31. A customer purchases 200 shares of ABC at $49.00 per share. Then the customer sells 2 ABC 50 calls at $2.50. At expiration, what is the customer's break-even point?
Answer: A
The customer's break-even point is $46.50.
To determine the break-even point for the customer's investment, we need to calculate the initial cost of purchasing the shares and consider the income from selling the call options. The break-even point is found by subtracting the total premium received from the call options from the purchase price of the shares.
A) $46.50
This option is correct because the customer initially purchased 200 shares at $49.00 each, totaling $9,800. The sale of 2 call options at $2.50 each generates income of $500. Thus, the break-even point is calculated as $49.00 - ($500 / 200 shares) = $46.50.
B) $47.50
This option is incorrect as it does not accurately reflect the break-even calculation. To reach $47.50, one would need to consider a different premium or purchase price that does not align with the provided data, making this a miscalculation.
C) $51.50
This option is also incorrect. A break-even point of $51.50 would imply that the costs associated with purchasing the shares and the premiums from the call options were not accounted for properly, leading to an inflated break-even calculation.
D) $52.50
This option is incorrect as well. A break-even point of $52.50 suggests that the customer would need to recover more than the initial investment after accounting for the premium received, which contradicts the correct analysis of the situation.
Conclusion
The correct break-even point of $46.50 is derived from accurately calculating the initial investment and the income from selling call options. All other options fail to align with the calculations based on the purchase price and call premiums, demonstrating a misunderstanding of how to calculate the break-even point in this context.