What is the cost of debt?
– The cost of debt is the effective interest rate a company pays on borrowed funds (loans, bonds, or other liabilities). It represents the annual interest expense as a percentage of the debt and signals how lenders view the company’s credit risk: higher perceived risk → higher cost of debt.
Key definitions (first use)
– Cost of debt: the interest cost borne by a borrower, expressed as a rate.
– Pretax cost of debt: the nominal interest rate or yield before any tax effects.
– After‑tax cost of debt: the pretax cost reduced by the tax benefit of deductible interest.
– Risk‑free rate: the theoretical return on a zero‑risk investment (commonly proxied by U.S. Treasury yields).
– Credit spread: the extra yield over the risk‑free rate that compensates lenders
for default risk, liquidity differences, and other lender‑specific considerations.
How to calculate the cost of debt — step by step
1) Choose the correct pretax rate
– For publicly traded debt (bonds): use the yield to maturity (YTM) on the company’s market‑priced bonds. YTM is the internal rate of return that equates the bond’s market price with its remaining coupon and principal payments.
– For private or bank debt, or when market prices are unavailable: use the effective interest rate implied by the company’s interest expense: pretax cost of debt ≈ total annual interest expense / average outstanding debt balance.
– If a company has multiple debt instruments, compute a weighted average pretax rate using each instrument’s market value (preferred) or book value if market values are unavailable.
2) Convert pretax to after‑tax cost
– Interest is generally tax‑deductible for corporations, so after‑tax cost of debt = pretax cost × (1 − tax rate).
– Use the company’s marginal (statutory or effective) tax rate depending on the analysis. For forward-looking WACC calculations, the marginal tax rate is commonly used.
Key formulas (compact)
– Pretax cost of debt (instrument level, approximate from interest and balance): r_d,pretax = Interest expense / Average debt
– Pretax cost from bond prices (approximate YTM formula): YTM ≈ (Coupon + (Face − Price)/n) / ((Face + Price)/2) where n = years to maturity (this is an approximation; exact YTM requires solving the present‑value equation)
– After‑tax cost of debt: r_d,aftertax = r_d,pretax × (1 − TaxRate)
– Weighted average cost of debt (multiple instruments): r_d,pretax,WA = Σ(w_i × r_i) where w_i = weight (market or book) of debt i
– Use r_d,aftertax in WACC: WACC includes (Weight of debt × r_d,aftertax)
Worked numeric examples
Example A — using interest expense (simple)
– Company reports annual interest expense = $50 million.
– Average outstanding debt during year = $1,000 million.
– Pretax cost of debt = 50 / 1,000 = 0.05 = 5.00%.
– Assume corporate tax rate = 21%.
– After‑tax cost of debt = 5.00% × (1 − 0.21) = 5.00% × 0.79 = 3.95%.
Example B — using bond market price (approximate YTM)
– Bond face value = $1,000, annual coupon = 6% → coupon = $60.
– Market price = $950, years to maturity n = 10.
– Approximate YTM ≈ (60 + (1,000 − 950)/10) / ((1,000 + 950)/2)
= (60 + 5) / 975 = 65 / 975 ≈ 0.0667 = 6.67%.
– After‑tax cost at 21% = 6.67% × 0.79 ≈ 5.27%.
Practical checklist when estimating cost of debt
– Decide whether to use market values (preferred) or book values (if market prices unavailable).
– Gather: current bond yields or market prices, coupon terms, maturity dates, latest interest expense, and average debt balances.
– Select the appropriate tax rate (marginal vs effective).
– Account for floating‑rate debt: use current reference rate
– …use the current reference rate (for example, SOFR, LIBOR replacement, or the prime rate) plus the contractual spread to estimate the floating rate at the next reset date.
– For leases or other financing obligations, decide whether to include them (IFRS 16 / ASC 842 capitalization may make them effectively debt).
– Treat convertible or deeply subordinated instruments separately — their effective cost depends on conversion features and call/put options.
– If you have multiple borrowings, compute a weighted average cost of debt (WACD) using market values for each tranche when possible.
– If using book-value interest expense (when market yields are unavailable), calculate a book‑value after‑tax cost as: kd = (Interest expense / Average debt balance) × (1 − tax rate). Document the period used for averages.
– Include issuance (flotation) costs when important: issuance fees reduce net proceeds and raise the effective yield; either solve for the yield that equates cash flows to net proceeds or adjust the price in an approximate YTM formula.
– Keep currency consistent: if debt is in a foreign currency, express cost in that currency (and note any hedging costs).
– Record assumptions (tax rate chosen, use of marginal vs effective tax rate, market prices used, and valuation date) and run a sensitivity check on key inputs.
Worked examples
1) Weighted average after‑tax cost (market‑value method)
– Debt A: bond market value = $1,000, YTM = 6.00% → after‑tax kd_A = 6.00% × (1 − 0.21) = 4.74% (using 21% tax).
– Debt B: bank loan outstanding = $500, contractual rate = 8.00% → after‑tax kd_B = 8.00% × (1 − 0.21) = 6.32%.
– Total market debt = $1,500. Weights: w_A = 1,000/1,500 = 0.6667; w_B = 500/1,500 = 0.3333.
– WACD = w_A × kd_A + w_B × kd_B = 0.6667×4.74% + 0.3333×6.32% ≈ 3.16% + 2.11% = 5.27%.
This example shows how to blend different instruments and matches the earlier single‑bond after‑tax calculation.
2) Effect of issuance (flotation) costs on effective yield (approximate)
– Bond face = $1,000; annual coupon = 6% → coupon = $60. Maturity n = 10 years. Gross market price = $980; issuance costs = $15 →