BA2034 Corporate Finance

Q1. The market value of the assets of a corporation is currently $15 million. The firm has on issue a debt outstanding that has a par value of $13.2 million and a due date of exactly five years. No intermediate interest payments are required. The risk-free (continuous) rate is 5.5% and the standard deviation of returns of the firm’s assets is 60%. Fortunately, for the bank loan officer, she learns that a dividend of $1.2 million will be paid within days. (Hint: It can be assumed that the dividend will be paid immediately.) 

What should be the 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.

Q2. Suppose a borrower knows at time t = 0 that it will have available at time t = 1 an opportunity to invest $85 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 $85 investment. If the borrower invests in S at time t = 1, the project will yield a gross payoff of $155 with a probability of 0.8 and $45 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 $170 with a probability of 0.6 and $25 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 10%. 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 8% (with probability 0.65) or 15% (with probability 0.35). 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 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. 

a) What advice should you give this borrower? Assume a competitive loan market in which each bank is constrained to earn zero expected profit.

The bank has granted a special loan that has 3 years to maturity and has repayments of $357.875 million at the end of year 1, no payment at the end of year 2 and $357.875 million payment at the end of year 3. The loan is trading at par and the yield to maturity is 5 percent per annum.
 
The yield curve is flat and the interest rate is 5%. The financial institution decides to use a 3- year swap. The swap is composed of a three-year bond with a fixed coupon rate of 5 percent paid annually and a floating-rate bond with duration of approximately zero. 

Using this swap, determine the notional principal of the swap and advise the financial institution on whether it should be a fixed or floating payer. Present an explanation including pertinent assumptions of how the swap you have recommended works.

b)    What impact does the suspension of loan repayments as the crisis hits borrowers have on your analysis? No calculations are required.