Use the following information on a mortgage$-$backed security for Problems $6$

$10.$

You are examining a mortgage$-$backed security with the following features:

$$500$ million in underlying mortgages $($e$.$g$.,$ principal value $=$$$500$ million$)$

Three credit tranches $($or default tranches$).$ A$,$ B$,$ and C where the par value

of $A$ is $$200$ million, the par value of $B$ is $$100$ million, and the par value of

$C$ is $$200$ million. $A$ is senior to $B$ and $B$ is senior to $C.$

The weighted average coupon $($WAC$)$ is $6\%$; the pass$-$through rate is $5\%$

The security has a weighted average maturity $($WAM$)$ of $3$ years and

payments are made annually $($e$.$g$.,$ so it will only make $3$ payments$).$

For Questions $6-7,$ assume that there is no default and no prepayment.

Total MBS Issue:

Tranche A:

Tranche B:

Tranche C:

Question $6$: What is the value of $x?$

Question $7$

Use the information given in question $6.$

What is the value of $Y?$

Question $8$

Use the information given in question $6,$ but now suppose that investors

default on $$75$ million in loans immediately after the payments in year $1.$

Redo the tables and obtain the value of $Y.$

Question $9$

Use the information given in question $6,$ but now suppose that investors

prepay $$75$ million in loans immediately after the payments in year $1.$ Assume

that there are no defaults.

Redo the tables and obtain the value of $Y.$