Unit 7: Cost of Capital

I. Orientation — The Required Return on Corporate Financing

The cost of capital is the minimum rate of return that a company must earn on its investments to preserve the market value of the firm and satisfy providers of finance. It represents both the firm’s financing cost and investors’ opportunity cost for committing funds to securities of comparable risk.

A. Meaning and Concept

Cost of capital provides the benchmark for financing, investment appraisal, and corporate valuation decisions.

• Core definition: It is the required return on funds supplied by creditors, preference shareholders, and equity shareholders.
• Opportunity-cost principle: Investors sacrifice returns available from comparable alternatives; therefore, historical accounting costs do not determine the relevant cost.
• Risk–return relationship: Required return rises with systematic business and financial risk. A riskier company must generally offer a higher expected return.
• Marginal concept: Capital budgeting normally uses the cost of raising the next unit of finance rather than the cost originally paid for existing funds.
• After-tax basis: Investment cash flows and discount rates must be measured consistently. Because corporate cash flows are usually estimated after tax, the weighted average cost of capital is also generally calculated after tax.
• Market-value basis: Financing weights should ordinarily reflect current market values because these measure investors’ present claims and opportunity costs.
• Major components:
  • Debt capital: Borrowed funds carrying contractual interest and repayment obligations.
  • Equity capital: Shareholders’ funds carrying residual risk and no guaranteed return.
  • Retained earnings: Profits reinvested instead of distributed to shareholders.
• Decision roles:
  • Capital budgeting: A project creates value when its expected return exceeds the risk-appropriate cost of capital.
  • Valuation: Expected cash flows are discounted at a rate reflecting their timing and risk.
  • Financing policy: Management compares the costs and risk effects of alternative capital sources.
• Acceptance rule: For a conventional project evaluated using WACC:

Accept if NPV = Σ[CFₜ / (1 + WACC)ᵗ] − I₀ > 0

Here, CFₜ is after-tax cash flow in period t, I₀ is initial investment, and t is the time period.

• Important limitation: The company-wide cost of capital is appropriate only when a project has risk broadly similar to the firm’s existing operations and does not materially change its financing structure.

II. Debt Capital — Contractual Financing and the Tax Shield

A. Cost of Debt

The cost of debt is the effective return required by lenders on the company’s interest-bearing borrowings.

• Relevant measure: The current yield to maturity or market-required return is preferable to the historical coupon rate because it represents the opportunity cost of debt today.
• Irredeemable debt: For perpetual debt with constant annual interest:

k_d = I / P₀

Here, k_d is the before-tax cost of debt, I is annual interest, and P₀ is the debt’s current net market price.

• Redeemable debt: The precise cost is the internal rate of return equating net debt proceeds with future interest and principal payments:

P₀ = Σ[Iₜ / (1 + k_d)ᵗ] + RV / (1 + k_d)ⁿ

Here, Iₜ is interest in year t, RV is redemption value, and n is years to maturity.

• Approximate redeemable-debt formula:

k_d ≈ [I + (RV − NP) / n] / [(RV + NP) / 2]

Here, NP is net proceeds after issue costs; the other symbols retain their earlier meanings.

• Tax adjustment: Interest is commonly deductible in calculating taxable corporate income, creating an interest tax shield:

k_d(after tax) = k_d(before tax)(1 − T)

Here, T is the marginal corporate tax rate. If debt costs 8% before tax and T = 25%, its after-tax cost is 8%(1 − 0.25) = 6%.

• Issue costs: Flotation fees reduce net proceeds and therefore increase the effective cost of newly issued debt.
• Default and financial risk: Additional borrowing can raise credit risk, promised yields, refinancing exposure, and expected distress costs; debt is not indefinitely cheap.
• Non-taxable or loss-making firms: The full tax adjustment is inappropriate if the company cannot use interest deductions when they arise.

III. Equity Capital — Return Required by Ordinary Shareholders

A. Cost of Equity

The cost of equity is the return required by ordinary shareholders for bearing residual business and financial risk.

• Residual position: Equity holders receive cash flows only after operating expenses, taxes, interest, and other prior claims; consequently, equity normally costs more than debt.
• Dividend growth model: For shares whose dividends are expected to grow perpetually at a constant rate:

k_e = D₁ / P₀ + g

Here, k_e is the cost of equity, D₁ is the expected dividend next year, P₀ is the current share price, and g is the constant dividend growth rate.

• Growth estimation: Sustainable growth may be approximated as:

g = b × ROE

Here, b is the earnings retention ratio and ROE is the expected return on equity, assuming stable profitability and payout policy.

• CAPM approach: The capital asset pricing model links required return to non-diversifiable market risk:

k_e = R_f + β_e(R_m − R_f)

Here, R_f is the risk-free rate, β_e is equity beta, R_m is expected market return, and (R_m − R_f) is the market risk premium.

• CAPM example: If R_f = 4%, β_e = 1.2, and the market risk premium is 6%, then:

k_e = 4% + 1.2(6%) = 11.2%

• Beta interpretation:
  • β = 1: Equity has market-level systematic risk.
  • β > 1: Equity is more sensitive than the market.
  • β < 1: Equity is less sensitive than the market.
• Model contrast:
  1. Dividend growth model: Direct and forward-looking, but unsuitable when dividends are absent, unstable, or not expected to grow constantly.
  2. CAPM: Explicitly incorporates systematic risk, but depends on uncertain beta, risk-free-rate, and market-premium estimates.
• New equity issues: Flotation costs lower net issue proceeds, making newly issued equity more expensive than otherwise identical internally generated equity.

IV. Internally Generated Equity — Reinvestment of Shareholders’ Funds

A. Cost of Retained Earnings

The cost of retained earnings is the return shareholders forgo when profits are reinvested rather than distributed for investment elsewhere.

• Economic cost: Retained earnings are not free merely because no interest or dividend must be paid immediately; they belong economically to shareholders.
• Opportunity-cost measure: The basic cost is generally the ordinary shareholders’ required return:

k_r = k_e

Here, k_r is the cost of retained earnings and k_e is the cost of equity.

• Reasoning: A firm should retain one monetary unit only when reinvestment is expected to create at least as much value as shareholders could obtain from comparably risky alternatives.
• Flotation-cost distinction: Retained earnings avoid underwriting, registration, and issue expenses. Thus, where new shares bear flotation costs, k_r may be lower than the cost of new external equity.
• Dividend-adjusted approach: Some treatments adjust for shareholders’ personal taxes and brokerage costs:

k_r = k_e(1 − t_p)(1 − b_c)

Here, t_p is the shareholder’s personal tax rate and b_c is the proportional brokerage cost. In corporate valuation, these investor-specific adjustments are often omitted because shareholders face different tax circumstances.

• Example: If the estimated equity return is 12% and no personal-tax adjustment is applied, retained earnings also cost 12%, despite producing no explicit financing payment.
• Allocation implication: Retaining earnings is justified by value-creating opportunities, not by management’s preference to avoid external financing.

V. Composite Financing Cost — Combining Capital Sources

A. Calculation of WACC

The weighted average cost of capital combines component costs according to their proportions in the firm’s financing mix.

• Standard formula:

WACC = w_d k_d(1 − T) + w_p k_p + w_e k_e

Here, w_d, w_p, and w_e are the market-value weights of debt, preference shares, and equity; k_d, k_p, and k_e are their respective costs; and T is the marginal corporate tax rate.

• Weight condition:

w_d + w_p + w_e = 1

• Preference-share cost: For irredeemable preference shares:

k_p = D_p / P_p

Here, D_p is the annual preference dividend and P_p is the current net market price. Preference dividends do not ordinarily generate a corporate tax shield.

• Market-value weights: Current market values are conceptually superior because WACC measures present investor-required returns. Book-value weights may be used when market data are unavailable but can distort the result.
• Worked calculation: Suppose financing is 40% debt and 60% equity, before-tax debt costs 8%, equity costs 12%, and tax is 25%:

WACC = 0.40[8%(1 − 0.25)] + 0.60(12%)
     = 0.40(6%) + 7.20%
     = 9.60%

• Target capital structure: Long-run target weights may be preferable when current proportions are temporary or management intends to rebalance financing.
• Use in appraisal: WACC discounts free cash flow available to all capital providers; interest should not also be deducted from project cash flows, because doing so would double-count financing costs.
• Limits: A single WACC can misvalue projects with different operating risk, country risk, currency exposure, or leverage. Such projects require a project-specific discount rate.

VI. Cross-Border Financing — Currency, Country, and Market Effects

A. International Dimensions in Cost of Capital

International operations affect the cost of capital through differences in currencies, inflation, taxation, political risk, and financial-market integration.

• Currency consistency: Cash flows and discount rates must use the same currency. Dollar cash flows require a dollar-denominated required return; euro cash flows require a euro-denominated rate.
• Nominal-rate relationship: Inflation affects nominal costs of capital through the Fisher relation:

(1 + k_n) = (1 + k_r)(1 + π)

Here, k_n is the nominal required return, k_r is the real required return, and π is expected inflation.

• Country risk: Sovereign default exposure, capital controls, expropriation, regulatory instability, and restrictions on profit remittance may increase required returns.
• Risk treatment: Country risk may be incorporated through probability-adjusted cash flows or an evidence-based discount-rate premium, but applying both to the same exposure would double-count risk.
• International CAPM perspective: If capital markets are globally integrated, systematic risk should be measured against a world market portfolio; segmented markets may instead make local market risk more relevant.
• Tax differences: Corporate tax rates, withholding taxes, tax treaties, foreign tax credits, and limits on interest deductibility alter after-tax financing costs.
• Financing opportunities: Access to deeper international debt and equity markets can reduce funding costs through greater liquidity, investor diversification, and competition among capital providers.
• Exchange-rate exposure: Currency volatility affects translated cash flows and debt-servicing capacity. Matching foreign-currency debt with foreign-currency operating cash flows can provide a natural hedge.
• Political-risk caution: Diversifiable project-specific risks belong primarily in expected cash flows, while genuinely systematic and priced risks may justify a higher required return.
• Practical principle: A multinational should estimate a currency-consistent, after-tax, project-specific cost of capital rather than mechanically adding a country premium to its domestic WACC.