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Work out what debt costs a firm after tax

CFA® Level I · Corporate Issuers · Capital Structure · CI.3.b

The idea

The cost of debt is the yield a company would pay on new borrowing today, not the coupon on debt it issued years ago. For a listed bond that is its yield to maturity; where no bond trades, it is estimated from the yields of comparable issuers with similar ratings and maturities. Because interest is deductible, the figure entering the weighted average cost of capital is multiplied by one minus the tax rate. Using the historical coupon is the standard error: it describes what the company agreed to in the past, not what capital costs now.

Formulas

After-tax cost of debt

after-tax cost of debt = rd × (1 − t)

rd
the before-tax cost of debt — the yield the market demands now, not the coupon on old bonds
t
the marginal tax rate

Interest is deductible, so the government pays part of it. The deduction is worth nothing to a company with no taxable profit, and there the cost of debt is the full rate.

A practice question

From the question bank, with the reason each wrong option is wrong.

A company's bonds yield 6% and its tax rate is 25%. What is its after-tax cost of debt?

  1. 4.50% — correct
  2. 6.00%Why not: The pre-tax yield, before the interest deduction is taken into account.
  3. 7.50%Why not: Divides by 0.8 or multiplies by 1.25, grossing the rate up when the deduction brings it down.

6% × (1 − 0.25) = 4.50%. Deductible interest means the company bears only part of the coupon; the tax authority bears the rest.

A harder one

Why is the current yield to maturity used rather than the coupon on existing debt?

  1. Because coupons are not tax deductibleWhy not: Coupon interest is exactly what is deductible; the objection to the coupon is that it is a historical rate.
  2. Because the cost of capital concerns what new funding would cost today — correct
  3. Because yields are always lower than couponsWhy not: They can be higher or lower, and which it is depends on what has happened since issue.

The cost of capital is a forward-looking opportunity cost used to judge new projects. A coupon fixed years ago says nothing about what the market would charge now.

The hardest tier

How is the cost of debt estimated for a private company with no traded bonds?

  1. It is assumed equal to the risk-free rateWhy not: That would credit a private company with government credit quality and no spread at all.
  2. It cannot be estimated, so equity financing must be assumedWhy not: Private companies borrow routinely, and comparable yields give a serviceable estimate.
  3. From the yields of comparable issuers with similar credit quality and maturity — correct

A synthetic rating based on the company's financial ratios maps to the spread the market charges comparable credits. That spread over the risk-free rate is the estimate.

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