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 find the asset beta, we need to calculate the weighted average of the equity beta and the debt beta.
Step 1: Calculate the equity beta.
The equity beta is given by the formula: Equity Beta = Weight of the Stock * Return on Stock / Return on Market
Using the given information, the equity beta can be calculated as follows:
Equity Beta = (0.1 * 3 / 5) + (0.3 * 8 / 10) + (0.4 * 20 / 15) + (0.2 * 15 / 20)
Simplifying the equation, we get:
Equity Beta = 0.06 + 0.24 + 0.5333 + 0.075
Adding up the values, we get:
Equity Beta = 0.9083
Step 2: Calculate the debt beta.
The debt beta represents the sensitivity of the company's debt to changes in market returns. Since the debt return and market return are the same (both equal to 10 in this case), the debt beta is 1.
Step 3: Calculate the asset beta.
The asset beta is calculated as the weighted average of the equity beta and the debt beta, using the debt-to-equity ratio.
Given the debt-to-equity ratio is 0.5, this means that for every $1 of equity, there is $0.5 of debt. Therefore, the weight of equity is 2/3 and the weight of debt is 1/3.
Asset Beta = (Weight of Equity * Equity Beta) + (Weight of Debt * Debt Beta)
Asset Beta = (2/3 * 0.9083) + (1/3 * 1)
Simplifying the equation, we get:
Asset Beta = 0.6055 + 0.3333
Thus, the asset beta of the medical equipment company is approximately 0.94.