Cost of Capital
Contents
Financing Activities..............................................................................................................................................................................................................................2
Cost of Capital ........................................................................................................................................................................................................................................4
Long-term Debt .............................................................................................................................................................................................................................. 11
Before tax cost of debt ........................................................................................................................................................................................................ 14
After tax cost of debt............................................................................................................................................................................................................. 18
Preferred Stock ..............................................................................................................................................................................................................................20
Common Stock .............................................................................................................................................................................................................................. 23
Gordon-growth model ......................................................................................................................................................................................................... 24
Capital Asset Pricing Model (CAPM) ............................................................................................................................................................................ 27
Cost of Retained Earnings .................................................................................................................................................................................................30
Cost of New Issues of Common Stock ...................................................................................................................................................................... 31
Weighted Average Cost of Capital ......................................................................................................................................................................................... 34
Weighting Schemes ........................................................................................................................................................................................................................38
book value weights .................................................................................................................................................................................................................... 40
market value weights ................................................................................................................................................................................................................. 41
Historical weights ......................................................................................................................................................................................................................... 42
Target weights ................................................................................................................................................................................................................................ 42
Financing Activities
Cash flows activities
• Operating Activities
• Investing Activities
• Financing Activities
BALANCE SHEET
ASSETS
LIABILITIES
Current Assets
Current Liabilities
Noncurrent Assets
Noncurrent Liabilities
SHAREHOLDERS’ EQUITY
Ordinary Shares
Preference Share
Retained Earnings
Cost of Capital
Accept or Reject?
Investment Cost of Capital
A
12%
B
5%
C
6%
D
10%
E
15%
Rate of return
10%
8%
6%
12%
11%
cost of capital Represents the firm’s cost of financing and is the
minimum rate of return that a project must earn to increase firm
value. #threshold #ExpectedReturn
Investments with a rate of return above the cost of capital will
increase the value of the firm, and projects with a rate of return
below the cost of capital will decrease firm value.
Accept or Reject?
Investment Cost of Capital
A
12%
B
5%
C
6%
D
10%
E
15%
Rate of return
10%
8%
6%
12%
11%
Answer
Reject
Accept
Accept
Accept
Reject
Financial managers are ethically bound to invest only in projects
that they expect to exceed the cost of capital.
A firm’s cost of capital is estimated at a given point in time and
reflects the expected average future cost of funds over the long
run.
A firm is currently faced with an investment opportunity. Assume
the following:
Best project available today
Cost = 100,000
Life = 20 years
Expected Return = 7%
Least costly financing source available
Debt = 6%
Because it can earn 7% on the investment of funds costing only
6%, the firm undertakes the opportunity.
Imagine that 1 week later a new investment opportunity is
available:
Best project available 1 week later
Cost = 100,000
Life = 20 years
Expected Return = 12%
Least costly financing source available
Equity = 14%
In this instance, the firm rejects the opportunity because the 14%
financing cost is greater than the 12% expected return.
Long-term Debt
cost of long-term debt The financing cost associated with new
funds raised through long-term borrowing. (e.g corporate
bonds)
net proceeds Funds actually received by the firm from the sale
of a bond or security.
flotation costs The total costs of issuing and selling a security.
These costs apply to all public offerings of securities—debt,
preferred stock, and common stock. They include two
components:
(1) underwriting costs—compensation earned by investment
bankers for selling the security—and
(2) administrative costs—issuer expenses such as legal,
accounting, and printing.
Total proceeds
100%
Less: Flotation costs
Underwriting costs
2%
Administrative costs
3%
Net proceeds
95%
1,000
20
30
50
950
Premium vs Discount
Effective Interest Rate vs Nominal Rate
Yield to maturity (yield rate) vs Coupon Rate
Before tax cost of debt
Using market quotation
yield to maturity (YTM) Compound annual rate of return earned
on a debt security purchased on a given day and held to
maturity
aka Effective Interest Rate
Calculating the cost
Exercise:
A firm raises capital by selling $20,000 worth of debt with
flotation costs equal to 2% of its par value. If the debt matures in
10 years and has a coupon interest rate of 8%, what is the bond’s
YTM?
Approximating the cost
r = {[ i + (par value – net proceed)/n ] / (net proceeds + par value / 2) }
After tax cost of debt
r = rate before tax ( 1 – tax rate)
Exercise:
Currently, Warren Industries can sell 15-year, $1,000-par-value
bonds paying annual interest at a 12% coupon rate. As a result of
current interest rates, the bonds can be sold for $1,010 each;
flotation costs of $30 per bond will be incurred in this process.
The firm is in the 40% tax bracket.
Find the net proceeds from sale of the bond
Use the approximation formula to estimate the before-tax and
after-tax costs of debt.
Preferred Stock
Preferred stock represents a special type of ownership interest
in the firm. It gives preferred stockholders the right to receive
their stated dividends before the firm can distribute any
earnings to common stockholders.
preferred stock dividends are stated as a dollar amount:
“x-amount preferred stock.” = “Php4 preferred stock”
Sometimes preferred stock dividends are stated as an annual
percentage rate.
cost of preferred stock The ratio of the preferred stock dividend
to the firm’s net proceeds from the sale of preferred stock.
r = annual dividends per share / net proceeds
Exercise
Your firm, People’s Consulting Group, has been asked to consult
on a potential preferred stock offering by Brave New World. This
15% preferred stock issue would be sold at its par value of $35
per share. Flotation costs would total $3 per share. Calculate the
cost of this preferred stock.
Common Stock
cost of common stock equity, The rate at which investors
discount the expected dividends of the firm to determine its
share value.
Two techniques are used to measure the cost of common stock
equity. One relies on the constant-growth valuation model, the
other on the capital asset pricing model (CAPM).
Gordon-growth model
constant-growth valuation (Gordon growth) model Assumes
that the value of a share of stock equals the present value of all
future dividends (assumed to grow at a constant rate) that it is
expected to provide over an infinite time horizon.
r = dividends per share / price per share + growth rate
r = dividend yield + capital gains yield
growth rate:
r = (FVn / PV)1/n – 1
derive from FVn = PV * (1 + r) n
or use interpolation formula below:
Exercise:
Duke Energy has been paying dividends steadily for 20 years.
During that time, dividends have grown at a compound annual
rate of 7%. If Duke Energy’s current stock price is $78 and the
firm plans to pay a dividend of $6.50 next year, what is Duke’s
cost of common stock equity?
Capital Asset Pricing Model (CAPM)
Capital asset pricing model (CAPM) Describes the relationship
between the required return and the non-diversifiable risk of the
firm as measured by the beta coefficient.
rs = RF + [b * (rm - RF)]
where:
rs = required return on common stock
RF = risk-free rate of return
rm = market return; return on the market portfolio of assets
b = beta coefficient or index of nondiversifiable risk for common
stock
Using the CAPM indicates that the cost of common stock equity
is the return required by investors as compensation for the firm’s
nondiversifiable risk, measured by beta.
Exercise:
J&M Corporation common stock has a beta, b, of 1.2. The riskfree rate is 6%, and the market return is 11%.
a. Determine the risk premium on J&M common stock.
b. Determine the required return that J&M common stock
should provide.
c. Determine J&M’s cost of common stock equity using the
CAPM.
Cost of Retained Earnings
cost of retained earnings, rr The same as the cost of an
equivalent fully subscribed issue of additional common stock,
which is equal to the cost of common stock equity, rs.
Cost of New Issues of Common Stock
cost of a new issue of common stock, rn The cost of common
stock, net of underpricing and associated flotation costs.
underpriced Stock sold at a price below its current market price,
P0.
issue price, the price paid by the primary market investors
r = dividends per share / net proceeds + growth rate
net proceeds = underpriced less floatation cost
or net proceeds = underpriced x (1 – floatation cost rate)
The net proceeds from sale of new common stock, Nn, will be
less than the current market price, P0. Therefore, the cost of new
issues, rn, will always be greater than the cost of existing issues,
rs, which is equal to the cost of retained earnings, rr. The cost of
new common stock is normally greater than any other longterm financing cost.
Exercise:
Ross Textiles wishes to measure its cost of common stock
equity. The firm’s stock is currently selling for $57.50. The firm
expects to pay a $3.40 dividend at the end of the year (2013). The
dividends for the past 5 years are shown in the following table.
Year
2012
2011
2010
2009
2008
Dividend
$3.10
2.92
2.60
2.30
2.12
After underpricing and flotation costs, the firm expects to net
$52 per share on a new issue. Growth rate is 9.97%.
Using the constant-growth valuation model, determine the cost
of new common stock, rn.
Weighted Average Cost of Capital
weighted average cost of capital (WACC), ra Reflects the
expected average future cost of capital over the long run; found
by weighting the cost of each specific type of capital by its
proportion in the firm’s capital structure.
Exercise:
Weekend Warriors, Inc., has 35% debt and 65% equity in its
capital structure. The firm’s estimated after-tax cost of debt is
8% and its estimated cost of equity is 13%. Determine the firm’s
weighted average cost of capital (WACC).
Oxy Corporation uses debt, preferred stock, and common stock
to raise capital. The firm’s capital structure targets the following
proportions: debt, 55%; preferred stock, 10%; and common stock,
35%. If the cost of debt is 6.7%, preferred stock costs 9.2%, and
common stock costs 10.6%, what is Oxy’s weighted average cost
of capital (WACC)?
Equity Lighting Corp. wishes to explore the effect on its cost of
capital of the rate at which the company pays taxes. The firm
wishes to maintain a capital structure of 30% debt, 10% preferred
stock, and 60% common stock. The cost of financing with
retained earnings is 14%, the cost of preferred stock financing is
9%, and the before-tax cost of debt financing is 11%. Calculate
the weighted average cost of capital (WACC) given the tax rate
assumptions in parts a to c.
a. Tax rate 40%
b. Tax rate 35%
c. Tax rate 25%
d. Describe the relationship between changes in the rate of
taxation and the weighted average cost of capital.
Weighting Schemes
book value weights Weights that use accounting values to
measure the proportion of each type of capital in the firm’s
financial structure.
market value weights Weights that use market values to
measure the proportion of each type of capital in the firm’s
financial structure.
historical weights Either book or market value weights based on
actual capital structure proportions
target weights Either book or market value weights based on
desired capital structure proportions
Market value weights are clearly preferred over book value
weights.
the preferred weighting scheme is target market value
proportions
The theoretically preferred approach uses target weights based
on market values.
book value weights
Exercise:
Ridge Tool has on its books the amounts and specific (after-tax)
costs shown in the following table for each source of capital.
Source of capital
Book value Individual cost
Long-term debt
$700,000
5.3%
Preferred stock
50,000
12.0
Common stock equity
650,000
16.0
a. Calculate the firm’s weighted average cost of capital using
book value weights.
b. Explain how the firm can use this cost in the investment
decision-making process.
market value weights
Webster Company has compiled the information shown in the
following table.
Source of capital
Long-term debt
Preferred stock
Common stock
equity
Totals
Book value Market value
$4,000,000
$3,840,000
40,000
60,000
1,060,000
$5,100,000
3,000,000
$6,900,000
After-tax
cost
6.0%
13.0
17.0
a. Calculate the weighted average cost of capital using book
value weights.
b. Calculate the weighted average cost of capital using market
value weights.
c. Compare the answers obtained in parts a and b. Explain the
differences.
Historical weights
Target weights
After careful analysis, Dexter Brothers has determined that its
optimal capital structure is composed of the sources and target
market value weights shown in the following table.
Source of capital
Long-term debt
Preferred stock
Common stock equity
Total
Target market value weight
30%
15
55
100%
The cost of debt is estimated to be 7.2%; the cost of preferred
stock is estimated to be 13.5%; the cost of retained earnings is
estimated to be 16.0%; and the cost of new common stock is
estimated to be 18.0%. All of these are after-tax rates. The
company’s debt represents 25%, the preferred stock represents
10%, and the common stock equity represents 65% of total
capital on the basis of the market values of the three
components. The company expects to have a significant
amount of retained earnings available and does not expect to
sell any new common stock.
a. Calculate the weighted average cost of capital on the basis of
historical market value weights.
b. Calculate the weighted average cost of capital on the basis of
target market value weights.
c. Compare the answers obtained in parts a and b. Explain the
differences.