A $50 par value convertible preferred stock is convertible into 5 shares (exercise price of $10). The preferred is selling for $75, and the price of the common stock is $12. If the price of the common stock rises to $20, what is the minimum percentage price increase the holder of the preferred stock should experience?

33.3%

Explanation:

Cost of one common stock = $12

Cost of 5 common stock = $60

Price of preferred stock = $75, which is more than $60

Hence, it would not make sense to convert the preferred stock shared into common stock as of now.

Now, if P is $20, then price of 5 stocks:

= 5 * 20

= $100

Hence, the Preferred stock price must increase to at least $100 otherwise there will be arbitrage opportunity.

Increase in price:

= price of 5 stocks - Price of preferred stock

= $100 - $75

= $25

% increase = (Increase in price : Price of preferred stock) * 100

= (25 : 75) * 100

= 33.3%