195.kc cost of capital lecture -kisk

Kevin Campbell, University of Stirling, November 2005 11

2008

KOSZT I STRUKTURA KAPITAŁU


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


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


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)


with stock with debtEBIT 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 debtfinancing with debt

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


with stock with debtEBIT 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) 0Retained earnings 214,000 231,000

Example: Tax effects of Example: Tax effects of financing with debtfinancing with debt


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


After-tax Before-tax Marginal % cost of % cost of x tax Debt Debt rate

Kd = kd (1 - T)

.066 = .10 (1 - .34)

-= 11

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?

EXAMPLE: Cost of Debt


Pre-tax cost of debt:950 = 100(PVIFA 20, Kd) + 1000(PVIF 20, Kd)

using a financial calculator: Kd = 10.61%After-tax cost of debt: Kd = Kd (1 - T) Kd = .1061 (1 - .34) Kd = .07 = 7%

EXAMPLE: Cost of Debt

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


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


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 KP


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


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


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


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


The Dividend Growth Model Approach

Estimating the cost of equity: the dividend growth model approachAccording to the constant growth (Gordon) model, D1 P0 = RE - g

Rearranging D1

RE = + g P0


Example: Estimating the Dividend Growth Rate

PercentageYear Dividend Dollar Change Change

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%


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


Capital Asset Pricing Model (CAPM)

)( fmf RRβRkj

Cost ofcapital Risk-free

return

Average rate of returnon common stocks

(WIG)

Co-varianceof returns against

the portfolio(departure from the average)

B < 1, security is safer than WIG averageB > 1, security is riskier than WIG average


The Security Market Line (SML)

Required rate of return Percent

0.5 1.0 1.5 2.0

SML = Rf + (Km – Rf)

Beta (risk)

Market risk premium

20.0

18.0

16.0

14.0

12.0

10.0

8.0

5.5Rf


Finding the Required Return on Common Stock using the Capital Asset Pricing ModelThe Capital Asset Pricing Model (CAPM) can be used to estimate the required return on individual stocks. The formula:

RK R K fmjfj where jK = Required return on stock j fR = Risk-free rate of return (usually current rate on Treasury Bill). j = Beta coefficient for stock j represents risk of the stock mK = Return in market as measured by some proxy portfolio (index) Suppose that Baker has the following values:

fR = 5.5% j = 1.0 mK = 12%

.


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

.


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


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


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

Mi

σσ

RVarRRCovβ


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


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


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

Corporations Financial Advisors90-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)


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


WACC IllustrationABC 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%


WACC IllustrationWACC = (E/V) x RE + (D/V) x RD x (1-Tc)

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

= .088126 or 8.81%


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 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.


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


Marginal cost of capital and investment projects16.0

14.0

12.0

10.0

8.0

6.0

4.0

2.0

0.0

Percent

10 15 19 5039Amount of capital ($ millions)

11.23%

70 85 95

Marginal cost of capital

Kmc

A

BC

D EF

GH

10.77%

10.41%

---------


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.

195.kc cost of capital lecture -kisk

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