hard · Principles of Finance valuation

Holding the unlevered cost of capital, target leverage, and pre-tax cost of debt all constant, which statement most accurately describes how the Miles–Ezzell levered value compares to the Modigliani–Miller (fixed-dollar-debt) levered value, and why?

1. Miles–Ezzell yields a lower value because only the very first year's tax shield gets discounted at the cost of debt, while every later shield instead uses the riskier unlevered rate throughout the horizon.
2. Miles–Ezzell yields a higher value because rebalancing debt to a fixed target ratio makes every period's tax shield certain, so shields are discounted at the risk-free rate rather than the unlevered cost of capital.
3. Miles–Ezzell yields an identical value because both methods capitalize the exact same steady-state tax shield, differing only in a cosmetic timing convention for exactly when each interest payment actually gets made each year.
4. Miles–Ezzell yields a lower value because the tax shield grows with firm value and so is discounted at the unlevered cost of capital from year two onward, capturing its dependence on future uncertain cash flows.

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