The following table lists possible rates of return for company X stock and debt and on the market portfolio. The probability is listed.
State Probability Return on Stock (%) Return on Debt (%) Return on Market (%)
1 0.1 3% 8% 5%
2 0.3 8% 8% 10%
3 0.4 20% 10% 15%
4 0.7 15% 10% 20%
a. What is the Beta of Company X debt?
b. What is the Beta of Company X stock?
c. If the debt-to equity Ratio of Company X is 0.5, what is the asset beta of Company X? Assume no taxes.
The solution calculates the beta of debt, equity and assets, given the probability distribution of return on equity, debt and market and the debt-equity ratio.