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:

Female Managers

Women who hold management positions in organizations, supervising the work of others and involved in strategic decision-making.

Male-Dominated Industries

Sectors of the economy where the workforce or leadership is predominantly male.

Formal Mentoring Programs

are structured initiatives within organizations that pair less experienced employees with more experienced colleagues to facilitate personal and professional growth.

ROPES

An acronym in the field of education and training that stands for Review, Overview, Presentation, Exercise, and Summary, a methodical approach to teaching and learning.