Final answer:
Smith's firm value is $7,000,000 with a cost of capital at 12%, while Jones's firm has a total value of $7,333,333.33, with $2,000,000 of debt at 10%, and cost of capital remains at 12% since the firm is evaluated as an all equity-financed entity in Case I no tax environment.
Step-by-step explanation:
When we consider two firms, Smith and Jones that are identical except for capital structure, and each firm expects EBIT of $840,000 each year forever, we can evaluate their value and the cost of capital assuming no taxes (Case I). We start with Smith, which has no debt. The firm’s value can be calculated as the present value of perpetual EBIT using the cost of equity as the discount rate. Therefore, the value of Smith is $840,000 / 0.12 = $7,000,000.
As for firm Jones, it has $2.0 million in perpetual debt with a coupon rate of 10%. The annual interest payments are $200,000 (10% of $2,000,000), which means the EBIT after interest (Earnings Before Taxes, because there are no taxes in this case) for Jones is $840,000 - $200,000 = $640,000. The value of equity in Jones is then the present value of this perpetual income, which gives us $640,000 / 0.12 = $5,333,333.33. The total value of the firm is the value of equity plus the value of debt, which is $5,333,333.33 + $2,000,000 = $7,333,333.33.
The cost of capital for each firm in this Case I environment without taxes will be Smith's cost of equity at 12%, and for Jones, a weighted average of the cost of debt and cost of equity. For Jones, since it's all equity-financed, the cost of capital equals the cost of equity, which is also 12%.