hard · Principles of Finance valuation

An analyst values a stable firm with a single APV pass: unlevered value of operations plus the present value of the interest tax shield, discounting the shield at the cost of debt r_d. The firm maintains a CONSTANT market-value debt-to-value RATIO (rebalancing debt each period to a fixed fraction of value), not a fixed dollar debt level.

Holding everything else constant, what is the most precise consequence of discounting the tax shield at r_d rather than at the unlevered cost of equity r_U?

  1. It overstates firm value, because under ratio rebalancing the shield inherits the business risk of operations after the first period and should be discounted at r_U.
  2. It correctly states firm value, because interest is a contractual obligation and the tax shield always carries debt-like risk no matter which debt policy is chosen.
  3. It understates firm value, because ratio rebalancing actually makes the shield safer than the debt itself, so it should be discounted below the cost of debt, r_d, each period.
  4. It overstates firm value, because the shield should instead be discounted at the WACC, which always exceeds r_d whenever the firm carries any equity in its capital structure.

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