Geothermal’s Cost of Capital

Definition and Importance

The cost of capital represents the return that a firm's investors could expect to earn if they invested in securities with comparable degrees of risk. It is a critical concept in financial accounting and corporate finance, as it serves as the benchmark for evaluating investment opportunities and financing decisions.

• Capital Structure: The mix of long-term debt and equity financing used by a firm.

• Cost of Capital: The weighted average of the required returns on the firm’s debt and equity.

Example: Calculating Cost of Capital

Suppose Geothermal Inc. has the following capital structure:

If Geothermal pays 8% for debt and 14% for equity, the company cost of capital is calculated as:

• Portfolio Return:

Distribution of Income and Risk

• Debtholders (30% of capital) receive a smaller, fixed share of income (8%), which is less risky and often guaranteed.

• Stockholders (70% of capital) bear more risk and, on average, receive a greater return (14%).

• If an investor owns all the debt and equity, they receive all the income generated by the firm.

The Weighted-Average Cost of Capital (WACC)

Definition and Formula

The Weighted-Average Cost of Capital (WACC) is the expected rate of return on a portfolio of all the firm's securities, adjusted for tax savings due to interest payments. WACC is used as a discount rate for evaluating investment projects and valuing businesses.

• Tax Considerations: Interest payments on debt are tax-deductible, reducing the effective cost of debt.

Formula for After-Tax Cost of Debt:

General WACC Formula:

• = Market value of debt

• = Market value of equity

• = Total market value of the firm

• = Firm's average tax rate

• = Yield to maturity (YTM) on bonds

• = Cost of equity, often estimated using CAPM

CAPM Formula for Cost of Equity:

• = Risk-free rate

• = Expected market return

• = Firm's equity beta

Example: Calculating WACC

Given Geothermal Inc. pays 8% for debt and 14% for equity, with a 21% tax rate:

• After-tax cost of debt:

• WACC:

Steps to Calculating Cost of Capital

1. Calculate the value of each security as a proportion of the firm's market value.

2. Determine the required rate of return on each security.

3. Calculate a weighted average of the after-tax return on the debt and the return on the equity.

WACC with Preferred Stock

When a firm has preferred stock, the WACC formula expands:

• = Market value of preferred stock

• = Preferred dividend / price of preferred stock

Example: WACC with Preferred Stock

Executive Fruit has issued debt ($4 million), preferred stock ($2 million), and common stock ($6 million). Required returns are 6%, 12%, and 18%, respectively.

• Firm Value: million

• WACC:

• Actual calculation from notes:

Measuring Capital Structure

Market vs. Book Value

When estimating WACC, always use the market value of securities, not book value. Market values reflect the true value of the firm's securities in the market.

• Market Value of Bonds: Present value of all coupons and par value, discounted at current YTM.

• Market Value of Equity: Market price per share multiplied by the number of outstanding shares.

Example: Calculating Market Value

If long-term bonds pay an 8% coupon and mature in 10 years, their market value (assuming a 9% YTM) is calculated using present value formulas.

Estimating Expected Returns

Required Rates of Return

• Debt: Use YTM on bonds.

• Common Stock: Use CAPM:

• Preferred Stock: Use dividend/price of preferred.

Example: Required Rate of Return

If a firm has a beta of 0.85, risk-free rate of 6%, market risk premium of 7%, YTM on bonds of 9%, and tax rate of 21%:

• Cost of equity:

• After-tax cost of debt:

• WACC:

Dividend Discount Model (DDM) for Cost of Equity

The DDM estimates the cost of equity using expected dividends and growth:

• = Expected dividend next year

• = Current price per share

• = Growth rate of dividends

Preferred Stock Return

Valuing Entire Businesses

Free Cash Flow (FCF) and Business Valuation

The value of a business or project is usually computed as the discounted value of Free Cash Flows (FCF) out to a valuation horizon (terminal value). FCF is a more accurate measurement of present value than dividends or earnings per share.

• Present Value of FCF:

• Horizon Value (Terminal Value):

Example: Deconstruction Company

• Capital structure: 60% equity, 40% debt

• Required rate of return on equity: 12%

• Interest rate on debt: 5%

• Tax rate: 21%

• WACC:

• Business value is calculated by discounting FCFs and the horizon value at WACC.

Interpreting WACC

Appropriate Use of WACC

• WACC is an appropriate discount rate only for projects that are carbon copies of the firm's existing business.

• Changing capital structure affects both the explicit cost of debt (interest rate) and the implicit cost (required return on equity due to increased risk).

Summary Table: Key Formulas

Additional info:

• These notes expand on the original slides by providing full definitions, formulas, and context for each concept.

• Examples and tables have been reconstructed and clarified for academic completeness.