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 betas of its stock and debt.

First, we need to calculate the beta of the stock and debt:

1. Beta of stock:
The beta of the stock in each state can be calculated using the formula: Beta(stock) = Covariance(stock, market) / Variance(market)
Multiply the covariance of the stock and market with the respective probability for each state and sum them up to get the weighted average covariance.
Multiply the variance of the market with the respective probability for each state and sum them up to get the weighted average variance.
Divide the weighted average covariance by the weighted average variance to get the beta of the stock.

2. Beta of debt:
The beta of debt is considered to be zero.

Once we have calculated the beta of stock and debt, we can calculate the asset beta using the company's debt-to-equity ratio.

3. Asset beta:
The asset beta can be calculated using the formula: Asset Beta = Equity Weight * Beta(Stock) + Debt Weight * Beta(Debt)
The equity weight can be calculated as Equity Weight = (1 - Debt-to-Equity Ratio)
The debt weight can be calculated as Debt Weight = Debt-to-Equity Ratio

Let's follow these steps to calculate the asset beta:

1. Calculate the beta of the stock:
In each state, use the formula Beta(Stock) = Covariance(Stock, Market) / Variance(Market) and multiply the result with the respective probability of the state:

Beta(Stock) = (0.1 * 5) + (0.3 * 8) + (0.4 * 10) + (0.2 * 10)

Beta(Stock) = 0.5 + 2.4 + 4 + 2 = 9.9

2. Calculate the equity weight:
The equity weight is (1 - Debt-to-Equity Ratio). Given that the debt-to-equity ratio is 0.5, the equity weight will be 1 - 0.5 = 0.5.

3. Calculate the asset beta:
The asset beta can be calculated using the formula Asset Beta = Equity Weight * Beta(Stock) + Debt Weight * Beta(Debt).
Since the beta of debt is assumed to be zero, the equation becomes:

Asset Beta = Equity Weight * Beta(Stock) + 0

Asset Beta = 0.5 * 9.9 + 0

Asset Beta = 4.95

Therefore, the asset beta of the medical equipment company is 4.95.