Question

An investor with $105,000 to invest feels that XYZ’s stock price will increase over the next 3 months. The current stock price is $105 and the price of a 3-month call option with a strike of 110 is $5. To make money, the investor can either buy the stock or invest in call options on the stock. How high does the stock price have to rise for the option strategy to be as profitable as an investment in the stock?

please provide formula and calculation step

Answer 1

Number of shares purchased=105000/105=1000
Number of calls purchased=105000/5=21000

Profit from shares=Number of shares*(Final Share Price-Purchase Price)=1000*(S-105)

If call is exercised, profit from calls=Number of calls*(Final Share Price-Strike Price-Call Price)=21000*(S-110-5)

To have same profits
21000*(S-110-5)=1000*(S-105)
=>S=(21*115-105)/20
=>S=115.5