Joyce and Anthony are in the process of renewing their mortgages. Each mortgage is an interest-only mortgage (i.e., the borrower pays only interest and has a balloon payment at the end) for $100,000. Anthony, having an excellent credit history, is offered the choice between a fixed rate mortgage at + 3 percent and a floating rate mortgage at prime + 1 percent (“prime” rate is the domestic version of LIBOR). Joyce is offered the choice between a fixed rate mortgage at 7 percent and a floating rate mortgage at prime + 3 percent. The current prime rate is 3 percent. Floating rate mortgages are reset at the start of each year.
Anthony and Joyce have both recently retired—Anthony’s future income is closely tied to market interest rates (he has his retirement funds invested in bonds) while Joyce has a fixed retirement income (the Canada Pension Plan).
a. Ignoring interest costs, which mortgage would Anthony prefer—fixed or floating? Why?
Which mortgage would Joyce prefers—fixed or floating? Why?
b. Assume that Anthony chose a fixed rate mortgage and Joyce chose a floating rate mortgage.
i. Design a swap agreement between Anthony and Joyce that will make them both better off.
ii. What is this type of swap called and what are the risks associated with it?
iii. If the prime rate for the next four years is: 3%, 5%, 4%, and 2%, respectively:
1. Show the cash flows between Anthony and Joyce.
2. Demonstrate that the swap will make Anthony and Joyce better off.