Final answer:
In a rights offering, the action that provides the least total wealth for shareholders is A) Do not sell or exercise the rights. By not engaging with the rights, the shareholder misses out on their potential value, while the other options involve realizing that value through exercising or selling the rights or new shares obtained.
Step-by-step explanation:
The question pertains to the least total wealth for shareholders in a rights offering scenario. Of the options presented, A) Do not sell or exercise the rights is the action that would provide shareholders with the least total wealth.
This is because the rights themselves have value, as they give the holder the ability to purchase additional shares at a discount.
By neither selling nor exercising these rights, the shareholder fails to capitalize on their intrinsic value, effectively forfeiting any potential gains from selling the rights or acquiring discounted shares through exercising them. In contrast, options B) and C) involve shareholders actively participating in the rights offering to either obtain new shares or to benefit from the sale afterwards, respectively.
Option D), selling the rights and keeping the cash and existing shares, also allows the shareholder to realize the value of the rights. Hence, it is clear that not utilizing the rights in any way leads to the least total wealth for shareholders.