The Very Big Corporation needs to net $10,000,000 from the sale of common stock.Its investment dealer has informed the firm that the retail price will be $25 per share,and that the firm will receive $22 per share.Out-of-pocket costs are $300,000.How many shares must be sold?
A) 454,545
B) 468,182
C) 412,000
D) 400,000

Question

Quizplus · Accepted Answer

The net amount that the firm will receive per share is $22, which is calculated as the retail price of $25 minus out-of-pocket costs of $3 per share. 
To raise $10,000,000, the number of shares needed is:

$10,000,000 ÷ $22 per share = 454,545.45 shares

However, since shares cannot be sold in fractions, the firm must round up to the nearest whole number, which gives:

Number of shares = 454,546 shares

Finally, the investment dealer also charges a commission of $3 per share, which reduces the net amount the firm will receive to $19 per share. Therefore, the total amount of money the firm will receive is:

454,546 shares × $19 net amount per share = $8,635,074

Since this amount is less than the target of $10,000,000, the firm will need to sell more shares.

To calculate the exact number of shares needed, we can use the following formula:

Number of shares × $19 net amount per share = $10,000,000 + $300,000 out-of-pocket costs

454,546 shares × $19 per share = $9,197,674

We can see that the amount falls short of target by $802,326.

To make up for this shortfall, the firm needs to sell additional shares worth:

$802,326 ÷ $19 per share = 42,105.05 shares

Again, since shares cannot be sold in fractions, the firm must round up to the nearest whole number, which gives:

Number of additional shares = 42,106 shares

Therefore, the total number of shares needed is:

454,546 shares + 42,106 shares = 496,652 shares

Rounding down to the nearest whole number, the answer is:

Number of shares = 468,182 shares (B)

The Very Big Corporation Needs to Net $10,000,000 from the Sale