Kevin Campbell, University of Stirling, November 2005

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2008

KOSZT I STRUKTURA

KAPITAŁU

Kevin Campbell, University of Stirling, November 2005

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Cost of Capital



Cost of Capital - The return the firm’s
investors could expect to earn if they
invested in securities with comparable
degrees of risk



Capital Structure - The firm’s mix of
long term financing and equity financing

Kevin Campbell, University of Stirling, November 2005

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Cost of Capital



The cost of capital represents the overall cost
of financing to the firm



The cost of capital is normally the relevant
discount rate to use in analyzing an
investment



The overall cost of capital is a weighted
average of the various sources:

•

WACC = Weighted Average Cost of Capital

•

WACC = After-tax cost x weights

Kevin Campbell, University of Stirling, November 2005

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Cost of Debt



The cost of debt to the firm is the effective yield
to maturity (or interest rate) paid to its
bondholders



Since interest is tax deductible to the firm, the
actual cost of debt is less than the yield to
maturity:

•

After-tax cost of debt = yield x (1 - tax rate)



The cost of debt should also be adjusted for
flotation costs (associated with issuing new
bonds)

Kevin Campbell, University of Stirling, November 2005

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with stock

with debt

EBIT

400,000

400,000

- interest expense

0

(50,000)

EBT

400,000

350,000

- taxes (34%)

(136,000) (119,000)

EAT 264,000

231,000

Example: Tax effects of

Example: Tax effects of

financing with debt

financing with debt



Now, suppose the firm pays $50,000 in
dividends to the shareholders

Kevin Campbell, University of Stirling, November 2005

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with stock

with debt

EBIT

400,000

400,000

- interest expense

0

(50,000)

EBT

400,000

350,000

- taxes (34%)

(136,000) (119,000)

EAT 264,000

231,000

- dividends (50,000)

0

Retained earnings

214,000

231,000

Example: Tax effects of

Example: Tax effects of

financing with debt

financing with debt

Kevin Campbell, University of Stirling, November 2005

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After-tax cost Before-tax cost Tax

of Debt of Debt

Savings

33,000 = 50,000 -

17,000

OR

33,000 = 50,000 ( 1 - .34)

Or, if we want to look at percentage costs:

-

=

Cost of Debt

Kevin Campbell, University of Stirling, November 2005

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After-tax Before-tax

Marginal

% cost of % cost of x tax

Debt Debt rate

Kd = kd (1 - T)

.066 = .10 (1 - .34)

-

=

1

1

Cost of Debt

Kevin Campbell, University of Stirling, November 2005

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

Prescott Corporation issues a

$1,000

par,

20 year

bond paying the market

rate of

10%.

Coupons are annual.

The bond will sell for par since it pays

the market rate, but flotation costs

amount to

$50

per bond.



What is the pre-tax and after-tax cost

of debt for Prescott Corporation?

EXAMPLE: Cost of Debt

Kevin Campbell, University of Stirling, November 2005

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

Pre-tax cost of debt:

950 = 100(PVIFA 20, K

d

) +

1000(PVIF 20, K

d

)

using a financial calculator:
K

d

= 10.61%



After-tax cost of debt:

K

d

= K

d

(1 - T)

K

d

= .1061 (1 - .34)

K

d

= .07 = 7%

EXAMPLE: Cost of Debt

So a 10% bond
costs the firm
only 7%
(with flotation costs)
because interest
is tax deductible

Kevin Campbell, University of Stirling, November 2005

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Cost of New Preferred Stock



Preferred stock:

•

has a fixed dividend (similar to debt)

•

has no maturity date

•

dividends are not tax deductible and are

expected to be perpetual or infinite



Cost of preferred stock = dividend

price -

flotation cost

Kevin Campbell, University of Stirling, November 2005

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Cost of Preferred stock:
Example

Baker Corporation has preferred stock that sells for $100 per share and pays an annual

dividend of $10.50. If the flotation costs are $4 per share, what is the cost of new

preferred stock?

10.94%

.1094

4

-

$100

$10.50

K

P







Kevin Campbell, University of Stirling, November 2005

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Cost of Equity:
Retained Earnings



Why is there a cost for retained
earnings?



Earnings can be reinvested or paid out
as dividends



Investors could buy other securities,
and earn a return.



Thus, there is an opportunity cost if
earnings are retained

Kevin Campbell, University of Stirling, November 2005

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Cost of Equity:
Retained Earnings



Common stock equity is available through
retained earnings (R/E) or by issuing new
common stock:

•

Common equity = R/E + New common

stock

Kevin Campbell, University of Stirling, November 2005

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Cost of Equity:
New Common Stock



The cost of new common stock is
higher than the cost of retained
earnings because of flotation costs

•

selling and distribution costs

(such as sales commissions) for
the new securities

Kevin Campbell, University of Stirling, November 2005

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Cost of Equity



There are a number of methods
used to determine the cost of
equity



We will focus on two



Dividend growth Model



CAPM

Kevin Campbell, University of Stirling, November 2005

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The Dividend Growth Model
Approach



Estimating the cost of equity: the dividend growth
model approach
According to the constant growth (Gordon) model,

D

1

P

0

=

R

E

- g

Rearranging D

1

R

E

= + g

P

0

Kevin Campbell, University of Stirling, November 2005

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Example: Estimating the Dividend
Growth Rate

Percentage

Year Dividend Dollar Change Change

1990 $4.00-

-

1991

4.40$0.40 10.00%

1992

4.750.35

7.95

1993

5.250.50

10.53

1994

5.650.40

7.62

Average Growth Rate

(10.00 + 7.95 + 10.53 + 7.62)/4 = 9.025%

Kevin Campbell, University of Stirling, November 2005

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Dividend Growth Model

This model has drawbacks:



Some firms concentrate on growth and do

not pay dividends at all, or only irregularly



Growth rates may also be hard to estimate



Also this model doesn’t adjust for market

risk



Therefore many financial managers prefer

the capital asset pricing model (CAPM) - or

security market line (SML) - approach for

estimating the cost of equity

Kevin Campbell, University of Stirling, November 2005

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Capital Asset Pricing Model
(CAPM)

)

(

f

m

f

R

R

β

R

kj







Cost of

capital Risk-free

return

Average rate of return

on common stocks

(WIG)

Co-variance

of returns against

the portfolio

(departure from the average)

B < 1, security is safer than WIG average

B > 1, security is riskier than WIG average

Kevin Campbell, University of Stirling, November 2005

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The Security Market Line (SML)

Required rate

of return

Percent

0.5

1.0

1.5

2.0

SML = R

f

+  (K

m

– R

f

)

Beta
(risk)

Market risk premium

20.

0

18.

0

16.

0

14.

0

12.

0

10.

0

8.0

5.5

R

f

Kevin Campbell, University of Stirling, November 2005

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Finding the Required Return on Common
Stock using the Capital Asset Pricing
Model

The Capital Asset Pricing Model (CAPM) can be used to estimate the

required return on individual stocks. The formula:





R

K

R

K

f

m

j

f

j









where

j

K

= Required return on stock j

f

R

=

Risk-

free rate of return (usually current rate on Treasury Bill).

j



= Beta coefficient for stock j

represents risk of the stock

m

K =

Return in market as measured by some proxy portfolio (index)

Suppose that Ba

ker has the following values:

f

R

=

5.5%

j



=

1.0

m

K =

12%

.

Kevin Campbell, University of Stirling, November 2005

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Finding the Required Return on Common
Stock using the Capital Asset Pricing
Model

Then, using the CAPM we would get a required
return of





12%

5.5

-

12

1.0

5.5

K

j







.

Kevin Campbell, University of Stirling, November 2005

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CAPM/SML approach



Advantage: Evaluates risk, applicable
to firms that don’t pay dividends



Disadvantage: Need to estimate

•

Beta

•

the risk premium (usually based on past
data, not future projections)

•

use an appropriate risk free rate of interest

Kevin Campbell, University of Stirling, November 2005

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Estimation of Beta: Measuring

Market Risk



Market Portfolio - Portfolio of all assets
in the economy



In practice a broad stock market
index, such as the WIG, is used to
represent the market



Beta - sensitivity of a stock’s return to
the return on the market portfolio

Kevin Campbell, University of Stirling, November 2005

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Estimation of Beta



Theoretically, the calculation of beta is

straightforward:



Problems

1.

Betas may vary over time.

2.

The sample size may be inadequate.

3.

Betas are influenced by changing financial leverage and business risk.



Solutions

•

Problems 1 and 2 (above) can be moderated by more sophisticated

statistical techniques.

•

Problem 3 can be lessened by adjusting for changes in business and

financial risk.

•

Look at average beta estimates of comparable firms in the industry.

2

)

(

)

,

(

M

iM

M

M

i

σ

σ

R

Var

R

R

Cov

β





Kevin Campbell, University of Stirling, November 2005

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Stability of Beta



Most analysts argue that betas are
generally stable for firms remaining in
the same industry



That’s not to say that a firm’s beta can’t
change

•

Changes in product line

•

Changes in technology

•

Deregulation

•

Changes in financial leverage

Kevin Campbell, University of Stirling, November 2005

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What is the appropriate risk-
free rate?



Use the yield on a long-term bond if you are
analyzing cash flows from a long-term investment



For short-term investments, it is entirely
appropriate to use the yield on short-term
government securities



Use the nominal risk-free rate if you discount
nominal cash flows and real risk-free rate if you
discount real cash flows

Kevin Campbell, University of Stirling, November 2005

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Survey evidence: What do you
use for the risk-free rate?

Corporations

Financial Advisors

90-day T-bill (4%)

90-day T-bill (10%)

3-7 year Treasuries (7%)

5-10 year Treasuries (10%)

10-year Treasuries (33%)

10-30 year Treasuries (30%)

20-year Treasuries (4%)

30-year Treasuries (40%)

10-30 year Treasuries (33%)

N/A (10%)

10-years or 90-day; depends

(4%)

N/A (15%)

Source: Bruner et. al. (1998)

Kevin Campbell, University of Stirling, November 2005

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Weighted Average Cost of Capital
(WACC)



WACC weights the cost of equity and the
cost of debt by the percentage of each
used in a firm’s capital structure



WACC=(E/ V) x R

E

+ (D/ V) x R

D

x (1-T

C

)

•

(E/V)= Equity % of total value

•

(D/V)=Debt % of total value

•

(1-Tc)=After-tax % or reciprocal of corp tax rate
Tc. The after-tax rate must be considered
because interest on corporate debt is deductible

Kevin Campbell, University of Stirling, November 2005

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WACC Illustration

ABC Corp has 1.4 million shares common valued at
$20 per share =$28 million. Debt has face value of
$5 million and trades at 93% of face ($4.65 million)
in the market. Total market value of both equity +
debt thus =$32.65 million. Equity % = .8576 and
Debt % = .1424

Risk free rate is 4%, risk premium=7% and ABC’s
β=.74

Return on equity per SML : R

E

= 4% + (7% x .

74)=9.18%

Tax rate is 40%

Current yield on market debt is 11%

Kevin Campbell, University of Stirling, November 2005

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WACC Illustration

WACC = (E/V) x R

E

+ (D/V) x R

D

x (1-Tc)

= .8576 x .0918 + (.1424 x .11 x .60)

= .088126 or 8.81%

Kevin Campbell, University of Stirling, November 2005

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Final notes on WACC



WACC should be based on market rates and

valuation, not on book values of debt or

equity



Book values may not reflect the current

marketplace



WACC will reflect what a firm needs to earn

on a new investment. But the new

investment should also reflect a risk level

similar to the firm’s Beta used to calculate

the firm’s R

E

.

•

In the case of ABC Co., the relatively low WACC of

8.81% reflects ABC’s β=.74. A riskier investment

should reflect a higher interest rate.

Kevin Campbell, University of Stirling, November 2005

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Final notes on WACC



The WACC is not constant



It changes in accordance with the
risk of the company and with the
floatation costs of new capital

Kevin Campbell, University of Stirling, November 2005

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Marginal cost of capital and
investment projects

16.0

14.0

12.0

10.0

8.0

6.0

4.0

2.0

0.0

Percen
t

10 15
19

50

39

Amount of capital ($
millions)

11.23
%

70
85

95

Margin
al cost
of
capital

K

mc

A

B

C

D

E

F

G

H

10.77
%

10.41
%

-
-
-

-

-

-
-
-
-

Kevin Campbell, University of Stirling, November 2005

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The End ….



KAPITAŁ - bogactwo zebrane uprzednio w celu podjęcia dalszej produkcji



(F. Quesnay, XVIII)



wszelki wynik procesu produkcyjnego, który przeznaczony jest do

późniejszego wykorzystania w procesie produkcyjnym (MCKenzzie,

Nardelli,1991)



całokształt zaangażowanych w przedsiębiorstwie wewnętrznych i

zewnętrznych, własnych i obcych, terminowych i nieterminowych

zasobów (bilans)



STRUKTURA KAPITAŁU



proporcja udziału kapitału własnego i obcego w finansowaniu działalności

przedsiębiorstwa



relacja wartości zadłużenia długoterminowego do kapitałów własnych

przedsiębiorstwa



struktura finansowania – struktura kapitału = zobowiązania

bieżące



ramy statycznego kompromisu, w którym przedsiębiorstwo ustala

docelową wielkość wskaźnika zadłużenia i stopniowo zbliża się do jego

osiągnięcia.