For the problems with answers, please explain in a few sentences how you came to the solution. Please also do this for problems without the answer. Please only complete word in Word and copy and paste any spreadsheets used in Excel directly into this document.

3.1. São Paulo Company has made a portfolio of these three securities:

Security / Cost / E(R) / σ(R)
Treasury bond / $45,000 / 4% / 0
Salvador Corporation / $55,000 / 15% / 45%
Brasilia Company / $60,000 / 17% / 55%

The correlation coefficient between Salvador and Brasilia is 0.6.

(A) Find the expected return of the portfolio and its standard deviation.

E(Rp) = 12.66%, σ(Rp) = 32.37% ♥

(B) If the returns are normally distributed, find the probability that the return of the portfolio is more than 16%. Prob(Rp > 16%) 45.89% ♥

3.2. Suppose you have $70,000 that you want to invest in two companies in the following table. Their correlation coefficient is 55%. Your portfolio should have a return of 14%.

Security / Price/share / E(R) / σ(R)
Manaus Oil Company / $50 / 12% / 45%
Curitiba Copper Company / $60 / 15% / 55%

(A) Approximately how many shares of stock of each company should you buy?

(B) What is the σ of the portfolio? 46.63% ♥

3.3. Rio de Janeiro Corporation’s common stock sells for $173 a share and its current annual dividend is $16. The β of this stock is 1.5. It has shown 3% annual growth in dividends for many years. The current riskless rate is 4%. Today, the analysts downgraded the stock from ‘buy’ to ‘hold’. In response to the news, the stock dropped in price by $7 to $166 a share. Assume that the stock will maintain the growth in dividends. Write two equations and solve them simultaneously to calculate the following.

(A) The new β of the stock. 1.57 ♥

(B) Expected return of the market. 9.684% ♥

3.4. Recife Corporation stock has a β of 1.39 and it will pay a dividend of $1.50 next year. The following table shows the various possible economic conditions.

State of the economy
for the next year / Probability / Expected return
of the market
Good / 40% / 15%
Fair / 30% / 10%
Poor / 30% / 0%

The current riskless rate is 5%. The expected long-term rate of growth of Recife is 8%. Find the value of its common stock. Hint: Assume that the predictions of the economy are short-term, perhaps over the next year. Also, assume that the growth of the dividends are long term, perhaps forever. Answer not given ♥

3.5. Belém Company stock currently sells at $21 a share. Given the uncertainty in the economy, you have estimated that after one year, the stock price and its dividend will have the following probability distribution.

Probability / Price/share / Dividend/share
10% / $26 / $1.20
40% / $24 / $1.10
40% / $22 / $1.00
10% / $15 / $0.90

The expected return of the market is 13% and the risk-free rate is 5%. Estimate the β of the stock. β = .8929 ♥

3.6. Goiânia Company has the same growth rate as Campinas Corporation. The current stock price of Goiânia is $43 a share, and its dividend this year is $3. The riskless rate is 4% and the expected return on the market is 12%. Campinas stock is selling at $75 a share. Its dividend next year will be $4 a share and its β is 1.3. Find the β of Goiânia stock. Answer not given

3.7. Guarulhos Autos has β = 1.4. It is interested in buying São Luís Tires which has β = 1.2. Guarulhos believes that after the acquisition, its β will become 1.3. The expected after-tax earnings from São Luís will be $1.37 million for the first year, but this figure will continue to increase by 4% per year in future. The expected return on the market is 14%, and the riskless rate is 6%. Find the amount that Guarulhos should spend on this acquisition. $11.048 million ♥

3.8. Calculate the β of Maceió Corporation from the following data.

Year / Price of
Maceió stock / Dividend
per share / S&P 500
index / S&P 500
dividend / Riskless
rate
beginning / end / beginning / end
2010 / $26 / $29 / $1.00 / 1450 / 1450 / 3.00% / 2.00%
2011 / 29 / 32 / $1.05 / 1450 / 1500 / 3.20% / 2.50%
2012 / 32 / 35 / $1.10 / 1500 / 1550 / 3.00% / 3.50%
2013 / 35 / 38 / $1.15 / 1550 / 1500 / 3.20% / 3.50%

β = .3115844147 » .31 ♥