# What is the NPV of refinancing? If fees are 2 points plus \$12,000, what is the regulation-Z required APR?

1. [10 pts] You have had a 20yr FA FRM at 9% for 6 years. The original principal was 2,500,000. You are considering a cash-out refi into a 15-year mortgage at 7%. The old mortgage has a prepay penalty of 3% if payoff occurs before year 8. The new mortgage has fees of 4% plus \$8,000, and no prepay penalty. The additional cash is for a \$75,000 car, and can be borrowed at 9% over 5 years, with upfront fees of 1%.

Assume that all fees will be financed, and that under either scenario you will be moving 9 years from now.

What is the NPV of refinancing?

2. [10 pts] Consider a 30 year, FA graduated payment mortgage for \$300,000 at 5%, with 4 payment increases of 20%. If fees are 2 points plus \$12,000, what is the regulation-Z required APR?

3. [12 pts] A reverse annuity mortgage is made with a balance not to exceed \$500,000 on a property now valued at \$800,000. The loan calls for monthly payments to be made to the borrower for 120 months at an interest rate of 8% MEY.

A [3] What will the monthly payments be?

B [3] What will the RAM balance be at the end of year 3?

C [4] Assume that the borrower must have monthly draws of \$4,000 for the first 60 months of the loan. The remaining draws from months 61 to 120 must be determined so that the \$300,000 maximum is not exceeded in month 120. What will the draws by the borrower be during months 61 to 120?

D [2] Suppose property experiences a 5% appreciation (MEY, starting today), and the borrower has a balance of \$500,000 at year 10 (by receiving payments computed in A). No payments are made thereafter. How many years from loan closing will the loan balance begin to exceed the house value?

4. [8 pts] Download the paper “Measuring Housing Affordability…,” by Davidson and Levin which was posted along with this HW document on BB. Discuss why the authors disagree with the NAR about the affordability of homeownership as of the date of the article.

5. [10 pts] Using excel, plot graphs of the modified duration and convexity versus the note rate c (for 1% ≤ c ≤ 20%) of a 30 year, fully amortizing, fixed rate, par mortgage. Annotate cells to show work. Assume that the mortgage never prepays/curtails, nor does it ever default (we deal with these later in the course).

6. [10 pts] Use the duration and convexity for c=5% in the previous question to plot the error in the percentage price change in the mortgage when yields change in the range of 0% to 3%, using

a. Duration only, and

b. Duration and convexity together.

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