9.1 Components of the Cost of Capital

Cost of Capital and its Significance

Definition and Role in Financial Decision-Making

The cost of capital is the minimum rate of return a company must earn on its investments to keep its investors satisfied. Think of it as a hurdle rate: any project the company takes on needs to clear this bar, or it's destroying value rather than creating it.

The weighted average cost of capital (WACC) combines the costs of all capital sources (debt, preferred stock, common equity), weighted by how much of each the company actually uses. WACC is the single number that represents a firm's blended financing cost.

• Acts as the discount rate in discounted cash flow (DCF) analysis and other valuation models to find the present value of future cash flows
• Guides capital budgeting decisions: accept projects that return more than the cost of capital, reject those that don't
• A key objective in corporate finance is minimizing the cost of capital through an optimal capital structure, which in turn maximizes shareholder value

Importance in Valuation and Corporate Finance

A lower cost of capital increases the net present value (NPV) of investment projects. That means more projects become worth pursuing, which expands the company's growth potential.

The optimal capital structure balances two competing forces: the tax benefits of debt (interest is tax-deductible) versus the financial risk that comes with too much leverage (higher chance of financial distress or bankruptcy).

• Cost of capital serves as a benchmark for evaluating whether management is generating adequate returns on the company's investments
• Accurate estimation matters for major decisions like capital budgeting, mergers and acquisitions, and dividend policy. Get the cost of capital wrong, and every downstream decision built on it will be off too.

Sources of Capital and Their Costs

Companies raise capital from three main sources. Each has a different cost, calculated in a different way.

Debt Financing

Debt includes bonds, bank loans, and other borrowings from creditors. The cost of debt is unique because interest payments are tax-deductible, which lowers the effective cost to the company.

• The before-tax cost of debt is typically the yield to maturity (YTM) on the company's bonds or the stated interest rate on its loans
• The after-tax cost of debt adjusts for the tax shield: you multiply the before-tax cost by $(1 - \text{marginal tax rate})$
• Example: A company issues bonds with a 6% YTM and faces a 25% tax rate. The after-tax cost of debt is $6\% \times (1 - 0.25) = 4.5\%$

Because of this tax advantage, debt is almost always the cheapest source of capital.

Preferred Stock

Preferred stock is a hybrid security that sits between debt and equity. It pays a fixed dividend (similar to interest on a bond), but those dividends are not tax-deductible for the issuing company. That's a critical distinction from debt.

• The cost of preferred stock equals the annual preferred dividend divided by the net issuance price (market price minus flotation costs)
• Flotation costs are expenses like underwriting fees that reduce the actual cash the company receives when issuing shares
• Example: A company issues preferred stock with a $2 annual dividend. The market price is $25 per share, and flotation costs are $1 per share. The cost of preferred stock is $\frac{2}{25 - 1} = \frac{2}{24} = 8.33\%$

Common Equity

Common equity represents ownership in the company. It can come from two places: retained earnings (profits reinvested instead of paid as dividends) or new share issuances.

• The cost of retained earnings is an opportunity cost. Shareholders expect a return on those reinvested profits just as they would on dividends they could have received.
• The cost of new common stock is slightly higher than retained earnings because the company incurs flotation costs when issuing new shares.
• Common equity is the most expensive source of capital because equity holders bear the most risk (they're last in line if the company fails).

Three models are commonly used to estimate the cost of common equity: CAPM, the Dividend Growth Model, and the Bond Yield Plus Risk Premium approach (detailed below).

Calculating the Cost of Debt, Preferred Stock, and Common Equity

Cost of Debt

The after-tax cost of debt reflects the true cost to the company after accounting for the tax deductibility of interest.

Formula:

$\text{After-tax cost of debt} = \text{Before-tax cost of debt} \times (1 - \text{Marginal tax rate})$

Steps:

1. Find the before-tax cost of debt (YTM on existing bonds or the interest rate on new borrowings)
2. Identify the company's marginal tax rate
3. Multiply the before-tax cost by $(1 - \text{tax rate})$

Example: A company issues bonds with a 5% YTM and faces a 30% tax rate.

$5\% \times (1 - 0.30) = 5\% \times 0.70 = 3.5\%$

Cost of Preferred Stock

Since preferred dividends are not tax-deductible, there's no tax adjustment here.

Formula:

$\text{Cost of preferred stock} = \frac{\text{Annual preferred dividend}}{\text{Net issuance price}}$

where net issuance price = market price − flotation costs.

Steps:

1. Identify the annual preferred dividend
2. Subtract flotation costs from the market price to get the net issuance price
3. Divide the dividend by the net issuance price

Example: A company issues preferred stock with a $1.50 annual dividend. The market price is $20 per share, and flotation costs are $0.50 per share.

$\frac{1.50}{20 - 0.50} = \frac{1.50}{19.50} = 7.69\%$

Cost of Common Equity

There's no single "correct" way to calculate the cost of equity, so analysts typically use multiple approaches and compare results.

Capital Asset Pricing Model (CAPM)

CAPM says the required return on a stock equals the risk-free rate plus compensation for the stock's systematic risk (measured by beta).

$\text{Cost of equity} = R_f + \beta \times (R_m - R_f)$

where $R_f$ is the risk-free rate, $\beta$ is the stock's beta, and $(R_m - R_f)$ is the market risk premium.

Steps:

1. Find the current risk-free rate (typically the yield on long-term government bonds)
2. Determine the stock's beta (measures sensitivity to market movements; a beta of 1.0 means the stock moves with the market)
3. Estimate the market risk premium (the expected return on the market minus the risk-free rate)
4. Plug into the formula

Example: Risk-free rate = 3%, beta = 1.2, market risk premium = 5%.

$3\% + 1.2 \times 5\% = 3\% + 6\% = 9\%$

Dividend Growth Model (DGM) / Gordon Growth Model

The DGM works well for companies that pay steady, growing dividends. It estimates the cost of equity as the current dividend yield plus the expected growth rate of dividends.

$\text{Cost of equity} = \frac{D_1}{P_0} + g$

where $D_1$ is next year's expected dividend, $P_0$ is the current stock price, and $g$ is the expected constant dividend growth rate.

Steps:

1. Find the company's current annual dividend per share (or calculate next year's expected dividend)
2. Find the current market price per share
3. Estimate the expected long-term dividend growth rate (from historical trends or analyst forecasts)
4. Divide the dividend by the price, then add the growth rate

Example: Current annual dividend = $2, stock price = $40, expected growth rate = 4%.

$\frac{2}{40} + 4\% = 5\% + 4\% = 9\%$

Bond Yield Plus Risk Premium Approach

This is the simplest method. You take the yield on the company's own long-term debt and add a risk premium to compensate equity holders for bearing more risk than bondholders. The risk premium is typically estimated at 3–5%, though it varies.

$\text{Cost of equity} = \text{Company's long-term debt yield} + \text{Equity risk premium}$

Example: Long-term debt yield = 6%, estimated equity risk premium = 4%.

$6\% + 4\% = 10\%$