# Real Estate Finance

**Educator2**

Sharon plans to borrow from a bank to finance her investment in a real estate project. She considers an ARM loan with three-year loan term, $100,000 loan amount. The loan has the following terms: 1) **initialinterest rate **=8.5%; 2)margin = 3%; 3) loan amortization period = 15 years; 4) frequency of adjustment = 1 year(monthly compounding); 5) interest rate cap = none; 6) payment cap = none; and 7)discount points = 3%; 8) no negative amortization is allowed. The index rates (i.e., based on 3 year treasure rate) for next two years (i.e., the 2^{nd} and 3^{rd} year) are expected to be 11% and 8%, respectively.

**(a) ****If the loan will be repaid after 3 years, what would be the monthly payment and the ending loan balance for each of the three years? [2pts] IS THIS RIGHT**

**100,000x3%= PV 97,0000 I 8.5% N 180**

**Year 1 Year 2 Year 3**

**PV 97,000 PV 93,654.28 PV 90,789.82**

**I 8.5% I 11.5% I 11.5%**

**N 15x12=180 N14x12=168 N 14x12=168**

PMT $955.30 / 93,654.28 PMT $1,123.90 /$90,789.82 PMT $1,123.90 /$87,578.02

(b) **What isthe effective mortgage yield for borrowing this mortgage**? [5pts]

(c) **Now suppose that there is an annual interest rate cap of 2% specified in the loan contract. What isthe effective mortgage yield for borrowing this mortgage, assuming that no negative amortization is allowed? [5pts] **

**(d) Now suppose, instead of the annual interest rate cap of 2%, the bank prefers a 3% annual payment cap. Assume that negative amortization is allowed, what is the effective mortgage yield for borrowing this mortgage?** [3 pt

1. Luistook a mortgage loan **5 years ago** for $120,000 at 7% interest for 15 years, to be paid in monthly payments. Now, a lender is offering him a new mortgage loan at 5% for 10 years. The new loan amount is $92,895, the outstanding loan balance of the existing loan. Suppose that a prepayment penalty of 3 % must be paid if Luis refinances the existing loan. Moreover, the lender who is making the new loan requires an origination fee of $3,000. Luis plans to hold the property for 10 years. Note: in this case, Luis has to pay the refinancing fees (i.e., the origination fee and the prepayment penalty) out of his pocket.

(c**) Now suppose thatLuis’s current income is low. The new lender allows him to pay a monthly payment of $200 for the new loan (i.e., the actual monthly payment to the lender is only $200, while the loan interest rate is 5%). In this situation, negative amortization occurs. What will be the accrued interest or the amount of increased loan balancefor the loan three years later from now? [3pts]**

**(d) Assume that Luis has to borrow two loans in order to refinance. That is, he has to borrow a new mortgage ($70,000) at 5% for 10 years (i.e., the loan maturity and the amortization period are the same, 10 years) and another mortgage ($22,895) at 9% for 5 years (the loan maturity and the amortization period are the same, 5 years). In this case, with the same**

- 9 years ago

**Real Estate Finance**

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- sharon_real_estate_finance.xls