A stock price with no dividends is $50 and the strike price of a 1-year European put option is $54. The risk-free rate is 5% (continuously compounded). Compute the lower bound for the put option such that there are arbitrage opportunities if the price is below the lower bound and no arbitrage opportunities if it is above the lower bound?

John is a 45-year-old manager who enjoys playing basketball in his spare time with his teenage sons and their friends. at work he finds that he is better able to solve problems that come up because of his many years of experience, but while on the court, he finds he is not as good keeping track of the ball while worrying about the other players. john's experience is:

Onsider the following subscription behavior information from genie, a web site that provides tools for constructing a family tree (ancestor search). subscriptions cost $9.99 per month, but you are charged for the entire year at the time of purchase. there is a one-year minimum term when you sign up for the service. once purchased, subscriptions are set to renew automatically unless the subscriber cancels them. when a membership renews, it renews for a one-year term and again you are charged for the entire year. there are no variable costs associated with providing this service to an individual customer, but genie does engage in customer relationship activities that they believe will increase customer retention. these customer relationship activities cost genie about $10 per year per customer. based on a sample of 1000 customers that joined genie five years ago, near the time when the company was founded, they were able to determine how many of those customers remained subscribers in the second year, third year etc. based on this information, genie calculated the average annual retention rate to be 20%. genie uses an annual discount rate of 8%. a. last year, genie spent $10,000 placing advertisements on google. genie management believes that these advertisements were responsible for about 300 new subscribers. would you recommend to genie management that they purchase more google ads? b. suppose a newly-introduced loyalty program increases the number of customers that remained to 30%. does this new data change your answer to 9.a? c. do you have any hesitations or concerns about making recommendations to management based on your above estimate of customer lifetime value?

There is a small, family-owned store that sells food and household goods in a small town. the owners have good relations with the community, especially with local farmers who supply much of the food. the farmers aren't organized into a cooperative or union, and the store deals with each individually. suppose the store wanted to buy some farms to control the supply of certain vegetables. how would you classify this strategic move? select one: a. horizontal integration b. forward integration c. backward integration d. concentric integration