**Question 1**

Lee Ltd and Ng Corporation negotiate a $25 million, 5-year interest-rate swap in which Lee will pay a 4.25% fixed rate to Ng, and Ng will pay Libor to Lee. The firms will net payments half-yearly. Lee generally pays Libor plus 20 basis points for borrowing, and Ng borrows at 4.10%.

Determine the “all-in-cost” for Lee and Ng. It may be useful to create a diagram showing the payment responsibilities of each firm.

Suppose that after two years, the market offers a swap rate of 3.35% against Libor. A swap dealer offers to take the swap off Lee’s hands. How much will Lee have to pay the dealer?

For question 1 (a), explain why interest only is paid or why interest and principal are paid.

Suppose a borrower knows at time t = 0 that it will have available at time t = 1 an opportunity to invest $330 in a risky project that will pay off at time t = 2. The borrower knows that it will be able to invest in one of two mutually exclusive projects, S or R, each requiring a $330 investment. If the borrower invests in S at time t = 1, the project will yield a gross payoff of $610 with a probability of 0.8 and $175 with a probability of 0.2 at time t = 2. If the borrower invests in R at time t = 1, the project will yield a gross payoff of $685 with a probability of 0.6 and $95 with a probability of 0.4 at time t = 2. The borrower’s project choice is not observable to the bank.The riskless, single-period interest rate at time t = 0 is 3%. It is not known at time t = 0 what the riskless, single-period interest rate at time t = 1 will be, but it is common knowledge that this rate will be 4% (with probability 0.70) or 10% (with probability 0.30). Assume universal risk neutrality and that the borrower has no assets than the project on which you (as the lender) can have a claim.

Suppose you are this borrower’s bank, and both you and the borrower recognize that this borrower has two choices: (1) it can do nothing at time t = 0 and simply borrow at the spot market at the interest rate prevailing for it at time t = 1, or (2) it can negotiate at time t = 0 with you (or some other bank) for a loan commitment that will permit it to borrow at predetermined terms at time t = 1.

What advice should you give this borrower? Assume a competitive loan market in which each bank is constrained to earn zero expected profit. Determine the NPV of the alternative(s) that you recommend.

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**Question 2**

The market value of the assets of a corporation is currently $15 million. The firm has on the issue a debt outstanding with a par value of $13.2 million and a due date of exactly four years. No intermediate interest payments are required. The risk-free (continuous) rate is 4.5%, and the standard deviation of returns of the firm’s assets is 70%.

Fortunately for the bank loan officer, she learns that a dividend of $1.8 million will be paid within days.

What should be today’s equity value and debt value and the fair interest rate required by the debt holders? State any simplifying assumptions made in your calculations.

If the bank requires repayment of debt (D), what is the payoff to the bank based on the value of the firm’s assets? Using the diagram below, describe the bank’s payoff depending on the value of D relative to A.

**Question 3**

Suppose you are required to fund a portfolio of homogeneous $330 million fixed-rate loans with 3-year maturities and 8 percent interest per annum with repayments in equal yearly installments using two types of bonds. One bond is an 8%, $1,000 bond maturing in 3 years, and the other is an 8%, $1,000 bond maturing in 1 year. Assume annual coupon payments for both bonds.

If the treasury management section of the bank is attempting to minimize interest rate risk, how many bonds should be issued? Your manager has suggested that both bonds should be used. Explain the rationale for your manager’s suggestion.

The other alternative that the manager has suggested is to use a 2-year swap. The swap comprises a two-year bond with a fixed coupon rate of 8.0 percent paid annually and a floating-rate bond with a duration of approximately zero.

Assume the yield curve that can be applied for these instruments is flat at 8%.

Examine both alternatives and advise the treasury management section.

**Question 4**

What strategies would you recommend to limit the interest rate exposure caused by a positive duration gap if interest rates rose?

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**Question 5**

“Credit enhancements” (such as banks retaining a subordinate claim in a pool of loans or obtaining a third-party guarantee in the form of a letter of credit) are needed when loans are securitized because investors who buy loans tend to be risk averse. Discuss.

**Question 6**

Suppose that a bank with a positive net worth perfectly matches the duration of its assets and liabilities. What will happen to the value of this bank’s shares if interest rates rise unexpectedly?

**Question 7**

Review the article by Brei, Borio, and Gambacorta (2020) and show how you can apply what was covered in BUS307 in a real-world situation. Insightful observations and discussion will attract a superior grade. Conversely, inserting paragraphs/sections from your texts, the internet, and the Brei et al. (2020) article will not be viewed favorably.

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