You have been charged with doing calibration of Alpha Banks structural pricing models for corporate debt. Of particular interest to you is determining a reasonable recovery rate on defaulted debt, as percentage of face value. As a starting point you notice that USTs recent consol bond debt issuance was priced to yield 12% (using continuous compounding). The consol bond had constant coupon flow equal of B = 50 (Billion) per instant. USTs flow of EBIT at the time the bond was issued was X equal to $100 (Billion) per instant. This EBIT has a growth rate of 3.5% and a volatility of 20%. UST will default on this debt obligation at the first time X hits B. The market currently charges a one-time fee equal to (B/X)2 to provide investors with $1 of perpetual credit protection in the event of default by UST on this debt [that is, the holder of such insurance is entitled to $1 at the first passage to default]. The face value F of the debt is expressed as B/r, where r is the risk-free rate of interest. Risk-free government bonds have a yield of r = 10% (using continuous compounding). What assumed recovery rate, expressed as a fraction of face value, would be required so that your calibrated model replicates the observed market yield on UST debt?

Please answer only if you are 100% confident.