Problem 22.15. A company has issued 3- and 5-year bonds with a coupon of 4% per annum payable annually. The yields on the bonds (expressed with continuous compounding) are 4.5% and 4.75%, respectively. Risk-free rates are 3.5% with continuous compounding for all maturities. The recovery rate is 40%. Defaults can take place half way through each year. The risk-neutral default rates per year are Q for years 1 to 3 and Q2 for years 4 and 5. Estimate Q1 and Q2. The table for the first bond is Time Def. (yrs) Prob. Recovery Amount ($) Risk-free Loss Given Discount PV of Expected Value ($) Default ($) Factor Loss ($) 0.5 Q1 40 103.01 63.01 0.9827 61.92Q1 1.5 Q1 40 102.61 62.61 0.9489 59.41Q1 2.5 Q1 40 102.20 62.20 0.9162 56.98Q1 Total 178.31Q1