Following are rates of return on a medical equipment company stock, debt, and market portfolio, along with probablity of each state
State Prob Ret.on Stock Ret.on Debt Ret.on Market
1 .1 3 8 5
2 .3 8 8 10
3 .4 20 10 15
4 .2 15 10 20
If the company's dept-to-equity ratio is .5, what is its asset beta?
To calculate the asset beta, we need to calculate the weighted average of the beta of the stock, debt, and market portfolio.
Step 1: Calculate the weights
First, we need to calculate the weights of the stock, debt, and market portfolio based on the company's debt-to-equity ratio.
Debt-to-Equity Ratio = Debt / Equity
Given that the debt-to-equity ratio is 0.5, we can assume that the equity is equal to 1. So the debt is also 0.5.
The weight of debt = Debt / (Debt + Equity)
Weight of debt = 0.5 / (0.5 + 1) = 0.5 / 1.5 = 1/3
The weight of equity = Equity / (Debt + Equity)
Weight of equity = 1 / (0.5 + 1) = 1 / 1.5 = 2/3
Step 2: Calculate the asset beta
Next, we can calculate the asset beta using the formula:
Asset Beta = Weight of Stock * Beta of Stock + Weight of Debt * Beta of Debt + Weight of Market * Beta of Market
Given the following data:
Weight of Debt = 1/3
Weight of Equity = 2/3
We also need the beta values for the stock, debt, and market portfolio, which were not provided in the question. The beta value represents the risk associated with each asset. Please provide the beta values, and I'll be able to calculate the final asset beta for you.