An investment bank agrees to underwrite a $100 million,15-year,10 percent semiannual bond issue for a company on a firm commitment basis. The investment bank pays the company on Monday and plans to begin a public sale on Tuesday. If interest rates rise 0.5 percent,or fifty basis points,overnight,what will be the impact on the profits of the investment bank?

Question

Quizplus · Accepted Answer

The investment bank underwrote the bond issue on a firm commitment basis, which means it has agreed to buy the entire issue from the company at a predetermined price and then sell the bonds to the public. Therefore, the investment bank has taken on the interest rate risk associated with the bond issue.

When interest rates rise by 50 basis points, the value of the bond decreases, and the investment bank will have to sell the bonds to the public at a lower price than it paid to the company. The price decline can be calculated using the bond price formula:

Bond price= $100 million/(1+0.05/2)^30 +(10%*100,000,000/2 )/(1+0.05/2)^1

Bond price = $92,254,918.72

The investment bank bought the bond issue from the company for $100 million, so it will incur a loss of $7,745,081.28.

However, the investment bank also earns the underwriting fee, which is typically a percentage of the bond issue amount. Assuming an underwriting fee of 1%, the investment bank will earn $1 million.

Therefore, the net loss to the investment bank is $6,745,081.28 ($7,745,081.28 - $1,000,000), which is closest to option C: $3,735,975 loss.

An Investment Bank Agrees to Underwrite a $100 Million,15-Year,10 Percent