Consider again Exercise 4. Imagine that back on October 16, 2007, the firm decided to sell the equipment for $98.78 million receiving the cash in 6 months. The CFO looks at the 3-month LIBOR at the time and sees that it is at 5.2088%. If the rate holds for only 6 months he could invest the proceeds from the sale and make a $67,000 gain because the return will be $100,067 million at the time of the lawsuit payment. So, he decides to forgo any type of hedging.
(a) Given past data on the 3-month LIBOR, compute the statistical distribution of possible cash flows in nine months. Specifically, proceed as follows:
i. Using past data, compute the change in the 3-month LIBOR over six-month periods. Use these changes as possible scenarios about the fluctuations in the 3-month LIBOR over the next six months, and compute the distribution of the total amount available in nine months. How frequently would the firm have enough cash to pay for the lawsuit?
ii. Alternatively, use past data to run the regression
rt+1 = ( + (rt + ϵt+1
Where rt is the LIBOR rate at time t, and ϵt+i ~ N(0,(2). Use the estimated parameters (, ( and ( together with the current LIBOR rate rtoday = 5.2088% to simulate LIBOR rates at t = today+ six months. According to this calculation, how frequently would the firm have enough cash to pay for the lawsuit?
(b) On an ex post basis, will the firm have enough cash to pay the lawsuit? How much will the surplus / deficit be?