Finance

1.    The current earnings of Video Inc. are $2.00 a share, and it has just paid an annual dividend of 40 cents.  You forecast that the company’s earnings and dividends will grow at the rate of 25% a year over the period.  From year 5 on, you expect the subsequent growth rate to decline to 8%.  If the capitalization rate for the stock is 15%, calculate its price and the present value of growth opportunities [PVGO].

2.    Assume that an individual can either invest all of his resources in one of the two securities, A or B; or, alternatively, he can diversify his investment between the two. The distributions of the returns are as follows:
Security A                     Security B
Return     Probability             Return     Probability
-10         1/2                 -20        1/2
50        1/2                60        1/2
Assume that the correlation between the returns from the two securities is zero, and answer the following questions:
(a)    Calculate each security’s expected return, variance and standard deviation.
(b)    Calculate the probability distribution of the returns on a mixed portfolio comprised of equal proportions of securities A and B. Also calculate the portfolio’s expected return, variance and standard deviation. You need to find all possible returns on this portfolio and the probability that you observe each of them.
(c)    Calculate the expected return and the variance of a mixed portfolio comprised of 75% of security A and 25% of security B.

3.    The securities of companies Z and Y have the following expected returns and standard deviations:
Company Z            Company Y
Expected Return (%)    15    35
Standard Deviation (%)    20    40
Assume that the correlation between the returns of the two securities is 0.25.
(a)    Calculate the expected return and standard deviation for the following portfolios:
(1) 100%Z
(2) 75%Z + 25%Y
(3) 50%Z + 50%Y
(4) 25%X + 75%Y
(5) 100%Y
(b)    Graph your results.
(c)    Which of the portfolios in part (a) is not optimal? Explain.

4.    Consider two assets A and B for which return distributions can be summarized as follows

AB = 0

What is the risk of the minimum risk portfolio composed of these two Stocks? (Hint: Use Solver in Excel to minimize p2). Is the risk of the minimum risk portfolio below that of every constituent asset? What is the expected rate of return on the minimum risk portfolio?

5.    Consider two other assets A’ and B’, which are identical (in statistical summary), respectively, to A and B above except that AB = 1.
a.    Draw the graph of the efficient frontier in this case
b.    Write down the answers to the same questions as in problem 4.

6.    Assume N securities. The expected returns on all the securities are equal to 0.01 and the variances of their returns are all equal to 0.01. The covariances of the returns between two securities are all equal to 0.005.
i.    What are the expected return and the variance of the return on an equally weighted portfolio of all N securities? Please, note that the variance is presented by the formula, which depends on N.
ii.    What value will the variance approach as N gets large?
iii.    From parts (i) and (ii): Can you conclude what characteristic of the securities is most important when determining the variance of a well-diversified portfolio?

7.    The returns on stocks A and B are perfectly negatively correlated ( ). Stock A has an expected return of 21 % and a standard deviation of return of 40%. Stock B has a standard deviation of return of 20%. The risk-free rate of interest is 11 %. What must be the expected return to stock B?

8.    (a) The risk-free rate of return is 8 percent, the required rate of return on the market, E[Rm] is 12 percent, and Stock X has a beta coefficient of 1.4. If the dividend expected during the coming year, D1, is $2.50 and g = 5%, at what price should Stock X sell?

(b)    Now suppose the following events occur:
(1)    The Federal Reserve Board increases the money supply, causing the riskless rate (Rf) to drop to 7 percent.
(2)    Investors’ risk aversion declines: this fact, combined with the decline in Rf, causes Rm to fall to 10 percent.
(3)    Firm X has a change in management. The new group institutes policies that increase the growth rate to 6 percent. Also, the new management stabilizes sales and profits, and thus causes the beta coefficient to decline from 1.4 to 1.1.
After all these changes, what is Stock X’s new equilibrium price? (Note: D1 goes to $2.52.)

 

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