Question

For this assignment, you should use your FINANCIAL CALCULATOR, NOT EXCEL. It is not enough to provide answers without any explanation. You are required to write down the inputs into your calculator and the output. All your calculations should be performed using your calculator’s PV, I, PMT, FV, and N keys.

Problem 2 (40 points)

1. We now have a $20 million partially-amortizing (balloon) mortgage to be repaid over 10 years with constant annual payments and a final balloon payment of $15 million. The fixed interest rate on the mortgage is 8%.
   1. What is the periodic debt payment?
   2. Using the PV method, compute the outstanding balance at the end of year 5.
   3. Redo the calculation in b using the FV method.
   4. What would be the periodic debt payments if they were made monthly rather than annually?
   5. Would the borrower pay more or less interest in total compared to annual payments?

Answer 1

a). PV = principal = 20,000,000; FV = balloon payment = -15,000,000; N = 10; rate = 8%; Mode = 0, solve for PMT.

Annual payment = 1,945,147.44

b). Outstanding balance after 5 years: PMT = 1,945,147.44; N = remaining payments = 5; rate = 8%; FV = 15,000,000; Mode = 0, solve for PV.

PV = 17,975,157.68

c). Outstanding balance using FV method: PV = -20,000,000; PMT = 1,945,147.44; rate = 8%; N = 5; Mode = 0, solve for FV.

FV = 17,975,157.68

d). Periodic debt payments if made monthly: N = 10*12 = 120; rate = 8%/12 = 0.67%; PV = 20,000,000; FV = -15,000,000; Mode = 0, solve for PMT.

Monthly payment = 160,663.80

e). Amount paid if made monthly = monthly payment*number of payments = 160,663.80*120 = 19,279,655.66

Total amount paid = 19,279,665.66 + 15,000,000 = 34,279,655.66

Interest paid = Total amount paid - principal = 34,279,655.66 - 20,000,000 = 14,279,655.66

Amount paid if made annually = annual payment*number of payments = 1,945,147.44*10 = 19,451,474.43

Total amount paid = 19,451,474.43 + 15,000,000 = 34,451,474.43

Interest paid = Total amount paid - principal = 34,451,474.43 - 20,000,000 = 14,451,474.43

Interest paid is more in case of annual payments.