Question

"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?"A) $4,258,365; loss B) $4,258,365; gain C) $3,735,975; gain D) S1,239,175

Answer 1

The impact on the profits of the investment bank: Loss of $3,735,976.

Step-by-step explanation:

The yield to maturity at the issuance ( Tuesday) = 10% + 0.5% = 10.5%.

As the interest rate increases from the time the bank paid to the firm to the time of public issuance, the price of the bond will decrease.

Thus, the investment bank suffer a loss from the interest rate increase.

The total impact of the loss from the 0.5% interest rate increase in the market is the difference between the market value of the bond at issuance and $100 million initially underwritten

The market value of the bond at issuance is the total present value of the cash flow from the bond ( $5 million each from 30 semiannual coupon payments and $100 million principal repayment at maturity) being discounted at the yield to maturity at the issuance time 5.25% (10.5%/2). It is calculated as ( unit in the calculation is million $):

(5/5.25%) x [1 - 1.0525^(-30)] + 100/1.0525^30 = $96.264025 million.

Loss impact = $96.264025 million - $100 million = $(3,735,976).

So, the impact on the profits of the investment bank: Loss of $3,735,976.