Cost of Capital

Chapter 13

Cost of Capital Defined

• Cost of capital: percentage cost of permanent funds employed in business, or firm’s capital structure

• Capital structure: mix of long-term debt and equity by firm for its permanent financing needs

Cost of Capital Defined

Sample Restructured Balance Sheet(“mix” of company’s permanent financing)

• Firm only has two categories of assets: net working capital and fixed assets

• Net working capital is current assets minus current liabilities.• “Restructured” right-hand side represents firm’s capital structure such

that there are two categories of financing for two categories of assets.

Net workingCapital

Long-termdebt

Fixed Assets Equity

Cost of Capital Defined• Two costs of capital

1. Average cost of capital (ACC): weighted average after-tax cost of new capital raised during given year• Analysis of current financial decisions requires focus on

current costs2. Marginal cost of capital (MCC): represents

incremental ACC as function of total dollar amount of capital raised• As increasing amounts of capital are raised, cost of capital

begins to increase• Increased cost occurs at increments such that MC of

additional dollar of capital is greater than AC of capital• AC increases more slowly than MC

Cost of Capital Defined

• Consider an analogy of average and marginal tax rates. Example:– Corporate tax rate

• 15% on first $50,000 of income• 25% on next $25,000• 35% on all income above $75,000

– If corporation earned $50,000 before taxes, both average and marginal tax rates are 15%.

– At $60,000, average tax rate is 16.7% and marginal tax rate is 25%.

– Above $75,000, marginal tax rate is 35%.

Cost of Capital Defined

• Same general pattern holds for corporate cost of capital as in example.– As more capital is raised, cost increases at margin,

increasing marginal cost in increments.– Average cost increases at slower rate and

eventually approached marginal cost.– See exhibit 13.2

Marginal Cost and Capital Budgeting

• MCC is the capital cost that should be used for making capital budgeting decisions.

• Firm is inclined to make capital budgeting decisions based on comparison of cost of each additional dollar of capital raised with expected rate of return on each additional dollar of capital invested.

• Firm should accept all investment projects where IRR ≥ MCC in order to maximize value of firm.

• See exhibit 13.3

Calculating the Average Cost of Capital

1. Calculate after-tax cost of individual capital components.

2. Calculate average of component costs, weighted by percentage that each comprises of total capital structure.

3. Calculate cost of debt and preferred stock4. Estimate cost of equity

Cost of Debt

• Before-tax cost of debt: interest paid divided by principal amount borrowed

• Convert to after-tax basis by multiplying before-tax cost by 1 minus firm’s effective tax rate– 1 minus tax rate represents percentage of interest

that is paid by firm after taking into account tax deductibility of interest payments

• Tax rate multiplied by dollars of interest paid represents amount of interest that is “paid” through tax savings.

Cost of Debt

• Effective after-tax cost of debtKd = I/P (1 – T)

where Kd = after-tax cost of debt

I = interest in dollars P = principal amount borrowed T = effective tax rate

Cost of Debt• If firm raises debt capital by selling bonds publicly, then it

will incur some sales costs.– Flotation costs: cost of taking the issue public and include

expenses such as legal research, underwriting expenses, salesperson’s commissions• Flotation costs (fixed costs) as a percentage of size of issue become

larger as issue size becomes smaller.• Adjust after-tax cost of debt calculation to account for

flotation costs. Let F equal flotation costs as percentage of face value of bond issue:

Kd = [(I/P(1-F)] (1-T)• Principal amount on which interest is calculated is reduced

by amount of flotation costs

Cost of Debt

Cost of Preferred Stock• Since preferred stock is an equity security, dividends

represent profit distributions to owners of corporation and are not tax deductible to corporation.

• Before-tax cost of preferred stick is the same as after-tax cost:

Kp = D/Pwhere Kp = cost of preferred stock

D = dividend in dollars P = price of preferred stock

Cost of Debt

Cost of Preferred Stock• Adjust for flotation costs for newly issued

preferred stock that is publicly marketed:Kp = D/[P(1-F)]

Cost of Debt

Cost of Common Equity• Cost of common stock must be estimated• Common equity: rate of return stockholders

require on equity capital– Rate of return on equity that firm must earn in

order to maintain value of its own common stock– Expected rate of return necessary to induce

investors to invest in firm’s common stock

Cost of Debt

Cost of Common Equity• Two components of stockholders’ expected

rate of return:(Ke represents cost of equity) Ke = Expected dividend yield + Expected capital gain

Cost of DebtCost of Common Equity• Use company’s dividend divided by its price as dividend yield

and expected growth rate of earnings and dividends as measure of expected capital gain:

Ke = (D/P) + gwhere Ke = cost of equity

D = dividend in dollars P = price of stock g = expected growth rate

• Adequate to measure cost of equity capital generated by reinvested earnings.

• Measurement is cost of retained earnings portions of equity capital

Cost of Debt

Cost of Common Equity• Adjust for flotation costs to measure cost of

equity capital generated through new issues of common stock:

Ke = [D/(P(1-F)] + g

Cost of DebtA Computational Example• Calculate average cost of capital for firm having capital structure

consisting of 40% debt 10% preferred stock 50% equity

• Debt bears interest at 8%• Preferred stock sells for $100 (its par value) and pays dividend of $8• Common stock sells for $55 and pays dividend of $2.20• Expected growth rate of earnings and dividends is 9%• Firm’s effective tax rate is 34%• No flotation costs will be incurred

– Newly issued debt and preferred stock will be privately placed– Required equity capital will be generated through reinvested earnings

Cost of Debt

A Computational Example• See exhibit 13.4– Cost of debt is 5.3% after tax– Cost of preferred stock is 8%– Cost of common equity is 13% (4% dividend yield

plus 9% growth rate)– Weighted average cost of capital is 9.42%

(calculated by multiplying each component cost by percentage of capital structure it comprises and summing results)

The Capital Asset Pricing Model

• Capital asset pricing model (CAPM): stockholders’ required rate of return on equity capital is function of risk-free rate of return, rate of return earned on stocks in general (“market return”), and riskiness of particular stock in which investor may be considering investing

Ke = Risk-free rate + Risk premium• Risk premium is determined by riskiness of particular

stock relative to market and by difference between market rate of return and risk-free rate.

The Capital Asset Pricing Model• Riskiness of individual stock is measured by stock’s

beta factor: measure of volatility of stock relative to market– Beta of 1.0: stock has same volatility as market– Beta of 0.5: stock is about half as volatile as market– Beta of 2.0: stock is approximately twice as volatile as

market• Stock’s beta is estimated by regressing stock’s price

against level of some broad market index• Ex. Standard and Poor’s Index of 500 Common Stocks (S&P

500)• Beta factor is slope of regression line and measure of

company’s systematic risk

The Capital Asset Pricing Model

• CAPM in equation form:Ke = Rf + (Rm – Rf)B

where Ke = cost of equity capital

Rf = risk-free rate of return

Rm = market rate of return

B = beta

Capital Structure Management

• From perspective of capital markets, cost of equity capital must be greater than cost of debt.

• Investors are averse to risk. • Investors must demand a higher rate of return on

equity than on debt because investing in equity is riskier than investing in debt.

• Capital structure management focuses on finding appropriate combination of debt and equity such that combined weighted average cost of capital is minimized.

Capital Structure Management

• See exhibit 13.5– Ke and Kd are constant over a broad range, but at some

point begin to increase as leverage gets higher.– Risk causes increase. As firm becomes increasingly debt

heavy, increased risk of insolvency drives up both Kd (return to creditors) and Ke (return to stockholders).

– If firm is 100% equity financed (leverage = 0), its ACC is at maximum.

– If firm employs some debt financing, relatively expensive equity is combined with relatively inexpensive debt. This reduces weighted ACC.

Capital Structure Management

• In theory, operate on minimum point of ACC curve.

• In practice, ACC tends to be flat over fairly broad range so optimal-capital-structure theory is useful as broad policy guideline.– Effective capital structure management requires

capital structure mix that is within “range of optimality.”

Capital Structure Management

• Location of range of optimality varies with riskiness of particular industry.

• In general, the higher the business risk in industry, the less leverage firm may employ before cost curves turn up.– Riskier firms will have higher cost curves to begin

with.