An investment bank has been asked to underwrite an issue of 5 million shares by

Question

An investment bank has been asked to underwrite an issue of 5 million shares by a company. It is trying to decide between a firm commitment where it buys the shares for $8 per share and a best effort where it charges a fee of 45 cents for each share sold. If the investment bank expects the shares to be sold at $10 by a probability of 30%, at $8.5 with a probability of 30%, and at $7.5 with a probability of 40%, would it be more reasonable for it to go ahead with the firm commitment option or the best effort option? Show your calculations.

Explanation / Answer

Expected selling price of the share on the basis of probabilities:

Selling Price of share = ($10 * 30%) + ($8.5 * 30%) + ($7.5 * 40%) = $8.55

Profit earned per share = $8.55 - $8.00 = $0.55 or 55 cents

Since the expected earning under firm commitment is higher, the investment bank should go with this option. This will result in additional 10 cents ($0.55 - $0.45) of earnings compared to best effort option.

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