Mr. T’s Corp, whose stock is now valued at $25, needs to raise $25’000’000 in common stock. Goldman Investment Bank has advised T’s Corp that they must price the new issues to the public at $21/share. Underwriter’s compensation will be 7% of the issue price and $200’000 of flotation expenses. How many shares must T’s Corp sell in order to net $25’000’000, after underwriting and flotation fees? Show calculations.

Question

BlackTom AI · Accepted Answer

We start by identifying the key financial facts in the problem: the new issue will be priced at $21 per share, Goldman’s underwriter compensation is 7% of the issue price, and there are $200,000 in flotation Expenses. The company needs to net $25,000,000 after all fees.

First, compute the per-share net proceeds after the underwriter’s fee. Since the underwriter takes 7% of the issue price, the deduction per share is 0.07 × 21 = 1.47. Therefore, the net amount received by the company from each new share, before accounting for the fixed flotation costs, is 21 − 1.47 = 19.53 dollars per share.

Next, account for flotation expenses. These are fixed costs of $200,000 regardless of the number of shares sold. If N shares are sold, the total net proceeds would be: N × 19.53 − 200,000.

Set this equal to the required net amount of $25,000,000 to solve for N:
N × 19.53 − 200,000 = 25,000,000
N × 19.53 = 25,000,000 + 200,000 = 25,200,000
N = 25,200,000 / 19.53

Now perform the division. 25,200,000 ÷ 19.53 ≈ 1,290,323 shares (to the nearest whole share). To check the calculation, multiply 19.53 by 1,290,323 and compare with 25,200,000; the product will be extremely close, reflecting the rounding.

Optional cross-check: compute total gross from 1,290,323 shares: 1,290,323 × 21 = 27,096,783; underwriter fees: 7% of 27,096,783 ≈ 1,896,775.81; flotation costs: 200,000. Net proceeds ≈ 27,096,783 − 1,896,776 − 200,000 ≈ 25,000,007, very close to the target 25,000,000, accounting for rounding.

Thus, the calculation yields a share count around 1,290,323 shares to meet the net requirement after underwriting and flotation fees.

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