HW 3 FIN/RES 9776Real Estate Finance
Professor Rui Yao
Due date: 03/22/11before the start of class
Q1. Do Problem A-2 of CH 4, Appendix (part c only; part a and b were in HW2)
Q2. This question helps you to understand the relationship of mortgage points/fees and mortgage contract rate for a FRM with constant payment.
You are in the market for a $500,000 house with 20% down payment, and face lots of options. One example is the offerings at Citizen Bank:
To keep things simple, let us limit ourselves to 20 year fixed rate mortgage with constant payments. The rates / points offerings are downloaded here.
20 Year Fixed RateRate / Points / Rebate / APR / Payment / Closing Fees / Total Cost / Apply
6.250% / 1.625% / $0.00 / 6.502% / $2,923.71 / $19,018.00 / /
6.500% / 0.875% / $0.00 / 6.657% / $2,982.29 / $16,018.00 / /
6.750% / 0.000% / $0.00 / 6.795% / $3,041.46 / $12,518.00 / /
7.000% / 0.000% / $2,500.00 / 7.046% / $3,101.20 / $10,018.00 / /
7.250% / 0.000% / $3,500.00 / 7.296% / $3,161.50 / $9,018.00 / /
7.500% / 0.000% / $5,500.00 / 7.546% / $3,222.37 / $7,018.00 / /
You can see the closing costs if you hit “Total Cost” button.Note that closing costs have several components here (again using the 0 point loan as an example) :
i. RBS Citizens, N.A. Fees
ii. Third Party Fees
iii. Taxes and other Unavoidable Fees
iv. Required Advances
v. Closing credits
i. RBS Citizens, N.A. Fees
Application Fee $350.00
Processing Fee $365.00
Underwriting Fee $300.00
Total RBS Citizens, N.A. Fees $1,015.00
ii. Third Party Fees
Tax Service Fee $67.00
Flood Determination $7.00
Settlement or Closing Fee $700.00
Title Insurance $3,475.00
Total Third Party Fees $4,249.00
iii. Taxes and other Unavoidable Fees
Recording Fee $100.00
Local Mortgage Tax $7,170.00
Total Taxes and other Unavoidable Fees $7,270.00
iv. Required Advances
Interest Due at Closing $2,178.08
Hazard Insurance Premium $1,250.00
Hazard Insurance Escrow Deposit $416.67
Property Tax Escrow Deposit $2,666.67
Total Required Advances $6,511.41
v. Closing Cost Credit $0.00
Your New Loan Amount -$400,000.00
Estimated Cash Required at Closing $119,045.41
- Let us first look at the 0.0% points and $0 rebate loan (in BOLD).
Let us figure out what costs are included in quoting APR.
Calculate APR using item i only.
For the loan with zero point and zero rebate, back out the net cash flow at time zero using quoted APR.
Confirm that the amount is close to item i above only (i.e. RBS Citizens, N.A. Fees).
b.The above APR is from the lender’s perspective. The fees go to third party or government are not included. So it is an APR for lender’s “yield” not a homeowner’s “cost”. However from the perspective of a buyer, all fees in items i, ii, and iii should be included. iv however should be ignored. Redo the APR calculation using item i, ii, and iii.
c. Recall APR assumes the borrower will stay for the entire loan term. Now let us think about your optimal loan choice, given your expected stay in the property. Assume that item i, ii, and iii in closing costs should be taken into account for calculating effective borrowing costs, in addition to any additional points and rebates. Find out effective borrow rates for loans with
- no point/no rebate;
- 1.625% point @ 6.25% – note: the points are added to item i.
- $5,500 rebate @ 7.5% - note the credit is added to item v.
while varying your expected stay in the house from 1 to 120months.
What is your optimal mortgage choice at different length of expected stay?