A firm undergoes a leveraged recapitalization at the end of 2021. After the leveraged recapitalization, the firm has substantial bank debt outstanding. The bank debt carries an interest rate of 7%. The principal outstanding of the bank debt is (in $ million): 600 at the end of 2021 and 2022, 400 at the end of 2023, and 200 at the end of 2024 and afterwards in perpetuity. Assume that the principal is paid down in equal installments over the year and interest is also paid equally throughout the year. long-term risk-free rate is 2% and expected market risk premium 6%.

The firm's debt is rated AA before the leveraged recapitalization and BB afterwards. Its pre-recap leverage ratio (D/(D+E)) is 20% and its equity beta at this capital structure is 1.2. Assume that in the last 20 years, the average returns on corporate bonds with an AA (BB) rating have exceeded those of Treasury bonds with the same maturity by 70 (280) basis points (0.7 (2.8) percentage points). The marginal corporate tax rate is 20%.

Part 1 -  Forecast promised interest tax shields from 2022 until 2024.

Part 2 - Calculate the discount rate for the expected post-recap interest tax shields.