Question

Under pro-rata allotment, a company receives applications for 20,000 shares but allots only 10,000 shares to applicants. If a shareholder was allotted 400 shares under this scheme, how many shares did they originally apply for?

• A. \( 800 \text{ shares} \)
• B. \( 200 \text{ shares} \)
• C. \( 400 \text{ shares} \)
• D. \( 600 \text{ shares} \)

Hint:

When an issue is oversubscribed, an individual's applied shares will always be greater than their allotted shares. If your calculation results in a smaller number, you accidentally reversed your adjustment fraction.

Answer 1

The Correct Option is A

Concept: Pro-rata allotment distributes shares proportionally when an issue is oversubscribed. To find an individual's applied or allotted shares, we use the ratio of total applications received to total shares allotted: \[ \text{Applied Shares} = \text{Allotted Shares} \times \left( \frac{\text{Total Applications Received}}{\text{Total Shares Allotted}} \right) \]

Step 1: Determine the general pro-rata allotment ratio.
Using the company's total issue figures: \[ \text{Allotment Ratio} = \frac{\text{Total Applied}}{\text{Total Allotted}} = \frac{20,000}{10,000} = \frac{2}{1} \] This means applicants were allotted exactly 1 share for every 2 shares they applied for.

Step 2: Calculate the individual shareholder's applied shares.
Multiply the individual's allotted shares (400) by the allotment ratio: \[ \text{Individual Applied Shares} = 400 \times \frac{2}{1} = 800 \text{ shares} \]