1. Suppose you have $60,000 that you want to invest in two companies, whose information is available as follows.
|
Company
|
Price/share
|
E(R)
|
σ(R)
|
|
Vienna
|
$30
|
14%
|
35%
|
|
Graz
|
$40
|
18%
|
45%
|
The correlation coefficient between them is 0.4. Your portfolio should have a return of 15%. How many shares of each company should you buy? Find the standard deviation of this portfolio's returns.
2. Linz Company has made a portfolio of these three securities:
|
|
Cost
|
E(R)
|
σ(R)
|
|
Treasury bond
|
$20,000
|
4%
|
0
|
|
Salzburg Corporation
|
$35,000
|
16%
|
35%
|
|
Innsbruck Company
|
$45,000
|
17%
|
40%
|
The correlation coefficient between Salzburg and Innsbruck is 0.3. If the returns are normally distributed, find the probability that the return of the portfolio is more than 18%.
3. The Klagenfurt Corp stock has a β of 1.75 and it will pay a dividend of $2.25 next year. The expected rate of return of the market is 12% and the current riskless rate is 4%. The expected rate of growth of Klagenfurt is 3.5%. Find the value of its common stock.
4. Villach Corporation preferred stock sells for $65 a share and pays an annual dividend of $3.50. The β of this stock is 1.7. The current riskless rate is 3%. The common stock of Villach was upgraded by the analysts from 'hold' to 'buy' today. In response to the news, the preferred stock jumped in price by $1.50. Find the new β of Villach preferred. 1.613
5. Wels Company has β = 1.25, whereas the return on the market is expected to be 11%, with a standard deviation of 18%. The riskless rate is 5% at present. The stock of Wels is selling at $40 a share, but it does not pay any dividends. Find the probability that it will be selling for more than $48 by next year. Assume that the entire change in the stock price is due to the change in the market.
6. Sankt Pölten Corp stock is selling at $140 a share. Its dividend next year will be $3.00 a share and its β is 1.15. Dornbirn Company has the same growth rate as Sankt Pölten. The current stock price of Dornbirn is $65 a share, and its dividend this year is $1.50. The riskless rate is 4% and the expected return on the market is 11%. Find the β of Dornbirn stock.
7. Steyr Corporation has β = 1.2. It is interested in buying Feldkirch Corporation for $600,000, which also has β = 1.2. Steyr believes that after the acquisition, its β will be 1.1. The expected after-tax earnings from Feldkirch will be $50,000 for the first year, which will continue to grow in future. The expected return on the market is 12%, and the riskless rate is 6%. Find the minimum growth rate of earnings to make it a profitable acquisition.
8. Calculate the β of Bregenz Corporation from the following data. The prices are at the beginning and at the end of each year:
|
Year
|
Price of Bregenz
|
Dividend of Bregenz
|
S&P 500 index
|
S&P 500 dividend
|
Riskless rate
|
|
2010
|
25-27
|
$2.00
|
100-105
|
3.05%
|
3.0%
|
|
2011
|
27-29
|
$2.00
|
105-110
|
3.20%
|
3.5%
|
|
2012
|
29-32
|
$2.50
|
110-120
|
3.50%
|
2.5%
|
|
2013
|
32-33
|
$2.50
|
120-125
|
4.00%
|
2.5%
|
β = 0.97265175 ≈ 0.97