Considering Your Answers for Questions 78 Through 83,please State How $P _ { t + 1 } = P _ { t } e ^ { r + a N ( 0,1 ) }$

question 55

Essay

Considering your answers for Questions 78 through 83,please state how many units of capacity you think the plant should be built for and explain why.
An executive has been offered a compensation package that includes stock options.The current stock price is $30/share,and she has been offered a call option on 2000 shares,which can be exercised five years from now at a price of $42/share.Therefore,if the market price of the shares in five years is more than $42/share,she can buy 2000 shares at $42/share,and then immediately sell the shares at the market price,earning a riskless profit.If the market price of the shares was less than $42/share,she will obviously choose not to exercise the option,and would have zero profit.
Assume the price of the stock can be modeled as exponential growth (compounding),which could be calculated as: $P _ { t + 1 } = P _ { t } e ^ { r + a N ( 0,1 ) }$
where, $$P _ { t + 1 }$$
stock price in next period (i.e. ,price next year) $$P _ { t }$$
current stock price $f$
annual growth rate of the stock price,which has been 10% $\sigma$
annual volatility,which is estimated to be 18% $N ( 0,1 ) =$
normal random variable with mean of zero and standard deviation of 1

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Definitions:

Economic Efficiency

A situation where resources are allocated in such a way that maximizes the production of goods and services, minimizing waste and inefficiency in an economy.

Sherman Act

A landmark federal statute in the U.S. that prohibits monopolistic practices and promotes competition among businesses.

McCarran-Ferguson Act

A U.S. federal law enacted in 1945 that exempts the business of insurance from most federal regulation, leaving regulation primarily to the states.

Robinson-Patman Act

A 1936 U.S. law aimed at preventing anticompetitive practices by producers, specifically addressing price discrimination.