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?
- 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.
- It correctly states firm value, since interest is contractual and the tax shield always carries debt-like risk regardless of the debt policy.
- It understates firm value, because ratio rebalancing makes the shield safer than debt and it should be discounted below r_d.
- It overstates firm value, because the shield should be discounted at the WACC, which exceeds r_d whenever the firm carries any equity.
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