Cost of Debt

TL;DR

You'll learn how to calculate a company's cost of debt using yield to maturity and the after-tax adjustment. You'll understand why interest's tax deductibility lowers the real cost of borrowing. You'll be able to work through a bond-pricing example by hand and know exactly which numbers finance teams plug into WACC.

1. The Mental Model

Debt isn't free — lenders charge interest because they're taking a risk and giving up other uses of their money. But because interest payments are tax-deductible, the government effectively subsidizes part of that cost. So the "true" cost of debt to a company is always less than the rate printed on the loan agreement. Cost of debt is what you actually pay lenders, minus what you save in taxes for paying them.

2. The Core Material

2.1 What "cost of debt" actually means

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Cost of debt is the effective rate a company pays to borrow money — it's the return lenders demand for lending, expressed as a percentage. It shows up in two forms:

• Pre-tax cost of debt (Kd): the raw rate lenders require. For a simple bank loan, this is just the stated interest rate. For bonds, it's the yield to maturity (YTM) — the rate that makes the present value of all future coupon and principal payments equal the bond's current market price.
• After-tax cost of debt: the number that actually matters for capital budgeting and WACC, because interest expense reduces taxable income.

The after-tax formula is simple:

$$K_{d,\text{after-tax}} = K_d \times (1 - T)$$

where $T$ is the marginal corporate tax rate. If a company borrows at 8% and faces a 25% tax rate, its after-tax cost of debt is:

$$8\% \times (1 - 0.25) = 6\%$$

That 2-point gap is the tax shield — real money the company saves every year simply because interest is deductible while dividends to shareholders are not. This asymmetry is a big reason debt is often cheaper than equity.

2.2 Finding Kd when debt isn't a simple bank loan

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For bonds trading in the market, you can't just read the coupon rate off the certificate — the coupon rate is fixed at issuance, but the market price of the bond moves as interest rates change. If a bond's price has fallen below face value, the effective yield to a new buyer is higher than the coupon. This effective yield — the YTM — is what you should use as Kd, not the coupon rate.

YTM is the discount rate $r$ that solves:

$$P_0 = \sum_{t=1}^{n} \frac{C}{(1+r)^t} + \frac{F}{(1+r)^n}$$

where $P_0$ is the current bond price, $C$ is the annual coupon payment, $F$ is face value, and $n$ is years to maturity. There's no clean algebraic solution for $r$ when $n > 1$ — you solve it by trial-and-error, interpolation, or a financial calculator/spreadsheet function (RATE or YIELD in Excel).

A useful approximation formula gets you close without a calculator:

$$YTM \approx \frac{C + \frac{F - P_0}{n}}{\frac{F + P_0}{2}}$$

This averages the coupon income with the amortized capital gain/loss, divided by the average of face and market value. It's an estimate — good for sanity-checking, not for final answers.

2.3 Weighting multiple debt sources

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Most companies don't have just one loan — they have bank debt, multiple bond issues, leases, etc., each with different rates. The overall cost of debt used in WACC is a weighted average, weighted by market value (not book value) of each source:

$$K_d = \sum_{i=1}^{n} w_i \times K_{d,i}$$

where $w_i$ is the proportion of total debt that source $i$ represents. Using market values matters because book value (what's on the balance sheet) can be very different from what the debt is actually worth if rates have shifted since issuance.

flowchart TD
    A["Identify all debt sources<br/>(bonds, bank loans, leases)"] --> B["Find pre-tax rate for each<br/>(YTM for bonds, stated rate for loans)"]
    B --> C["Weight each rate by market value of that debt"]
    C --> D["Compute weighted average pre-tax Kd"]
    D --> E["Apply tax shield: Kd x (1 - T)"]
    E --> F["After-tax cost of debt<br/>feeds into WACC"]

2.4 Why the tax rate matters more than people think

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The tax shield isn't a fixed number — it depends on the company actually having taxable profit to shield. A company with large losses (zero taxable income) gets no benefit from interest deductibility that year, so its effective after-tax cost of debt equals its pre-tax cost. This is why in practice, analysts sometimes use an "effective tax rate" (taxes actually paid / pre-tax income) rather than the statutory rate, especially for firms with tax credits, carryforwards, or multinational tax structures. Always check whether the tax rate you're using reflects reality or just the textbook rate.

3. Worked Example

Let's build a company's after-tax cost of debt from scratch using two debt sources.

Debt Source 1 — Corporate Bond
- Face value: $1,000
- Coupon rate: 6% annual (so $60/year)
- Years to maturity: 5
- Current market price: $950 (trading below par because market rates have risen)

First, find YTM using the approximation:

$$YTM \approx \frac{60 + \frac{1000 - 950}{5}}{\frac{1000+950}{2}} = \frac{60 + 10}{975} = \frac{70}{975} \approx 7.18\%$$

Let's verify this is in the right ballpark by checking the exact PV at 7.18%:

$$PV = \sum_{t=1}^{5}\frac{60}{(1.0718)^t} + \frac{1000}{(1.0718)^5}$$

Coupon PVs: $60/1.0718 + 60/1.0718^2 + 60/1.0718^3 + 60/1.0718^4 + 60/1.0718^5$
≈ $55.98 + 52.23 + 48.72 + 45.45 + 42.40 = 244.78$

Principal PV: $1000 / 1.0718^5 ≈ 1000 / 1.4142 ≈ 707.35$

Total PV ≈ $244.78 + 707.35 = 952.13$, very close to our $950 price — confirming YTM ≈ 7.18% is accurate.

Debt Source 2 — Bank Term Loan
- Principal: $500,000
- Stated interest rate: 5% (fixed, no market trading, so the stated rate is the pre-tax cost)

Step 1: Determine market value weights.

Assume the bond issue has 1,000 bonds outstanding, each priced at $950:
Bond market value = 1,000 × $950 = $950,000

Bank loan market value = $500,000 (loans usually valued at book/principal since they don't trade)

Total debt = $950,000 + $500,000 = $1,450,000

Weights:
- Bond weight = 950,000 / 1,450,000 = 0.655 (65.5%)
- Loan weight = 500,000 / 1,450,000 = 0.345 (34.5%)

Step 2: Weighted average pre-tax cost of debt.

$$K_d = (0.655 \times 7.18\%) + (0.345 \times 5\%) = 4.70\% + 1.73\% = 6.43\%$$

Step 3: Apply the tax shield. Assume a 25% marginal tax rate:

$$K_{d,\text{after-tax}} = 6.43\% \times (1 - 0.25) = 6.43\% \times 0.75 = 4.82\%$$

So this company's true, after-tax cost of borrowing is 4.82% — the number that should flow into the WACC calculation, not the 5-7% headline rates on the individual instruments. Notice how far this after-tax number sits below the raw rates: that gap (about 1.6 percentage points) is the tax shield doing real work.

4. Key Takeaways

4.1 Most Important Concepts

• Cost of debt ≠ coupon rate. For traded bonds, use YTM (the market-implied yield), not the historical coupon printed on the bond.
• The tax shield is essential, not optional. Always convert pre-tax to after-tax cost of debt using $K_d(1-T)$ before using it in WACC or any investment decision.
• Weight by market value, not book value. Book value on the balance sheet reflects historical cost, not what the debt is actually worth today.
• YTM has no simple closed-form solution for multi-year bonds — you solve it iteratively or approximate it.
• The tax rate should reflect economic reality. Use an effective tax rate if the statutory rate overstates the benefit the firm actually captures (e.g., due to losses).
• Debt is generally cheaper than equity largely because of the interest