A CDO of $$100$ million notional value with five year maturity has the following structure respectively: Tranche, Size $($million$),$ Spread $($bps$),$ O$/$C target, I$/$C target

A $601001\mathrm{.}351\mathrm{.}6$

B $102001\mathrm{.}251\mathrm{.}4$

C $105001\mathrm{.}131\mathrm{.}2$

Equity $=20$ million size but no spread, O$/$C or I$/$C target

The CDO collateral has an average annual coupon rate of $10\%$ payable semiannually.

The CDO manager charges a deal structuring fee of $100$ bps of the notional amount

amortized over the life span of the CDO at $5\%$ per annum. The yearly manager fee is $40$

bps for the senior tranche and $20$ bps for the subordinated tranches. The current risk free

interest rate is $6\%$ on a BEY basis.

$($i$)$ If there is no default, find the semiannual cash flow distributions to deal restructuring

fees, asset manager fees, payments to tranches A$,$ B$,$ and C$,$ and payment to equity

tranche. Calculate the O$/$C and I$/$C ratios for tranches A$,$ B$,$ and C$.$ Are these ratios

above their target levels?