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Capital Structure

Corporate Issuers

The Cost of Capital

Learning Outcome Statement:

calculate and interpret the weighted-average cost of capital for a company

Summary:

The weighted-average cost of capital (WACC) is a crucial financial metric used by companies to evaluate the cost of financing their operations through debt and equity. It represents the average rate of return required by all security holders and is used as a hurdle rate for capital investments. WACC is calculated by weighting the costs of debt and equity financing according to their respective proportions in the company's capital structure, adjusted for tax impacts.

Key Concepts:

Cost of Debt

The cost of debt is the return that lenders demand on the firm's debt. It is usually calculated using the interest rate on existing debt. This cost is adjusted for taxes since interest expenses are tax-deductible, reducing the effective cost of debt.

Cost of Equity

The cost of equity is the return that equity investors require on their investment in the firm. Unlike debt, there is no explicit cost like interest rate; instead, it is typically estimated using models like the Capital Asset Pricing Model (CAPM) or based on historical equity returns adjusted for company-specific risks.

Capital Structure

Capital structure refers to the proportion of debt and equity that a company uses to finance its operations. This mix impacts the WACC because debt and equity have different costs and risk profiles.

Tax Shield

The tax shield refers to the reduction in income taxes that results from taking allowable deductions from taxable income. In the context of WACC, the interest expense on debt is tax-deductible, which lowers the after-tax cost of debt.

Formulas:

Weighted Average Cost of Capital (WACC)

WACC=(Costdebt×Weightdebt×(1−Taxrate))+(Costequity×Weightequity)WACC = (Cost_{debt} \times Weight_{debt} \times (1 - Tax_{rate})) + (Cost_{equity} \times Weight_{equity})

This formula calculates the overall cost of capital for a firm, blending the costs of debt and equity financing, adjusted for the tax deductibility of interest expenses.

Variables:
CostdebtCost_{debt}:
Cost of debt
WeightdebtWeight_{debt}:
Proportion of debt in the capital structure
TaxrateTax_{rate}:
Corporate tax rate
CostequityCost_{equity}:
Cost of equity
WeightequityWeight_{equity}:
Proportion of equity in the capital structure
Units: percentage

Factors Affecting Capital Structure

Learning Outcome Statement:

Explain factors affecting capital structure and the weighted-average cost of capital

Summary:

The factors affecting capital structure include business models, life cycle stages, and external and internal factors. These factors influence the amount and type of financing needed, and the costs of debt and equity. Capital structure decisions aim to minimize the weighted-average cost of capital (WACC) to maximize firm value.

Key Concepts:

Business Model and Life Cycle

The business model and stage in the corporate life cycle determine the amount and type of financing a company needs. Capital-intensive businesses require significant asset investments, influencing higher capital needs, while capital-light businesses have lower asset and capital requirements. The life cycle stage (startup, growth, mature) affects the type of financing (equity, convertible debt, secured/unsecured debt) and the cost of capital.

Weighted-Average Cost of Capital (WACC)

WACC is the average rate of return a company is expected to pay to its security holders to finance its assets. It is calculated using the market value weights of debt and equity, cost of debt, cost of equity, and the corporate tax rate. Companies aim to minimize WACC to maximize shareholder value.

Determinants of Costs of Debt and Equity

Costs of debt and equity are influenced by top-down factors like economic conditions and industry-specific factors, and issuer-specific factors such as sales risks, profitability risks, and financial leverage. These costs are crucial as they directly impact the WACC and, consequently, the valuation and financial strategy of the company.

Formulas:

Weighted-Average Cost of Capital (WACC)

WACC=(Wd×rd×(1−Tc))+(We×re)WACC = (W_d \times r_d \times (1-T_c)) + (W_e \times r_e)

This formula calculates the overall cost of capital for a company, combining the costs of debt and equity financing, adjusted for the tax shield provided by debt.

Variables:
WdW_d:
Weight of debt
rdr_d:
Cost of debt
TcT_c:
Corporate tax rate
WeW_e:
Weight of equity
rer_e:
Cost of equity
Units: Percentage (%)

Operating Leverage

Operating leverage=Fixed costsTotal costsOperating \, leverage = \frac{Fixed \, costs}{Total \, costs}

This ratio measures the proportion of fixed costs in a company's total costs, indicating how a change in sales volume will affect operating income.

Variables:
FixedcostsFixed costs:
Total fixed costs incurred by the company
TotalcostsTotal costs:
Sum of fixed and variable costs
Units: Ratio

Interest Coverage Ratio

Interest coverage=Profit before interest and taxesInterest expenseInterest \, coverage = \frac{Profit \, before \, interest \, and \, taxes}{Interest \, expense}

This ratio indicates how easily a company can pay interest expenses on outstanding debt with its operating income.

Variables:
ProfitbeforeinterestandtaxesProfit before interest and taxes:
Earnings before interest and taxes (EBIT)
InterestexpenseInterest expense:
Total interest expenses for the period
Units: Ratio

Modigliani-Miller Capital Structure Propositions

Learning Outcome Statement:

Explain the Modigliani–Miller propositions regarding capital structure

Summary:

The Modigliani-Miller propositions, developed by economists Franco Modigliani and Merton Miller, state that under certain ideal conditions, the value of a firm is unaffected by its capital structure. These propositions are divided into scenarios with and without taxes. Without taxes, the capital structure is irrelevant to the firm's value (Proposition I) and the cost of equity increases with leverage but does not affect the overall weighted average cost of capital (WACC) (Proposition II). With taxes, the value of a levered firm is higher due to the tax shield on debt (Proposition I with taxes), and the cost of equity still increases with leverage but at a slower rate due to the tax shield, leading to a decrease in WACC (Proposition II with taxes).

Key Concepts:

Capital Structure Irrelevance (MM Proposition I without Taxes)

Under no-tax conditions, the firm's value is not affected by changes in the capital structure due to the ability of investors to create homemade leverage.

Higher Financial Leverage Raises the Cost of Equity (MM Proposition II without Taxes)

While increasing debt lowers the cost of capital due to debt being cheaper than equity, it increases the cost of equity due to higher financial risk, keeping the WACC unchanged.

Firm Value with Taxes (MM Proposition I with Taxes)

Introduces the concept of a tax shield on debt, which increases the value of a levered firm over an unlevered firm by the tax rate times the value of the debt.

Cost of Capital (MM Proposition II with Taxes)

Even with the tax shield, increasing debt increases the cost of equity but at a slower rate, resulting in a lower overall WACC and higher firm value.

Cost of Financial Distress

Financial distress costs, including direct and indirect costs, can negate the benefits of debt financing, especially in highly leveraged firms.

Formulas:

Cost of Equity without Taxes

re=r0+(r0−rd)DEr_e = r_0 + (r_0 - r_d) \frac{D}{E}

Shows how the cost of equity increases linearly with the debt-to-equity ratio in a no-tax scenario.

Variables:
rer_e:
Cost of equity
r0r_0:
Cost of capital for a company financed only with equity
rdr_d:
Cost of debt
DD:
Market value of debt
EE:
Market value of equity
Units: Percentage

Cost of Equity with Taxes

re=r0+(r0−rd)(1−t)DEr_e = r_0 + (r_0 - r_d)(1 - t)\frac{D}{E}

Adjusts the increase in cost of equity for the tax shield provided by debt, showing a slower rate of increase compared to the no-tax case.

Variables:
rer_e:
Cost of equity
r0r_0:
Cost of capital for a company financed only with equity
rdr_d:
Cost of debt
tt:
Marginal tax rate
DD:
Market value of debt
EE:
Market value of equity
Units: Percentage

Value of Levered Firm with Taxes

VL=VU+tDV_L = V_U + tD

Calculates the increased value of a levered firm over an unlevered firm due to the tax shield on debt.

Variables:
VLV_L:
Value of the levered company
VUV_U:
Value of the unlevered company
tt:
Marginal tax rate
DD:
Market value of debt
Units: Monetary units

Optimal Capital Structure

Learning Outcome Statement:

describe optimal and target capital structures

Summary:

The optimal capital structure is the specific mix of debt and equity that maximizes a company's firm value while minimizing its cost of capital. In practice, firms aim for a target capital structure that balances these considerations along with internal and external factors, such as market conditions and corporate strategy. The static trade-off theory, pecking order theory, and considerations of agency costs and asymmetric information play significant roles in determining and understanding a firm's capital structure.

Key Concepts:

Static Trade-Off Theory

This theory suggests that firms balance the tax benefits of debt against the costs of financial distress. Debt provides a tax shield that enhances firm value, but high levels of debt increase the risk and costs of financial distress, which reduces firm value.

Optimal Capital Structure

The specific mix of debt and equity that maximizes a company's value and minimizes its overall cost of capital. It is determined at the point where the marginal benefit of debt equals its marginal cost.

Target Capital Structure

A firm's target capital structure is an ideal mix based on balancing the factors that influence capital costs and the firm's value. It may not always be achievable due to market conditions and internal constraints.

Pecking Order Theory

Developed by Myers and Majluf, this theory suggests that firms prioritize their sources of financing (from internal financing to equity) according to the principle of least effort, preferring to issue debt over equity if external financing is required, due to asymmetric information.

Agency Costs

Costs arising from conflicts of interest among various stakeholders in a firm, which can influence capital structure decisions. Higher debt levels can reduce agency costs by reducing the free cash flow available to managers, thereby limiting potential wasteful spending.

Formulas:

Weighted Average Cost of Capital (WACC)

WACC=DD+E×rd×(1−t)+ED+E×reWACC = \frac{D}{D+E} \times r_d \times (1-t) + \frac{E}{D+E} \times r_e

WACC is the average rate of return a company is expected to pay to its security holders to finance its assets. It is calculated based on the proportion of debt and equity in the firm's capital structure.

Variables:
DD:
total market value of debt
EE:
total market value of equity
rdr_d:
cost of debt
rer_e:
cost of equity
tt:
corporate tax rate
Units: percentage

Value of Levered Firm (VL)

VL=VU+tD−PV(Costs of financial distress)VL = VU + tD - PV(\text{Costs of financial distress})

This formula represents the static trade-off theory, showing how the value of a levered firm is calculated by considering the tax shield benefits of debt and the costs associated with financial distress.

Variables:
VLVL:
value of the levered firm
VUVU:
value of the unlevered firm
tt:
corporate tax rate
DD:
value of debt
PVPV:
present value
Units: monetary value
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