity?

In one of my ongoing research work I however realized that one can still find the cost of capital, market value of company, debt and equity even when one does not know the market value of either equity or debt. That is in valuation there are two (and not one as I have believed so far) degrees of freedome available.

What this means is that even if we do not two of the parameters, we can always derive them from the other available parameretrs.