Problem:
The price of a stock is $25 and the price of a three-month call option on the stock with a $27 strike is $2.50. Suppose a trader has $2,500 to invest and is trying to choose between buying 1,000 options (10 contracts) or 100 shares of stock.
Task:
How high does the stock price have to rise for an investment in options to be as profitable as an investment in the stock? Please provide all calculations and formulas.