hard · Investment Banking valuation-core
You value a firm by APV. The unlevered value is $1,000m at an unlevered cost of capital k_u=10%. The firm carries $400m of debt at k_d=5% and a 25% tax rate, generating an annual tax shield of T,k_d,D=$5m. The treasury policy is to rebalance debt continuously to a constant percentage of firm value (Harris–Pringle assumption).
What is the PV of the interest tax shield, and the resulting levered value?
- $50m tax shield (discounted at k_u), for a levered value of about $1,050m, because rebalanced debt makes future shields as risky as the assets.
- $100m tax shield, discounted at k_d, for a levered value of about $1,100m, equal to T× D, which is correct only for permanent, fixed-dollar debt.
- $50m tax shield, correctly discounted at k_u, but a levered value of $950m, mistakenly subtracting rather than adding the shield to unlevered value.
- $40m tax shield, discounted at k_u but on an already after-tax basis, for a levered value of about $1,040m, an unnecessary extra haircut.
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