COST OF DEBT

Definition

The Cost of Debt (Kd) is the effective interest rate a company pays on its borrowed funds, including bonds, loans, and other forms of debt financing. It reflects the cost of borrowing from creditors and is a crucial component of the Weighted Average Cost of Capital (WACC).

Since interest is tax-deductible, the after-tax cost of debt is typically lower than the pre-tax cost, making debt financing attractive relative to equity in some cases.

Origins

The term “debt” originates from the Latin debitum, meaning “something owed.” The modern concept of the cost of debt as a key input in corporate finance was significantly shaped by groundbreaking theories on capital structure in the mid-20th century. For instance, the work of Modigliani and Miller provided the theoretical framework that led to a deeper understanding of the trade-offs between debt and equity financing.

Usage

• Corporate Finance – Used to evaluate financing strategies.

• Valuation Models – Input for calculating WACC.

• Bond Markets – Measured as yield to maturity on issued bonds.

• Credit Risk Analysis – Higher perceived risk → higher cost of debt.

• Capital Budgeting – Helps determine hurdle rates for projects.
  
  

How Cost of Debt Works

1. A company borrows funds via loans, bonds, or credit facilities.

2. Creditors charge an interest rate based on risk, inflation, and market rates.

3. The company deducts interest expenses from taxable income (tax shield).

4. The effective cost = interest paid, adjusted for tax savings.
   
   

Key Takeaway

• Measures cost of borrowing capital from debt holders.

• Must account for tax shield from interest deductibility.

• Lower than cost of equity, but increases with higher credit risk.

• Critical in determining optimal capital structure.

Context in Financial Modeling

• WACC Calculation – Cost of debt is weighted by the firm’s debt proportion.

• DCF Valuations – Discount rate includes debt financing impact.

• M&A Transactions – Buyers analyze cost of debt for leveraged deals.

• Risk Management – Sensitivity analysis on debt cost under different market conditions.
  
  

Types of Cost of Debt

1. Explicit Cost – Contractual interest rates on debt.

2. Implicit Cost – Opportunity cost of debt financing (credit ratings, restrictions).

3. Marginal Cost – Cost of issuing new debt.

4. Effective Interest Rate – Actual cost after fees and issuance costs.
   
   

Nuances & Complexities

• Subjectivity – Choice of discount rate dramatically changes valuation.

• Country risk premiums – Emerging markets require higher rates.

• Inflation adjustments – Must align with nominal vs. real cash flows.

• Policy impact – Central banks’ discount rate influences market interest rates.
  
  

Mathematical Formulas

Pre-Tax Cost of Debt:

$$K_d = \frac{\text{Total Interest Expense}}{\text{Total Debt}}$$

Or, for bonds:

$$K_d \approx YTM$$
(where YTM = Yield to Maturity on bonds)

After-Tax Cost of Debt:

$$K_d (after-tax) = K_d \times (1 - T)$$

Where:

• $K_d$ = Pre-tax cost of debt

• $T$ = Corporate tax rate

$$\text{Credit Spread} = Y_{\text{corporate bond}} - Y_{\text{risk-free bond}}$$

Related Terms

• Cost of Equity

• Weighted Average Cost of Capital (WACC)

• Credit Spread

• Yield to Maturity (YTM)

• Tax Shield

• Leverage Ratio
  
  

Real-World Applications

Corporate Bonds – A company issues bonds at 6% YTM; with a 25% tax rate, the after-tax cost of debt is calculated as:

Bank Loan – A firm pays $2M annual interest on a $40M loan, with a pre-tax cost of debt of:

With a 25% tax rate, the after-tax cost is $5\%\times (1-0.25)=3.75\%$.

High-Yield Debt – Junk bond issuers pay much higher rates due to default risk.

References & Sources

• Inspired Economist: Cost of Debt: Understandings Its Impact on Financial Decisions