Question: (Yield Maintenance) A commercial mortgage is written for $1 million at 8% with 30-year amortization and a 10-year balloon payment. A yield-maintenance (YM) prepayment penalty is included as follows. If the borrower pays the loan off early, she must pay the lender an amount such that if the lender reinvests the proceeds (including the prepayment penalty) in U.S. Treasury bonds maturing on the same date as the original maturity of the mortgage, the lender will receive the same 8% mortgage-equivalent YTM on the loan's outstanding balance as she would have received in the mortgage over the remaining time until the loan's original maturity.
Now suppose the borrower prepays the loan after seven years. Suppose that on that date three-year government bonds are yielding 6% (bond-equivalent yield). How much prepayment penalty must the borrower pay? Compute your answer based on coupon equivalent yield, converting the mortgage MEY to its equivalent BEY. (This is an example of a Treasury flat yield maintenance prepayment structure with the remaining cash flows discounted at the then prevailing Treasury yield with no added margin or spread. In principle, it is identical to the defeasance premium associated with prepaying a CMBS conduit loan. Additional details on different prepayment penalty structures and their evolution as CMBS have become a major force, specifically in the text box, ‘‘Call Protection in CMBS Bonds: Defeasance.'')