Consider a $$1,000-$par junk bond paying a $12\%$ annual coupon with two years to maturity. The issuing com$-$ pany has a $20\%$ chance of defaulting this year; in which case, the bond would not pay anything. If the company survives the first year, paying the annual coupon payment, it then has a $25\%$ chance of default$-$ ing in the second year. If the company defaults in the second year, neither the final coupon payment nor par value of the bond will be paid.a$.$ What price must investors pay for this bond to expect a $10\%$ yield to maturity?b$.$ At that price, what is the expected holding period return and standard deviation of returns? Assume that periodic cash flows are reinvested at $10\%.$