Cost of Capitalintermediate

Cost of Debt

The cost of debt $k_d$ is the return lenders require, best measured by the yield to maturity (YTM) on the firm’s traded bonds. The YTM can be read as the risk-free rate plus a default spread tied to the firm’s credit rating, so a weaker rating means a wider spread. Because interest is tax deductible, the figure that enters the WACC is the after-tax cost, $k_d (1 - t)$ . The pre-tax yield is the promised return, while the expected cost can be lower once the probability of default and the recovery rate are taken into account.

Try it yourself

Building the after-tax WACC

A firm's cost of capital is the market-value-weighted blend of what debt and equity holders require: WACC = w_d·k_d·(1 − T) + w_e·k_e. Equity is priced by the CAPM, k_e = r_f + β·ERP, while debt is taken after the interest tax shield, k_d·(1 − T). Only debt earns the shield, so it usually sits below equity in the blend.

Weighted average cost of capital7.50%

Cost of equity k_e 9.50%After-tax k_d 4.50%WACC 7.50%

Weight of debt w_d40%

Equity weight w_e = 60%

Pre-tax cost of debt k_d6.0%

Tax rate T25%

Cost of equity (CAPM)

Risk-free rate r_f4.0%

Equity beta β1.10x

Equity risk premium ERP5.0%

Equity costs 9.50% (=4.0% + 1.10x × 5.0%), debt costs 4.50% after the 25% shield. Blended at 40/60 they give a WACC of 7.50%.

Try this

Shift weight toward debt and WACC usually falls, because shielded debt is cheaper than equity. Raising the tax rate deepens the shield and lowers the after-tax cost of debt.

Note: only debt carries the (1 − T) tax shield, since interest is tax-deductible and dividends are not. The weights w_d and w_e should be market values of debt and equity, not book values, because WACC is the return the market requires today.

Reflect: if cheap shielded debt always lowers WACC, why not finance the firm almost entirely with debt? What does this model leave out about how k_d and k_e respond as leverage climbs?

Why it matters

Lenders set a price for risk just as equity investors do. Start from the safe Treasury yield, then add a spread for the chance the borrower fails to pay. The market already does this work, so the YTM on the firm’s own bonds is the cleanest signal. The last step is the tax shield. Since interest reduces taxable profit, the government effectively subsidises part of the interest bill, which is why the tax shield must not be forgotten.

Formulas

After-tax cost of debt

k_d^{after\text{-}tax} = k_d\,(1 - t)

The pre-tax cost

k_d

is the YTM on the firm’s debt. Multiplying by

(1 - t)

captures the interest tax shield, since interest is deductible.

YTM as risk-free plus spread

k_d = k_{rf} + \text{default spread}

The default spread widens with credit risk. For example, a bond yielding 5 percent when the risk-free rate is 2 percent implies a default spread of 3 percent.

Worked examples

Scenario

A target firm has a bond with 25 years to maturity, a 9 percent coupon paid semi-annually, currently priced at US$908.72 per US$1,000 of face value. Solving for the yield gives 5 percent per semi-annual period. The tax rate is 25 percent. Find the pre-tax and after-tax cost of debt.

Solution

A semi-annual yield of 5 percent corresponds to a pre-tax annual cost of debt of about 10 percent. Apply the tax shield. The after-tax cost is $\,10\% \times (1 - 0.25) = 7.5\%$ . The bond trades below par precisely because its 9 percent coupon is worth less than the 10 percent the market now demands, so investors only pay US$908.72.

Common mistakes

✗The coupon rate is the cost of debt. The cost of debt is the current YTM, which reflects today’s market price. A bond priced below par yields more than its coupon.
✗You use the pre-tax cost of debt in the WACC. The WACC uses the after-tax cost, $k_d(1 - t)$ . Skipping the shield inflates the WACC and can wrongly reject good projects.
✗The promised yield equals the expected cost of debt. For risky borrowers the expected cost is lower than the promised YTM once default probability and the recovery rate are factored in.
✗Corporate debt is risk-free. Only Treasuries come close. Corporate bonds carry credit risk, shown in the yield spread over a matched Treasury.

Revision bullets

•Cost of debt is the YTM on the firm’s traded bonds, not the coupon
•YTM equals the risk-free rate plus a default spread set by the credit rating
•The WACC uses the after-tax cost, $k_d(1 - t)$ , because interest is deductible
•For risky debt, expected cost reflects default probability and recovery rate
•Private or unrated debt is priced off comparable bonds of similar rating and maturity
•Bond below par means the market yield exceeds the coupon

Quick check

A firm’s bonds yield 7 percent to maturity and the tax rate is 30 percent. The after-tax cost of debt used in the WACC is

A bond trades below its face value. This tells you that

Connected topics

WACC Cost of Equity (CAPM)Debt Beta Risk Premiums Tax Shield

Sources

Titman & Martin
Titman, S. & Martin, J. D. Valuation: The Art and Science of Corporate Investment Decisions. Pearson.
Chapter on the cost of debt capital. The YTM, default-spread and after-tax treatment follow this text, illustrated with the semi-annual bond example.
Damodaran (2012), Ch. 4
Damodaran, A. Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. 3rd ed. Wiley, 2012.
Estimating the cost of debt from ratings, synthetic spreads and default probabilities when traded bonds are unavailable.

How to cite this page

Dr. Phil's Quant Lab. (2026). Cost of Debt. Derivatives Atlas. https://phucnguyenvan.com/concept/sabv-cost-of-debt

← Back to the atlas See in the network →