Astro Investment Bank offers Lunar Vacations the following options on its initial

a) a best efforts arrangement will yield income of $290,160 (2.4% of 1,000,000 x $12.09) to Astro Investment Bank.

b) a firm commitment arrangement of $10,200,000 will yield income of $1,890,000 (1,000,000x $12.09 minus $10,200,000) to Astro Investment Bank.

c) If 100% of the shares are sold, the better choice for Lunar Vacations is under the best efforts arrangement whereby Astro keeps 2.4% of the retail sales.  This amounts to only $290,160.

d) If 100% of the shares are sold, the better choice for Astro Investment Bank is under the firm commitment arrangement because it will earn $1,890,000 from the deal.

Explanation:

Best efforts arrangement is an agreement whereby the underwriting firm undertakes to make best efforts to sell the shares of the issuer without a firm commitment guaranteeing that all the shares will be sold.  This implies that the underwriter does not take liability for unsold issues.

Usually, the underwriter and the issuer agree on a minimum level of shares to be sold.  And once the minimum is reached, the underwriter is not under obligation to guarantee the unsold portion.

On the other hand, a firm commitment arrangement means that the underwriter guarantees to assume liability for any unsold issue.  For this risk, it is usually arranged for the shares to be sold at a spread, which compensates the underwriter for the assumed risk.  For example, an issue at a price of $10 per share can assume a spread of 10%.  The implication is that the issuer will receive 10% less per share.  For this example, it will be ready to receive $9 per share as against the $10 per share issue price.