Question

1. A lender wants an EY of 4.00% and expects an average loan payoff in 7 years. However, a particular borrower wants to borrow $400,000 for 30 years at 3.20%, compounded monthly. First, without charging a prepayment penalty, how many discount points must the lender charge to have an EY of 4%. Assume no other fees to close the loan other than discount points. Second, without charging discount points, how much of a prepayment penalty (in terms of dollars) will the lender need to charge to have an EY of 4%. 2. Choose a city or county area in the U.S. and make an evaluation/analysis of your chosen area's current housing market. See the lecture on Current Housing Market Evaluation for Palm Beach County as a sample of the type work expected. (Note – you cannot analysis the Palm Beach, Broward, or Miami Dade housing markets.) 3. In class, we discussed how longer-term loans are inferior to shorter-term loans. Develop an example and explain the concept.

Answer 1

1. Monthly interest rate to borrower = 3.2%/12 =0.0026667

No of payments = 30*12 = 360

The monthly payment by borrower (A) is given by

A/0.0026667*(1-1/1.0026667^360) = 400000

A *231.231 = 400000

A = $1729.87

Loan Amount outstanding after 7 years (23*12 =276)

= 1729.87/0.0026667*(1-1/1.0026667^276)

=$337651.31

Let the lender Charge X discount points at the closing of loan , So on net basis the loan amount given

=$400000* (1-X/100) so that net 4% effective yield is earned i.e monthly yield 1.04^(1/12)-1 = 0.00327374 is earned

So,

-400000*(1-X/100) + 1729.87/0.00327374*(1-1/1.00327374^84)+ 337651.31/1.00327374^84 =0  

=> -400000*(1-X/100) + 383448.39 =0

X = 4.1379

So, Discount points charged at the closing of loan should be 4.1379% (no other charges)

If a prepayment penalty of $X is to be charged, then

-400000 + 1729.87/0.00327374*(1-1/1.00327374^84)+ 337651.31/1.00327374^84 + X/1.00327374^84 = 0

=> X = 16551.61*1.00327374^84 = $21780.79

So, a prepayment penalty of $21780.79 has to be charged to earn effective yield of 4%