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1. Consider two stocks, of equal systematic riskiness:

- Stock A is expected to pay a dividend of $10 a share forever.
- Stock B is expected to pay a dividend of $5 a year next year, and thereafter each year's dividend is expected to be 5% above the previous year's dividend.

2. Suppose that we have two stocks, each of which will pay out $5 per share next year in dividends, and report $10 per share in earnings. Suppose that the required rate of return is 10%, that one of the stocks--stock C--has a price/earnings ratio of 10, and that the other stock--stock D--has a price/earnings ratio of 20.

- Explain how two stocks with identical earnings and dividends this year can nevertheless sell for different prices.
- What is the expected long-run dividend growth rate g for stock C? For stock D?
- What is the PVGO--the present value of growth opportunities--for stock C? For stock D?

- What--assuming that you dealt, and did not cheat--is your expected gain (or loss) from this hand?
- What is the
*variance*of your return from this hand? What is the standard deviation? - Your opponent offers you $0.25 if you will cancel this hand and deal another one. Should you accept or reject his or her offer? Why or why not?

- What is your expected gain (or loss) from this game?
- What is the
*variance*of your return from this game? What is the standard deviation? - Your opponent offers you $0.80 if you will cancel this game. Should you accept or reject his or her offer? Why or why not?

A

Project | C(0) |
C(1) | C(2) |

Project | -500 | 480 | 144 |

Project B | -100 | 65 | 84.5 |

- What are the internal rates of return (IRR) associated with the two projects?
- If you can undertake only one of them, and if the cost of capital is 10%, which should you undertake?
- Explain why IRR analysis gives the same (or different) answer as net present value analysis.
- Suppose the cost of capital is 20%; which should you undertake?

A

Year | Machine
| Machine B |

0 | $20,000 | $25,000 |

1 | $5,000 | $4,000 |

2 | $5,000 + replace | $4,000 |

3 | $4,000+replace |

Which machine should you buy? Why? What assumptions are you making about what happens in year 2 (or 3) when you have to replace the machine bought in year 0?

7. What was the average gap between the annual returns on a diversified portfolio of small stocks and the returns on a diversified portfolio of U.S. Treasury bonds between 1926 and 1994? Why does anyone invest in Treasury bonds at all--what advantage do investments in Treasury bonds have over investments in the stocks of small firms?

8. You believe that there is a 50% chance that stock E will rise by 20% and a 50% chance that stock E will fall by 10%. You also believe that there is a 1/3 chance that stock F will rise by 30% and a 2/3 chance that stock F will remain constant. The correlation coefficient between the two stocks is .25

- Calculate the expected return, the variance, and the standard deviation of each stock.
- Calculate the expected return, the variance, and the standard deviation of a portfolio made up of equal investments in each stock.

- How many variance terms are there in your calculation?
- How many covariance terms?
- Suppose that each of the stocks has a standard deviation of annual returns of 25% and a correlation with each other stock of .5. What is the standard deviation of a portfolio that places 1/500 of your wealth in each of the 500 stocks?
- What is the standard deviation of a portfolio that places all of your wealth in one of the stocks?

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