Note to answer this question you dont need the principal bal

Note: to answer this question you don’t need the principal balance of the loan. If you want to use the principal balance and answer the questions in dollar terms vs. percent terms that’s fine but it’s more calculations to arrive at the same conclusions. You work in the finance department of a real estate equity investment firm and you have been thinking about re-financing a $1MM mortgage on a hotel that’s been doing well as the economy has recovered. The current loan is low leverage, so finding a lender willing to provide the same or more proceeds doesn’t seem to be a problem. However, you have to pay a yield maintenance penalty or defease the loan if you want to prepay the loan early. The interest rate on the existing loan is 6.1% and there’s a remaining term of 3 years. The three year U.S. Treasury Rate is 0.66%. You decide to set up a yield maintenance calculation on your calculator to figure out what the prepayment penalty would be:

a) What’s the difference between the current loan’s interest rate and the three year U.S. Treasury rate? ______ Hint, this amount, divided by 12, would be the payment in a PV calculation.

b) What’s the number of monthly payment periods remaining on the loan? ______ Hint: this is the ‘n’ number of period you’ll have to use to discount the payments to PV.

c) Is there a future value associated with this Yield Maintenance income stream, or is it‘0’? ______ Hint: your answer is the FV amount for the HP12C.

d) What periodic discount rate ( i ) should you use for discounting the monthly yield maintenance cash flows to Present Value? ____% (annual) _____% (periodic). Hint: it is usually the risk free rate for the appropriate # of years.

e) What would the present value (PV) of the income stream you set up be ? If you followed the steps above, the PV is expressed as a percent of the loan. ______% (aka ‘points’)

f) You Google a Mortgage Defeasance Calculator and conclude that defeasing, after paying fees, will cost about 11.4 points or 11.4% of the current principal balance of the loan you want to retire. Which prepayment penalty, Defeasance or Yield Maintenance, is cheaper to pursue? _________

Solution

a) The difference between the current loan’s interest rate and the three year U.S. Treasury rate is 5.44 % (i.e. 6.1% - 0.66)

b) The number of monthly payment periods remaining on the loan are 36 ( i.e. 12 * 3)

c) IF we Consider 3 year U.S. Treasury rate, the Future Value will be 0

d) The Discounting rate are 0.66% (Annual) and 0.055% (periodic)