The MZ Mortgage Company is issuing a CMO with three tranches. The A tranche will consist of $$40\mathrm{.}64$ million with a coupon of $8\mathrm{.}25$ percent. The $B$ tranche will be issued with a coupon of $9\mathrm{.}0$ percent and a principal of $$22\mathrm{.}64$ million. The $Z$ tranche will carry a coupon of $10\mathrm{.}0$ percent with a principal of $$45\mathrm{.}14$ million. The mortgages backing the security issue were originated at a fixed rate of $10$ percent with a maturity of $10$ years $($annual payments$).$ The issue will be overcollateralized by $$4\mathrm{.}5$ million, and the issuer will receive all net cash flows after priority payments are made to each class of securities$.$ Priority payments will be made to the class A tranche and will include the promised coupon, all amortization from the mortgage pool, and interest that will be accrued to the $Z$ class until the principal of $$45\mathrm{.}1$ million due to the A tranche is repaid. The $B$ class securities will receive interest$-$only payments until the A class is repaid, and then will receive priority payments of amortization and accrued interest. The $Z$ class will accrue interest at $10$ percent until both A and $B$ classes are repaid. It will receive current interest and principal payments at that time.

Required:

a$.$ What will be the weighted average coupon $($WAC$)$ on the CMO when issued?

b$.$ What will be the maturity of each tranche assuming no prepayment of mortgages in the pool?

c$.$ What will be the WAC at the end of year $3?$ year $4?$ year $8?$

d$.$ If class $A,B,$ and $Z$ investors demand an $8\mathrm{.}5$ percent, $9\mathrm{.}5$ percent, and $9\mathrm{.}75$ percent yield to maturity, respectively, at the time of issue, what price should MZ Mortgage Company ask for each security? How much will the company receive as proceeds from the CMO issue?

e$.$ What are the residual cash flows to MZ$?$ What rate of return will be earned on the equity overcollateralization?

f$.$ Optional. Assume that the mortgages in the underlying pool prepay at the rate of $10$ percent per year.