Corporate Issuers
foundationAfter-Tax Cost of Debt
- the pre-tax cost of debt: the yield lenders demand (roughly, the coupon on new borrowing)
- the marginal tax rate — the rate saved on the last dollar of deduction
- the fraction of the interest bill the company truly bears after the tax refund
- the after-tax cost: what borrowing really costs per dollar per year
Reading the notation
Why it must be true
Interest is paid with pre-tax dollars: every dollar of interest expense reduces taxable income by a dollar, so the government quietly refunds a slice of it. If the company borrows at 8% and pays 25% tax, each dollar of interest saves 25 cents of tax — the true cost of the borrowed dollar is only 6 cents.
That refund is the "tax shield," and it is the reason debt is the cheap seat in the capital structure: lenders take less risk than shareholders AND the tax code subsidizes their coupon. The after-tax rate — not the coupon — is what belongs in a WACC.
The derivation
Borrow $1 at rate . The year's interest bill is , but deducting it cuts the tax bill by . Net cash out:
The shield exists only while there is taxable income to shield — a loss-making firm gets no refund this year, which is one of the formula's honest limits.
When to reach for it
Preparing the debt component of a WACC, or comparing financing costs on a like-for-like (after-tax) basis.
Listen for
Back-of-the-envelope
Estimate it in your head first — then the calculator only confirms.
- ≈
Complement first: t = 25% → keep 75%. Then 8% × 0.75 = 6% is a one-step multiply.
- ≈
The answer must sit BELOW the pre-tax rate — a candidate answer above r_d has the adjustment backwards.
- ≈
Common exam pairs are clean: 30% tax → ×0.7; 25% → ×0.75; 21% → ×0.79. Memorize the complements, not the rates.
Traps in applying it
- ✗Multiplying by t instead of (1 − t) — that computes the tax SAVING, not the cost.
- ✗Applying the shield to the cost of equity — dividends are NOT tax-deductible; only debt gets this haircut.
- ✗Using the average tax rate instead of the marginal rate — the deduction operates at the margin.
Limits & criticisms
The shield assumes the firm has profits to shield: loss-makers and firms with expiring carryforwards capture less or none of it, and tax-code ceilings (like the US interest-deductibility caps introduced in 2017) can cut the deduction off entirely at high leverage. The formula also uses today's marginal rate for cash flows that stretch decades of tax regimes.
Where it came from
The tax shield entered finance's center stage with Modigliani and Miller's 1963 correction to their famous irrelevance theorem: once taxes exist, debt financing adds value precisely because interest is deductible — a result that fueled decades of leverage, LBO math and policy debate about the "debt bias" in tax codes. Every WACC computed in every valuation and every board's capital-structure review starts from this one-line adjustment.
One identity, 1 questions
The exam can hide any variable. Each face below is the same equation solved for a different unknown — drill them separately.
The shielded rate
The WACC-input face: the coupon is the lender's return; the shielded rate is the shareholder's cost.
On the BA II Plus
Worked example: New bonds would be issued at a yield of 8%; the marginal tax rate is 15%. What debt cost belongs in the company's WACC?
- 1.1 [−] 0.15 [=]the kept fraction (1 − t)
- 2.[×] 0.08 [=]times the pre-tax rate (decimal)
→ 6.8%
Where it leads
Master this and the following come almost for free: