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# dominant strategy in game theory

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1. In game theory analysis, what is a "dominant strategy"?

2. A firm's most recent annual dividend was \$2 per share; its shares sell for \$40 in the stock market, and the company expects its dividend to grow at a constant rate of 5% in the foreseeable future. Using the dividend growth (Gordon) model, what would you estimate its equity cost of capital to be? Show all the steps leading to your answer.

3. Two projects have the following NPV's and standard deviations:

Project A Project B

NPV 200 300

Standard deviation 75 100

a) Which of the two projects is more risky? Show all the steps leading to your answer.

b) Why?

4. What are the major ways that the risks of exchange rate changes can be hedged against?

5. What are the ways a multinational corporation can reposition its funds to increase its profits?

6. A function of government is to regulate "natural monopolies."

a) Explain what is a natural monopoly, and

b) Why it requires government regulation

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#### Solution Preview

1. In game theory analysis, what is a "dominant strategy"?

A dominant strategy is one which always gives a player the best possible outcome, regardless of what the other player does. If strategy gives a player the highest payout for each of his opponent's moves, he will choose it, making it his dominant strategy.

2. A firm's most recent annual dividend was \$2 per share; its shares sell for \$40 in the stock market, and the company expects its dividend to grow at a constant rate of 5% in the foreseeable future. Using the dividend growth (Gordon) model, what would you estimate its equity cost of capital to be? Show all the steps leading to your answer.

The Gordon growth model gives us the formula: stock value = d/k-g, where

d = Expected dividend per share one year from now
k = Required rate of return for equity investor which is equal to the cost of equity for that company
g = Growth rate in dividends (in perpetuity)

So we have:
40 = 2 /k-5
Solving for k:
k -5 =2/40
k ...

\$2.19