Chap 4.pdf beta

Cost of Capital and Leverage.WACC

Chapter 4

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Outline

�Project selection for a levered firm

�Beta and cost of equity of a levered firm

� Hamada equation

�WACC

�Project selection in a diversified firm

� Mensac case

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What types of capital do firms use?

�Debt

�Preferred stock

�Common equity

� Existing shareholders

� New stock

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Do different investors ask for the same return?

� Example: A company has the following EBIT every year (see the table next page). kRF=4%, the market risk premium is 6%. If the company is all-equity financed, its beta is 1

• What is the cost of equity in this case? What is the company value? If there are 1,000 shares outstanding, what is the share price?

• If company wants to issue � 40,000 of debt to buy back some shares, what is the cost of debt and the new cost of equity assuming no taxes?

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EconomyBad Avg. Good

Prob. 0.25 0.50 0.25EBIT �5,000 �10,000 �15,000

Example (2)

� Cost of equity is • 4%+6%x1=10%

� The company value is• (0.25x5,000 + 0.5x10,000 + 0.25x15,000)/.1 =100,000 �

� The share price is 100 �

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Example (3)

Probability 0.25 0.5 0.25EBIT 5,000.00$ 10,000.00$ 15,000.00$ Interest -$ -$ -$ EBT 5,000.00$ 10,000.00$ 15,000.00$ Taxes -$ -$ -$ NI 5,000.00$ 10,000.00$ 15,000.00$ EPS 5.00$ 10.00$ 15.00$ Average NI 10,000$ Average EPS 10$ Standard deviation 3.54

Value of equity 100,000$ Share price 100.00$

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Debt 40,000$ Interest rate 4%Number of shares 600 Probability 0.25 0.5 0.25EBIT 5,000.00$ 10,000.00$ 15,000.00$ Interest 1,600.00$ 1,600.00$ 1,600.00$ EBT 3,400.00$ 8,400.00$ 13,400.00$ Taxes -$ -$ -$ NI 3,400.00$ 8,400.00$ 13,400.00$ EPS 5.67$ 14.00$ 22.33$ Average NI 8,400$ Average EPS 14.00$ Standard deviation 5.89

Example (4)

� For the levered firm let us assume that the debt is risk-free and check, whether this is the case or not:

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Example (5)

�The cost of equity of the levered firm becomes

cost of equity kLS = EPS/Share price = 14/100

= 14%

�Why?

� Return to shareholders is riskier now (look at EPS volatility)

� It should be higher

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Beta and cost of equity of a levered firm:Hamada equation (risk-free debt)

� Because the increased use of debt causes both the costs of debt and equity to increase, we need to estimate the new cost of equity

� The Hamada equation attempts to quantify the increased cost of equity due to financial leverage

� It uses the unlevered beta of a firm, which represents the risk of a firm as if it had no debt

� Hamada equation assumes that the debt is risk-free

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βL = βU [1 + (1 – T)(D/E)]

where T is the tax rate; D/E is the debt-equity ratio and βU is the beta of equity of an unlevered firm with the same operating cash flow

In our example βU = 1, D/E = 400/600 = 2/3

βL = 1(1+0.67)=1.67

kLS = 4% + 1.67 x 6% = 14 %

Notice that

Hamada equation (cont’d)

kLS = kU

S [1 + (1 – T)(D/E)]-kRF (1 – T)(D/E)

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Beta and cost of equity of a levered firm:risky debt

� If debt is risky, the cost of equity of a levered firm is found using the following equation:

where kD is the cost of risky debt. Similarly, for beta we can write

( ) ( )DUS

US

LS kk

ED

Tkk −−+= 1

( ) ( ) DUS

LS E

DT

ED

T β−−��

��

� −+β=β 111

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Example

� The risk-free rate is 6%, as is the market risk premium. The unlevered beta of the firm is 1.0. The total assets are �2,000,000

• Find the cost of equity of a levered firm if it has 250,000 of a risk-free debt

• The same if the beta of debt is 0.2

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ββββL = ββββU[1 + (1 – T)(D/E)]

kL = kRF + (kM – kRF)ββββL

Example (2)

�For riskless debt we have

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ββββL = 1.0[1 + (1 – 0.4)(�250/�1,750)]


kL = 6.0% + (6.0%)1.0857

Example (3)


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kL = 6.0% + (6.0%)1.0857 = 12.51%

ββββL = 1.0[1 + (0.6)(0.1429)]= 1.0857

Example (4)


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ββββL = ββββU[1 + (1 – T)(D/E)]-(1 – T)(D/E)ββββD

kL = kU + (1 – T)(D/E)(kU - kD)

kL = 12% + (0.6)(0.1429)(4.8%) = 12.411%

kD = kRF + (kM – kRF)ββββD=6%+(6%)0.2 =7.2%

ββββL = 1.0[1 + (0.6)(0.1429)]- (0.6)(0.1429)0.2 = 1.0857-0.0171 = 1.0686

Example (5)

�For risky debt we have

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How to determine the cost of equity for a new company?

� Identify the peer companies

� For each peer, find its unlevered β and cost of equity using their cost of debt and D/E ratio

• Try using market values of debt and equity

� Find the average unlevered β and kSU

� Find β and kSL for your company, using its

cost of debt and D/E ratio

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ED

t

kED

tkk

c

DcLS

US

)1(1

)1(

−+

−+=

( ) ( )DUSC

US

LS kk

ED

tkk −−+= 1

Determining levered cost of equity, kLs

�Find kU directly

�Find average kUs

�Find kLs

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( )

( ) ��

��

� −+==

−+=

VD

tVE

kWACCkk

ktVD

kVE

WACC

cUSfD

DcLS

1 , if

1

WACC

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Example: Find WACC, given these inputs:

Target D/E ratio = 66.7 %

kD = 10%

kRF = 7%

Tax rate = 40%

Market risk premium = 6%

Industry Beta = 0.95

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( )

( )

%4.11

10.67.1

67.4.115.

67.11

%1515.006.33.107.

33.132

4.01195.0

=

×+

×−+×+

=

==×+=

=��

��

� −+×=β

WACC

WACC

kLS

L

Example: Find WACC

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Company WACCIntel 12.9%General Electric 11.9Motorola 11.3Coca-Cola 11.2Walt Disney 10.0 AT&T 9.8Wal-Mart 9.8Exxon 8.8H. J. Heinz 8.5BellSouth 8.2

WACC Estimates for Some Large U. S. Corporations, Nov. 1999

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Should the company use the composite (company average) WACC as the hurdle

rate for each of its projects?

�NO! The composite WACC reflects the risk of an average project undertaken by the firm. Therefore, the WACC only represents the “hurdle rate” for a typical project with average risk.

�Different projects have different risks. The project’s WACC should be adjusted to reflect the project’s risk.

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Rate of Return(%)

WACC

Rejection Region

Acceptance Region

Risk

L

B

A

H12.0

8.0

10.010.5

9.5

0 RiskL RiskA RiskH

Risk and the Cost of Capital

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Rate of Return(%)

WACC

Project H

Division H’s WACC

Risk

Project L

Composite WACCfor Firm A

13.0

7.0

10.0

11.0

9.0

Division L’s WACC

0 RiskLRiskAverage

Risk H

Divisional Cost of Capital

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What are the types of project risk?

�Stand-alone risk

�Corporate risk

�Market risk

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How is each type of risk used?

�Market risk is theoretically best in most situations.

�However, creditors, customers, suppliers, and employees are more affected by corporate risk

�Therefore, corporate risk is also relevant

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How to determine the risk-adjusted cost of capital for a particular project or division?

�By making subjective adjustments to the firm’s composite WACC

� Not very scientific!

�By attempting to estimate what the cost of capital would be if the project/division were a stand-alone firm with the same capital structure. This requires estimating the project’s beta

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Methods for Estimating a Project’s Beta

�Pure play:

� Find several publicly traded companies exclusively in project’s business

� Use average of their betas as proxy for project’s beta

�Difficulties: Sometimes it is hard to find such companies

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Methods for Estimating a Project’s Beta

� Using Accounting beta (won’t use in the class)

• Estimate the project’s beta by running regression between project’s ROA and market ROA (S&P index)

� Problems: • Accounting betas are not perfectly

correlated with market betas (correlation is about 0.5–0.6)

• Normally can’t get data on new projects’ ROAs before the capital budgeting decision has been made

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Example

�Find the division’s market risk and cost of capital based on the CAPM, given these inputs

� Target debt/value ratio = 40% (D/E = 66.7%)

� kD = 10%

� kRF = 7%

� Tax rate = 40%

� betaDivision = 1.7

� Market risk premium = 6%.

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Example (contd.)

�Levered beta = 1.7, so division has more market risk than the company on average (1.33).

�Division’s required return on equity:

� ks = kRF + (kM – kRF)βDiv.

= 7% + (6%)1.7 = 17.2%

� WACCDiv. = wdkd(1 – T) + wcks

= 0.4(10%)(0.6) + 0.6(17.2%)

= 12.72%

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Mensac case

Chap 4.pdf beta

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