In practice, when doing CDS valuations, we need to estimate the default probability and the recovery rate, just as we need to estimate the volatility in order to use the Black-Scholes formula when valuing options. Suppose we have two CDS contracts on the same company's bonds. One is a 3-year CDS on a junior subordinated bond with a spread of 282.35bp and the other is a 5-year CDS on a senior subordinated bond with a spread of 244.71pb. Both contracts have a value of zero right now. Suppose the LIBOR rate is 4.5%, defaults occur in the middle of the year, and payments are made in arrears. Historically, the recovery rate for senior subordinated bonds is 8% higher than the recovery rate for junior subordinated bonds (e.g., if the former is 30%, then the latter is 38%). Further suppose that all bonds are in default if default occurs. Please estimate the recovery rate and the default probability during a year conditional on no early defaults. (Hint: Do this question using Excel Solver with a similar method as in the Merton's model - i.e., by setting the sum of squared terms to zero. Also, for better convergence, please multiply the difference between the given CDS spread and the calculated CDS spread by a large constant, e.g, 1,000,000, if spreads are expressed in decimal forms)