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Work out what debt costs a firm after tax

CFA® Level I · Corporate Finance · 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.

Why is the cost of debt multiplied by one minus the tax rate?

  1. Because interest is tax deductible, so the net cost is lower - correct
  2. Because lenders pay tax on the interest they receiveWhy not: That is the lender's position. The adjustment here reflects the borrower's deduction.
  3. Because market yields are quoted before any adjustment for inflationWhy not: Inflation is not what the adjustment captures; it reflects the company's own tax saving.

Interest is a tax-deductible expense, so every dollar of interest lowers the tax bill. The government therefore bears part of the cost. Formula: After-tax cost of debt = Pre-tax cost x (1 - Tax rate). For example, at a 6% pre-tax cost and a 30% tax rate, 6% x (1 - 0.30) = 4.2%. This tax saving assumes the company has taxable profit to claim the deduction against. It is one reason debt is cheaper than equity, along with lenders ranking ahead of shareholders.

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 yield to maturity is already quoted after taxWhy not: Yield to maturity is a pre-tax figure. The tax deduction is applied to it separately.

The cost of capital is used to judge new projects, so it should show what raising money would cost today. The coupon on old debt is the fixed interest rate set when the bond was issued, which may be years out of date. The yield to maturity is the return investors demand on that bond now. For example, a bond issued with an 8% coupon when yields were 8% may now trade at a yield of 5%, so 5% is what new borrowing would cost. Idea: use today's market rate, not a historical one.

The hardest tier

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

  1. As the government bond yield plus a small fixed marginWhy not: That ignores the borrower's credit quality; the spread depends on the company's own risk.
  2. From the company's accounting return on its assetsWhy not: Return on assets measures how profitable the business is. It is not what lenders charge for credit.
  3. From yields on similar-risk issuers with comparable maturity - correct

A private company has no bonds trading, so there is no market yield to read off. Lenders charge more for riskier borrowers, so the best guide is what similar borrowers pay. The analyst can build a synthetic rating from the company's financial ratios, such as interest coverage (operating income divided by interest). Formula: Cost of debt = Risk-free rate + Credit spread, where the spread comes from bonds with the same rating and a similar maturity. The risk-free rate alone ignores credit risk, and return on assets measures profitability, not borrowing cost.

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