Reading: Leverage and Cost of Capital

To illustrate the key principles, let's assume the world lasts only one year and that we are at the beginning of that year. At year-end, there are only two possible states of the world, State I and State II, both with 50% probability. Suppose there is a firm without any debt (unlevered firm) with the following year-end free cash flows:

Suppose the type of business the firm is doing commands a return on its assets (\(k_A\)) of 20%, on average. Under these assumptions, our unlevered firm has a value (\(V_U\)) of:

\( V_U=\frac{FCF}{(1+k_A)}=\frac{1.5}{1.2}=1.25 \)

Since there is no debt outstanding, 1.25 million is also the firm's market value of equity. The cost of equity (\(k_E\))  is also 20%.

Of course, the actual return shareholders will earn depends on the future state of the world. As we can show, that return is either -20% or 60%. But, on average, it is 20%: