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On January 1, 2017, Dave Coates, a 23-year-old mathematics teacher at Xavier High School, received a tax refund of $1,100. Because Dave didn’t need this money for his current living expenses, he decided to make a long-term investment. After surveying a number of alternative investments costing no more than $1,100, Dave isolated two that seemed most suitable to his needs.
Each of the investments cost $1,050 and was expected to provide income over a 10-year period. Investment A provided a relatively certain stream of income. Dave was a little less certain of the income provided by investment B. From his search for suitable alternatives, Dave found that the appropriate discount rate for a relatively certain investment was 4%. Because he felt a bit uncomfortable with an investment like B, he estimated that such an investment would have to provide a return at least 4% higher than investment A. Although Dave planned to reinvest funds returned from the investments in other vehicles providing similar returns, he wished to keep the extra $50 ($1,100 − $1,050) invested for the full 10 yeas in a savings account paying 3% interest compounded annually.
As he makes his investment decision, Dave has asked for your help in answering the questions that follow the expected return data for these investments.
- Assuming that investments A and B are equally risky and using the 4% discount rate, apply the present value technique to assess the acceptability of each investment and to determine the preferred investment. Explain your findings.
- Recognizing that investment B is more risky than investment A, reassess the two alternatives, adding the 4% risk premium to the 4% discount rate for investment A and therefore applying a 8% discount rate to investment B. Compare your findings relative to acceptability and preference to those found for question a.
- From your findings in questions a and b, indicate whether the IRR for investment A is above or below 4% and whether that for investment B is above or below 8%. Explain.
- Use the present value technique to estimate the IRR on each investment. Compare your findings and contrast them with your response to question c.
- From the information given, which, if either, of the two investments would you recommend that Dave make? Explain your answer.
- Indicate to Dave how much money the extra $50 will have grown to by the end of 2026, assuming he makes no withdrawals from the savings account.
Case Problem 4.2 The Risk-Return Tradeoff: Molly O’Rourke’s Stock Purchase Decision
Over the past 10 years, Molly O’Rourke has slowly built a diversified portfolio of common stock. Currently her portfolio includes 20 different common stock issues and has a total market value of $82,500.
Molly is at present considering the addition of 50 shares of either of two common stock issues—X or Y. To assess the return and risk of each of these issues, she has gathered dividend income and share price data for both over the last 10 years (2007–2016). Molly’s investigation of the outlook for these issues suggests that each will, on average, tend to behave in the future just as it has in the past. She therefore believes that the expected return can be estimated by finding the average HPR over the past 10 years for each of the stocks. The historical dividend income and stock price data collected by Molly are given in the accompanying table.
- Determine the HPR for each stock in each of the preceding 10 years. Find the expected return for each stock, using the approach specified by Molly.
- Use the HPRs and expected return calculated in question a to find the standard deviation of the HPRs for each stock over the 10-year period.
- Use your findings to evaluate and discuss the return and risk associated with stocks X and Y. Which stock seems preferable? Explain.
- Ignoring her existing portfolio, what recommendations would you give Molly with regard to stocks X and Y?
Case Problem 2.1 Traditional Versus Modern Portfolio Theory: Who’s Right?
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Walt Davies and Shane O’Brien are district managers for Lee, Inc. Over the years, as they moved through the firm’s sales organization, they became (and still remain) close friends. Walt, who is 33 years old, currently lives in Princeton, New Jersey. Shane, who is 35, lives in Houston, Texas.Recently, at the national sales meeting, they were discussing various company matters, as well as bringing each other up to date on their families, when the subject of investments came up. Each had always been fascinated by the stock market, and now that they had achieved some degree of financial success, they had begun actively investing.
As they discussed their investments, Walt said he thought the only way an individual who does not have hundreds of thousands of dollars can invest safely is to buy mutual fund shares. He emphasized that to be safe, a person needs to hold a broadly diversified portfolio and that only those with a lot of money and time can achieve independently the diversification that can be readily obtained by purchasing mutual fund shares.
Shane totally disagreed. He said, “Diversification! Who needs it?” He thought that what one must do is look carefully at stocks possessing desired risk-return characteristics and then invest all one’s money in the single best stock. Walt told him he was crazy. He said, “There is no way to measure risk conveniently—you’re just gambling.” Shane disagreed. He explained how his stockbroker had acquainted him with beta, which is a measure of risk. Shane said that the higher the beta, the more risky the stock, and therefore the higher its return. By looking up the betas for potential stock investments on the Internet, he can pick stocks that have an acceptable risk level for him. Shane explained that with beta, one does not need to diversify; one merely needs to be willing to accept the risk reflected by beta and then hope for the best.
The conversation continued, with Walt indicating that although he knew nothing about beta, he didn’t believe one could safely invest in a single stock. Shane continued to argue that his broker had explained to him that betas can be calculated not just for a single stock but also for a portfolio of stocks, such as a mutual fund. He said, “What’s the difference between a stock with a beta of, say, 1.2 and a mutual fund with a beta of 1.2? They have the same risk and should therefore provide similar returns.”
As Walt and Shane continued to discuss their differing opinions relative to investment strategy, they began to get angry with each other. Neither was able to convince the other that he was right. The level of their voices now raised, they attracted the attention of the company’s vice president of finance, Elinor Green, who was standing nearby. She came over and indicated she had overheard their argument about investments and thought that, given her expertise on financial matters, she might be able to resolve their disagreement. She asked them to explain the crux of their disagreement, and each reviewed his own viewpoint. After hearing their views, Elinor responded, “I have some good news and some bad news for each of you. There is some validity to what each of you says, but there also are some errors in each of your explanations. Walt tends to support the traditional approach to portfolio management. Shane’s views are more supportive of modern portfolio theory.” Just then, the company president interrupted them, needing to talk to Elinor immediately. Elinor apologized for having to leave and offered to continue their discussion later that evening.
a. Analyze Walt’s argument and explain why a mutual fund investment may be overdiversified. Also explain why one does not necessarily have to have hundreds of thousands of dollars to diversify adequately.
b. Analyze Shane’s argument and explain the major error in his logic relative to the use of beta as a substitute for diversification. Explain the key assumption underlying the use of beta as a risk measure.
c. Briefly describe the traditional approach to portfolio management and relate it to the approaches supported by Walt and Shane.
d. Briefly describe modern portfolio theory and relate it to the approaches supported by Walt and Shane. Be sure to mention diversifiable risk, undiversifiable risk, and total risk, along with the role of beta.
e. Explain how the traditional approach and modern portfolio theory can be blended into an approach to portfolio management that might prove useful to the individual investor. Relate this to reconciling Walt’s and Shane’s differing points of view.
Case Problem 5.2 Susan Lussier’s Inherited Portfolio: Does It Meet Her Needs?
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Susan Lussier is 35 years old and employed as a tax accountant for a major oil and gas exploration company. She earns nearly $135,000 a year from her salary and from participation in the company’s drilling activities. An expert on oil and gas taxation, she is not worried about job security—she is content with her income and finds it adequate to allow her to buy and do whatever she wishes. Her current philosophy is to live each day to its fullest, not concerning herself with retirement, which is too far in the future to require her current attention.
A month ago, Susan’s only surviving parent, her father, was killed in a sailing accident. He had retired in La Jolla, California, two years earlier and had spent most of his time sailing. Prior to retirement, he managed a children’s clothing manufacturing firm in South Carolina. Upon retirement he sold his stock in the firm and invested the proceeds in a security portfolio that provided him with supplemental retirement income of over $30,000 per year. In his will, he left his entire estate to Susan. The estate was structured in such a way that in addition to a few family heirlooms, Susan received a security portfolio having a market value of nearly $350,000 and about $10,000 in cash.
Susan’s father’s portfolio contained 10 securities: 5 bonds, 2 common stocks, and 3 mutual funds. The following table lists the securities and their key characteristics. The common stocks were issued by large, mature, well-known firms that had exhibited continuing patterns of dividend payment over the past five years. The stocks offered only moderate growth potential—probably no more than 2% to 3% appreciation per year. The mutual funds in the portfolio were income funds invested in diversified portfolios of income-oriented stocks and bonds. They provided stable streams of dividend income but offered little opportunity for capital appreciation.
Now that Susan owns the portfolio, she wishes to determine whether it is suitable for her situation. She realizes that the high level of income provided by the portfolio will be taxed at a rate (federal plus state) of about 40%. Because she does not currently need it, Susan plans to invest the after-tax income primarily in common stocks offering high capital gain potential. During the coming years she clearly needs to avoid generating taxable income. (Susan is already paying out a sizable portion of her income in taxes.) She feels fortunate to have received the portfolio and wants to make certain it provides her with the maximum benefits, given her financial situation. The $10,000 cash left to her will be especially useful in paying brokers’ commissions associated with making portfolio adjustments.
- Briefly assess Susan’s financial situation and develop a portfolio objective for her that is consistent with her needs.
- Evaluate the portfolio left to Susan by her father. Assess its apparent objective and evaluate how well it may be doing in fulfilling this objective. Use the total cost values to describe the asset allocation scheme reflected in the portfolio. Comment on the risk, return, and tax implications of this portfolio.
- If Susan decided to invest in a security portfolio consistent with her needs—indicated in response to question a—describe the nature and mix, if any, of securities you would recommend she purchase. Discuss the risk, return, and tax implications of such a portfolio.
- From the response to question b, compare the nature of the security portfolio inherited by Susan with what you believe would be an appropriate security portfolio for her, based on the response to question c.
- What recommendations would you give Susan about the inherited portfolio? Explain the steps she should take to adjust the portfolio to her needs.
Case Problem 13.1 Assessing the Stalchecks’s Portfolio Performance
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Mary and Nick Stalcheck have an investment portfolio containing four investments. It was developed to provide them with a balance between current income and capital appreciation. Rather than acquire mutual fund shares or diversify within a given class of investments, they developed their portfolio with the idea of diversifying across various asset classes. The portfolio currently contains common stock, industrial bonds, mutual fund shares, and options. They acquired each of these investments during the past three years, and they plan to purchase other investments sometime in the future.
Currently, the Stalchecks are interested in measuring the return on their investment and assessing how well they have done relative to the market. They hope that the return earned over the past calendar year is in excess of what they would have earned by investing in a portfolio consisting of the S&P 500 Stock Composite Index. Their research has indicated that the risk-free rate was 7.2% and that the (before-tax) return on the S&P 500 portfolio was 10.1% during the past year. With the aid of a friend, they have been able to estimate the beta of their portfolio, which was 1.20. In their analysis, they have planned to ignore taxes because they feel their earnings have been adequately sheltered. Because they did not make any portfolio transactions during the past year, all of the Stalchecks’s investments have been held more than 12 months, and they would have to consider only unrealized capital gains, if any. To make the necessary calculations, the Stalchecks have gathered the following information on each investment in their portfolio.
Common stock. They own 400 shares of KJ Enterprises common stock. KJ is a diversified manufacturer of metal pipe and is known for its unbroken stream of dividends. Over the past few years, it has entered new markets and, as a result, has offered moderate capital appreciation potential. Its share price has risen from $17.25 at the start of the last calendar year to $18.75 at the end of the year. During the year, quarterly cash dividends of $0.20, $0.20, $0.25, and $0.25 were paid.
Industrial bonds. The Stalchecks own eight Cal Industries bonds. The bonds have a $1,000 par value, have a 9.250% coupon, and are due in 2027. They are A-rated by Moody’s. The bonds were quoted at 97.000 at the beginning of the year and ended the calendar year at 96.375%.
Mutual fund. The Stalchecks hold 500 shares in the Holt Fund, a balanced, no-load mutual fund. The dividend distributions on the fund during the year consisted of $0.60 in investment income and $0.50 in capital gains. The fund’s NAV at the beginning of the calendar year was $19.45, and it ended the year at $20.02.
Options. The Stalchecks own 100 options contracts on the stock of a company they follow. The value of these contracts totaled $26,000 at the beginning of the calendar year. At year-end the total value of the options contracts was $29,000.
- Calculate the holding period return on a before-tax basis for each of these four investments.
- Assuming that the Stalchecks’s ordinary income is currently being taxed at a combined (federal and state) tax rate of 38% and that they would pay a 15% capital gains tax on dividends and capital gains for holding periods longer than 12 months, determine the after-tax HPR for each of their four investments.
- Recognizing that all gains on the Stalchecks’s investments were unrealized, calculate the before-tax portfolio HPR for their four-investment portfolio during the past calendar year. Evaluate this return relative to its current income and capital gain components.
- Use the HPR calculated in question c to compute Jensen’s measure (Jensen’s alpha). Use that measure to analyze the performance of the Stalchecks’s portfolio on a risk-adjusted, market-adjusted basis. Comment on your finding. Is it reasonable to use Jensen’s measure to evaluate a four-investment portfolio? Why or why not?
- On the basis of your analysis in questions a, c, and d, what, if any, recommendations might you offer the Stalchecks relative to the revision of their portfolio? Explain your recommendations.