fin3004 2011-2012s2 lecture04 cost of capital

8/2/2019 FIN3004 2011-2012s2 Lecture04 Cost of Capital

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Lecture 4

Cost of Capital



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Learning Outcome

Know how to determine a firm’scost of equity capital

Understand the impact of beta indetermining the firm’s cost of equity capital

Know how to determine the firm’s

overall cost of capital Understand the impact of flotation

costs on capital budgeting



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Lecture Outline

The Cost of Equity Capital

Estimating the Cost of Equity Capital with theCAPM

Estimation of Beta

Beta, Covariance and Correlation

Determinants of Beta

Dividend Discount Model

Cost of Capital for Divisions and Projects

Cost of Fixed Income Securities

The Weighted Average Cost of Capital

Estimating Eastman Chemical’s Cost of Capital

Flotation Costs and the Weighted Average Cost of Capital



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Where Do We Stand?

Earlier discussions on capitalbudgeting focused on the

appropriate size and timing of cash flows.

This lecture discusses the

appropriate discount rate whencash flows are risky.



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Invest in project


Firm with

excess cash

Shareholder’sTerminal

Value

Pay cash dividend

Shareholder

invests in

financial

asset

Because stockholders can reinvest the dividend in risky financial assets,

the expected return on a capital-budgeting project should be at least asgreat as the expected return on a financial asset of comparable risk.

A firm with excess cash can either pay adividend or make a capital investment



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From the firm’s perspective, theexpected return is the Cost of EquityCapital:

)( F M iF i R R β R R • To estimate a firm’s cost of equity capital, we need

to know three things:

1. The risk-free rate, RF

F M R R 2. The market risk premium,

2

,

)(

),(

M

M i

M

M ii

σ

σ

RVar

R RCov β 3. The company beta,



Example

Suppose Quantram has a beta of 1.3,and the firm is 100% equity financed.

Assume a risk-free rate of 5% and a

market risk premium of 8.4%.

What is the appropriate discount rate foran expansion of this firm?

)( F M iF R R β R R

%92.15

%,4.83.1%5

R

R



Example

Suppose the stock of StansfieldEnterprises, a publisher of PowerPointpresentations, has a beta of 2.5. The

firm is 100% equity financed. Assume a risk-free rate of 5% and a

market risk premium of 10%.

What is the appropriate discount rate for

an expansion of this firm?

)( F M iF R R β R R

%105.2%5 R

%30 R



Example

Suppose Stansfield Enterprises is evaluating

the following independent projects. Each costs$100 and lasts one year.

Project Project b Project’sEstimated Cash

Flows Next

Year

IRR NPV at30%

A 2.5 $150 50% $15.38

B 2.5 $130 30% $0

C 2.5 $110 10% -$15.38



Using the SML

An all-equity firm should accept projects whose

IRRs exceed the cost of equity capital and reject

projects whose IRRs fall short of the cost of capital.

P r o j e c t

I R R

Firm’s risk (beta)

SML

5%

Good

project

Bad project

30%

2.5

A

B

C

Reject Region



The Risk-free Rate

Treasury securities are close proxies forthe risk-free rate.

The CAPM is a period model. However,projects are long-lived. So, averageperiod (short-term) rates need to be used.

The historic premium of long-term (20-year) rates over short-term rates forgovernment securities is 2%.

So, the risk-free rate to be used in theCAPM could be estimated as 2% belowthe prevailing rate on 20-year treasurysecurities.



The Market Risk Premium

Method 1: Use historical data

Method 2: Use the Dividend

Discount Model:

Market data and analyst forecasts

can be used to implement the DDMapproach on a market-wide basis

gP D R

0

1



Estimation of Beta

Market Portfolio - Portfolio of allassets in the economy. In practice,

a broad stock market index, such asthe S&P 500 or the Hang SengIndex, is used to represent themarket.

Beta - Sensitivity of a stock’s returnto the return on the market

portfolio.



Estimation of Beta

)(

),(

M

M i

RVar

R RCov β

• 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 can be moderated by more sophisticated statisticaltechniques.

– Problem 3 can be lessened by adjusting for changes in business andfinancial risk.

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



Stability of Beta

Most analysts argue that betas aregenerally stable for firms remainingin the same industry.

That is not to say that a firm’s betacannot change.

Changes in product line

Changes in technology

Deregulation

Changes in financial leverage



Using an Industry Beta

It is frequently argued that one can betterestimate a firm’s beta by involving the

whole industry.

If you believe that the operations of thefirm are similar to the operations of therest of the industry, you should use theindustry beta.



Using an Industry Beta

If you believe that the operations of thefirm are fundamentally different from theoperations of the rest of the industry, you

should use the firm’s beta. Do not forget about adjustments for

financial leverage.



Example

Microsoft 0.86

Apple 2.43

ADP 0.76

EDS

1.13

Oracle 1.54

Computer Sciences 1.19

CA 2.03

Fiserv 1.24 Accenture 1.18

Symantec 0.64

Paychex 0.96

Equally Weighted Portfolio 1.27



Example

Given Rf = 1.2%, Rm – Rf = 7%

Cost of capital of Symantec =

1.2% + 0.64 * 7% = 5.68% Or, Symantec wants to use

industry beta, so

Cost of capital will be

1.2 % + 1.27 * 7% = 10.09%



Beta, Covariance and Correlation

Beta is qualitatively similar to the covariance since thedenominator (market variance) is a constant.

Beta and correlation are related, but different. It ispossible that a stock could be highly correlated to themarket, but it could have a low beta if its deviation wererelatively small.

)(

)(

)(

)(

2

,

M

i

M

M i

i R

R

R

R RCov

b



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Determinants of Beta

Business Risk

Cyclicality of Revenues

Operating Leverage Financial Risk

Financial Leverage



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Cyclicality of Revenues

Highly cyclical stocks have higher betas.

Empirical evidence suggests that retailers andautomotive firms fluctuate with the business cycle.

Transportation firms and utilities are less dependent

on the business cycle.

Note that cyclicality is not the same asvariability — stocks with high standard

deviations need not have high betas.

Movie studios have revenues that are variable,depending upon whether they produce ―hits‖ or―flops,‖ but their revenues may not be especiallydependent upon the business cycle.



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Operating Leverage

The degree of operating leveragemeasures how sensitive a firm (orproject) is to its fixed costs.

Operating leverage increases as fixedcosts rise and variable costs fall.

Operating leverage magnifies the

effect of cyclicality on beta. The degree of operating leverage is

given by: DOL =

EBIT D Sales

SalesD EBIT×



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Operating Leverage

Sales

$

Fixed costs

Total

costs

D EBIT

D Sales

Operating leverage increases as fixed costs rise

and variable costs fall.

Fixed costs

Total

costs



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Financial Leverage and Beta

Operating leverage refers to the sensitivity tothe firm’s fixed costs of production.

Financial leverage is the sensitivity to a firm’s

fixed costs of financing. The relationship between the betas of the

firm’s debt, equity, and assets is given by:

• Financial leverage always increases the equity beta relative

to the asset beta.

b Asset =Debt + Equity

Debt× b Debt +

Debt + Equity

Equity× b Equity



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Financial Leverage and Beta

The beta of debt is low in practice, sosometimes it is convenient to assumebeta of debt = 0 and a simplified version

of the above formula will be:

)1(,S

Band

S B

S

Asset Equity

Equity Asset

b b

b b



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ExampleConsider Grand Sport, Inc., which is

currently all-equity financed and has abeta of 0.90.

The firm has decided to lever up to a capital

structure of 1 part debt to 1 part equity.

Since the firm will remain in the sameindustry, its asset beta should remain0.90.



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ExampleHowever, assuming a zero beta for its debt,

its equity beta would become twice aslarge:

b Asset = 0.90 =

1 + 1

1× b Equity

b Equity

= 2 × 0.90 = 1.80



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Example

Rapid is currently all equity and hasa beta of 0.8. The firm desires tohave 1 part of debt and 2 parts of equity.

Because the firm stays in the sameindustry, its asset beta remain the

same. Assuming a beta of 0 for debt,we have:



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Example

If 1 part of debt to 1 part of equity, equitybeta will be:

2.1,2

118.0

),1(

Equity Equity

Asset EquityS

B

b b

b b

6.11

118.0

Equity b



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Dividend Discount Model

The DDM is an alternative to the CAPM forcalculating a firm’s cost of equity.

The DDM and CAPM are internally consistent,

but academics generally favor the CAPM andcompanies seem to use the CAPM moreconsistently.

This may be due to the measurement error associated

with estimating company growth.

gP

RD

1



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Capital Budgeting & Project Risk

A firm that uses one discount rate for all projects may over

time increase the risk of the firm while decreasing its value.

P r o j e c t I R R

Firm’s risk (beta)

SML

r f

b FIRM

Incorrectly rejected

positive NPV projects

Incorrectly accepted

negative NPV projects

Hurdle

rate)( F M FIRM F R R β R

The SML can tell us why:



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Suppose the Conglomerate Company has a cost of capital,based on the CAPM, of 17%. The risk-free rate is 4%, themarket risk premium is 10%, and the firm’s beta is 1.3.

17% = 4% + 1.3 × 10%

This is a breakdown of the company’s investment projects:

1/3 Automotive Retailer b = 2.0

1/3 Computer Hard Drive Manufacturer b = 1.3

1/3 Electric Utility b = 0.6

average b of assets = 1.3

When evaluating a new electrical generation investment,

which cost of capital should be used?




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P r o j e c t I R

R

Project’s risk (b)

17%

1.3 2.00.6

R = 4% + 0.6×(14% – 4% ) = 10%

10% reflects the opportunity cost of capital on an investmentin electrical generation, given the unique risk of the project.

10%

24%

Investments in harddrives or auto retailing

should have higher

discount rates.

SML



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Cost of Debt

Interest rate required on new debtissuance (i.e., yield to maturity onoutstanding debt)

Adjust for the tax deductibility of interest expense

Cost of debt (after corporate tax) =

RB x (1 – tC)



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Example

Borrowing Rate (RB)= 10%

Tax Rate (tC) = 40%

After tax cost of debt = RB x (1 – tC) = 10% x (1 – 0.4) = 6%



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Cost of Preferred Stock

Preferred stock is a perpetuity,so its price is equal to the

coupon paid divided by thecurrent required return.

Rearranging, the cost of

preferred stock is: RP = C / PV



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The Weighted Average Cost of Capital

The Weighted Average Cost of Capital is givenby:

• Because interest expense is tax-deductible, wemultiply the last term by (1 – T C ).

RWACC =Equity + Debt

Equity × R Equity +Equity + Debt Debt × R Debt × (1 – T C )

RWACC =S + B

S× RS +

S + B

B× R B × (1 – T C )



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Example: International Paper

First, we estimate the cost of equityand the cost of debt.

We estimate an equity beta toestimate the cost of equity.

We can often estimate the cost of debt by observing the YTM of the

firm’s debt.

Second, we determine the WACC byweighting these two costs

appropriately.



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The industry average beta is0.82, the risk free rate is 3%,

and the market risk premium is8.4%.

Thus, the cost of equity capital

is: RS = RF + bi × ( R M – RF )

= 3% + 0.82×8.4%= 9.89%



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The yield on the company’s debtis 8%, and the firm has a 37%marginal tax rate.

The debt to value ratio is 32%

8.34% is International’s cost of capital. It should be used to

discount any project where one believes that the project’s risk

is equal to the risk of the firm as a whole and the project has

the same leverage as the firm as a whole.

= 0.68 × 9.89% + 0.32 × 8% × (1 – 0.37)

= 8.34%

RWACC = S + B

S× RS +

S + B

B× R B × (1 – T C )



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Flotation Costs

Flotation costs represent theexpenses incurred upon the issue, orfloat, of new bonds or stocks.

These are incremental cash flows of the project, which typically reducethe NPV since they increase the initial

project cost (i.e., CF0).



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Flotation Costs

Amount Raised = NecessaryProceeds / (1-% flotation cost)

The % flotation cost is a weightedaverage based on the average cost of issuance for each funding source andthe firm’s target capital structure:

f A = (E/V)* f E + (D/V)* f D



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Example

If Spatt is an all equity firm andwants to raise $100M throughequity. If flotation cost of equity is

10%, how much equity should Spattsell?

$100 M = (1 – 0.1) X AmountRaised, so Amount Raised = $100 M

/ 0.9 = $111.11 M



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Example

Now if Spatt is financed by 60%equity and 40% debt, and f S =10%as before, and f B = 0.05

The weighted average flotation costwill be: f A = (E/V)* f E + (D/V)* f D = 0.6 * 0.1 +

0.4*0.05 = 0.08

Amount raised will be $100 M / (1-0.08) =$108.70 M



Revision Topics and Checkpoints

How do we determine the cost of equity capital?

How can we estimate a firm or

project beta? How does leverage affect beta?

How do we determine the weighted

average cost of capital? How do flotation costs affect the

capital budgeting process?

fin3004 2011-2012s2 lecture04 cost of capital

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