Firm A on 1 January X1 has 5,000 shares outstanding (valued at 14.5 CU per share on the market)and holds 600 shares in treasury stock.On 1 July,it issues 1,000 new shares that are fully subscribed and fully paid for in cash at 15 CU per share.On 1 October,managers exercise their stock options and the firm sells them the 600 shares it held in treasury at a price of 12 CU per share as agreed when the options were granted.The current market value of a share on 1 October is 16 CU per share.What is the time weighted average number of share for the year X1.On 31 December X1,the share is still valued by the market at 16 CU per share.

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The time-weighted average number of shares for the year X1 is calculated by taking into account the number of shares outstanding at the beginning of the year, any share issues or buybacks during the year, and the timing of these transactions. - Start with 5,000 shares on 1 January.- Add 1,000 shares issued on 1 July, which contributes for half the year (6/12 months).- Add 600 shares sold from treasury stock on 1 October, which contributes for the last quarter of the year (3/12 months).$$ \text{Time-weighted average} = 5,000 + (1,000 \times \frac{6}{12}) + (600 \times \frac{3}{12}) = 5,000 + 500 + 150 = 5,650 $$

Firm a on 1 January X1 Has 5,000 Shares Outstanding