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 working
Capital
Long-term
debt
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 costs
2. 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 stock
4. 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 beforetax 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 debt
Kd = 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 aftertax cost:
Kp = D/P
where 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 Debt
Cost 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) + g
where 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 Debt
A 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.