Question 1 Company XYZs current return on equity (ROE) is 14%. It pays out one-half of earnings as cash dividends (payout ratio = 0.5). Current book value per share is R50. Book value per share will grow as XYZ reinvests earnings. Assume that the ROE and payout ratio stay con- stant for the next four years. After that, competition forces ROE down to 11.5% and the pay- out ratio increases to 0.8. The cost of capital is 11.5%. a. What are XYZs EPS and dividends next year? How will EPS and dividends grow in years 2, 3, 4, 5, and subsequent years? (6 marks) b. What is XYZs stock worth per share? How does that value depend on the payout ratio and growth rate after year 4? (4 marks) Question 2 Kagiso Dimba, aged 40, is the operations director at his familys company, Dimba Holdings (Pty) Ltd. (DH). Kagiso earns a salary ZAR 1.2 million per year before taxes. Amahle Dimba, Kagisos spouse, aged 38, sits at home to take care of the couples newborn twins. Amahle re- cently inherited ZAR 13.5 million (after wealth-transfer taxes) in cash from her fathers es- tate. In addition, the Dimbas have accumulated the following assets: ZAR 75,000 in cash, ZAR 2.4 million in stocks and bonds, and ZAR 3.3 million in the DH stock. The value of the couples holdings in the DH stock has appreciated substantially as a result of the companys growth in sales and profits during the last ten years. Kagiso is confident that the company and its stock will continue to perform well. The Dimbas now need ZAR 450,000 for a down payment on the purchase of a house and plan to make a ZAR 300,000 non-tax-deductible donation to a charity in memory of Amahles fa- ther. The Dimbas living expenses are ZAR 1.11 million per year. After-tax increments on Kagisos salary will offset any future increases in their living expenses. During their recent discussion with their financial advisor, Dineo Lekota, the Dimbas ex- pressed concern about achieving their educational goals for their children and their own re- tirement goals. The Dimbas told Dineo They want to have sufficient funds to retire in 18 years when their children begin their future years of college education. They have been unhappy with the portfolio volatility that they have experienced in re- cent years and they do not want to experience a loss greater than 12% in any one year. They do not want to invest in alcohol and tobacco stocks. They will not have any additional children. After their discussion, Dineo calculates that in 18 years, the Dimbas will need ZAR 30 million to meet their educational and retirement goal. Dineo suggests that the portfolio be structured to limit shortfall risk (defined as the expected total return minus two standard deviations) to no lower than a 12% return in any one year. Kagisos salary and all capital gains and in- vestment income are taxed at 40% and no tax-sheltering strategies are available. Dineos next step is to formulate an investment policy statement for the couple. Required: a. Formulate the risk objective of an investment policy statement for the Dimbas. (2 marks) b. Formulate the return objective of an investment policy statement for the Dimbas. Cal- culate the pretax rate of return that is required to achieve this objective. Show all your workings. (4 marks) c. Formulate the constraints portion of an investment policy statement for the Dimbas, ad- dressing each one of the following: i. Time horizon (1 mark) ii. Liquidity requirements (2 marks) iii. Tax concerns (2 marks) iv. Unique circumstances (2 marks) Suppose that the Dimbas have now purchased their house and made the donation to the local charity. Now that the investment policy has been prepared for them, Dineo Lekota, the finan- cial analyst, has recommended that they consider the strategic asset allocation described in Table 2. Asset class Recommended allocation(%) Current yield (%) Projected annualized pretax total return (%) Expected standard deviation (%) Cash 15.0 1.0 1.0 2.5 SA corporate bonds 55.0 4.0 5.0 11.0 SA small cap equities 0.0 0.0 11.0 25.0 SA large cap equities 10.0 2.0 9.0 21.0 US equities 5.0 1.5 10.0 20.0 DH common stock 15.0 1.0 16.0 48.0 Total Portfolio 100.0 - 6.7 12.4 Table 2: Recommended asset allocation for the Dimbas Required d. Identify aspects of the recommended asset allocation in Table 2 that are inconsistent with the Dimbas investment objectives and constraints. Support your responses (4 marks) e. After further discussion, Dineo and the Dimbas agree that any suitable strategic asset al- location will include 5 10% in South African small capitalization equities and 10 15% in South African large capitalization equities. For the remainder of the portfolio, Dineo is considering the asset ranges describes in Table 3. Recommend the most appropriate allocation range for each of the asset classes in Table 3. Justify each appropriate allocation range with a reason based on the Dimbas investment objectives and constraints. (No calculations are required.) (8 marks) Asset class Proposed allocation ranges (%) Cash 0-3 5-10 15-20 SA corporate bonds 10-20 30-40 50-60 US equities 0-5 10-15 20-25 DH common stock 0-5 10-15 20-25 Table 3: Proposed strategic asset class ranges for the Dimbas Question 3 Noxolo Makeba owns a newly issued ten-year SA government Treasury bond and wants to evaluate the sensitivity of its cash flows to interest rate changes. The bond has a sinking fund whose terms require that the principal be amortized at a constant rate over the final five years of the bond. Thus, sinking fund payments are scheduled to begin at the end of the sixth year and are payable directly to the trustee to the indenture. Bond investors expect to be paid the principal amount of the bond at its maturity. The coupon rate of interest is 9% payable annually, and each bond has a face value of ZAR 1,000. Investors required rate of return on bonds with a similar risk is 12%. Noxolo has predicted the following interest rate scenario: Interest rates simultaneously decline today by 250 basis points for all maturities, remain there for one year and then, Interest rates simultaneously increase by 350 basis points for all maturities and remain there for the next year. Currently, the Treasury bond is priced close to par and the yield curve is flat. Noxolo does not expect the shape of the yield curve to change during the next three years. Required: a. State whether, in the interest rate scenario described, the Treasury bonds cash flows: Increase or decrease in the first year. (2 marks) Increase or decrease in the second year. (2 marks) Explain why the bonds cash flows change. (2 marks) b. Noxolo also wants to evaluate the price sensitivity of her bond to changes in interest rates. She knows that the modified duration and the convexity are two possible measures she could use to evaluate price sensitivity. i. Select and justify with one reason which measure Noxolo should use to evaluate the price sensitivity of her bond. (2 marks) ii. Would it be theoretically correct to use any of the above measures in isolation? Why or why not? (2 marks) c. Thako Capital Inc., a client of Ms Tozi Mxenge, has entered into a transaction requiring a payment of ZAR 25,000 million in two years time. Thako has ZAR 23,500 million avail- able to meet this liability. Tozi recommends a technique called dedication. Under certain market conditions, this technique can provide Thako with a safety margin or cushion in meeting its liability. Tozi notes that a South African government bond with a bond equiva- lent yield of 3.82% is available. Thako agrees to implement dedication using this bond. i. Identify and explain the advantages to Thako of using dedication rather than immu- nization. (2 marks) ii. Tozi discusses opportunities to use immunization with Nomxolisi Ndzelani, the finan- cial manager at Thako. Nomxolisi makes the following statements: Statement 1: Thako should use corporate bonds for immunization in the future as this will achieve a lower cost of immunization. Statement 2: Whenever Thako implements a multiple-liability immunization plan, the market value of the assets should be compared with the present value of the remain- ing liabilities by discounting the liabilities using zero coupon South African Treasury yields. Explain why each of Nomxolisis statements is incorrect. (Note: Simply reversing the state- ments will not earn credit.) (4 marks) d. You are the fund manager for a large unit trust fund that specializes in fixed income. You have gathered some information, presented in Table 4, about three instruments that are of interest to you in forming a new fixed income portfolio: Coupon (%) Maturity Year Price ZAR Call Price ZAR Yield to maturity (%) Bond 1 (new issue) 14.00 2022 101.750 114.00 13.75 Bond 2 (new issue) 6.00 2022 48.125 103.00 13.80 Bond 3 (2012 issue) 6.00 2022 48.875 103.00 13.40 Table 4: Some facts about some fixed income instruments Suppose that you expect a decline in interest rates over the next three years. Identify and justify which one of these three bonds you would select. Assume that the three bonds are of the same quality. (Show all your workings.) (9 marks) Question 4 You have been recently appointed chief investment officer of a major charitable organization. The organizations large endowment fund is currently invested in a broadly diversified port- folio of stocks (60%) and (40%). The organizations board of trustees is a group of prominent individuals whose knowledge of modern investment theory and practice is superficial. You de- cide a discussion of basic investment principles would be helpful. a. Explain the concepts of idiosyncratic risk, systematic risk, standard deviation and beta as they relate to investment management. (8 marks) b. You believe that the addition of other asset classes to the endowment portfolio would im- prove the portfolio by reducing risk and enhancing return. You are aware that depressed conditions in South African real estate markets are providing opportunities for property acquisition at levels of expected return that are unusually high by historical standards. You believe that an investment in real estate would be both appropriate and timely and have decided to recommend a 20% position to be established with funds taken equally from stocks and bonds. Preliminary discussions revealed that several trustees believe that real estate is too risky to include in the portfolio. The board chairman, however, has scheduled a meeting for further discussion of the matter and has asked you to provide background information that will clarify the risk issue. To assist you, the expectations data presented in Table 5 have been developed: Return Standard Correlation Matrix Asset Class (%) Deviation(%) Stocks Bonds Real Estate Treasury Bills Stocks 12.0 21.0 1.00 Bonds 8.0 10.5 0.14 1.00 Real Estate 12.0 9.0 -0.04 -0.03 1.00 Treasury Bill 4.00 0.0 -0.05 -0.03 0.25 1.00 Table 5: Assets descriptive statistics Required: i. Explain the effect on both portfolio risk and portfolio return that would result from the addition of real estate. Include in your answer two reasons for any change you expect in portfolio risk. (Note: It is not necessary to compute the expected return and risk.) (5 marks) ii. Your understanding of capital market theory causes you to doubt the validity of the expected return and risk estimates for South African real estate. Justify your scepti- cism. (4 marks) c. Identify and describe four criticisms that can be levelled against the Capital Assert Pricing Model. (8 marks) Question 5 Consider stocks A and B whose data are presented in Table 6. The risk-free rate over the period was 6%; the markets average return was 14% with standard deviation, 23%. Perfor- mance is measured using an index model regression on excess return. Required: Stock A Stock B Index model regression estimates 1% + 1.2(rM rf ) 2% + 0.8(rM rf ) R-square 0.576 0.436 Residual standard deviation 10.3% 19.1% Standard deviation of excess returns 21.6% 24.9% Table 6: The performance of stocks a. Compare the performance of stocks A and B using the following measures: i. The Sharpe ratio (5 marks) ii. M-squared (5 marks) b. Suppose that an investor would like to add either stock A or stock B to a diversified port- folio with a Sharpe ratio of 0.8. Assume that the expected return on portfolios A and B were respectively 16.5% and 13%. Which one of the two stocks (A and B) should the in- vestor choose? Why? (5 marks) c. Explain, in terms of relative returns and volatility, the circumstances under which M-squares for a portfolio or asset would equal M-squared for the market. (3 marks) d. Assume that using the Sharpe ratio to measure performance, the JSE All-shares index out- performed some portfolio, but using the Treynor measure, the portfolio outperformed the JSE All-share index. Explain, in terms of systematic and unsystematic risks, how this in- consistency in ranking could have occurred.