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##### FNCE 370v8 - Assignment 4

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Question;6. (15 marks) The expected returns, return variances, and the correlation between the returns of four securities are shown below.Security ExpectedReturn Variance ofReturns Correlation A B C DA 0.17 0.0169 1.0 0.4 0.7 0.2B 0.13 0.0361 1.0 0.6 0.5C 0.09 0.0049 1.0 0.9D 0.07 0.0050 1.0a. 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% securityA 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% securityC 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 equally-weighted portfolio of securities A, B, and C.o An equally-weighted portfolio of A, B, and D.o An equally-weighted portfolio of B, C, and D.e. If a risk-adverse 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 BetaA 15% 8% 1.2B 12% 14% 0.9a. 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 inA 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 risk-free 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 risk-free asset via borrowing at the risk-free 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 OccursState of economy Probability of state of economy Stock A Stock B Stock CBoom 0.5 0.2 0.35 0.6Normal 0.3 0.15 0.12 0.05Bust 0.2 0.01 -0.25 -0.5a. 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 T-Bill 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 T-Bill 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 firm?s cost of equity is 16% and its pre-tax cost of debt is 8%. The flotation costs of debt and equity are 2% and 8%, respectively. Assume the firm?s tax rate is 34% and ignore the effects of CCA depreciation. (10 marks)a. What is the firm?s 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 after-tax cash savings of $2 million at the end of the first year, and these savings will grow at a rate of6% per year indefinitely. The firm has a target debt-equity ratio of 1.5, a cost of equity of 20%, and an after-tax cost of debt of 7%. The cost-saving 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 riskyprojects.Under what circumstances should Photosynthesis take on the project? (10 marks) 12. ABC Co. has the following dividend payment history: (10 marks)Year Dividend2003 $1.002004 1.152005 1.252006 1.352007 1.45a. How many periods of growth are there in the information given?b. What is the compound growth rate of dividends?c. Calculate the year-to-year growth rates in dividends.d. What is the average year-to-year 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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