Introductory Corporate Finance: Cost of Capital Cost of Debt rd Yield to Maturity on Existing Debt AfterTax Cost rd 1 T

What This Is

The cost of debt (rd) is the rate at which a company borrows money from lenders, such as banks or bondholders. It is an essential component of a company's capital structure, as it affects the company's weighted average cost of capital (WACC). For example, let's consider Tesla, Inc. (TSLA), which has a debt-to-equity ratio of 0.25 and an after-tax cost of debt of 4.5%. If Tesla's tax rate is 25%, its after-tax cost of debt would be 3.375% (4.5% x (1 - 0.25)).

Key Formulas & Models

• rd = Yield to Maturity on Existing Debt: the rate at which a company borrows money from lenders, such as banks or bondholders.
• rd (1 - T) = After-Tax Cost of Debt: the cost of debt after considering the tax benefits of interest payments.
• WACC = wd × rd(1‑T) + wps × rps + we × re: the weighted average cost of capital, used as a discount rate for capital budgeting decisions.
• DOL = Q(P‑V) / (Q(P‑V)‑F): the degree of operating leverage, which measures EBIT sensitivity to sales.
• Interest Tax Shield (ITS) = rd × D: the tax benefit of interest payments, which reduces the company's tax liability.
• Debt-Equity Ratio (DER) = D / E: the ratio of a company's debt to its equity, which affects the company's cost of capital.
• After-Tax Cost of Debt (ATCD) = rd (1 - T): the cost of debt after considering the tax benefits of interest payments.
• Tax Shield (TS) = rd × D × T: the tax benefit of interest payments, which reduces the company's tax liability.

Step-by-Step Calculation

1. Determine the company's debt-to-equity ratio (DER) by dividing its total debt by its total equity.
2. Calculate the company's after-tax cost of debt (ATCD) by multiplying its cost of debt (rd) by (1 - T), where T is the company's tax rate.
3. Calculate the company's interest tax shield (ITS) by multiplying its cost of debt (rd) by its total debt (D).
4. Calculate the company's weighted average cost of capital (WACC) by using the formula: WACC = wd × rd(1‑T) + wps × rps + we × re, where wd is the weight of debt, wps is the weight of preferred stock, and we is the weight of equity.
5. Calculate the company's degree of operating leverage (DOL) by using the formula: DOL = Q(P‑V) / (Q(P‑V)‑F), where Q is the company's sales, P is the company's price, V is the company's variable costs, and F is the company's fixed costs.

Common Mistakes

1. Mistake: Using book value instead of market value for WACC.
   • Correction: Use market value instead of book value to reflect the company's current market capitalization.
   • Counterexample: Suppose a company has a book value of $100 million and a market value of $200 million. Using book value instead of market value would result in an incorrect WACC calculation.
2. Mistake: Ignoring flotation costs when calculating WACC.
   • Correction: Include flotation costs in the WACC calculation to reflect the company's actual cost of capital.
   • Counterexample: Suppose a company has a flotation cost of 5% and a WACC of 10%. Ignoring flotation costs would result in an incorrect WACC calculation.
3. Mistake: Confusing sunk cost with opportunity cost.
   • Correction: Use opportunity cost instead of sunk cost to reflect the company's actual cost of capital.
   • Counterexample: Suppose a company has a sunk cost of $100 million and an opportunity cost of $150 million. Using sunk cost instead of opportunity cost would result in an incorrect WACC calculation.

Exam / CFA Tips

1. Tip: When calculating WACC, use market value instead of book value to reflect the company's current market capitalization.
2. Tip: When calculating DOL, use the formula: DOL = Q(P‑V) / (Q(P‑V)‑F) to measure EBIT sensitivity to sales.
3. Tip: When calculating ITS, use the formula: ITS = rd × D to calculate the tax benefit of interest payments.

Quick Practice Problem

A company has EBIT of $10 million, interest of $2 million, and a tax rate of 25%. Calculate the company's degree of operating leverage (DOL).

Answer: DOL = $10 million / ($10 million - $2 million) = 2.5

Explanation: The company's DOL is 2.5, which means that a 1% increase in sales will result in a 2.5% increase in EBIT.

Last-Minute Cram Sheet

1. Cost of debt (rd): the rate at which a company borrows money from lenders.
2. After-tax cost of debt (ATCD): the cost of debt after considering the tax benefits of interest payments.
3. Interest tax shield (ITS): the tax benefit of interest payments, which reduces the company's tax liability.
4. Debt-equity ratio (DER): the ratio of a company's debt to its equity, which affects the company's cost of capital.
5. Weighted average cost of capital (WACC): the weighted average of a company's cost of debt and equity.
6. Degree of operating leverage (DOL): a measure of EBIT sensitivity to sales.
7. Flotation costs: the costs associated with issuing new debt or equity.
8. Opportunity cost: the cost of a decision that is not taken, which reflects the company's actual cost of capital.
9. Sunk cost: a cost that has already been incurred, which does not reflect the company's actual cost of capital.
10. Tax shield: the tax benefit of interest payments, which reduces the company's tax liability.