Reference no: EM131060967

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