#### [SOLUTION]-Wells Fargo issues a CMBS security. The mortgages in the pool are interest only loans, with a total loan amount of \$15 million. For simplicity, assume that the interest rate for the mortgages is 11%, and the loan maturity

1. Wells Fargo issues a CMBS security. The mortgages in the pool are interest only loans, with a total loan amount of \$15 million. For simplicity, assume that the interest rate for the mortgages is 11%, and the loan maturity is 4 years. Further, assume that the mortgages are annually compounded.
The bank issues three tranches of securities based on the mortgage pool: i) Senior Class or Tranche A, with an amount of \$10 million at 8% coupon rate; ii) Subordinated Class or Trance B, with an amount of \$3 million at 10% coupon rate; and iii) Residual tranche, with an amount of \$2 million. These securities have a maturity of four years.
a. Suppose that there is no default in the mortgage pool over the four year period. Calculate the returns for the investors who purchase the three tranches of securities.
b. Now assume that the value of the properties associated with the mortgage pool at the end of the fourth year is only 70% of the outstanding loan balance. What are the returns for the investors for the three tranches of securities?
a.)
Year CF from the pool Senior Class Subordinated Class Residual Class
1
2
3
4
Return = —
b.)
Year CF from the pool Senior Class Subordinated Class Residual Class
1
2
3
4
Return = —
2. Bank of America issues a MBS security based on a mortgage pool with the following terms:

Mortgage pool value \$25,000,000
Mortgage interest rate 6.5%
Loan Term 3 years

a) Suppose that the MBS has only one class of security, i.e., the basic MBS discussed during the class. What is the price of this MBS if the market interest rate is 6%? Assume annual compounding as well as a constant annual prepayment rate of 10% (based on the outstanding loan amount at the beginning of each year, the same as we discussed during the class).

b) Why MBS securities are often considered a “callable” bond? How can this callable feature affect MBS pricing? Briefly discuss.
Now, another investment bank suggests that, instead of issuing the single-class MBS security as above, two classes of securities can be issued based on the same mortgage pool, i.e., an IO and a PO security.

c) Determine the price of the IO and PO security, assuming that there is no prepayment. Further assume that the IO investors require a market rate of return of 4.5% and the PO investors require a market return of 6%.
d) Now suppose future interest rate will fall, so there is a 15% prepayment for each year (again, prepayment calculation is based on the loan balance at the beginning of the year). The IO and PO investors require a market rate of return of 4% and 5.5%, respectively. Determine the prices of the IO and the PO security.
3. Consider a construction loan made to Middleton Development Co. The loan amount is \$6 million, which will be drawn evenly (i.e., a \$1,000,000 monthly draw) during the next six months to redevelop an existing apartment building. Note that each disbursement occurs at the end of the month. The annualized interest rate is expected to remain the same at 8% for the first three (3) months. For the next three (3) months, the annualized interest rate will be 8%. What is the total loan amount (including interest) required to finance this project and what is the total interest carry?

Month Draws Interest Carry Cumulative Loan Bal.
1
2
3
4
5
6
Total
4.
A multifamily property is expected to produce the following income stream over the next three years:

Year NOI
1 \$575,000
2 600,000
3 625,000

A lender is willing to make a \$6,000,000 participation mortgage, at 6% interest rate, a 30 year amortization period, with a balloon payment at the end of year 3. For simplicity, annual compounding for this mortgage is assumed. In addition, the lender gets 10% of each year’s net operating income, and 20% of the net sales proceeds (note: the net sales proceeds will be calculated as: the sales proceeds – the selling expenses – the mortgage balance). The purchase price of the property is \$8 million. The investor of the property expects to sell the property for \$9 million at the end of the third year with the selling expenses of 6.5% (based on the sales price).
a) Calculate the before-tax mortgage yield for the loan, assuming that the loan is held for 3 years.
b) What is lender’s before-tax mortgage yield if the property ends up with selling for \$8 million at the end of the third year, instead of selling for \$9 million?
c) Why do lenders issue participation loans? What are the benefits and risks associated with this type of loans for borrowers and lenders? Briefly discuss.

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