Final answer:
The concept of pro-rata allotment of shares requires additional information that is not provided in the question to accurately determine how many shares an applicant who received 1200 shares must have originally applied for.
Step-by-step explanation:
The question pertains to pro-rata allotment of shares in a business scenario where more shares are subscribed for than are available. Pro-rata allocation means that the shares are allotted to applicants in proportion to the amount they applied for relative to the total amount of shares they could have received. To calculate the number of shares initially applied for by an investor who was allotted 1200 shares on a pro-rata basis, we would need to know the total number of shares applied for and the relationship between the shares applied for and allotted.
However, the additional examples provided regarding the Darkroom Windowshade Company and the PDV (Present Discounted Value) calculations are unrelated in context to the original pro-rata question, illustrating problems in shareholder voting power and stock valuation, which would not inform the answer to the initial question.
In conclusion, without additional information on the total shares applied for in the pro-rata example, we cannot accurately respond to the question about how many shares the shareholder must have originally applied for to be allotted 1200 shares.