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Business Administration 130

Problem Set # 2

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1. Consider two stocks, of equal systematic riskiness:
At what required rate of return r would the market price of these two stocks be equal? What would the value of these two stocks be at that required rate of return?

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.
3. Suppose that you are playing a card game (using a normal deck of 52 cards, with ace high; and with spades higher than hearts higher than diamonds higher than clubs) with one other person: each is dealt a card which he or she does not examine, but instead shows to his or her opponent. After a round of negotiation and discussion, the cards are turned over, and the low card holder pays the high card holder $1. You look at your opponent's card: it is the eight of diamonds.
4. Suppose that you are playing a dice game (using two normal, fair, six sided dice). If you roll a seven using the two dice, your opponent pays you $1; if you roll an 11, you pay your opponent $1; if you roll anything else you roll again until you do roll a 7 or an 11.
5. Mr. Cyrus Clops has to make a choice between two possible investments:

A
 Project C(0) C(1) C(2)
Project  -500  480  144
 Project B  -100 65 84.5

6. Suppose that you have to choose between two machines which do the same job but have different lives. You must buy one of the two machines. The two machines have the following costs, measured in real, inflation-adjusted dollars:

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
Suppose your cost of capital is 10% per year.

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
9. Suppose that you are trying to calculate the variance of a portfolio made up of all the stocks in the S&P 500 index--500 stocks--from knowledge of the variances and covariances of the stocks alone.
10. Brealey and Myers say that diversification is of the utmost importance for investors making portfolio decisions. Is diversification important for businesses making investment decisions? Why or why not?


Adam Smith
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