6. (15 marks) The expected returns, return variances, and the correlation between the returns of four securities are shown below.
Security Expected
Return Variance of
Returns Correlation
A B C D
A 0.17 0.0169 1.0 0.4 0.7 0.2
B 0.13 0.0361 1.0 0.6 0.5
C 0.09 0.0049 1.0 0.9
D 0.07 0.0050 1.0
a. Determine the expected return and variance for a portfolio composed of 25% of security A and 75% of security B.
b. Determine the expected return and variance of a
portfolio that contains 78% security
A and 22% security B. Is this portfolio superior to that one
in (a) above?
c. Calculate the expected return and variance of a
portfolio that contains 60% security
C and 40% security D.
d. If an investor were to select among the following three portfolios, which one would he or she prefer?
o An equallyweighted portfolio of securities A, B, and C.
o An equallyweighted portfolio of A, B, and D.
o An equallyweighted portfolio of B, C, and D.
e. If a riskadverse investor desires to hold a portfolio
of only two securities and expects a return of 11%, what would you
advise the investor to do?
7. Use the following information to answer the
questions
below.
(10 marks)
Security Return Standard Deviation Beta
A 15% 8% 1.2
B 12% 14% 0.9
a. Which of A and B has the least total risk? The least systematic risk?
b. What is the value of systematic risk for a portfolio
with 75% of the funds invested in
A and 25% of the funds invested in B?
c. Calculate the risk free rate of return and the market
risk premium
(i.e., Rf and RM Rf).
d. What is the portfolio expected return and the portfolio
beta if you invest 30% in A,
30% in B, and 40% in the riskfree asset?
(For questions (d) and (e), assume the risk free rate of
return is 5%.)
e. What is the portfolio expected return with 125% invested in A and the remainder in the riskfree asset via borrowing at the riskfree interest rate?
f. What is the beta of the portfolio created in part (e)?
8. Consider the following information on three stocks. (10 marks)
Rate of Return if State Occurs
State of economy Probability of state of
economy Stock A Stock B Stock C
Boom 0.5 0.2 0.35 0.6
Normal 0.3 0.15 0.12 0.05
Bust 0.2 0.01 0.25 0.5
a. If your portfolio is invested 40% each in A and C, and 20% in B, what is the portfolio expected return?
b. What is the variance of this portfolio?
c. What is the standard deviation of this portfolio?
d. If the expected TBill rate is 5%, what is the expected risk premium on the portfolio?
e. If the expected inflation rate is 2.50%, what are the approximate and exact expected real returns on the portfolio?
f. If the expected TBill rate is 5% and the
expected inflation rate is 2.50%, what are the approximate and
exact expected real risk premiums on the portfolio?
9. Briefly discuss the advantages and disadvantages of
using the dividend growth model to estimate the cost of
equity.
(5 marks)
10. Mustard Patch Doll Company needs to purchase new plastic moulding machines to meet the demand for its product. The cost of the equipment is $100,000. It is estimated that the firm will generate, after tax, operating cash flow (OCF) of $22,000 per year for the next seven years. The firm is financed with 40% debt and 60% equity, both based on market values. The firms cost of equity is 16% and its pretax cost of debt is 8%. The flotation costs of debt and equity are 2% and 8%, respectively. Assume the firms tax rate is 34% and ignore the effects of CCA depreciation. (10 marks)
a. What is the firms tax adjusted WACC?
b. Ignoring flotation costs, what is the NPV of the proposed project?
c. What is the weighted average flotation cost, fA, for the firm?
d. What is the dollar flotation cost of the proposed financing?
e. After considering flotation costs, what is the NPV of the proposed project?
11. Photosynthesis, Inc. is considering a project that will
result in initial aftertax cash savings of $2 million at the end
of the first year, and these savings will grow at a rate of
6% per year indefinitely. The firm has a target debtequity
ratio of 1.5, a cost of equity of 20%, and an aftertax cost of
debt of 7%. The costsaving proposal is somewhat riskier than the
usual projects the firm undertakes; management uses the subjective
approach and applies an adjustment factor of +10% to the cost of
capital for such risky
projects.
Under what circumstances should Photosynthesis take on the
project? (10 marks)
12. ABC Co. has the following dividend payment
history:
(10 marks)
Year Dividend
2003 $1.00
2004 1.15
2005 1.25
2006 1.35
2007 1.45
a. How many periods of growth are there in the information given?
b. What is the compound growth rate of dividends?
c. Calculate the yeartoyear growth rates in dividends.
d. What is the average yeartoyear dividend growth rate?
e. Assume a retention ratio of 0.45 and a historical return on equity (ROE) of 0.18. Using these two additional pieces of information, calculate an alternative estimate of dividend growth rate, g.
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