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 beta of the stock, debt, and market portfolio.
1. Calculate the equity weight: Since the debt-to-equity ratio is 0.5, the equity weight is 1 - 0.5 = 0.5.
2. Calculate the beta of the stock: We need to multiply the return on stock by the equity weight for each state and sum them up.
Stock Beta = (Ret.on Stock1 * Prob1) + (Ret.on Stock2 * Prob2) + (Ret.on Stock3 * Prob3) + (Ret.on Stock4 * Prob4)
Stock Beta = (3 * 0.1) + (8 * 0.3) + (20 * 0.4) + (15 * 0.2)
3. Calculate the beta of the debt: Similar to step 2, we need to multiply the return on debt by the equity weight for each state and sum them up.
Debt Beta = (Ret.on Debt1 * Prob1) + (Ret.on Debt2 * Prob2) + (Ret.on Debt3 * Prob3) + (Ret.on Debt4 * Prob4)
Debt Beta = (8 * 0.1) + (8 * 0.3) + (10 * 0.4) + (10 * 0.2)
4. Calculate the beta of the market portfolio: Similar to step 2, we need to multiply the return on the market by the equity weight for each state and sum them up.
Market Beta = (Ret.on Market1 * Prob1) + (Ret.on Market2 * Prob2) + (Ret.on Market3 * Prob3) + (Ret.on Market4 * Prob4)
Market Beta = (5 * 0.1) + (10 * 0.3) + (15 * 0.4) + (20 * 0.2)
5. Calculate the asset beta: The asset beta is calculated using the formula:
Asset Beta = (Stock Beta + Debt Beta) / (1 + (Debt-to-Equity Ratio))
Asset Beta = (Stock Beta + Debt Beta) / (1 + 0.5)
Now, plug in the values we calculated in steps 2, 3, and 4 into the formula to get the asset beta.