Task $3$: CMBS

$(1)$ Why are bond rating agencies so vital in the MBS market? $(1$ point$)$

$(2)$ Consider a $$100$ million loan pool, packaged, and sold in securities of $$1,000$ each. The loans in the pool have five years to run, a $9\%$ interest rate, they are fully amortizing, and there is no prepayment or default. The loan servicing charge is $1\mathrm{.}5\%$ of the loan balance outstanding.

a$.$ If you want to offer a security at a yield of $10\mathrm{.}5\%,$ what is the price of the security? $(2$ points, $1$ for correct cash flows, $1$ for correct price$)$

b$.$ What discount does that represent to the face value of the security? $(1$ point$)$

$(3)$ A mortgage pool has $$1$ billion in par value. The senior $($A$)$ tranche has $30\%$ credit support $($subordination$).$ The next tranche $($B$)$ has $25\%$ credit support $($subordination$).$

a$.$ How much par value $($principal$)$ was issued in the A tranche? $(1$ point$)$

b$.$ How much par value $($principal$)$ was issued in the B tranche? $(1$ point$)$