Intro to Finance: Cost of Capital Cost of Debt Aftertax Rd Rd 1 Tax Rate

What This Is

The cost of debt, also known as the after-tax cost of debt, is the cost of borrowing money for a company. It's an essential concept in finance because it affects a company's weighted average cost of capital (WACC) and ultimately its stock price. For example, suppose Apple borrows $1 billion at a 5% interest rate, and the corporate tax rate is 21%. The after-tax cost of debt would be 3.9% (5% x (1 - 0.21)).

Key Formulas & Symbols

• Rd = Rd × (1 – Tax Rate) where Rd = after-tax cost of debt, Rd = cost of debt, Tax Rate = corporate tax rate.
• Cost of Debt (Rd) = Coupon Rate + Credit Spread where Coupon Rate = periodic interest rate, Credit Spread = additional return for taking on credit risk.
• After-Tax Cost of Debt (Rd) = (1 – Tax Rate) × Cost of Debt where Tax Rate = corporate tax rate.
• Tax Shield = Interest Expense × (1 – Tax Rate) where Tax Shield = tax benefit from interest expense, Interest Expense = interest paid on debt.
• WACC = (E/V × Re) + (D/V × Rd × (1 – Tax Rate)) where WACC = weighted average cost of capital, E/V = market value of equity, Re = cost of equity, D/V = market value of debt, Rd = cost of debt.
• Cost of Debt (Rd) = (1 + (Coupon Rate / 2)) × (1 + (Coupon Rate / 2))^n - 1 / ((1 + (Coupon Rate / 2))^n - 1) where Coupon Rate = periodic interest rate, n = number of periods.
• Credit Spread = Rd - Coupon Rate where Rd = cost of debt, Coupon Rate = periodic interest rate.

Step-by-Step Calculation

1. Determine the cost of debt (Rd) using the formula Rd = Coupon Rate + Credit Spread.
2. Calculate the after-tax cost of debt (Rd) using the formula Rd = (1 – Tax Rate) × Cost of Debt.
3. Calculate the tax shield using the formula Tax Shield = Interest Expense × (1 – Tax Rate).
4. Calculate the weighted average cost of capital (WACC) using the formula WACC = (E/V × Re) + (D/V × Rd × (1 – Tax Rate)).

Common Mistakes

• Mistake: Using the wrong tax rate (e.g., using the marginal tax rate instead of the effective tax rate).
• Correction: Use the effective tax rate, which is the average tax rate over a period of time.
• Mistake: Forgetting to adjust the cost of debt for taxes.
• Correction: Remember to multiply the cost of debt by (1 – Tax Rate) to get the after-tax cost of debt.
• Mistake: Confusing the cost of debt with the after-tax cost of debt.
• Correction: Make sure to use the after-tax cost of debt in calculations, not the cost of debt.

Exam / CFA Tips

• Tip: Be careful with the formula Rd = (1 + (Coupon Rate / 2)) × (1 + (Coupon Rate / 2))^n - 1 / ((1 + (Coupon Rate / 2))^n - 1), as it's easy to get confused with the formula for the cost of equity.
• Tip: Make sure to use the correct tax rate in calculations, as it can affect the after-tax cost of debt.
• Tip: Be prepared to calculate the weighted average cost of capital (WACC) using the formula WACC = (E/V × Re) + (D/V × Rd × (1 – Tax Rate)).

Quick Practice Problem

Apple borrows $1 billion at a 5% interest rate, and the corporate tax rate is 21%. What is the after-tax cost of debt?

Answer: 3.9% (5% x (1 - 0.21)) Explanation: The after-tax cost of debt is calculated by multiplying the cost of debt by (1 – Tax Rate).

Last-Minute Cram Sheet

• ⚠️ The after-tax cost of debt is calculated by multiplying the cost of debt by (1 – Tax Rate).
• The cost of debt (Rd) = Coupon Rate + Credit Spread.
• The after-tax cost of debt (Rd) = (1 – Tax Rate) × Cost of Debt.
• The tax shield = Interest Expense × (1 – Tax Rate).
• The weighted average cost of capital (WACC) = (E/V × Re) + (D/V × Rd × (1 – Tax Rate)).
• ⚠️ The effective tax rate is the average tax rate over a period of time.
• ⚠️ The after-tax cost of debt is used in calculations, not the cost of debt.
• ⚠️ The formula Rd = (1 + (Coupon Rate / 2)) × (1 + (Coupon Rate / 2))^n - 1 / ((1 + (Coupon Rate / 2))^n - 1) is used to calculate the cost of debt.