Today is year t = 0. Consider 5 mortgages, M1 to M5, each with one payment left of $100 to be made at t = 1. Each mortgage has a default probability of 10% and a 50% recovery rate in foreclosure after creating an SPV that purchases all 5 mortgages and issues CMOs. The CMOs consist of 10 tranches: Senior, Mezzanine1, ..., Mezzanine8, and Junior Each tranche is a zero-coupon, 1-year to maturity bond with face value $50 The Junior tranche ranks lowest in seniority Default correlation between all mortgages is 0 Assume the risk free rate is 0% and that investors are risk-neutral.

What is the fair price of the Junior tranche?