FIN 3710 - City University of New York



RES9776 Department of Real Estate

Real Estate Finance Baruch College

Spring 2010

|RES 9776 |

|Midterm (Practice) Exam 04/14/11 |

SESSION: 7:35 – 8:50 PM ________

Name: __________________________

1. The exam is closed book and closed notes. You can bring in one page, single-sided, 8(11 formula sheet.

2. You can (and probably have to) use a calculator.

3. You have a total of 60 minutes for the exam.

4. The whole exam has a total of 20 points. It will count 20% for your final course grade.

5. Do not separate the exam book. Turn in the entire exam at the end.

6. Budgeting your time efficiently.

7. Good luck.

Q1. Think about Price Level Adjusted Mortgage (textbook page 115).

The loan has a fixed interest rate of 4%. In addition, the loan balance will adjust upward each year by the CPI. If the first year’s realized inflation is 6%,, assuming an initial loan amount of $60,000 what is the loan balance at the beginning of the 2nd year (2 pts)? What is the 2nd year monthly payment (3 pts)?

Q2. Think about Share Appreciation Mortgage.

Consider two loans for a $500,000 house with 20% down payment. Both have 4% for fees and points. One is 30-year FRM with CPM at 8%. The other is SAM at 6% interest rate, and amortizes over 30 years. THE SAM gives the lender 50% of capital gains when the loan at maturity or if the house is sold. If the expected house price appreciation is 4% per year, what is the expected yield for both loans (3 pts), if we assume 5 year horizon?

Questions 3-6 are based on the following information for an adjustable rate mortgage (ARM):

i. Loan amount - $150,000;

ii. Loan term is 30 years, while the borrower is only expected to stay for 5 years;

iii. Introduction rate – 6%;

iv. Index – one year treasury;

v. Payment adjusted annually;

vi. Margin is a constant 2%;

vii Discount points 2%;

viii. Expected end of year (EOY) index numbers are: EOY1=10%; EOY2=8%; EOY3=12%; EOY4=14%

3. If the loan has a payment cap of 5% (negative amortization allowed), what is the monthly loan payment in the second year (2 pts)?

4. If the loan has a payment cap of 5% (no negative amortization beyond original loan balance allowed), what is the loan balance by the end of the second year (2 pts)?

5. If the loan has no payment cap, yet a 2% annual and 5% lifetime interest cap, what is the loan payment in the second year (2 pts)?

6. If the loan has no payment cap, yet a 2% annual and 5% lifetime interest cap, what is the loan balance by the end of the second year (2 pts)?

7. What is the APR for the following 30-year 5/1 ARM mortgage (4 points)?

i. Intro rate of 4.75%;

ii. 2% of loan balance for fees and discount points;

iii. Market index of 1.5% at closing;

iv. Margin of 2.50%;

v. Initial adjustment and life time interest cap of 5.0 %, and annual interest cap of 2.0%

vi. Fees and points amount to 2% of loan balance.

8. What is the effective cost of borrowing after 10 years if the index interest rate become 5% for year 6 and 7, and 8% for year 8, 9, and 10 (4 pts)?

Q1. a. Monthly PMT in first year = PMT (nper=360, int=4%/12, PV=-60,000) = $286

Loan balance by the end of the 1st year:

OLB12 = FV(nper=12, int=4%/12, pmt = $286, PV=-60,000) = $58,964

The balance will then adjust up by inflation rate to

(1+6%) * $58,964 = $62,480

b. What is the monthly loan payment in the 2nd year (2 pts)?

PMT in the 2nd year is based on the new balance and same 4% rate for the remaining 29 years:

Monthly PMT in 2nd year = PMT (nper=348, int=4%/12, PV=-62,480) = $304

Alternatively, you can do $286 * (1+6%) = $304

Q2. Assume a property value of $500,000. In 5 years, the property is expected to be worth

|P0 |500000 | |P0 |500000 |

|Mortgage |400000 | |Mortgage |400000 |

|Mortgage rate |6% | |Mortgage rate |8% |

|Percentage shared |50% | |Percentage shared |0% |

|Fees and points |4% | |Fees and points |4% |

| | | | | |

|P5 |608326.4512 | |P5 |608326.4512 |

|Gain |108326.4512 | |Gain |108326.4512 |

|Shared gain |54163.2256 | |Shared gain |0 |

| | | | | |

|PMT |$2,398.20 | |PMT |$2,935.06 |

|OLB60 |$372,217.43 | |OLB60 |$380,279.43 |

| | | | | |

|Eff cost |9.24% | |Eff cost |9.02% |

| Q3 |OLB0 |150000 |  |annual cap |100% |

|  |Loan term |30 | |lifetime cap |100% |

|  |Intro rate |6% | |pmt cap |5% |

|  |Margin |2% | |Max neg amort |100% |

|  | | | | |  |

|Year |Index |Loan rate |Monthly pmt |OLB |  |

|0 | | | | $ 150,000 |  |

|1 | |6% | $ 899 | $ 148,158 |  |

|2 |10% |12% | $ 944 | $ 154,972 |  |

|3 |8% |10% | $ 992 | $ 158,741 |  |

|4 |12% |14% | $ 1,041 | $ 169,121 |  |

|5 |14% |16% | $ 1,093 | $ 184,132 |  |

| | | | | |  |

|Q4 |OLB0 |150000 |  |annual cap |100% |

|  |Loan term |30 | |lifetime cap |100% |

|  |Intro rate |6% | |pmt cap |5% |

|  |Margin |2% | |Max neg amort |0% |

|  | | | | |  |

|Year |Index |Loan rate |Monthly pmt |OLB |  |

|0 | | | | $ 150,000 |  |

|1 | |6% | $ 899 | $ 148,158 |  |

|2 |10% |12% | $ 1,336 | $ 150,000 |  |

|3 |8% |10% | $ 1,332 | $ 148,970 |  |

|4 |12% |14% | $ 1,658 | $ 150,000 |  |

|5 |14% |16% | $ 2,000 | $ 150,000 |  |

|Q5-6 |OLB0 |150000 | |annual cap |2% |

| |Loan term |30 | |lifetime cap |5% |

| |Intro rate |6% | |pmt cap |100% |

| |Margin |2% | | | |

| | | | | | |

|Year |Index |Loan rate |Monthly pmt |OLB | |

|0 | | | | $ 150,000 | |

|1 | |6% | $ 899 | $ 148,158 | |

|2 |10% |8% | $ 1,096 | $ 146,806 | |

|3 |8% |10% | $ 1,304 | $ 145,799 | |

|4 |12% |11% | $ 1,410 | $ 144,873 | |

|5 |14% |11% | $ 1,410 | $ 143,841 | |

|Q7 |Mortgage |5/1 ARM | | |

Q8.

|OLB0 |$400,000 | |Year |Index |Mort Rate |PMT |OLB |

|Intro Rate |4.750% | |0 |1.50% | | |$400,000 |

|Margin |2.50% | |1 |1.50% |4.75% |$2,086.59 |$393,827.70 |

|Term |30 | |2 |1.50% |4.75% |$2,086.59 |$387,355.75 |

|Annual Cap |2.00% | |3 |1.50% |4.75% |$2,086.59 |$380,569.60 |

|Lifetime cap |5.00% | |4 |1.50% |4.75% |$2,086.59 |$373,454.00 |

|Initial Adj Cap |5.00% | |5 |1.50% |4.75% |$2,086.59 |$365,992.95 |

|Fees and points |2% | |6 |5.00% |7.50% |$2,704.66 |$360,810.82 |

| | | |7 |5.00% |7.50% |$2,704.66 |$355,226.39 |

| | | |8 |8.00% |9.50% |$3,172.08 |$350,714.85 |

| | | |9 |8.00% |9.75% |$3,231.11 |$345,925.97 |

| | | |10 |8.00% |9.75% |$3,231.11 |$340,648.73 |

| | | | | | | | |

| | | | | | | | |

Eff cost @ 10 yr |6.61% | | | | | | | |

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