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 first determine the equity beta of the company. The equity beta represents the sensitivity of the company's stock returns to the overall market returns.
1. Calculate the weighted average return on equity (ROE):
ROE = (P1 * Ret.on Stock) + (P2 * Ret.on Stock) + (P3 * Ret.on Stock) + (P4 * Ret.on Stock)
where P1, P2, P3, P4 are the probabilities of each state
ROE = (.1 * 3) + (.3 * 8) + (.4 * 20) + (.2 * 15)
ROE = 0.3 + 2.4 + 8 + 3
ROE = 13.7%
2. Calculate the weighted average return on debt (ROD):
ROD = (P1 * Ret.on Debt) + (P2 * Ret.on Debt) + (P3 * Ret.on Debt) + (P4 * Ret.on Debt)
where P1, P2, P3, P4 are the probabilities of each state
ROD = (.1 * 8) + (.3 * 8) + (.4 * 10) + (.2 * 10)
ROD = 0.8 + 2.4 + 4 + 2
ROD = 9.2%
3. Calculate the weighted average return on the market (ROM):
ROM = (P1 * Ret.on Market) + (P2 * Ret.on Market) + (P3 * Ret.on Market) + (P4 * Ret.on Market)
where P1, P2, P3, P4 are the probabilities of each state
ROM = (.1 * 5) + (.3 * 10) + (.4 * 15) + (.2 * 20)
ROM = 0.5 + 3 + 6 + 4
ROM = 13.5%
4. Calculate the equity beta (βe) using the following formula:
βe = (ROE - ROD) / (ROM - ROD)
βe = (0.137 - 0.092) / (0.135 - 0.092)
βe = 0.045 / 0.043
βe ≈ 1.047
5. Finally, calculate the asset beta (βa) using the debt-to-equity ratio (D/E):
βa = βe * (1 + (1 - tax rate) * D/E)
With a given D/E ratio of 0.5, we assume a tax rate of 0. Since the question does not provide a specific tax rate value, we can use 0 as a simplifying assumption:
βa = 1.047 * (1 + (1 - 0) * 0.5)
βa = 1.047 * (1 + 0.5)
βa = 1.047 * 1.5
βa ≈ 1.57
Therefore, the asset beta of the company is approximately 1.57.