Assume that the default probability for a company in a year, conditional on no earlier defaults is X and the recovery rate is R. The risk-free interest rate is 5% per annum. Default always occur half way through a year. The spread for a five-year plain vanilla CDS where payments are made annually is 120 basis points and the spread for a five-year binary CDS where payments are made annually is 160 basis points. Estimate R and X. Explain.