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Corporate Finance Problems - Essay Example

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b. Is the stock of firm A correctly priced according to the capital-asset- pricing model (CAPM) What about the stock of Firm B Firm C If these securities are not correctly priced, what is your investment recommendation for someone with a well-diversified-portfolio
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Corporate Finance Problems
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Question 10.39 You have been provided the following data on the securities of three firms, the market portfolio and the risk free asset. Security Expected Return
Standard Deviation
Correlation*
Beta
Firm A
0.13
0.12
0.75
0.9
Firm B
0.16
0.275
0.4
1.1
Firm C
0.25
0.24
0.75
1.8
The Market Portfolio
0.15
0.1
1
1
The risk-free asset
0.05
0
0
0
* With the market portfolio
a. Fill in the missing values in the table
Firm A
Correlation (security) = Beta* Stnd Dev Market/ Stnd Dev (security)
Correlation (security) = 0.9*0.1/0.12
Correlation (security) =0.75
Firm B
Stnd Dev(security)= Beta* Stnd Dev Market/Correlation
Stnd Dev (Security) = 1.1 * 0.1 / 0.4
Stnd Dev (Security) = 0.275
Firm C

Beta = Stnd Dev (security) * Correlation (Security) / Stnd Dev (market)
= 0.24*0.75/01.=1.8
The Market Portfolio
The average beta across all securities, when weighted by the proportion of each security's market value to that of the market portfolio, is 1.
The risk-free asset
Standard Deviation of the risk-free asset always equals 0. And beta is 0 as well, as it is a risk-free asset, so it can not have beta.
b. Is the stock of firm A correctly priced according to the capital-asset- pricing model (CAPM) What about the stock of Firm B Firm C If these securities are not correctly priced, what is your investment recommendation for someone with a well-diversified-portfolio
The CAPM says that the expected return of a security or a portfolio equals the rate on a risk-free security plus a risk premium. If this expected return does not meet or beat the required return, then the investment should not be undertaken.
For A, 0.05+0.9(0.15-0.05) =0.14 0.14 > 0.13 under priced
For B, 0.05+1.1(0.15-0.05) =0.16 0.16 = 0.16 priced correctly
For C, 0.05+1.8 (0.15-0.05) =0.23 0.23 < 0.25 overpriced
If the securities are not priced correctly, the recommendation we would like to give is to take securities with different betas, so in the case of shocks, they will compensate each other.
Question 11.2
Suppose a Three- Factor model is appropriate to describe the returns of a stock. Information about those 3 factors is presented in the following chart. Suppose this is the only information you have concerning these factors.
Factor
Beta of Factor
Expected Value
Actual Value
GNP
0.042
$4,416
$4,480
Inflation
-1.40
3.1%
4.3%
Interest Rate
-0.67
9.5%
11.8%
a. What is the systematic risk of the stock return
The systematic risk is any risk that affects a large number of assets. Such uncertainty about general economic conditions, such as GNP, Interest rate, Inflation is an example of systematic risk and is called beta coefficient, which tells us the response of the stock's return to a specific risk factor.
The total effect of the systematic risks on the stock return includes:
= Surprise in inflation
= Actual inflation - Expected inflation
= 4.3% -3.1% = 1.2%
= Surprise in GNP
= Actual GNP - Expected GNP
= 4480-4416=64
= Surprise in change in interest rates
=Actual change - Expected cnahge
= 11.8- 9.5% = 2.3%
So, the total systematic risk on the stock return is
b. Suppose unexpected bad news about the firm was announced that dampens the returns by 2.6 percentage points. What' the unsystematic risk of the stock returns
Then, the unsystematic risk of the stock return is -2.6%.
c. Suppose the expected return of the stock is 9.5%. What is the total return of this stock
Total return = Expected return + Unexpected return
R = E(R) + U
= E(R) + systematic portion + unsystematic portion


Bibliography:
Corporate Finance, Stephane A.Ross, Randolph W. Westerfield, Jeffrey Jaffe.-7th ed.- The McGraw-Hill/Irwin series in finance, insurance, and real estate. Read More
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