Unit 7: Cost of Capital - Subjective Questions

The cost of capital is the minimum rate of return that a company must earn on its investments to satisfy the expectations of its providers of finance. It represents the opportunity cost of investing funds in a particular business.

Significance:

• Investment decisions: It is used as the discount rate when evaluating capital projects.
• Financing decisions: It helps determine an appropriate mix of debt and equity.
• Performance evaluation: A return above the cost of capital indicates value creation.
• Business valuation: It is used to discount expected future cash flows.
• Dividend decisions: It assists in deciding whether earnings should be retained or distributed.

A project generally creates shareholder wealth when its expected return exceeds the relevant cost of capital.

The cost of capital can be classified as follows:

• Specific cost: The cost associated with an individual financing source, such as debt, equity, or retained earnings.
• Composite cost: The combined cost of all financing sources, generally measured through the Weighted Average Cost of Capital.
• Historical cost: The cost of funds already raised by the company.
• Future cost: The expected cost of obtaining additional finance in the future.
• Average cost: The weighted average cost of the company's existing sources of finance.
• Marginal cost: The cost of raising one additional unit of capital.
• Explicit cost: The discount rate that equates the present value of cash inflows from financing with the present value of associated cash outflows.
• Implicit cost: The opportunity cost arising from the use of funds for one purpose instead of their best alternative use.

Irredeemable debt has no fixed maturity date, so the company pays interest indefinitely.

If is annual interest and is the net proceeds from debt, the before-tax cost is:

Interest is normally deductible for corporate tax purposes. Therefore, the after-tax cost is:

where is the corporate tax rate.

The after-tax cost of debt is generally lower than its before-tax cost because the interest tax deduction creates a tax shield. If market value is used instead of net proceeds, is replaced by the current market price of debt.

Face value per debenture is .

Step 1: Calculate annual interest

Step 2: Calculate net proceeds

Step 3: Calculate before-tax cost of debt

Step 4: Calculate after-tax cost of debt

Thus, the before-tax cost of debt is approximately , while the after-tax cost is approximately .

Redeemable debt involves periodic interest payments and repayment of principal on maturity. Its precise cost is the internal rate of return that equates net proceeds with the present value of future after-tax interest and redemption payments.

An approximate formula is:

where:

• = annual interest,
• = corporate tax rate,
• = redemption value,
• = net proceeds,
• = number of years to redemption.

The numerator contains the annual after-tax interest and the annualized capital gain or loss. The denominator represents the average amount of debt outstanding. For greater accuracy, the cost should be calculated through trial-and-error interpolation or an IRR method.

The dividend growth model assumes that equity dividends will grow at a constant rate indefinitely. The current market price of a share equals the present value of its expected future dividends.

The cost of equity is:

where:

• = cost of equity,
• = expected dividend per share for the next year,
• = current market price per share,
• = constant dividend growth rate.

For a new issue involving flotation cost , the formula becomes:

Limitations:

• It applies mainly to dividend-paying companies.
• It assumes a constant growth rate forever.
• Its result is highly sensitive to the estimated growth rate.
• It may not be suitable when dividend policy is unstable.

The dividend growth model is:

The dividend just paid is . Therefore, the next expected dividend is:

Substituting the values:

Therefore:

The company's cost of equity is approximately .

The Capital Asset Pricing Model, or CAPM, relates the required return on equity to systematic market risk.

Its formula is:

where:

• = risk-free rate,
• = equity beta measuring systematic risk,
• = expected market return,
• = market risk premium.

The model states that investors require compensation for:

• Time value of money, represented by ; and
• Systematic risk, represented by .

A beta greater than indicates that the share has greater systematic risk than the market. CAPM does not compensate investors for company-specific risk because such risk can be diversified away.

Dividend growth model:

• Uses expected dividends, market price, and dividend growth.
• Is simple to understand and apply.
• Is suitable mainly for companies with stable dividend growth.
• Does not explicitly measure risk.
• Is highly sensitive to the growth-rate estimate.

CAPM:

• Uses the risk-free rate, beta, and market risk premium.
• Explicitly incorporates systematic risk.
• Can be used even when a company does not pay dividends.
• Depends on estimates of beta and the market risk premium.
• Relies on restrictive assumptions about efficient markets and investor behavior.

Neither model is universally superior. Companies often calculate the cost of equity under both models and use judgment to select a reasonable estimate.

The cost of retained earnings is the return that shareholders forgo when profits are retained by the company rather than distributed as dividends.

Retained earnings are not free because:

• Shareholders could have received the earnings as dividends.
• They could have invested those dividends in alternative securities.
• Retaining earnings therefore involves an opportunity cost.
• Management must earn at least the return shareholders could obtain on investments of comparable risk.

When personal taxes and transaction costs are ignored, the cost of retained earnings is generally treated as equal to the cost of existing equity:

Unlike a new equity issue, retained earnings normally do not involve flotation costs.

If earnings were distributed, shareholders would receive dividends after personal tax and could reinvest them after paying brokerage costs. A commonly used adjustment is:

where:

• = cost of retained earnings,
• = shareholders' required return,
• = shareholders' personal tax rate on dividends,
• = brokerage cost expressed as a proportion.

For example, if , , and :

The adjustment reflects the amount shareholders could actually reinvest. In practice, different shareholders face different tax rates and costs, making an exact estimate difficult.

Cost of new equity:

• Relates to funds raised by issuing new shares.
• Includes flotation expenses such as underwriting, legal, and issue costs.
• May involve underpricing of the new issue.
• Is generally calculated using net issue proceeds.

Cost of retained earnings:

• Relates to profits retained and reinvested in the business.
• Represents shareholders' opportunity cost.
• Does not normally involve flotation expenses.
• Is generally equal to the cost of existing equity when personal taxes and transaction costs are ignored.

Consequently, new equity is usually more expensive than retained earnings. Under the dividend growth approach:

while:

The Weighted Average Cost of Capital, or WACC, is the average required return on all long-term sources of finance, weighted according to their relative importance in the capital structure.

The general formula is:

For debt and equity:

Calculation steps:

1. Identify the relevant sources of long-term capital.
2. Determine the market value of each source.
3. Calculate each source's proportion in total financing.
4. Estimate the specific cost of each source.
5. Adjust debt cost for the corporate tax shield.
6. Multiply each cost by its weight.
7. Add the weighted costs.

WACC is an appropriate discount rate for projects that have risk similar to the company's existing operations and do not materially change its financing structure.

Step 1: Calculate total market value

Step 2: Calculate capital weights

Step 3: Calculate after-tax debt cost

Step 4: Calculate WACC

Therefore, the company's WACC is .

Book-value weights:

• Are based on values reported in the balance sheet.
• Are stable and readily available.
• Reflect historical financing amounts.
• May differ substantially from current economic values.

Market-value weights:

• Are based on current market prices of securities.
• Reflect investors' present valuation of debt and equity.
• Are forward-looking and economically relevant.
• May fluctuate with market conditions.

Market-value weights are generally preferred because the cost of capital is an opportunity cost based on current investor expectations. If exact market values are unavailable, target capital-structure weights may be used. Book values should mainly be used as a practical approximation rather than as the theoretically ideal basis.

The average cost of capital is the weighted average cost of the funds already employed by a company. It reflects the company's overall financing structure and is commonly represented by WACC.

The marginal cost of capital is the weighted average cost of the next additional amount of finance raised by the company.

Key differences:

• Average cost relates primarily to the existing capital base, whereas marginal cost relates to new finance.
• Marginal cost can rise when cheap sources, such as retained earnings, are exhausted.
• Average cost is useful for company valuation and evaluating projects comparable to existing operations.
• Marginal cost is especially relevant for new investment and financing decisions.

A company should compare the expected return from an additional project with the marginal cost of financing that project.

Major assumptions:

• The proposed project has the same business risk as the company's existing operations.
• The project does not materially alter financial risk or capital structure.
• Existing financing weights represent the target long-term capital structure.
• Corporate tax rates and financing costs remain reasonably stable.
• The estimated component costs reflect current market expectations.

Limitations:

• A single WACC may cause acceptance of excessively risky projects.
• Market values and expected returns can be difficult to estimate.
• WACC may change as more capital is raised.
• International projects may involve additional currency and country risks.
• Different divisions may have substantially different operating risks.

Therefore, WACC should be adjusted or replaced by a project-specific discount rate when project risk differs significantly from the company's normal risk.

Flotation costs are expenses incurred when new securities are issued, including underwriting fees, registration charges, legal costs, and selling expenses.

Their effects include:

• They reduce the net proceeds received from a security issue.
• Lower net proceeds increase the effective cost of debt or equity.
• New equity generally costs more than retained earnings because it incurs flotation costs.
• A higher component cost can increase the WACC for newly raised capital.

For new equity under the dividend growth model:

where is the flotation cost per share.

For debt, net proceeds after flotation costs are used when calculating its yield. In capital budgeting, flotation costs may alternatively be treated as an additional initial cash outflow rather than as a permanent adjustment to WACC.

A company needs a project-specific cost of capital when a proposed investment has business or financial risk different from its existing operations. Using the company-wide WACC could undervalue safe projects and overvalue risky projects.

Estimation methods:

• Pure-play method: Identify listed companies engaged mainly in a similar business and use their risk characteristics.
• Beta method: Ungear a comparable company's equity beta to obtain an asset beta, then regear it for the project's target capital structure.
• CAPM: Apply the project beta in the CAPM formula to estimate the project cost of equity.
• Risk-adjusted premium: Add an appropriate risk premium to the company WACC.
• Divisional WACC: Use a separate cost of capital for a business division with comparable risk.

The project-specific debt and equity costs are then combined using the project's target financing weights.

A multinational company's cost of capital is influenced by domestic factors and additional international considerations:

• Exchange-rate risk: Volatile currencies increase uncertainty about the home-currency value of cash flows.
• Political risk: Expropriation, capital controls, conflict, or policy changes can increase required returns.
• Country risk: Economic instability, sovereign default risk, and weak institutions raise financing costs.
• Interest-rate differences: Borrowing costs vary across countries and currencies.
• Tax systems: Different corporate tax rates, withholding taxes, and tax treaties affect after-tax returns.
• Market segmentation: Restricted capital flows may prevent equalization of required returns across markets.
• Inflation: Differences in expected inflation influence nominal interest and discount rates.
• Liquidity and disclosure: Less liquid markets and weak reporting standards usually lead investors to demand higher returns.

International diversification may reduce total risk, but this benefit can be offset by currency, political, and sovereign risks.