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 of the medical equipment company, we need to calculate the weighted average of the stock beta and debt beta. The formula for the asset beta is as follows:

Asset Beta = (Equity Proportion * Stock Beta) + (Debt Proportion * Debt Beta)

To calculate the equity proportion, we need to first find the market value of equity and debt. The market value of equity is given by the formula:

Market Value of Equity = Total Assets / (1 + Debt-to-Equity Ratio)

Given that the debt-to-equity ratio is 0.5, we can assume the total assets to be 1, as we are only interested in the proportions.

Market Value of Equity = 1 / (1 + 0.5) = 0.6667

The equity proportion is then calculated as:

Equity Proportion = Market Value of Equity / Total Assets = 0.6667 / 1 = 0.6667

Similarly, the debt proportion is calculated as:

Debt Proportion = 1 - Equity Proportion = 1 - 0.6667 = 0.3333

Now, let's calculate the weighted average of the stock beta and debt beta using the given probabilities and returns:

Weighted Stock Beta = (Probability of State 1 * Stock Beta of State 1) + (Probability of State 2 * Stock Beta of State 2) + (Probability of State 3 * Stock Beta of State 3) + (Probability of State 4 * Stock Beta of State 4)

Weighted Stock Beta = (0.1 * 3) + (0.3 * 8) + (0.4 * 20) + (0.2 * 15) = 2.8 + 2.4 + 8 + 3 = 16.2

Weighted Debt Beta = (Probability of State 1 * Debt Beta of State 1) + (Probability of State 2 * Debt Beta of State 2) + (Probability of State 3 * Debt Beta of State 3) + (Probability of State 4 * Debt Beta of State 4)

Weighted Debt Beta = (0.1 * 8) + (0.3 * 8) + (0.4 * 10) + (0.2 * 10) = 0.8 + 2.4 + 4 + 2 = 9.2

Now, we can calculate the asset beta using the weighted average:

Asset Beta = (Equity Proportion * Stock Beta) + (Debt Proportion * Debt Beta)

Asset Beta = (0.6667 * 16.2) + (0.3333 * 9.2) = 10.8 + 3.07 = 13.87

Therefore, the asset beta of the medical equipment company is approximately 13.87.