Transcript THE COST OF CAPITAL - Uniwersytet Gdański

KOSZT I
STRUKTURA
KAPITAŁU
2008
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

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
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
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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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Example: Tax effects of
financing with debt
EBIT
- interest expense
EBT
- taxes (34%)
EAT

with stock
400,000
0
400,000
(136,000)
264,000
with debt
400,000
(50,000)
350,000
(119,000)
231,000
Now, suppose the firm pays $50,000 in dividends
to the shareholders
Kevin Campbell, University of Stirling, November 2005
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Example: Tax effects of
financing with debt
with stock
EBIT
400,000
- interest expense
0
EBT
400,000
- taxes (34%)
(136,000)
EAT
264,000
- dividends
(50,000)
Retained earnings
214,000
Kevin Campbell, University of Stirling, November 2005
with debt
400,000
(50,000)
350,000
(119,000)
231,000
0
231,000
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Cost of Debt
After-tax cost
of Debt
33,000
=
Before-tax cost
of Debt
-
=
50,000
-
=
50,000 ( 1 - .34)
Tax
Savings
17,000
OR
33,000
Or, if we want to look at percentage costs:
Kevin Campbell, University of Stirling, November 2005
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Cost of Debt
After-tax
% cost of
=
Debt
Before-tax
% cost of
Debt
x
1
Marginal
- tax
rate
Kd
=
kd (1 - T)
.066
=
.10 (1 - .34)
Kevin Campbell, University of Stirling, November 2005
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EXAMPLE: Cost of Debt

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?
Kevin Campbell, University of Stirling, November 2005
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EXAMPLE: Cost of Debt

Pre-tax cost of debt:
950 = 100(PVIFA 20, Kd) + 1000(PVIF 20, Kd)
using a financial calculator:
So a 10% bond
Kd = 10.61%

After-tax cost of debt:
Kd
Kd
Kd
=
=
=
Kd (1 - T)
.1061 (1 - .34)
.07 = 7%
Kevin Campbell, University of Stirling, November 2005
costs the firm
only 7%
(with flotation costs)
because interest
is tax deductible
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Cost of New Preferred
Stock

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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?
KP 
$10.50
 .1094 10.94%
$100- 4
Kevin Campbell, University of Stirling, November 2005
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Cost of Equity:
Retained Earnings
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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

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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,
D1
P0 =
RE - g
Rearranging
D1
RE =
+g
P0
Kevin Campbell, University of Stirling, November 2005
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Example: Estimating the
Dividend Growth Rate
Dollar Change
Percentage
Change
Year
Dividend
1990
$4.00
1991
4.40
$0.40
10.00%
1992
4.75
0.35
7.95
1993
5.25
0.50
10.53
1994
5.65
0.40
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:

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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)
kj  Rf  β ( Rm  Rf )
Cost of
capital
Risk-free
return
Co-variance
of returns against
the portfolio
(departure from the average)
Average rate of return
on common stocks
(WIG)
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
20.0
SML = Rf +  (Km – Rf)
18.0
16.0
14.0
12.0
Market risk premium
10.0
Rf
8.0
5.5
0.5
1.0
1.5
Kevin Campbell, University of Stirling, November 2005
2.0
Beta (risk)
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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:
K j  R f   j (K m  R f )
where
Kj
=
Required return on stock j
Rf
j
=
=
Risk-free rate of return (usually current rate on Treasury Bill).
Beta coefficient for stock j represents risk of the stock
Km
=
Return in market as measured by some proxy portfolio (index)
Suppose that Baker has the following values:
=
5.5%
Rf
j
=
1.0
Km
=
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
K j  5.5  1.0 (12 - 5.5) 12%
.
Kevin Campbell, University of Stirling, November 2005
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CAPM/SML approach
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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

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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

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Theoretically, the calculation of beta is
straightforward:
Cov( Ri , RM ) σ iM
β
 2
Problems
Var ( RM )
σM
1. Betas may vary over time.
2. The sample size may be inadequate.
3. Betas are influenced by changing financial leverage and business risk.
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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.
Kevin Campbell, University of Stirling, November 2005
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Stability of Beta

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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?
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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 RE + (D/ V) x RD x (1-TC)
•
•
•
(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 =$32.65 million. Equity % = .8576
and Debt % = .1424
Risk free rate is 4%, risk premium=7% and ABC’s β=.74
Return on equity per SML : RE = 4% + (7% x .74)=9.18%
Tax rate is 40%
Current yield on market debt is 11%
Kevin Campbell, University of Stirling, November 2005
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WACC Illustration
WACC = (E/V) x RE + (D/V) x RD x (1-Tc)
= .8576 x .0918 + (.1424 x .11 x .60)
= .088126 or 8.81%
Kevin Campbell, University of Stirling, November 2005
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Final notes on WACC
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WACC should be based on market rates and
valuation, not on book values of debt or equity
Book values may not reflect the current
marketplace
WACC will reflect what a firm needs to earn on
a new investment. But the new investment
should also reflect a risk level similar to the
firm’s Beta used to calculate the firm’s RE.
•
In the case of ABC Co., the relatively low WACC of
8.81% reflects ABC’s β=.74. A riskier investment
should reflect a higher interest rate.
Kevin Campbell, University of Stirling, November 2005
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Final notes on WACC


The WACC is not constant
It changes in accordance with the risk of
the company and with the floatation
costs of new capital
Kevin Campbell, University of Stirling, November 2005
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Marginal cost of capital and
investment projects
Percent
16.0
14.0
12.0
10.0
8.0
-
A
B
10.77%
C
11.23%
Kmc Marginal
cost of
capital
10.41%
D
E
F
4.0 2.0 0.0 -
G
H
6.0
10 15 19
39
50
70
Amount of capital ($ millions)
Kevin Campbell, University of Stirling, November 2005
85
95
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The End ….
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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.
Kevin Campbell, University of Stirling, November 2005
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