Calculating Weighted Average Cost of Capital (WACC) in this example I am stuck with an exercise where I have to calculate the Weighted Average Cost of Capital (WACC) of the company X.
The data is as follows:

We have two periods (t = 0 and t = 1). Company can be found in t = 1 in two states. Each state has a probability of 0.5. In t=1 the value of the company in State 1 is 200.000 USD and the value of the company in State 2 is 70.000 USD.
The corporate tax rate is 40 %. The incurred costs if the firms becomes insolvent would be 20.000 USD in t = 1, which is subtracted from the firm's value. Contingent unit claims are both in State 1 and State 2 equal to 0.45 USD.

Since I am not the economist, I would have the following questions. In order to calculate WACC we need to calculate cost of equity (Re) and cost of debt (Rd). I found in the literature that the cost of equity (Re) is obtained by CAPM (capital asset pricing model), where Cost of equity (Re)  = risk free rate - beta * (market risk rate - risk free rate)
Now let us suppose that the firm's capital is 100% equity financed. I have no idea of how to calculate the cost of equity using CAPM model. Using the data that I have at disposal I guess that I can calculate risk free rate by inversing the sum of contingent claims in State 1 and State 2 which is equal to $\frac{1}{0.90}$
The problem remains how to calculate $beta$ and market risk rate having at disposal only data that I presented above.
You can't. Beta is observed from the value of the company respective to the market (beta represents volatility).
Also the market risk premium is the expected return for the market portfolio and cannot be calculated with what you have been given.