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# Risk Free Beta Calculations

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1. With a beta equal to .95 and a risk-free rate of 5%, if the required return on Carbo Certamics, Inc. is equal to 9%, what is the required return on the market, rm, assuming the maket is in equilibrium?

2. PowerShares Global Agricultural Investment Fund is holding a stock with a beta of 2.0 that is currently in equilibrium. The required rate of return on the stock is 15% versus a required return on an average stock of 10%. Now the required return on an average stock increases by 42.5% (not percentage points). The risk-free rate is unchanged. By what percentage (not percentage points) would the required retun on PowerShares Global Agricultural Investment Fund's stock increase as a result of this event?

3. Estee Lauder Co.'s deta is shown below. The expected inflation rate and thus the inflation premium increase by 2.0 percentage points, and Estee Lauder Co acquires risky assets that increase its beta by the indicated percentage. What is the firm's new required rate of return?
Beta: 1.50
Required return (rs) 10.20%
Rpm: 6.00%
Percentage increase in beta: 25%

4. You are given the following returns on "the market" and Coca Cola Co's stock during the last three years. We could calculate beta using data for Years 1 and 2 and then, after Year 3, calculate a new beta for Years 2 and 3. How different are those two betas, i.e., what's the value of beta 2- beta 1? (Hint: You can find betas using the Rise-Over-Run method, or using your calculator's regression function.)
Year Market Ratiopharm
1 6.10% -2.50%
2 14.00% -3.70%
3 10.20% 11.71%

5. Consider the following information and then calculate the required rate of return for Beacon Capital Partners Fund, which holds 4 stocks. The market's required rate of return is 8%, the risk-free rate is 4.0%, and the Fund's assets are as follows:
Stock Investments Beta
A \$200,000 1.50
B 300,000 -0.50
C 500,000 1.25
D 1,000,000 0.75

#### Solution Preview

1. With a beta equal to .95 and a risk-free rate of 5%, if the required return on Carbo Certamics, Inc. is equal to 9%, what is the required return on the market, rm, assuming the maket is in equilibrium?
Using the CAPM equation
Required return = Rf + (Rm-Rf) beta
Substituting
9% = 5% + (Rm-5%) 0.95
Rm = (9%-5%)/.95 + 5% = 9.21%
2. PowerShares Global Agricultural Investment Fund is holding a stock with a beta of 2.0 that is currently in equilibrium. The required rate of return on the stock is 15% versus a required return on an average stock of 10%. Now the required return on an average stock increases by 42.5% (not percentage points). The risk-free rate is unchanged. By what percentage (not percentage points) would the required retun on PowerShares Global Agricultural Investment Fund's stock increase as a result of this event?

The required return on average stock ...

#### Solution Summary

Risk free beta calculations are provided. The PowerShares Global Agricultural Investment Fund's stock increase as a result of this event is determined.

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