1. The Treasury wishes to conduct a yield auction to sell T-bonds with a maturity of 2 years. It would like to sell T-bonds with a face value of $2 million. The following bids were received:
| Investor | Quantity Demanded(Face Value) | Yield demanded(percent p.a.) |
| 1 | 300,000 | 15 |
| 2 | 200,000 | 14 |
| 3 | 500,000 | 14.38 |
| 4 | 500,000 | 10 |
| 5 | 300,000 | 12 |
| 6 | 200,000 | 15.5 |
| 7-10 | 1,000,000 | Noncompetitive |
Notes:
1. Assume that investors' horizons are exactly 1 year. Hence assume that the CAPM describes asset returns over 1 year holding periods. Suppose a 10 year zero-coupon sells for $295 and is known to have a beta of 0.15. Suppose further that the expected rate of return on the market is 25% per annum. What do you expect a 9 year bond to cost next year if the current yield on a 1 year bond is 5%?
The following data apply to questions 2 through 4:
Hennessey & Associates manages a $30 million equity portfolio for the multimanager Wilstead Pension Fund. Jason Jones, financial vice president of Wilstead, noted that Hennessy had rather consistently achieved the best record among the Wilstead's six equity managers. Performance of the Hennessy portfolio had been clearly superior to that of the S&P 500 in 4 of the past 5 years. In the one less favorable year, the shortfall was trivial.
Hennessy is a "bottom-up" manager. The firm largely avoids any attempt to "time the market." It also focuses on selection of individual stocks, rather than the weighting of favored industries.
There is no apparent conformity of style among the six equity managers. The five managers, other than Hennessy, manage portfolios aggregating $250 million made of more than 150 individual issues.
Jones is convinced that Hennessy is able to apply superior skill to stock selection, but the favorable results are limited by the high degree of diversification in the portfolio. Over the years, the portfolio generally held 40 to 50 stocks, with about 2% to 3% of total funds committed to each issue. The reason Hennessy seemed to do well most years was because the firm was able to identify each year 10 or 12 issues which registered particularly large gains.
Based on this overview, Jones outlined the following plan to the Wilstead pension committee:
"Let's tell Hennessy to limit the portfolio to no more than 20 stocks. Hennessy will double the commitments to the stocks that it really favors, and eliminate the remainder. Except for this one new restriction, Hennessy should be free to manage the portfolio exactly as before."
All the members of the pension committee generally supported Jones' proposal, because all agreed that Hennessy had seemed to demonstrate superior skill in selecting stocks. Yet, the proposal was a considerable departure from previous practice, and several committee members raise questions.
Respond to each of these questions, using no more than 5 lines each:
2. Answer the following:
a. Will the limitation of 20 stocks likely increase or decrease the risk of the portfolio? Explain.
b. Is there any way Hennessy could reduce the number of issues from 40 to 20 without significantly affecting risk? Explain.
3. One committee member was particularly enthusiastic concerning Jones' proposal. He suggested that Hennessy's performance might benefit further from reduction in the number of issues to 10. If the reduction to 20 could be expected to be advantageous, explain why reduction to 10 might be less likely to be advantageous. (Assume that Wilstead will evaluate the Hennessy portfolio independently of the other portfolios in the fund.)
4. Another committee member suggested that, rather than evaluate each managed portfolio independently of other portfolios, it might be better to consider the effects of a change in the Hennessy portfolio on the total fund. Explain how this broader point of view could affect the committee decision to limit the holdings in the Hennessy portfolio to either 10 or 20 issues.
5. Consider the following table, which gives a security analyst's expected return on two stocks for two particular market returns:
Market Return |
Aggressive Stock |
Defensive Stock |
0.05 |
0.02 |
0.035 |
0.20 |
0.32 |
0.14 |
Note: SML stands for Security Market Line. This line is typically drawn with the expected return on assets on the y-axis, and the asset beta on the x-axis.
The expected return should be equal to the required rate of return, but this equality will hold only if the market is in equilibrium.
1. You own 500 acres of timberland, with young timber worth $40,000 if logged now. This represents 1000 cords of wood worth $40 per cord net of costs of cutting and hauling. A paper company has offered to purchase your tract for $140,000. Should you accept the offer? You have the following information:
a)
| Years | Yearly Growth Rate of Cords per acre |
| 1-4 | 16% |
| 5-8 | 111% |
| 9-13 | 4% |
| 14 and subsequent years | 1% |
b) You expect the price per cord to increase at 4% per year indefinitely.
c) The cost of capital is 9 percent. Ignore taxes.
d) The market value of your land would be $100 per acre if you cut and removed the timber this year. The value of cut-over land is also expected to grow at 4 percent per year indefinitely.
2. The Fischer Corporation is considering an average risk investment in a mineral water spring project that has a cost of $150,000. The project will produce 1,000 cases of mineral water per year indefinitely. The current sales price is $138 per case, and the current cost per case is $105. Fischer is taxed at a rate of 46%. Both prices and costs are expected to rise at a rate of 6% per year. Fischer's cost of capital is 15%.
(a) Should Fischer accept the project?
(b) If total costs consisted of a fixed cost of $10,000 per year and variable costs of $95 per unit, and if only the variable costs were expected to increase with inflation, would this make the project better or worse? Continue with the assumption that the output price will rise with inflation.
I. You are in a world where there are only two possible future outcomes--i.e., two states of the world--boom and depression. There are two companies, Dizengoff and Elysee. The following table shows the total payoffs from each company in each state of the world (e.g. if there is depression, Dizengoff pays $20 and Elysee pays $0).
| State of the World | |||
| Boom | Depression | Present Market Value of Firm | |
| Dizengoff | $50 | $20 | $30 |
| Elysee | $50 | $0 | $15 |
Presumably, investors would hold portfolios of the two firm's shares to minimize the variability of their payoffs, all other things being the same. However, investors in this economy have other income in the two states of the world. Hence they would consider not simply the variability of the payoffs from holding the two shares described above, but rather, the variability of their total payoffs from all sources. (Recall the difference between considering an asset in isolation and as part of a portfolio.) Each investor's valuation of a dollar of income in a given state of the world would, thus, depend on his or her income from other sources in that state of the world, as well as on his or her willingness to take risks. (For example, an investor who already had income from other sources, say labor income, which gave him high payouts in the 'depression' state, and low payouts in the 'boom' state, would value more, a security that had a higher payout in the 'boom' state than in the 'depression' state.) The collective valuations of all investors in this economy would result in market prices for the shares of Dizengoff and Elysee. These market valuations for the two firms are given in the last column of the table above.
Answer the following questions, keeping in mind that short-selling of Dizengoff and Elysee shares is permitted. (Riskfree borrowing and lending is not permitted for questions a. through e.) You do not know the probabilities of occurrence of the two states. The solutions to the questions do not require assuming a particular value for the probabilities.:
I. Given the following information about Eastman Corporation, compute the expected rates of return on its debt, levered equity and assets as a function of its debt-equity ratio. Plot these rates of return as a function of Eastman's debt-equity ratio. Your graph should resemble the graph below, which has been created with the given information; however, your graph should extend the graph given below by showing expected rates of return for debt/equity ratios going upto 100. Do expected rates of return behave differently for higher values of the debt/equity ratio in this example? Why do you think this is so?
Confirm that Modigliani-Miller Proposition II (without taxes) holds.
Note: A state price is the market price of a security with a payoff of $1 in that state and zero otherwise.
| State price | Probability | Operating Earnings |
| 0.08 | 0.1 | 100 |
| 0.16 | 0.22 | 80 |
| 0.28 | 0.3 | 60 |
| 0.19 | 0.2 | 50 |
| 0.09 | 0.1 | 30 |
| 0.09 | 0.08 | 20 |
II. The market value of a firm with $500,000 of debt is $1,700,000. EBIT are expected to be a perpetuity. The pretax interest rate on debt is 10 percent. The company is in the 34-percent tax bracket. If the company was 100-percent equity financed, the equity holders would require a 20-percent return.
A. Assume that the personal tax rate of the company's security holders is zero percent.
B. Assume that the personal tax rate on equity income for the company's stockholders is 10%, while the personal tax rate on debt income for the company's bondholders is 25%.
III. The Branch Company's debt holders are promised payments of $25. The expected earnings if the firm does well are $45, but only $20 if it does poorly. The probability of the firm performing poorly or well is 50%. If Branch's bonds are selling at a price of $20, and the interest rate on the bonds is 10%, estimate the reduction in the value of the firm today because of bankruptcy costs.
IV. An entrepreneur has a patent on an invention that is likely to generate $100 million in one year with a probability of 20% and $40 million with a probability of 80%. He needs a capital outlay of $30 million. Since he is certain to make a minimum of $40 million, he should be able to borrow the $30 million at the risk- free rate of 10%.
Suppose, however, that the entrepreneur has another option: to invest in a hula hoop factory. If hula hoops come back into fashion, he will make a killing of $1500 million; if they don't, the best he can do is to recover costs. The probability of making a killing is 0.02.
Pick one of the companies for which data has been provided. Compute the beta for this firm's stock, using the instructions provided in Chapter 6 of the text. You might want to give some thought to the selection of the company, since you will be following this company and performing other financial analyses. You may also pick companies for which data has not been provided. If so, try to locate the firm's stock's CUSIP number. Information on what a CUSIP is can be obtained at the CUSIP Service Bureau site. If you do not know the stock's CUSIP, I will try to find it for you. If the company is not too obscure, and it is traded on the NYSE, I should be able to obtain the return data for you. The list of companies traded on the NYSE can be found at the NYSE's Traded Issues List site. The advantage to picking your own company is that you can use more recent data, and focus on a company that is of interest to you.
Compute the beta using its definition, and then compute it using regression. Confirm that your results match. How confident are you regarding your beta estimate? (Answer with respect to your regression.) How might you improve your beta estimate?
Use balance sheet data on this company to analyse the capital structure of this firm, using the approach laid out in Chapter 18 of the text (cost of capital approach). You can write to the company itself to obtain its annual statements. Get annual statements for the current year and for a few years in the past. Frequently, financial information is available on the Web, either on the company's own home page, or on a database, such as the SEC Database.
For the same company, analyse its dividend policy. Use the approach described in Chapter 21.
The analysis must be done using EXCEL. The report should be presented in any of the following ways: 1) an HTML document, capable of being uploaded to a Web site, 2) a Microsoft Word document, with the EXCEL file embedded. If you use any word processor, other than Word, you must either convert it to Microsoft Word, or convert it to ASCII. Unfortunately, ASCII documents do not look as good, and cannot support much formatting. The report must be submitted on a 3.5" diskette, or (preferably) emailed to me as an attachment. I would like for the groups to present a summary of the projects at the end of the term, using multimedia devices, such as Microsoft Powerpoint.