hard · Principles of Finance cost-of-capital-structure

A firm with a 25% statutory tax rate has $500M of perpetual debt at a 6% coupon (priced at par). It also carries a deferred tax asset from prior losses, and analysts project that for the next 3 years the firm will have NO taxable income against which to deduct interest (it remains in a tax-loss position), after which it returns to full taxability in perpetuity. A junior analyst computes the after-tax cost of debt as 6%×(1-0.25)=4.5% and uses it for all years.

What is the most defensible critique of this treatment for valuing the firm today?

  1. The interest tax shield should be deferred: for the first 3 years the marginal tax benefit is effectively zero (so the after-tax cost approaches the 6% pre-tax rate), and only the present value of shields realized in year 4 onward should be capitalized at the 4.5% equivalent.
  2. The analyst should gross up the cost of debt to 8% because tax-loss carryforwards make debt strictly more expensive than the coupon during the shelter period.
  3. The after-tax cost of debt is correct as computed because the statutory rate is the legally binding marginal rate regardless of the timing of taxable income.
  4. Because the firm has a deferred tax asset, the effective tax rate on interest is zero in perpetuity, so the full 6% pre-tax cost of debt should be used for the entire valuation horizon.

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