returns on cash of capital

15.1 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

Chapter 15Chapter 15Required Returns Required Returns

and the Cost of and the Cost of CapitalCapital


1. Explain how a firm creates value and identify the key sources of value creation.

2. Define the overall “cost of capital” of the firm. 3. 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. 4. 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.

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

6. Explain how the concept of economic Value added (EVA) is related to value creation and the firm’s cost of capital.

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

After Studying Chapter 15, After Studying Chapter 15, you should be able to:you should be able to:


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

Required Returns and Required Returns and the Cost of Capitalthe Cost of Capital


Growthphase ofproduct

cycle

Barriers tocompetitive

entry

Other --e.g., patents,

temporarymonopoly

power,oligopoly

pricing

CostMarketing

andprice

Perceivedquality

Superiororganizational

capability

Industry AttractivenessIndustry Attractiveness

Competitive AdvantageCompetitive Advantage

Key Sources of Key Sources of Value CreationValue Creation


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).

Overall Cost of Overall Cost of Capital of the FirmCapital of the Firm


Type of Financing Mkt Val WeightLong-Term Debt $ 35M 35%Preferred Stock $ 15M 15%Common Stock Equity $ 50M 50%

$ 100M 100%

Market Value of Market Value of Long-Term FinancingLong-Term Financing


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

ki = kd ( 1 – T )

P0 =Ij + Pj

(1 + kd)jn

j=1

Cost of DebtCost of Debt


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%.

$385.54 =$0 + $1,000

(1 + kd)10

Determination of Determination of the Cost of Debtthe Cost of Debt


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

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

= 1.1 kd = 0.1 or 10%

ki = 10% ( 1 – .40 )

kkii = 6%6%

Determination of Determination of the Cost of Debtthe Cost of Debt


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

kP = DP / P0

Cost of Preferred StockCost of Preferred Stock


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

kkPP = 9%9%

Determination of the Determination of the Cost of Preferred StockCost of Preferred Stock


• Dividend Discount ModelDividend Discount Model• Capital-Asset Pricing ModelCapital-Asset Pricing Model• Before-Tax Cost of Debt plus Before-Tax Cost of Debt plus

Risk PremiumRisk Premium

Cost of Equity Cost of Equity ApproachesApproaches


The cost of equity capitalcost 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. D1 D2 D

(1 + ke)1 (1 + ke)2 (1 + ke)+ . . . ++P0 =

Dividend Discount ModelDividend Discount Model


The constant dividend growth constant dividend growth assumptionassumption reduces the model to:

ke = ( D1 / P0 ) + g

Assumes that dividends will grow at the constant rate “g” forever.

Constant Growth ModelConstant Growth Model


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) + 0.08

kkee = 0.05 + 0.08 = 0.130.13 or 13%13%

Determination of the Determination of the Cost of Equity CapitalCost of Equity Capital


D0(1 + g1)t Da(1 + g2)t–a

(1 + ke)t (1 + ke)tP0 =

The growth phases assumption growth phases assumption leads to the following formula leads to the following formula

(assume 3 growth phases):(assume 3 growth phases):

t=1

a

t=a+1

b

t=b+1

Db(1 + g3)t–b

+

Growth Phases ModelGrowth Phases Model

(1 + ke)t


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).

ke = Rj = Rf + (Rm – Rf)j

Capital Asset Capital Asset Pricing ModelPricing Model


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 11.4%

ke = Rf + (Rm – Rf)j

= 4% + (11.4% – 4%)1.25 kkee = 4% + 9.25% = 13.25%13.25%

Determination of the Determination of the Cost of Equity (CAPM)Cost of Equity (CAPM)


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.

ke = kd + Risk Premium*

* Risk premium is not the same as CAPM risk premium

Before-Tax Cost of Debt Before-Tax Cost of Debt Plus Risk PremiumPlus Risk Premium


Assume that Basket Wonders (BW) typically adds a 2.75% premium to the

before-tax cost of debt.

ke = kd + Risk Premium

= 10% + 2.75% kkee = 12.75%12.75%

Determination of the Determination of the Cost of Equity (kCost of Equity (kdd + R.P.) + R.P.)


Constant Growth Model 13.00%13.00%Capital Asset Pricing Model 13.25%13.25%Cost of Debt + Risk Premium 12.75%12.75%

Comparison of the Comparison of the Cost of Equity MethodsCost of Equity Methods

Generally, the three methods will not agree.We must decide how to weight –

we will use an average of these three.


Cost of Capital = kx(Wx)

WACC = 0.35(6%) + 0.15(9%) + 0.50(13%)

WACC = 0.021 + 0.0135 + 0.065 = 0.0995 or 9.95%

n

x=1

Weighted Average Weighted Average Cost of Capital (WACC)Cost of Capital (WACC)


1.1. Weighting SystemWeighting System

• Marginal Capital Costs

• Capital Raised in Different Proportions than WACC

Limitations of the WACCLimitations of the WACC


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

a. Adjustment to Initial Outlayb. Adjustment to Discount Rate

Limitations of the WACCLimitations of the WACC


• 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 AddedEconomic 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 AddedEconomic Value Added


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

Impact: ReducesReduces the NPV

NPV = n

t=1

CFt

(1 + k)t– ( ICO + FC )

Adjustment to Adjustment to Initial Outlay (AIO)Initial Outlay (AIO)


Subtract Flotation Costs from the proceeds (price) of the security and

recalculate yield figures.Impact: IncreasesIncreases the cost for any

capital component with flotation costs.

Result: Increases the WACC, which decreasesdecreases the NPV.

Adjustment to Adjustment to Discount Rate (ADR)Discount Rate (ADR)


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

Use of CAPM in Project Selection:

Determining Project-Specific Determining Project-Specific Required Rates of ReturnRequired Rates of 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:

Difficulty in Determining Difficulty in Determining the Expected Returnthe Expected Return


SML

X

XX

X

XX

X

O O

O

O

O

O

O

SYSTEMATIC RISK (Beta)

EXPE

CTE

D R

ATE

OF

RET

UR

N

Rf

Accept

Reject

Project Acceptance Project Acceptance and/or Rejectionand/or Rejection


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

Rk = Rf + (Rm – Rf)k

2. Adjust for capital structure of thefirm (financing weights).

Weighted Average Required Return = [ki][% of Debt] + [Rk][% of Equity]

Determining Project-Specific Determining Project-Specific Required Rate of ReturnRequired 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 Project-Specific Required Rate of ReturnRate of Return ExampleExample


ke = Rf + (Rm – Rf)j

= 4% + (11.2% – 4%)1.5 kkee = 4% + 10.8% = 14.8%14.8%

WACCWACC = 0.30(6%) + 0.70(14.8%)= 1.8% + 10.36% = 12.16%12.16%

IRR IRR = 19%19% > WACC WACC = 12.16%12.16%

Do You Accept the Project?Do You Accept the Project?


• 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:

Determining Group-Specific Determining Group-Specific Required Rates of ReturnRequired Rates of Return


Group-SpecificRequired Returns

Company Costof Capital

Systematic Risk (Beta)

Expe

cted

Rat

e of

Ret

urn

Comparing Group-Specific Comparing Group-Specific Required Rates of ReturnRequired Rates of Return


• 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 Qualifications to Using Group-Specific RatesGroup-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 Project Evaluation Based on Total RiskBased on Total Risk


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

RADR and NPVRADR and NPV


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 Project Evaluation Based on Total RiskBased on Total Risk


B

C

A

IndifferenceCurves

STANDARD DEVIATION

EXPE

CTE

D V

ALU

E O

F N

PV

Curves show“HIGH”

Risk Aversion

Firm-Portfolio ApproachFirm-Portfolio Approach


B

C

A

IndifferenceCurves

STANDARD DEVIATION

EXPE

CTE

D V

ALU

E O

F N

PV

Curves show“MODERATE”Risk Aversion



B

C

A

IndifferenceCurves

STANDARD DEVIATION

EXPE

CTE

D V

ALU

E O

F N

PV

Curves show“LOW”

Risk Aversion



jj = = juju [ 1 + ( [ 1 + (B/SB/S)(1 – )(1 – TTCC) ]) ]

j: Beta of a levered firm.

ju: 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 Adjusting Beta for Financial LeverageFinancial 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.

APV = UnleveredProject Value + Value of

Project Financing

Adjusted Present ValueAdjusted Present Value


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 ExampleNPV and APV Example


What is the NPVNPV to an all-equity- to an all-equity-financed firmfinanced firm?

NPV = $100,000[PVIFA11%,6] – $425,000

NPV = $423,054 – $425,000NPVNPV = – $1,946– $1,946

Basket Wonders Basket Wonders NPV SolutionNPV Solution


What is the APVAPV?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%) = 6,300 Int Yr 5( 60,000)(7%) = 4,200Int Yr 6( 30,000)(7%) = 2,100

Basket Wonders Basket Wonders APV SolutionAPV 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



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 = PV = $13,513$13,513



What is the APVAPV?

APV = NPV + PV of TS – Flotation Cost APV = –$1,946 + $13,513 – $10,000

APVAPV = $1,567$1,567

Basket Wonders Basket Wonders NPV SolutionNPV Solution

returns on cash of capital

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