Final answer:
The additional premium that Ethier's shareholders require for financial risk is 0.6%, calculated using the CAPM formula and the differences between the costs of equity with and without leverage.
Step-by-step explanation:
The student is asking how to calculate the additional premium that shareholders of Ethier Enterprise require to be compensated for financial risk given that Ethier Enterprise has an unlevered beta of 1.25, it is financed with 40% debt, and has a levered beta of 1.35. The risk-free rate provided is 5% and the market risk premium is 6%. To determine the additional premium required by Ethier's shareholders, we can use the Capital Asset Pricing Model (CAPM) which states that the expected return on equity (or equity cost of capital) is equal to the risk-free rate plus the equity beta times the market risk premium.
First, we find the equity cost of capital using the levered beta: 5% + 1.35 * 6% = 13.1%. Next, we find the cost of capital with no leverage using the unlevered beta: 5% + 1.25 * 6% = 12.5%. The difference between the two, 13.1% - 12.5%, equals 0.6%, which is the additional premium for financial risk that Ethier's shareholders require.