Chapter 15

Required Returns and the Cost of Capital

Learning Objectives

After studying Chapter 15, you should be able to:• Explain how a firm creates value and identify the key sources of value

creation.• Define the overall “cost of capital” of the firm. • Calculate the costs of the individual components of a firm’s cost of

capital - cost of debt, cost of preferred stock, and cost of equity. • Explain and use alternative models to determine the cost of equity,

including the dividend discount approach, the capital-asset pricing model (CAPM) approach, and the before-tax cost of debt plus risk premium approach.

• Calculate the firm’s weighted average cost of capital (WACC) and understand its rationale, use, and limitations.

• Explain how the concept of Economic Value Added (EVA) is related to value creation and the firm’s cost of capital.

• Understand the capital-asset pricing model's role in computing project-specific and group-specific required rates of return.

• Creation of Value• Overall Cost of Capital of the Firm• Project-Specific Required Rates• Group-Specific Required Rates• Total Risk Evaluation

• Creation of Value• Overall Cost of Capital of the Firm• Project-Specific Required Rates• Group-Specific Required Rates• Total Risk Evaluation

Topics

Growthphase ofproductcycle

Barriers tocompetitive

entry

Other --e.g., patents,

temporarymonopoly

power,oligopolypricing

CostMarketing

& pricePerceived

quality

Superiororganizational

capability

Industry Attractiveness

Competitive Advantage

Key Sources of Value Creation

Overall Cost of Capital of the Firm

Cost of Capital is the required rate of return on the various types of financing. The overall cost of capital is a weighted average of the individual required rates of return (costs).

Type of Financing Mkt Val Weight

Long-Term Debt $ 35M 35%

Preferred Stock $ 15M 15%

Common Stock Equity $ 50M 50%

$ 100M 100%

Market Value of Long-Term Financing

Cost of Debt is the required rate of return on investment of the lenders of a company.

Cost of Debt

n

tt

d

tt

k

PIP

10 )1(

ki = kd ( 1 - T )

P0 = Current market priceIt = Interest payment at tPt = Principal payment at t

ki = After-tax cost of debtkd = Before-tax cost of debtT = Marginal tax rate

Assume that Basket Wonders (BW) has $1,000 par value zero-coupon bonds outstanding. BW bonds are currently trading at $385.54 with 10 years to maturity. BW tax bracket is 40%.

Cost of Debt: Example

$385.54 =$0 + $1,000

(1 + kd)10

(1 + kd)10 = $1,000 / $385.54 = 2.5938

(1 + kd) = (2.5938) (1/10) = 1.1

kd = .1 or 10%

ki = 10% ( 1 - .40 )

ki = 6%

Cost of Debt: Example

Year Cash Flow0 $ (385.54)1 $ - 2 $ - 3 $ - 4 $ - 5 $ - 6 $ - 7 $ - 8 $ - 9 $ -

10 $ 1,000.00 irr= 10.00%

Cost of Preferred Stock is the required rate of return on investment of the preferred shareholders of the company.

Cost of Preferred Stock

kP = DP / P0

kP = Cost of preferred stockDP = Stated annual dividendP0 = Current market price

Assume that Basket Wonders (BW) has preferred stock outstanding with par value of $100, dividend per share of $6.30, and a current market value of $70 per share.

kP = $6.30 / $70

kP = 9%

Cost of Preferred Stock: Example

A. Dividend Discount Model

B. Capital-Asset Pricing Model

C. Before-Tax Cost of Debt plus Risk Premium

Cost of Equity Approaches

The cost of equity capital, ke, is the discount rate that equates the present value of all expected future dividends with the current market price of the stock.

A. Dividend Discount Model

12

21

10 )1()1()1()1( t

te

t

eee k

D

k

D

k

D

k

DP

P0 = Current market priceDt = Dividend expected at tke = Cost of equity capital

The constant dividend growth assumption reduces the model to:

ke = ( D1 / P0 ) + g

Dividend Discount Model:Constant Growth

P0 = Current market priceD1 = Dividend expected at t=1ke = Cost of equity capitalg = Dividend growth rate

Assume that Basket Wonders (BW) has common stock outstanding with a current market value of $64.80 per share, current dividend of $3 per share, and a dividend growth rate of 8% forever.

ke = ( D1 / P0 ) + g

ke = ($3(1+.08) / $64.80) + .08

ke = .05 + .08 = .13 or 13%

Cost of Equity Capital:Example (Constant Growth)

The growth phases assumption leads to the following formula (assume 3 growth phases):

Dividend Discount Model:Growth Phases

1

3

1

2

1

100 )1(

)1(

)1(

)1(

)1(

)1(

btt

e

btb

b

att

e

ata

a

tt

e

t

k

gD

k

gD

k

gDP

P0 = Current market priceDt = Dividend expected at tke = Cost of equity capitalg = Dividend growth rate

The cost of equity capital, ke, is equated to the required rate of return in market equilibrium. The risk-return relationship is described by the Security Market Line (SML).

B. Capital Asset Pricing Model

jfmfje )R - R( R R k Rf = Risk-free rateRm = Expected return for market portfolio ke = Cost of equity capitalβj = Beta coefficient (responsiveness to market)

Assume that Basket Wonders (BW) has a company beta of 1.25. Research by Julie Miller suggests that the risk-free rate is 4% and the expected return on the market is 11.2%

ke = Rf + (Rm - Rf)bj

= 4% + (11.2% - 4%)1.25

ke = 4% + 9% = 13%

Cost of Equity (CAPM):Example

The cost of equity capital, ke, is the sum of the before-tax cost of debt and a risk premium in expected return for common stock over debt.

C. Before-Tax Cost of Debt Plus Risk Premium

ke = kd + Risk Premium*

*Risk premium is not the same as CAPM risk premium

Assume that Basket Wonders (BW) typically adds a 3% premium to the before-tax cost of debt.

ke = kd + Risk Premium

= 10% + 3%

ke = 13%

Cost of Equity (kd + R.P.):Example

Constant Growth Model 13%

Capital Asset Pricing Model 13%

Cost of Debt + Risk Premium 13%

Generally, the three methods will not agree.

Comparison of the Cost of Equity Methods

Cost of Capital

WACC = .35(6%) + .15(9%) + .50(13%)

= .021 + .0135 + .065 = .0995 or 9.95%

Weighted Average Cost of Capital (WACC)

n

xxx Wk

1

)(

1. Weighting System• Marginal Capital Costs• Capital Raised in Different Proportions than WACC

Limitations of the WACC

2. Flotation Costs are the costs associated with issuing securities such as underwriting, legal, listing, and printing fees.

a. Adjustment to Initial Outlay

b. Adjustment to Discount Rate

Add Flotation Costs (FC) to the Initial Cash Outlay (ICO).

Impact: Reduces the NPV

Adjustment to Initial Outlay (AIO)

)()1(1

FlotationICOk

CFNPV

n

tt

t

Subtract Flotation Costs from the proceeds (price) of the security and recalculate yield figures.

Impact: Increases the cost for any capital component with flotation costs.

Result: Increases the WACC, which decreases the NPV.

Adjustment to Discount Rate (ADR)

• A measure of business performance.• It is another way of measuring that firms are

earning returns on their invested capital that exceed their cost of capital.

• Specific measure developed by Stern Stewart and Company in late 1980s.

Economic Value Added

EVA = NOPAT – [Cost of Capital x Capital Employed]

• Since a cost is charged for equity capital also, a positive EVA generally indicates shareholder value is being created.

• Based on Economic NOT Accounting Profit.• NOPAT – net operating profit after tax is a

company’s potential after-tax profit if it was all-equity-financed or “unlevered.”

Economic Value Added

• Initially assume all-equity financing.• Determine project beta.• Calculate the expected return.• Adjust for capital structure of firm.• Compare cost to IRR of project.

Determining Project-Specific Required Rates of Return

Use of CAPM in Project Selection:

Difficulty in Determining the Expected Return

• Locate a proxy for the project (much easier if asset is traded).

• Plot the Characteristic Line relationship between the market portfolio and the proxy asset excess returns.

• Estimate beta and create the SML.

Determining the SML:

Project Acceptance and/or Rejection

SML

X

XX

X

XX

X

O O

O

O

O

O

O

SYSTEMATIC RISK (Beta)

EX

PE

CT

ED

RA

TE

OF

RE

TU

RN

Rf

Accept

Reject

1. Calculate the required return for Project k (all-equity financed).

Rk = Rf + (Rm - Rf)bk

2. Adjust for capital structure of the firm (financing weights).

Weighted Average Required Return =

[ki][% of Debt] + [Rk][% of Equity]

Determining Project-Specific Required Rate of Return

Assume a computer networking project is being considered with an IRR of 19%.

Examination of firms in the networking industry allows us to estimate an all-equity beta of 1.5. Our firm is financed with 70% Equity and 30% Debt at ki=6%.

The expected return on the market is 11.2% and the risk-free rate is 4%.

Project-Specific Required Rate of Return: Example

ke = Rf + (Rm - Rf)bj

= 4% + (11.2% - 4%)1.5

ke = 4% + 10.8% = 14.8%

WACC = .30(6%) + .70(14.8%) = 1.8% + 10.36% = 12.16%

IRR = 19% > WACC = 12.16%

Do You Accept the Project?

Determining Group-Specific Required Rates of Return

• Initially assume all-equity financing.• Determine group beta.• Calculate the expected return.• Adjust for capital structure of group.• Compare cost to IRR of group project.

Use of CAPM in Project Selection:

Comparing Group-Specific Required Rates of Return

Group-SpecificRequired Returns

Company Costof Capital

Systematic Risk (Beta)

Exp

ecte

d R

ate

of R

etur

n

• Amount of non-equity financing relative to the proxy firm. Adjust project beta if necessary.

• Standard problems in the use of CAPM. Potential insolvency is a total-risk problem rather than just systematic risk (CAPM).

Qualifications to Using Group-Specific Rates

Risk-Adjusted Discount Rate Approach (RADR)

The required return is increased (decreased) relative to the firm’s overall cost of capital for projects or groups showing greater (smaller) than “average” risk.

Project Evaluation Based on Total Risk

RADR and NPVRADR and NPV

Discount Rate (%)0 3 6 9 12 15

RADR – “high” risk at 15%

(Reject!)

RADR – “low” risk at 10%(Accept!)

Adjusting for risk correctlymay influence the ultimate

Project decision.

Net

Pre

sent

Val

ue

$000s15

10

5

0

-4

Probability Distribution Approach

Acceptance of a single project with a positive NPV depends on the dispersion of NPVs and the utility preferences of management.

Project Evaluation Based on Total Risk

Firm-Portfolio Approach

B

C

A

IndifferenceCurves

STANDARD DEVIATION

EX

PE

CT

ED

VA

LUE

OF

NP

V

Curves show“HIGH”

Risk Aversion

Firm-Portfolio Approach

B

C

A

IndifferenceCurves

STANDARD DEVIATION

EX

PE

CT

ED

VA

LUE

OF

NP

V

Curves show“MODERATE”Risk Aversion

Firm-Portfolio Approach

B

C

A

IndifferenceCurves

STANDARD DEVIATION

EX

PE

CT

ED

VA

LUE

OF

NP

V

Curves show“LOW”

Risk Aversion

bj = bju [ 1 + (B/S)(1-TC) ]

bj: Beta of a levered firm.

bju: Beta of an unlevered firm (an all-equity financed firm).

B/S: Debt-to-Equity ratio in Market Value terms.

TC : The corporate tax rate.

Adjusting Beta for Financial Leverage

Adjusted Present Value (APV) is the sum of the discounted value of a project’s operating cash flows plus the value of any tax-shield

benefits of interest associated with the project’s financing minus any flotation costs.

Adjusted Present Value

APV = UnleveredProject Value

+ Value ofProject Financing

Assume Basket Wonders is considering a new $425,000 automated basket weaving machine that will save $100,000 per year for the next 6 years. The required rate on unlevered equity is 11%.

BW can borrow $180,000 at 7% with $10,000 after-tax flotation costs. Principal is repaid at $30,000 per year (+ interest). The firm is in the 40% tax bracket.

NPV and APV Example

What is the NPV to an all-equity-financed firm?

NPV = $100,000[PVIFA11%,6] - $425,000

NPV = $423,054 - $425,000

NPV = -$1,946

Basket Wonders NPV Solution

What is the APV?First, determine the interest expense.

Int Yr 1 ($180,000)(7%) = $12,600Int Yr 2 ( 150,000)(7%) = 10,500Int Yr 3 ( 120,000)(7%) = 8,400Int Yr 4 ( 90,000)(7%) = 6,300Int Yr 5 ( 60,000)(7%) = 4,200Int Yr 6 ( 30,000)(7%) = 2,100

Basket Wonders APV Solution

Second, calculate the tax-shield benefits.

TSB Yr 1 ($12,600)(40%) = $5,040TSB Yr 2 ( 10,500)(40%) = 4,200TSB Yr 3 ( 8,400)(40%) = 3,360TSB Yr 4 ( 6,300)(40%) = 2,520TSB Yr 5 ( 4,200)(40%) = 1,680TSB Yr 6 ( 2,100)(40%) = 840

Basket Wonders APV Solution

Third, find the PV of the tax-shield benefits.

TSB Yr 1 ($5,040)(.901) = $4,541TSB Yr 2 ( 4,200)(.812) = 3,410TSB Yr 3 ( 3,360)(.731) = 2,456TSB Yr 4 ( 2,520)(.659) = 1,661TSB Yr 5 ( 1,680)(.593) = 996TSB Yr 6 ( 840)(.535) = 449

PV = $13,513

Basket Wonders APV Solution

What is the APV?

APV = NPV + PV of TS - Flotation Cost

APV = -$1,946 + $13,513 - $10,000

APV = $1,567

Basket Wonders NPV Solution

Basket Wonders NPV Solution

Year Cash Flow Loan Bal. Repayment Interest TS Benefit Flotation0 -425000 1800001 100000 150000 30000 12600 50402 100000 120000 30000 10500 42003 100000 90000 30000 8400 33604 100000 60000 30000 6300 25205 100000 30000 30000 4200 16806 100000 0 30000 2100 840

NPV= ($1,946.21) $13,512.26 10000APV= $1,566.04