Cost of Capital

Chapter

McGraw-Hill/IrwinCopyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.

Cost of Capital11

1-2

Chapter 11 - Outline

• Cost of Capital• Cost of Debt• Cost of Preferred Stock• Cost of Common Equity:

– Common Stock– Retained Earnings

• Optimum Capital Structure• Marginal Cost of Capital• The Security of Market Line• Summary and Conclusions

PPT 11-2

1-3

Cost of Capital

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

• The cost of capital is normally the relevant discount rate to use in analyzing an investment– It represents the minimal acceptable return from the investment– If your cost of funds is 10%, you must earn at least 10% on your investments

to break even!

• The cost of capital is a weighted average of the various sources of funds in the form of debt and equity

WACC = Weighted Average Cost of Capital

PPT 11-3

1-4

Steps in measuring a firm’s cost of capital

1. Compute the cost of each source of capital.

2. Assign weights to each source. Conversion of historical

cost of capital structure to market values may be required.

3. Compute the weighted average of the component costs.

1-5

Cost of Capital – Baker Corporation

1-6

Cost of Debt

• Measured by interest rate, or yield, paid to bondholders– Example: $1,000 bond paying $100 annual

interest – 10% yield– Calculation is complex discount rate or premium

from par value bonds

• To determine the cost of a new debt in the marketplace:– The firm will compute the yield on its currently

outstanding debt

1-7

Approximate Yield to Maturity (Y')

Annual interest payment + Number of years to maturity 0.6 (Price of the bond) + 0.4 (Principal payment)• Assuming:

Y' = $101. 50 +

20 .6 ($940) + .4 ($1,000) = $101.50 + 20 $564 + $400 Y’ = $101.50 + 3 = $104.50 = 10.84% $964 $964

Principal payment – Price of the bond

$1,000 - $940

60

1-8

Tax and flotation cost consideration

• Market-determined yields on various

financial instruments will equal the cost of

those instruments to the firm with adjustment

tax and flotation cost consideration

1-9

Adjusting Yield for Tax Considerations

• Yield to maturity indicates how much the firm has to pay on a before-tax basis

• Interest payment on a debt is a tax-deductible expense– Due to this, the true cost is less than the stated

cost

1-10

Adjusting Yield for Tax Considerations (cont’d)

• The after-tax cost of debt is calculated as shown below:

• Assuming:

1-11

Yield of 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

Yield of preferred stock = annual dividend

price of stock

Yield of new preferred stock = annual dividend price-flotation costs

Flotation costs: selling and distribution costs (such as sales commissions) for the new securities

PPT 11-6

1-12

Cost of Preferred Stock (cont’d)

• The cost of preferred stock is as follows:

• Where, = Cost of preferred stock; = Annual dividend on

preferred stock; = Price of preferred stock; F = Floatation, or selling cost

• Assuming annual dividend as $10.50, preferred stock is $100, and flotation, or selling cost is $4. Effective cost is:

= $10.50 = $10.50 = 10.94% $100 - $4 $96

1-13

Cost of Common Equity – Valuation Approach

• In determining the cost of common stock, the firm must be sensitive to pricing and performance demands of current and future stockholders

• Dividend valuation model:

• Where,

= Price of the stock today; = Dividend at the end of the year (or period); = Required rate of return; g = Constant growth rate in dividends

• Assuming = $2; = $40 and g = 7%, equals 12 percent

= $2 + 7% = 5% + 7% = 12%

$40

1-14

Alternate Calculation of the Required Return on Common Stock

• Capital asset pricing model (CAPM)

• Where:

= Required return on common stock; = Risk-free rate of return, usually the current rate on Treasury bill securities; = Beta coefficient (measures the historical volatility of an individual stock’s return relative to a stock market index; = return in the market as measured by an approximate index

• Assuming = 5.5%, = 12%, = 1.0, would be:

= 5.5% + 1.0 (12% - 5.5%) = 5.5% + 1.0 (6.5%)

= 5.5% + 6.5% = 12%

1-15

Cost of Retained Earnings

• Sources of capital for common stock equity: – Purchaser of the new shares – external source– Retained earnings – internal source

• Represent the present and past earnings of the firm minus previously distributed dividends

• Belong to the current stockholders – may be paid in the form of dividends or reinvested in the firm

• Reinvestments represent a source of equity capital supplied by the current stockholders

• An opportunity cost is involved

1-16

Cost of Retained Earnings (cont’d)

• The cost of retained earnings is equivalent to the rate of return on the firm’s common cost representing the opportunity cost

• represents both the required rate of return on common stock, and the cost of equity in the form of retained earnings

• For ease of reference,

= Cost of common equity in the form of retained earnings

= Dividend at the end of the first year, $2

= Price of stock today, $40

g = Constant growth rate in dividends, 7%

= $2 + 7% = 5% + 7% = 12%

$40

1-17

Cost of New Common Stock

• A slightly higher return than , representing the required rate of return of present stockholders, is expected– Needed to cover the distribution costs of the

new securities

Common stock

New common stock

1-18

Cost of New Common Stock (cont’d)

• Assuming = $2, = $40, F (Flotation or selling costs) = $4 and g = 7%;

= $2 + 7%

$40 - $4

= $2 + 7%

$36

= 5.6% + 7% = 12.6%

1-19

Overview of Common Stock Costs

1-20

Optimum Capital Structure

The optimum (best) situation is associated with the minimum overall cost of capital:– Optimum capital structure means the lowest

WACC– Usually occurs with 40-70% debt in a firm’s

capital structure– WACC is also referred to as the required rate of

return or the discount rate– Based upon the market value rather than the

book value of the firm’s debt and equity

PPT 11-8

1-21

Optimal Capital Structure – Weighting Costs (cont’d)

• Assessment of different plans (next slide):– Firm is able to initially reduce weighted average

cost of capital with debt financing– Beyond Plan B, continued use of debt becomes

unattractive and greatly increases costs of sources of financing

1-22

Optimal Capital Structure – Weighting Costs (cont’d)

Cost (After-tax) Weights Weighted CostFinancial Plan A:Debt………………………… 6.5% 20% 1.3%Equity………………………. 12.0 80 9.6 10.9%Financial Plan B:Debt………………………… 7.0% 40% 2.8%Equity………………………. 12.5 60 7.5

10.3%Financial Plan C:Debt………………………… 9.0% 60% 5.4%Equity………………………. 15.0 40 6.0 11.4%

1-23

Cost of Capital Curve

1-24

Debt as a Percentage of Total Assets (2006)

1-25

Capital acquisition and investment decision making

• The discount rate used in evaluating capital projects should be the weighted average cost of capital.

• If the cost of capital is earned on all projects, the residual claimants of the earnings stream, the owners, will receive their required rate of return. If the overall return of the firm is less than the cost of capital, the owners will receive less than their desired rate of return because providers of debt capital must be paid.

• For most firms, the cost of capital is fairly constant within a reasonable range of debt-equity mixes. Changes in money and capital market conditions (supply and demand for money), however, cause the cost of capital for all firms to vary upward and downward over time.

1-26

Cost of capital over time

Cost of capital (Ka)

x y

Debt-equity mix (percent)

Kat

Kat + 1

Kat + 2

1-27

Investment Projects Available to the Baker Corporation

1-28

Cost of capital and investment projects for the Baker Corporation

16.0

14.0

12.0

10.0

8.0

6.0

4.0

2.0

0.0

Percent

10 15 19 5039Amount of capital ($ millions)

10.41%

70 85 95

Weighted average cost of capital

Ka

A

BC

D

EF

GH

-----

----

1-29

The Marginal Cost of Capital

• The market may demand a higher cost of capital for each amount of fund required if a large amount of financing is required– Equity (ownership) capital is represented by

retained earnings• Retained earnings cannot grow indefinitely as the

firm’s capital needs to expand• Retained earnings is limited to the amount of past and

present earnings that can be redeployed into investments

1-30

The Marginal Cost of Capital (cont’d)

• Assumptions:– 60% is the amount of equity capital a firm must maintain to keep a

balance between fixed income securities and ownership interest– Baker Corporation has $23.40 million of retained earning available

for investment• There is adequate retained earning to support the capital structure as

shown below:

• Assuming: X = Retained earnings ; Percent of retained earnings in the capital structure

• Where X represents the size of the capital structure that retained earnings will support

X = $23.40 million = $39 million .60

1-31

Costs of Capital for Different Amounts of Financing

1-32

Increasing Marginal Cost of Capital

• Both and represent the cost of capital– The mc subscript after K indicates the increase

in cost of capital

• Increase is because common equity is now in the form of new common stock rather than retained earnings

• The aftertax cost of the new common stock is more expensive than retained earnings because of flotation costs

1-33

Increasing Marginal Cost of Capital (cont’d)

• Equation for the cost of new common stock:

= $2 + 7% = $2 + 7% = 5.6% + 7% = 12.6%

$40 - $4 $36

• The $50 million figure can be derived thus:

Z = Amount of lower-cost debt ; Percent of debt in the capital structure

Z = $15 million = $50 million .30• Where Z represents the size of the capital structure in which lower-cost

debt can be used

1-34

Cost of Capital for Increasing Amounts of Financing

1-35

Changes in the Marginal Costs of Capital

1-36

PPT 11-16Marginal cost of capital and Baker Corporation investment alternatives

16.0

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%

-----

----

1-37

Cost of Components in the Capital Structure

1-38

Basic form of the CAPM

The basic form of the CAPM is a linear relationship between returns on individual stocks and the market over time. Using least squares regression analysis, the return

Kj = α + βRm + e

Where:

Kj = return on individual common stock of company

α = Alpha, the intercept on the y-axis β = Beta, the coefficient Rm = Return on the stock market

e = Error term of the regression equation

1-39

Rate of Return on Stock

Year PAI Market

1 . . . . . . . . . . . . 12.0% 10.0%

2 . . . . . . . . . . . . 16.0 18.0

3 . . . . . . . . . . . . 20.0 16.0

4 . . . . . . . . . . . . 16.0 10.0

5 . . . . . . . . . . . . 6.0 8.0

Mean return 14.0% 12.4%

Standard deviation 4.73% 3.87%

PPT 11-18Table 11A-1

Performance of PAI and the market

1-40

Percent

21.0

15.0

9.0

3.0

Return on PAI common stock Kj

3.0 9.0 15.0 21.0Rm

Kj = j Rm + ej

= 2.8 + .9 (Rm ) + ej

Return on the market Rm

(x)

2.8

.9

Beta = j = Slope of the line(5)

(1)

(4)

(3)

(2)

(y)

Linear regression of returns between PAI and the market

1-41

Year Kj Rm

1. . . . . 12% 10%2. . . . . 16% 18%3. . . . . 20% 16%4. . . . . 16% 10%5. . . . . 6% 8%

70% 62%

Kj Rm Kj Rm Rm2 ( Rm )

2

936 4,340 844 3,844

n Kj Rm – Kj Rm 5(936) - 4,340j n Rm

2 – ( Rm )2 5(844) - 3,844

Kj – Rm 70 - 0.9 (62)n 5

PPT 11-20Linear regression of returns between PAI and the market

1-42

Linear regression of returns between PAI and the market

Calculator

Mode: Stat

Input 10 (x,y) 12 Data

18 (x,y) 16 Data

16 (x,y) 20 Data

10 (x,y) 16 Data

8 (x,y) 6 Data

2ndF a gives 2.79

2ndF b gives .90

2ndF r gives .74

Note that the values for the x axis(Rm) are input first

This is the alpha coefficient

This is the beta coefficient

This is the correlation coefficient, a measure of how well the formula describes the relationship. The closer to 1.00, the better the fit

PPT 11-21

1-43

Improved CAPM (risk premium model)

Investors expect higher returns if higher risks are taken Kj = Rf + β(Rm-Rf)

Where:

Kj= Required return on Common Stock

Rf = Risk-free rate of return

β= Beta coefficient. The beta measures the historical volatility of an individual stock's return relative to a stock market index. A beta greater than 1 indicates greater volatility (price movements) than the market, while the reverse would be true for a beta less than 1.

Rm-Rf _= Premium or excess return of the market versus the risk-free rate.

β(Rm-Rf) = Expect return above the risk-free rate for the stock of company j, given the level of risk.

1-44

The security market line (SML)

K.5

Required rates of return Percent

0.5 1.0 1.5 2.0

SML = Rf + (Rm – Rf)

Beta (risk)

6.5 % market risk premium

20.0

18.0

16.0

14.0

12.0

10.0

8.0

5.5

K2

K1

Rf

1-45

Required rates of return (percent)

0.5 1.0 1.5 2.0

20.0

18.0

16.0

14.0

12.0

10.0

7.5

5.5

Rf1

Rf0

SML1

Beta (risk)

Rf increased 2%

SML0

The security market line and changing interest rates

1-46

0.5 1.0 1.5 2.0

Rf

Required rates of return (percent) SML1

Beta (risk)

More risk aversion22.0

20.0

18.0

16.0

14.0

12.0

10.0

8.0

5.5

SML0

PPT 11-24The security market line and changing

investor expectations

1-47

Net income (NI) approach

Cost of capital (percent)

Debt/value ratio (percent)

Value of the firm ($)


Ke = Cost of Equity: Kd = Cost of debt; Ka = Cost of capitalValue is the market value of the firm

0 100 0 100

Kd

Ke

Ka

1-48

Net operating income (NOI) approach

Cost of capital (percent) Value of the firm ($)

Debt/value ratio (percent) Debt/value ratio (percent) 0 0 100 100

Ke

Ka

Kd

1-49

Traditional approach as described by Durand

Cost of capital (percent)


Value of the firm ($)


Ke

Ka

Kd

0 100 0 100

1-50

Modigliani and Miller with corporate taxes

Cost of capital (percent) Value of the firm ($)

Debt/value ratio (percent) Debt/value ratio (percent)0 100 0 100

Cost of debtadjusted for the tax effect of interest

Ke

Ka

Kd

VL

VU

1-51

Combined impact of the corporate tax effect and bankruptcy effect on valuation and cost of capital

A. Cost of capital (percent)

0Debt/value ratio (percent)

100

Ka (M +M with tax effect and bankruptcy effect)

Ka (original M + M)

Ka (M + M with tax effect)

1-52

Combined impact of the corporate tax effect and bankruptcy effect on valuation and cost of capital

B. Value of the firm ($)

0


100

VL (M + M with tax effect)

VU (original M +M)

(M + M with tax effect and bankruptcy effect)

Documents

Cost of Capital