Chapter 20 - Cost of Capital

7/30/2019 Chapter 20 - Cost of Capital

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Prepared byKen Hartviksen

INTRODUCTION TOCORPORATE FINANCELaurence Booth W. Sean Cleary

Chapter 20 Cost of Capital


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CHAPTER 20Cost of Capital


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CHAPTER 20 Cost of Capital 20 - 3

Lecture Agenda

Learning Objectives

Important Terms

Financing Sources

The Cost of Capital

Estimating the Component Costs The Effect of Operating and Financial Leverage

Growth Models and the Cost of Common Equity

Risk-Based Models and the Cost of Common Equity

The Cost of Capital and Investment Summary and Conclusions

Concept Review Questions

Appendix 1 Steep Hill Mines # 1


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Learning Objectives

1. How ROE and the required return by common equity investors arerelated to a firms growth opportunities

2. How to apply the steps involved in estimating a firms weightedaverage cost of capital, including how to estimate the marketvalues of the various components of capital, and how to estimatethe various costs of these components

3. How operating and financial leverage affect firms

4. The advantages and limitations of using growth models and/or riskmodels to estimate the cost of common equity.


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Important Chapter Terms

Asset turnover ratio

Beta coefficient

Capital asset pricing model

Capital structure

Cash cow Cost of capital

Debt-to-equity ratio

Dog

Earnings yield Hurdle rate

Investment opportunitiesschedule (IOS)

Issuing (or floatation) costs Marginal cost of capital (MCC) Market-to-book (M/B) ratio Market risk premium Multi-stage growth DDM

Operating leverage Present value of existing

opportunities (PVEO) Present value of growth

opportunities (PVGO) Return on assets (ROA) Return on invested capital

(ROIC) Return on equity (ROE)


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Important Chapter Terms

Risk-based model

Risk-free rate of return

Star

Turnaround

Weighted average cost ofcapital (WACC)


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Weighted Average Cost of Capital

A Quick Primer on the Subject


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The Short Story of WACCPurposes/Use

The weighted average cost of capital (WACC)

serves three primary purposes:1. To evaluate capital project proposals before-the-fact.2. To set performance targets in order for management to

sustain or grow market values, and

3. to measure management performance after-the-fact.


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The Short Story of WACCWhat Costs are Measured?

Costs associated with financing the firms invested

capital including:

Debt Costs: Bank loans

Long-term debt bonds/debentures

Equity Costs:

Preferred equity costs Common equity costs


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The Short Story of WACCWhy the Marginal Cost?

What capital cost the firm 5 months, 5 years or 5

decades ago is irrelevant. What is relevant is what the next dollar of capital will

cost in todays economic environment for this

particular firm.


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The Short Story of WACCSteps in Solving for the WACC

1. Identify the relevant sources of capital (debt andequity).

2. Estimate the market values for the sources ofcapital and determine the market value weights.

3. Estimate the marginal, after-tax, and after-floatationcost for each source of capital.

4. Calculate the weighted average.


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The Short Story of WACCThe Formula

Once you have the specific marginal costs of capital (after accounting for taxes

and floatation costs) and you have found the appropriate weights to use, the

actual calculation of a WACC is a simple matter.

)1(

V

DTK

V

SKKWACC dea

The cost of equitytimes the marketvalue weight of

equity

The cost of debtafter tax times the

market value weightof debt


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The Short Story of WACCThe Spreadsheet Approach

(1) (2) (3) (4) = (2)*(3)

Type of

Capital

Specific

Marginal Cost

after tax andfloatation

costs

MarketValue

Weights

Weighted

SpecificMarginal

CostLong-Term Debt 5.5% 43.0% 0.02365

Preferred Stock 11.4% 11.0% 0.01254

Common Stock 12.9% 46.0% 0.05934

WACC = 9.55%

WACC is the sum of the weightedspecific marginal costs of each source ofcapital.


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The Short Story of WACCFrequently Asked Questions

1. Why dont we include the cost of accruals andaccounts payable in the cost of capital?

These are spontaneous liabilities that rise and fall

with the volume of business activity, and are notsubject to formal lending arrangements.

Accruals (wages and taxes), it can be argued, dont

have an explicit cost.

For major corporations, spontaneous liabilities areoften a very small part of the overall capitalization ofthe firm (are immaterial for cost of capital purposes).


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2. Why is the cost of capital an estimate and does this matter? WACC is calculated based on a current estimate of what it will cost for

the next dollar of debt and equity. Since that next dollar hasnt yetbeen raised, we are attempting for forecast or estimate that cost.

To estimate the cost of debt we often assume it is equal to the

required rate of return on existing debt outstanding in the markets (Ofcourse, when a firm actually goes to the market, conditions may havechanged, underwriting costs may be greater, etc.)

Forecasting WACC also requires estimating the cost of equity. Theremay different approaches to this task, and will result in a range ofestimates.

In the end, WACC will still be an estimate. The key thing to ensure isthat the NPV of the project be positive over the range of possibleWACCs. (Graph an NPV profile and determine the range of WACCsthat will still produce a positive NPV.)


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3. Why is the component cost of capital greater than the investorsrequired return ?

Accruals

Accounts payable

Short-term debt

Total current liabilities

Total current as sets Long-term debt

Shareholders' equity

Total assets Total liabilities and shareholders' equity

Prepaid expenses

Net fixed assets

Table 20-1 Main Balance Sheet Accounts

Cash and marketable securities

Accounts receivable

Inventory

Investment

Dealer

Investor buys one

new share in acompany and paysthe investmentdealer $20 for it.

$20.00

Investment dealergives the issuingfirm $18.00 for the

share, and pockets$2.00 for providingunderwritingservices.

Issuing companyreceives $18.00.

$18.00

Investor requires a

10% return on herinvestment of $20.This is a $2.00return on investedcapital.

Conclusion: The cost of external capital is greater thanthe investors required return because of

floatation costs.

The company must produce$2.00 income on an $18.00investment to meet theinvestors expectations. This is

an 11.1% return.


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The Short Story of WACCSummary

WACC measures the firms cost of financing future growth today,based on current capital market conditions, and assuming the firmuse a long-term average of financing sources.

WACC is an estimate. WACC is used to make capital investment decisions.

WACC is used to set performance targets for sales, and ROE.

WACC is used to assess managements performance, answeringthe question, has management added value?


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Sources of Capital for Corporations

Cost of Capital


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Financing SourcesCapital Structure

Table 20 - 1 illustrates the basic structure of a firms balancesheet: This is a snapshot of the firms financial position at one point in

time.

Left-hand side of the Balance Sheet Assets the things the firm owns

Note the structure of assets (relative proportions of current assetsand net fixed assets)

Right-hand side of the Balance Sheet Liabilities the borrowed sources of financing

Note the structure of liabilities (the relative proportions of current versuslong-term debt)

Shareholders equity owners investment in the business Note the amount of capital invested versus the amount of earnings that

have been reinvested in the business


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Accruals

Accounts payable

Short-term debt

Total current liabilities

Total current assets Long-term debt

Shareholders' equity

Total assets Total liabilities and shareholders' equity

Prepaid expenses

Net fixed assets

Table 20-1 Main Balance Sheet Accounts


Accounts receivable

Inventory

The FinancialStructure

Capital Structure


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Important Terms

Financial Structure The whole right-hand side of the balance sheet

Includes both short-term and long-term sources of financing(debt and equity)

Capital Structure How the firm finances its invested capital Excludes accruals and accounts payable short-term liabilities

that are not strictly debt contracts, that spontaneously change inresponse to the operations of the business.

Includes: Bank Loans

Long-term debt

Common stock and retained earnings(See Table 20 2 for a typical example)


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$50 Accruals $100

200 Accounts payable 200

250 Short-term debt 50

0 Total current liabilities 350

Total current assets 500 Long-term debt 650

1,500 Shareholders' equity 1,000

Total assets $2,000 Total liabilities and shareholders' equity $2,000

Prepaid expenses

Net fixed assets

Table 20-2 A "Simplified" Balance Sheet


Accounts receivable

Inventory

Financial Structure = $2,000Capital Structure = $1,700


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Financing SourcesInterpreting Balance Sheets

Balance sheets are prepared in accordance with GAAP: Represent historical costs which may not be relevant for current

decision-making purposes.

Analysis of reported data should include ratios such as:

Debt to Equity: Interest bearing debt to shareholders equity plus minority interest

Convert book values to market values This is done by multiplying the market-to-book ratio times the book

value.

Interpret the ratios again.

(Table 20 2 will be used to illustrate the adjustment process from book valuesto market values)


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Financing SourcesDebt-to-Equity Ratio

$50 Accruals $100







Prepaid expenses

Net fixed assets



Accounts receivable

Inventory

70.0000,1$

$650$50RatioEquity-to-Debt

Debt =

Equity =


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Financing SourcesConverting Book Value to Market Values

Book Values

$50 Accruals $100







Prepaid expenses

Net fixed assets



Accounts receivable

Inventory

Market value of debt will be very close (if not equal) to the bookvalues stated on the balance sheet. This is because these arecontractual claims that are not negotiable (traded in secondarymarkets). The amounts stated are the amounts that are requiredto satisfy the financial claims of these creditors.

The market value of long-term debt will depend on interest ratechanges since the debt was originally issued. As the bondsapproach maturity, their market price will move progressively toequal their par (face) value. It is the face value of the debt that ispresented here.

Equity =

The market value of equity is greatly affected bymanagement. It is not uncommon to see market-to-bookratios of 2 or more, reflecting the growth prospects themarket sees for the firm. Lets convert the book value ofequity by a market-to-book ratio of 2.5.


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Financing SourcesConverting Book Value to Market Values

Book Values Market Values

$50 Accruals $100 $100

200 Accounts payable 200 200

250 Short-term debt 50 500 Total current liabilities 350 350

Total current assets 500 Long-term debt 650 650

1,500 Shareholders' equity 1,000 2,500

Total assets $2,000 Total liabilities and shareholders' equity $2,000 $3,500

Prepaid expenses

Net fixed assets



Accounts receivable

Inventory

28.0500,2$

$650$50RatioEquity-to-Debtued"Market val"

When adjusted for market value effects, the apparenthigh debt to equity ratio (.7) is a much lower 0.28.

This confirms the importance of using relevant data whenmaking decisions.


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The Most Important Corporate FinanceDecisions

It is the managers job to maximize shareholders wealth.

In this and the next chapter we will address two of the most

important ways manager can add value to the firm:

Changing the mix of financing used by the firm (changing therelative proportions of debt and equity), and

Determining the minimum rate of return needed to maintain thecurrent market value.


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Three Ways of Using the Valuation

Equation

Cost of Capital


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Valuation Equation for a PerpetuityThree Ways of Using the Valuation Equation

In Chapter 5 you learned how to determine the present valueof an infinite stream of equal, periodic cash flows (an infiniteannuity).

Where:

S= the present value of the perpetuityX= the forecast annual earnings

Ke= the investors required return

eK

XS[ 20-1] $20.00

10.0

00.2$S[ 20-1]

If the annual cashflow is$2.00 and the

investors requiredreturn is 10%, thepresent value of theperpetuity is $20.


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The equation can be rearranged to solve for the requiredreturn Ke also known as the earnings yield:

The earnings yield is not normally used as the investorsrequired return because it simply measures forecast earningsas a percentage of the market price, ignoring growthopportunities.

SXKe [ 20-2] 10%

$20.00$2.00

SXKe[ 20-2]


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The perpetuity valuation model can be further rearranged tosolve for the forecast earnings given the current market priceand investors required return.

This helps managers determine their earnings target that must

be met to support the current market value. If the manager knows the investor requires a 10% rate of return

and the market price is $20.00, she knows the firm mustgenerate $2.00 in EPS to sustain the stock price.

SKX e [ 20-3] $2.00$20.000.10 SKX e


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Setting Performance TargetsUsing Required Returns and Market Values

Given market values and required rates of return, it is possible toestablish performance targets for management to sustain marketvalues:

For a firm financed by bondholders and stockholders, the firm mustplan to earn sufficient returns as follows:

Working back from these requirements we can forecast the level ofsales the firm must earn in order to achieve these operatingresultsthereby setting a sales performance target for management.

(1) (2) (3) =(1)(2)

Market Value

Required

Return

Earnings

Required

Debt (D) $700 6.0% $42

Equity (S) 2500 12.0% 300

V=D+S = $3,200 $342


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Setting Performance TargetsDeriving the RequiredIncome Statement

Sales ? $1,000

Variable costs 300 300Fixed costs 158 158

EBIT ? $542

Interest 42 42

Tax (40%) #VALUE! 200

Net Income $300 $300

Table 20-3 A Forecasted Income StatementGiven the need toearn $42 to coverinterest, and toearn $300 after-tax for

shareholders, andgiven a fixedcorporate tax rateand other costs,we can determinethe Sales requiredto achieve thesegoals.

It is $1,000

542$500$42$.4)-(1

$300$42

)1(

T

IncomeNetInterestEBIT

$1,000$542$158$300

EBITCostsFixedCostsVariable

Sales

This is the very process that is used by regulators to approve regulatedutility rates based on market-determined required rates of return.

So, the cost of capital drives utility rate increases.


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Setting Performance TargetsHow Market Value is Related to Book Value and ROE

Once you have the sales performance target you can establish otheroperating targets through the application of ratios.

Since equity in this case is a perpetuity we can express the price pershare as:

Dividing both sides of Equation 20 4 by BVPS we get the basicrelationship that drives the M/B ratio:

eeK

BVPSROE

K

EPSP

[ 20-4]


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Setting Performance TargetsThe Relationship Between BVPS and MVPS How to Increase

Shareholder Value

Equation 20 5 tells us:

If the ROE exceeds the investors required return (Ke)then the price of the stock will rise above book value.

This is a crucial goal of the financial manager to addto shareholder value.

eK

ROE

BVPS

P[ 20-5]


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Weighted Average Cost of Capital

(WACC)

Cost of Capital


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The Cost of CapitalDetermining the Weighted Average Cost of Capital (WACC)

The overall market value of the firm is:

V = D + S

In our example V= $3,200

After-tax ROI = 19.13%

= (EBIT)(1-T) = ($542 (1-.4))

= $325.20

This is the required net income if the firm is financed 100% withequity (no deduction for interest.)


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Where the value of the firm is $3,200 and EBIT (1T) is $325.60,we can find the discount rate that sets them equal.

First rewrite EBIT minus taxes as ROI IC and re-express thevaluation equation as:

Equation 20 6 can be rearranged to solve forKa for an all equityfirm:

aK

ICROIV

[ 20-6]


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Using the numbers from the continuing example the WACC is:

On the following slide will show how we can now substitute incomponent costs for both equity and debt to develop the generalequation for WACC (Ka)

V

ICROIKa

[ 20-7]

10.16%$3,200

$325.20

V

ICROIK

a


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11

V

D-T)(K

V

SK

V

T)D(KSK

V

ICROIK de

dea

[ 20-8]

The WACC is simply the weightedaverage of the component costs.


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The equation for WACC including common equity, preferredshare financing and debt is:

In this case the value of the firm equals the sum of the valueof stock, preferred and debt:

V = S + P + D

1V

D-T)(K

V

PK

V

SKWACC dpe [ 20-9]


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Estimating Market Values

Cost of Capital


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Estimating Market ValuesMarket Value of Equity

The total market value of equity (marketcapitalization) is the price per share times thenumber of shares outstanding:

n0 PS[ 20-10]


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Estimating Market ValuesMarket Value of Preferred Stock

The market price for preferred is simply the annual preferreddividend divided by the preferred shareholders required return.

The market value of all preferred stock is simply the price per sharetimes the number of shares outstanding.

0

p

p

k

DP [ 20-11]

n0 PS[ 20-10]


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Estimating Market ValuesMarket Value of Bonds

As previously mentioned, the market value of bonds will differ fromtheir book value only if required rates of return in the market havechanged since the bonds original issue.

Knowing the term to maturity, the coupon rate and the bondholders

required return we can determine the market value of bonds with

equation 20 - 12:

1

11

11

nbb

n

b

)k(Fk

)k(

IB

[ 20-12]


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Estimating Market ValuesMarket Value of Bonds

Once you know the market value of the bonds, you multiply theirprice by the number of bonds outstanding to determine total marketvalue.

n bPB[ 20-10]


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A Simple Exercise in Determining

Market Value Weights

Cost of Capital


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Market Value WeightsAn Example

Given:

Market price for common stock = $21.50

Bonds are trading for 95% of face value

In order to calculate market value (MV) weights, you will need toknow the total market value of debt, and common stock (andpreferred stock if the company uses it.)

To calculate total MV you need to know the current price of thesecurity in each class, as well as the total number of securities

outstanding:Total Market Capitalization = Price Quantity

The following balance sheet date, when combined with market price data, will allow you to calculate MV weights.


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Market Value WeightsAn Example

XYZ Company Limited

Balance Sheet

as at January 30, 2xxx

ASSETS LIABILITIES:

Current Assets $147,000 Current Liabilities $75,250

Net Fixed Assets 15,000,250 8.5% 2020 Mortgage Bonds 4,000,000

Common stock (1,000,000 outstanding) 7,155,000

Retained earnings 3,917,000

TOTAL ASSETS $15,147,250 TOTAL LIABILITIES AND O. EQUITY $15,147,250

Number of common sharesoutstanding is read from thebalance sheet.

Face value of bonds are$1,000, therefore there mustbe 4,000 bonds outstanding.


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Market Value WeightsAn Example Continued

Total MV of Equity = Price per share times number of shares = 1M $21.50 = $21.5M

Total MV of Bonds = Price per bond times number of bonds = $950 4,000 = $3,800,000

Type of

Capital

Market

price Number

Total Market

Value

MarketValue

Weight

Bonds $950.00 4,000 $3,800,000 15.02%

Stock $21.50 1,000,000 $21,500,000 84.98%

TOTAL= $25,300,000 100.00%

These weights could now be used to calculate WACC.


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Bond ValueGeneral Formula

)k(F

k

)k(IB

n

bb

n

b

1

11

11

[ 20-12]

Where:I = interest (or coupon ) payments

kb = the bond discount rate (or market rate)

n = the term to maturity

F = Face (or par) value of the bond

In the example, you didnt have to calculate the bond value because you

were given the fact that it was trading at 95% of par.

In the event that you do, however, simply use equation 20 -12.


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Estimating the Component Costs

Cost of Capital


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Estimating the Component CostsFloatation Costs

Issuing or floatation costs are incurred by a firm when it raisesnew capital through the sale of securities in the primarymarket.

These costs include: Underwriting discounts paid to the investment dealer

Direct costs associated with the issue including legal andaccounting costs

The result: Net proceeds on the sale of each security is less than what the

investor invests, and

The component cost of capital > investors required return.

Table 20 4 illustrates average issuing costs for different forms of capital.


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Estimating the Component CostsFloatation Costs and the Marginal Cost of Capital (MCC)

Commercial paper 0.125%

Medium-term notes 1.0%

Long-term debt 2.0%Equity (large) 5.0%

Equity (small) 5.0% - 10.0%

Equity (private) 10.0% and up

Table 20-4 Average Issuing Costs

What issue costs mean is that there is a financing wedge between what theinvestor pays and what the firm receives, the difference being the moneythat is lost to these costs. Issue costs are responsible for the componentcost of capital being greater than the investors required return.

Floatation costs fordebt securities islowest because debt isnormally privatelyplaced with largeinstitutional investorsnot requiring

underwriting costs andbecause debt is eitherissued by high qualityissuers or sits at thetop of the priority ofclaims list in the caseof default.


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WACC versus MCCFloatation Costs and the Marginal Cost of Capital (MCC)

The Marginal Cost of Capital (MCC) is the weighted averagecost of the next dollar of financing to be raised.

At low levels of financing the WACC = MCC

As a firm raises more and more capital in a given year, it will

exhaust the supply of lower cost sources, and then have toaccess marginally higher cost sources.

Therefore MCC increases with the amount of capital to beraised.

The following figure illustrates the MCC concept.


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0 $2,000,000 $4,000,000 $6,000,000 $8,000,000 $10,000,000

(%)

Dollars of Capital to be Raised

15

10

5

The Marginal Cost of Capital MCC

MCC1=WACC= 9.44%MCC2= 10.64%

There is only one break in the MCC curve. It

occurs at $5,500,000. At this point the firm has

exhausted its internal equity and to raise more

equity capital will mean accessing external

equity using the services of an underwriter.%64.10%24.2%4.8

)4%(.6.5)6%(.14

100

40)3.1%(8

100

60%14

)1(2

V

DtK

V

SKMCC de

%44.9%24.2%2.7

)4%(.6.5)6%(.12

100

40)3.1%(8

100

60%12

)1(1

V

DtK

V

SKMCC de

2.24%

Each dollar of capital invested is financed 40% by debt. (40% after-tax cost = 2.24%)

Each dollar of capital invested up to$5.5 million is financed 60% byinternal equity (R/E). (60% cost

of retained earnings = 7.2%)

Each dollar of capital investedbeyond $5.5 million is financed60% by new equity. (60% cost of new equity = 8.4%)


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The Component Cost of Debt

The cost of debt is a function of: The investors required rate of return

The tax-deductibility of interest expense

The floatation costs incurred to issue new debt


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The Component Cost of Debt

%19.697.0

%6

.03-1

0.4)-(1.010%

f-1

T)-(1ReturnRequiredsInvestor'DebtofCost

d

If you know the debt investors required rate of return Kd , the corporate taxrate and the floatation cost percentage for debt, you can estimate the cost ofdebt in the following manner:

Assume:

Kd= 10% (debt investors required return)

T= 40% (corporate tax rate)

fd= 3% (floatation cost percentage)

The after tax cost ofdebt is lower than the

investors required

return because of thetax shield on interest

expense.


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Estimating the Component CostsDebt

Alternatively you can adjust the bond valuation formula for the tax-deductibility of interest expense and the net proceeds the firm wouldreceive on the sale of one bond (after floatation costs) and solve forthe rate (Ki) that causes the formula to become and equality:

Ki= the after-tax and after-floatation cost of debt.

1

11

11

)1(n

ii

n

i

)K(F

K

)K(TINP

[ 20-13]

Net proceeds on the sale of the bond = Selling pricefloatation cost per bond.

Coupon interest times 1 minus corporate

tax rate = after tax cost of interest


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Estimating the Component CostsPreferred Shares

If you know the preferred shareinvestors required rate of return

Kp , and the floatation costpercentage for preferred sharefinancing, you can estimate thecost of preferred shares in thefollowing manner:

Assume:

Kp= 14% (preferred investorsrequired return)

F = 5% (floatation cost percentage)

%74.1495.0

%14

.05-1

14%

f-1

ReturnRequiredsInvestor'PreferredofCost

p

NOTE: Preferred dividends are paid out of after-tax earnings, therefore there are no taxation effectson the preferred share component cost of capital.

Floatationcosts cause

the componentcost to be

greater thanthe investors

required

return.


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Estimating the Component CostsPreferred Shares

Alternatively, the component cost of preferred sharescan be found using equation 20 -14, where NP is theselling price per preferred share less the floatation costsper share.

NP

DK

p

p [ 20-14]


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Estimating the Component CostsCommon Shares

Estimating the component cost of common stock is the mostdifficult because:

Promised cash flows are uncertain

Growth opportunities, their timing and magnitude will influence

the cost The riskiness of the stock is influenced by corporate decisions

such as the use of leverage

There are numerous alternative approaches that we willpresent to estimate the component cost of equity.

Before doing so, we will first address the effect of leverage onshareholders.


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Effects of Operating and Financial

Leverage

Cost of Capital


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Leverage

The increased volatility in operating income overtime, created by the use of fixed costs in lieu ofvariable costs. Leverage magnifies profits and losses.

There are two types: Operating leverage

Financial leverage

Both types of leverage have the same effect on

shareholders but are accomplished in very differentways, for very different purposes strategically.


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Leverage Effects on Operating Income

Years

When a firm increases theuse of fixed costs itincreases the volatility ofoperating income.

Normal volatility ofoperating income

OperatingIncome

+

0

-

O i L


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Operating LeverageWhat is it? How is it Increased?

Your textbook defines operating leverage as:

The increased volatility in operating income caused by fixedoperating costs.

You should understand that managers do make decisionsaffecting the cost structure of the firm.

Managers can, and do, decide to invest in assets that giverise to additional fixed costs and the intent is to reducevariable costs.

This is commonly accomplished by a firm choosing to becomemore capital intensive and less labour intensive, therebyincreasing operating leverage.

O ti L


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Operating LeverageAdvantages and Disadvantages

Advantages: Magnification of profits to the shareholders if the firm is

profitable.

Operating efficiencies (faster production, fewer errors, higher

quality) usually result increasing productivity, reducingdowntime etc.

Disadvantages: Magnification of losses to the shareholders if the firm does not

earn enough revenue to cover its costs.

Higher break even point High capital cost of equipment and the illiquidity of such aninvestment make it:

Expensive (more difficult to finance)

Potentially exposed to technological obsolescence, etc.

Fi i l L


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Financial LeverageWhat is it? How is it Increased?

Your textbook defines financial leverage as:

The increased volatility in operating income causedby fixed financial costs.

Financial leverage can be increased in the firm by: Selling bonds or preferred stock (taking on financial

obligations with fixed annual claims on cash flow)

Using the proceeds from the debt to retire equity (if

the lenders dont prohibit this through the bondindenture or loan agreement)

Fi i l L


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Financial LeverageAdvantages and Disadvantages

Advantages: Magnification of profits to the shareholders if the firm is

profitable.

Lower cost of capital at low to moderate levels of financialleverage because interest expense is tax-deductible.

Disadvantages: Magnification of losses to the shareholders if the firm does not

earn enough revenue to cover its costs.

Higher break even point.

At higher levels of financial leverage, the low after-tax cost ofdebt is offset by other effects such as:

Present value of the rising probability of bankruptcy costs

Agency costs

Lower operating income (EBIT), etc.

Eff t f O ti d Fi i l L


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Effects of Operating and Financial LeverageSummary

Equity holders bear the added risks associated withthe use of leverage.

The higher the use of leverage (either operating orfinancial) the higher the risk to the shareholder.

Leverage therefore can and does affectshareholders required rate of return, and in turnthis influences the cost of capital.

HIGHER LEVERAGE = HIGHER COST OF CAPITAL


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Growth Models and the Cost of

Common Equity

Cost of Capital


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The Importance of Growth

To this point we have been valuing stock as a perpetuity:

This means that we are assuming the current dividend will bepaid each year in the future into infinity.

Table 20 8 illustrates the importance of growth opportunities

to the price of dividend paying stocks on the TSX.

On average, 62.22% of the market value of this sample offirms could be attributed to growth opportunities and theremaining 37.78% to the present value of the current dividend

(perpetuity value)

Growth Models and the Cost of Common


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Company Price ($) DPS ($) Dividend

Yield (%)

Perpetuity

($)

Growth

Value (%)

AGF 25.75 0.283 1.10 5.66 78.0BC Gas 30.60 1.13 3.70 22.60 26.0

CAE 11.50 0.161 1.40 3.22 72.0

Dennings 3.50 0.102 2.90 2.04 42.0

EL Financial 285 0.570 0.20 11.40 96.0

GSW (A) 26.75 0.428 1.60 8.56 68.0

Hammersen 14.05 0.197 1.40 3.94 72.0

Intrawest 6.95 0.292 4.20 5.84 16.0

Jannock 29.60 0.148 0.50 2.96 90.0

Average 1.89 62.22

Source: Booth, Laurence, Table 1 f rom "What Drives Shareholder Value."Financial Intelligence IV-6, Spring 1999.

Table 20-8 Stock Prices and Growth Prospects

Stock Market Time Horizon

G o t ode s a d t e Cost o Co oEquity

The Importance of Adjusting for Growth

Currentstock price

Perpetuityvalue ofcurrent

dividend

% of CurrentMarket Valueexplained by

growthopportunities.



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EquityThe Constant Growth Model

The Gordon model assumes constant growth in the stream ofdividends from t =1 through :

The price of a share (P0) today equals the expected dividendat t =1 dividend b the required shareholder return (Ke ) minus

the long-run growth rate (g) . This formula can be rearranged to solve for the investors

required rate of return (Ke ):

1

0 gK

D

P [ 20-15]

C t t G th M d l


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Constant Growth ModelThe Cost of Common Equity Using Internal Funds

Investors required rate of return consists of twocomponents:

1. Expected dividend yield

2. Expected long-run growth rate (g)

This is the cost of internal equity (the cost of retainedearnings where the firm does not need to incur floatationcosts)

0

1 gP

DKe [ 20-16]

Constant Gro th Model


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Constant Growth ModelThe Cost of New Equity

The model can be modified to solve for the cost ofnew equity by using NP (net proceeds the firmreceives for each new share sold after floatationcosts)

1 gNP

DKne [ 20-17]

Constant Growth Model


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Constant Growth ModelCaution

The constant growth model can only be used incases where it is reasonable to assume that thegrowth rate can be sustained in the very long term.

This usually means, using it only for large, matureblue-chip companies that already pay a significantdividend.

The Gordon model SHOULD NOT be used onsmaller, more rapidly growing firms where high

current growth rates are experienced, but cannot besustained in the long term.



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EquityGrowth and ROE

One way to estimate growth is the sustainablegrowth method:

Growth rate is the product of the firms retention rate

(b), times the forecast ROE:

This definition ofgcan be used in the Gordon model:

ROEbg [ 20-18]



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Substituting the sustainable growth rate into the Gordonmodel:

Now we can recognize that the expected dividend D1 is theexpected earnings per share (X1) times the dividend payoutratio (one minus the retention rate):

10 ROEbK

DP

e

[ 20-19]



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This equation shows that the price per share isdetermined by: The firms forecast EPS

Dividend payout (1 b)

ROE

Required return by common shareholders (Ke)

This equation shows the higher the growth rate, the higher the share pricebecause larger future dividends and earnings are forecast.

)1(10

ROEbK

bXP

e

[ 20-20]



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Rearranging Equation 20 20 by substituting alternativeexpressions forD1 and g:

When this equation is used to estimate the cost of equity

capital (internal) for three different growth scenarios (10%,12% and 14%) we get some unusual results summarized inTable 20 9:

1

0

1

0

1 ROEbP

b)(XgP

DKe

[ 20-21]



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ROE P0 Expected

Dividend

Yield

Sustainable

Growth RateKe

10% $14.29 7% 5% 12%

12% $16.67 6% 6% 12%

14% $20.00 5% 7% 12%

Table 20-9 Growth and Ke

Stock price rises asexpected growth rate rises.

Three different sustainablegrowth rates.

A lower dividend yield. Asprices rise, dividends as apercentage of share price,

fall.

The firms retention rate, and thus its dividend payout ratio, is reflected in the

constant growth DDM as b.

Table 20 10 on the next slide gives the share price if the retention ratechanges under the three scenarios where ROE is 10, 12 and 14%.



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b 14.0% 12.0% 10.0%

0.40 $18.75 $16.67 $15.00

0.41 18.85 16.67 14.94

0.42 18.95 16.67 14.87

0.43 19.06 16.67 14.81

0.44 19.18 16.67 14.74

0.45 19.30 16.67 14.670.46 19.42 16.67 14.59

0.47 19.56 16.67 14.52

0.48 19.70 16.67 14.44

0.49 19.84 16.67 14.37

0.50 20.00 16.67 14.29

0.51 20.16 16.67 14.20

0.52 20.34 16.67 14.12

0.53 20.52 16.67 14.03

0.54 20.72 16.67 13.94

0.55 20.93 16.67 13.85

0.56 21.15 16.67 13.75

0.57 21.39 16.67 13.65

0.58 21.65 16.67 13.55

0.59 21.93 16.67 13.44

0.60 22.22 16.67 13.33

Table 20-10 Retention Rates, ROE, and Share PricesROE

Retentionrate

increases

as you gosouth.

When ROE =10%, share

pricedecreases as

the firm retainsmore money.


price remains

the same asthe firmincreases theretention rate.


priceincreases as

the firm retainsmore money.

The shareholders

required return is 12%.

When a firm retains moreearnings and reinveststhem at a lower rate thanwhat shareholdersrequire, the value of thefirm falls.

Clearly, the key to share

price growth is toreinvest earnings at ratesgreater than the cost ofcapital.

Hurdle Rate


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Hurdle RateThe Cost of Capital

Table 20 -10 tells us that the cost of capital is ahurdle rate.

The HURDLE RATE is the return on an investment

required to create value; below this rate, aninvestment will destroy value.

G i Fi V G th Fi


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Growing Firms Versus Growth Firms

Growing Firms Reinvests in projects that offer rates equal to its cost

of capital:

ROE = Ke

Growth Firms Does something that shareholders cannot do

reinvest earnings at rates higher than the cost ofcapital.

ROE > Ke

Growth Firms


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Growth FirmsImportance of the Reinvestment Rate of Return

Growth Firms Does something that shareholders cannot do reinvest earnings

at rates higher than the cost of capital.

ROE > Ke

This is the reason earnings yield is not an appropriate estimate of thefirms cost of capital.

What is relevant is NOT whether dividends or earnings are growing,but rather WHETHER THE FIRM IS INVESTING AT RATES OF

RETURN GREATER THAN THE COST OF CAPITAL.Of course, this means, the firm should be investing in projects with

positive NPVs (IRRs > cost of capital)


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Multi-Stage Growth Models and theCost of Capital

Cost of Capital



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EquityMulti-Stage Growth Models

Multi-stage DDM is a version of the DDM thataccounts for different levels of growth in earningsand dividends.

There is no limit to the number of growth stages onecan forecast for a given company, so this is a veryflexible model.

See Chapter 7 for detailed pricing model description.

Simple Two-stage Growth Model


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Simple Two-stage Growth ModelMulti-Stage Growth Models

Equation 20 22 is a simple, two-stage growth model. It breaks the stock price into two components:

1. PVEO present value of existing opportunities (the value of the firmscurrent operations assuming no new investment) and

2. PVGO present value of growth opportunities the net present value

today of the firms future investments.

)()1(

210

e

e

ee

K

KROE

K

Inv

K

BVPSROEP

[ 20-22]

PVEO PVGO



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Simple Two stage Growth ModelPVEO and PVGO

PVGO is discounted back to the present by one year because itrepresents an incremental investment decision today that wont

result in the first cash flow until one year from now. PVGO does add a perpetual amount represented by the difference

between ROE2 earned on this added investment and Ke

)()1(

210

e

e

eeK

KROE

K

Inv

K

BVPSROEP

[ 20-22]

PVEO PVGO



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Simple Two stage Growth ModelPVGO and ROE2

If ROE2 = Ke then the future investment addsnothing to the value of the firm

If ROE2 > Ke then the future investment addsvalue to the firm

)()1(

210

e

e

eeK

KROE

K

Inv

K

BVPSROEP

[ 20-22]

PVGO

Simple Two-stage Growth Model Scenarios


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Simple Two stage Growth Model ScenariosPVEO and PVGO

Four Scenarios:

High PVEO and High PVGO - Star

High PVEO and Low PVGO - Cash Cow

Low PVEO and High PVGO - TurnaroundLow PVEO and Low PVGO - Dog

(These four scenarios are found in matrix form in Figure 20 -1 )

)()1(

210

e

e

ee K

KROE

K

Inv

K

BVPSROEP

[ 20-22]

PVGO



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Simple Two stage Growth ModelGrowth Opportunities and Firm Type

20 - 1 FIGURE



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Star Growth Company High PVEO and high PVGO DCF methods of valuation are unreliable due to high growth

Turnaround Growth Company Low PVEO and high PVGO Poor PVEO drags down stock price today

DCF methods of valuation are unreliable due to high growthCash Cow

High PVEO and low PVGO DCF methods of valuation are reliable due to lack of growth we are valuing a

perpetuity

Dog Low PVEO and low PVGO High earnings yield forecast to lose value from future investments depressing

the current share price.

(See Table 20 -11 for earnings yield and Market-to-book ratios for each type.)



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Earnings Yield (%) Market-to-Book

Star 8.84 2.26

Cash cow 12.00 1.67

Turnaround 2.63 0.76

Dog 114.29 0.02

Table 20-11 The Impact of Growth Opportunities on Share Prices


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The Fed ModelU.S. Federal Reserve

Cost of Capital

Growth Models and the Cost of CommonE it


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EquityThe Fed Model

Used by the U.S. central bank to estimate whetherthe stock market was over- or under-valued Used to decide whether the Central Reserve Bank

should send signals to the market to encourage

reason in the market place (to avoid speculativebubbles and the inevitable price collapse that follows)

Attempting to avoid irrational exuberance!

The Fed Model equation is found on the next slide.



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EquityThe Fed Model

)

%)0.1/()(

TBond

actual

Fed

actual

KEPSExp

V

V

V[ 20-23]

Actual value of the U.S. stock amarket. (Total marketcapitalization).

Estimate of the U.S. stockmarket value from the Fedmodel.

Expected EPS on S&P 500 indexdivided by yield on long U.S.Treasury bonds.

Aggregate valuation across the entire market is easier becauseunsystematic risk attached to individual securities is eliminated as a

factor for the market as a whole.



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EquityThe Fed Model

The Feds estimate of market value = Expected EPS on S&P 500divided by Yield on Long U.S. Treasury Bonds minus 1.0%.

All of this data is continuously, readily available so this estimate ofvalue is easy to produce and to track over time as illustrated inFigure 20 2 on the following slide:

)%)0.1(

)(

TBond

FedK

EPSExpV[ 20-24]

Aggregate valuation across the entire market is easier becauseunsystematic risk attached to individual securities is eliminated as afactor for the market as a whole.

The Fed Model


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Feds Stock Valuation Model

20 - 2 FIGURE



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EquityThe Fed Model

If the Fed Model is rearranged it can show when themarket is fairly valued:

%.-KP

XTBond

S&P

01500

[ 20-25]



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EquityThe Fed Model

When the earnings yield on the S&P 500 (market) is equal to thelong-term Treasury Bond yield minus 1.0 percent, the market is fairlyvalued.

The earnings yield is the appropriate discount rate for the no-growthcase. (perpetuities), whereas we would expect the market as a

whole to grow at the nominal GDP growth rate.

Required return on the market as a whole = Long Treasury Yield +4.0% risk premium. (5% nominal GDP 1%).

%.-KP

XTBond

S&P

01500

[ 20-25]

Growth Models and the Cost of CommonEquity


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EquityThe Fed Model

Required return on the market as a whole = Long Treasury Yield + 4.0%risk premium. (5% nominal GDP 1%).

The required rate of return on the market as a whole can serve as auseful benchmark for financial managers as they attempt to estimate

their own firms cost of capital.

%.-KP

X

TBondS&P

01500

[ 20-25]


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Risk-Based Models and the Cost ofCommon Equity

Cost of Capital

Risk-Based Models and the Cost of CommonEquity


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EquityUsing the CAPM to Estimate the Cost of Common Equity

CAPM can be used to estimate the required return bycommon shareholders.

It can be used in situations where DCF methods willperform poorly (growth firms)

CAPM estimate is a market determined estimate

because:

The RF (risk-free) rate is the benchmark return and is measureddirectly, today as the yield on 91-day T-bills

The market premium for risk (MRP) is taken from current marketestimates of the overall return in the market place less RF (ERM

RF)



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As a single-factor model, we estimate the common shareholders requiredreturn based on an estimate of the systematic risk of the firm (measured bythe firms beta coefficient)

Where:

Ke= investors required rate of return

e = the stocks beta coefficient

Rf = the risk-free rate of return

MRP= the market risk premium (ERM - Rf)

MRPRK eFe [ 20-26]



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EquityEstimating the Market Risk Premium

Rfis observable (yield on 91-day T-bills)

Getting an estimate of the market risk premium is one of the moredifficult challenges in using this model. We really need a forward looking of MRP or a forward looking

estimate of the ERM

One approach is to use an estimate of the current, expected MRPby examining a long-run average that prevailed in the past.

Table 20 -12 illustrates the % returns on S&P/TSX Compositeannually for the first five years of this century.

MRPRK eFe [ 20-26]



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Returns

2000 7.5072%

2001 -12.572%2002 -12.438%

2003 26.725%

2004 14.480%

2005 24.127%

Table 20-12 Returns on the S&P/TSX Composite Index Investors areunlikely to expectnegative returns

on the stockmarket. If they

did, no one would

hold shares!

Who would haveguessed before

hand, there wouldbe two

consecutive years

of aggregatemarket losses?

Such is the realityof investing since

none of us areclairvoyant.

It would bebetter to use

averagerealized

returns overan entire

business/market cycle.


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Financial Forecasts Average Annual Percent Return

Bank of Canada Overnight Rate 4.50

Cash: 3-Month T-bills 4.40

Income: Scotia Universe Bond Index 5.60

Canadian Equities: S&P/TSX Composite Index 7.30

U.S. Equities: S&P 500 Index 7.80

International Non-U.S. Equities: MSCI EAFE Index 7.50

Source: TD Economics

Table 20-14 Long-Run Financial Projections

An estimate of ERM is very important.

TD Economics recently generated the above estimates of forward

looking rates.

The Scotia Universe Bond Index is a long-term bond index thatcontains Canadas and corporate bonds with default risk.

Nevertheless, on a risk-adjusted basis, the TD forecast for MRP isconsistent with an arithmetic risk premium of 4.3%



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EquityEstimating Betas

After obtaining estimates of the two importantmarket rates (Rfand MRP), an estimate for the

company beta is required.

Figure 20 -3 illustrates that estimated betas formajor sub-indexes of the S&P/TSX have varied

widely over time:



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EquityEstimated Betas for Sub Indexes of the S&P/TSX Composite Index

20 - 3 FIGURE



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EquityEstimated Betas for Sub Indexes of the S&P/TSX Composite Index

Actual data for Figure 20 -3 is presented in Table 20 -15 onthe following slide:

You should note: IT sub index shows rapidly increasing betas

Other sub index betas show constant or decreasing trends.

Reasons: The weighted average of all betas = 1.0 (by definition they are

the market)

If one sub index is changingthat change alone affects allothers in the opposite direction.

What Happened in the 1995 2005 decade? The internet bubble of the late 1990s resulted in rapid growth in

the IT sector till it burst in the early 2000s.



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EquityEstimating Betas

Energy Materials Industrials ConsDisc ConsStap Health Fin IT Telco Utilities

1995 0.93 1.41 1.19 0.82 0.68 0.36 0.92 1.25 0.53 0.67

1996 0.93 1.28 1.10 0.83 0.66 0.39 1.02 1.36 0.61 0.65

1997 0.98 1.33 0.97 0.82 0.62 0.60 0.93 1.56 0.62 0.53

1998 0.85 1.12 0.94 0.80 0.60 1.02 1.11 1.40 0.92 0.55

1999 0.91 1.04 0.78 0.73 0.43 1.00 1.00 1.55 1.11 0.30

2000 0.67 0.74 0.73 0.69 0.23 1.10 0.79 1.78 0.92 0.14

2001 0.50 0.60 0.82 0.68 0.10 0.98 0.67 2.12 0.94 -0.03

2002 0.43 0.57 0.86 0.73 0.11 0.99 0.67 2.27 0.92 -0.06

2003 0.27 0.42 0.91 0.74 -0.04 0.85 0.39 2.75 0.82 -0.26

2004 0.17 0.42 1.04 0.81 -0.02 0.84 0.41 2.89 0.55 -0.14

2005 0.48 0.78 1.12 0.84 0.14 0.74 0.58 2.71 0.71 -0.01

Source: Data from Financial Post Corporate Analyzer Database

Table 20-15 S&P/TSX Sub Index Beta Estimates

ITBubble



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EquityNortel Stock Price

Nortels stock price reflects the IT bubble and crash.

(See Figure 20 -4 on the following slide for Nortel Stock Price history)



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EquityNortel Stock Price

20 - 4 FIGURE



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EquityIT Bubble effect on Betas of Other Companies Outside the Sector

The bubble in IT stocks has driven down the betas in othersectors.

This is demonstrated in Rothmans beta over the 1966 2004

period. Remember, Rothmans is a stable company and its beta

should be expected to remain constant.

(See Figure 20 -5 on the following slide for Rothmans beta history)



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EquityRothmans Beta Estimates

20 - 5 FIGURE



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EquityAdjusting Beta Estimates and Establishing a Range

When betas are measured over the period of asector bubble or crash, it is necessary to adjust thebeta estimates of firms in other sectors.

Take the industry grouping as a major input, plusthe individual company beta estimate.

Using current MRP and Rf Develop estimates of Keusing the range of Company betas prior to the bubble

or crash



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EquityUsing CAPM to Estimate Kne

We can scale our estimate of the equity holders

required return when accessing new equity andincurring floatation costs.

NPPKK ene /0[ 20-27]


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The Marginal Cost of Capital andInvestment Opportunity Schedule

Cost of Capital

The Investment Opportunity Schedule


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pp y

The IOS is the ranking of a firms investment

opportunities from highest to lowest profitabilityaccording to expected IRR.

When superimposed on the MCC curve, the firm is ableto identify projects that will increase the value of the firm.

A stylized version of this for Rothmans is found in Figure20 6.

Cost of Capital and InvestmentR th I IOS S h d l 2006


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Rothmans Inc.s IOS Schedule, 2006

20 - 6 FIGURE

$11,976Million

Rate ofReturn

WACC

Internal Funds Available

OPTIMAL INVESTMENT

IOS

$177,607Million

Projects expected toincrease the value of the

firm.

The break in the MCC at$177,607 millionindicates that the firm

has a surplus ofinternally-generatedfundsmore than

enough to fund the$11,976 of capital

investments.Projectsrejected.

Investment Opportunity ScheduleA D t il d E l


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A Detailed Example

In practice, the IOS is a detailed list, rank orderedfrom highest IRR to lowest of the investment projectproposals for one year.

As you can see on the following slides:

The width of the columns indicate the capitalinvestment each project requires, and

The height of the columns indicates the forecast IRRfor the project



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A Detailed Example

In any one year, a firm may consider a number of capital projects.

The greater the number of projects undertaken, the more moneythat the firm will have to raise in order to finance them.

There is a limit to the amount of money that can be raised in anyone year (ie. the capital markets are finite ie. there is a limit to the

number of investors and their investment dollars that will considerinvesting in any prospect in any given year.) hence it is important

that the capital budgeting analysis be extended to take this fact into

account.



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A Detailed Example

This Investment opportunity schedule is the prioritized list ofcapital projects, listed by IRR (internal rate of return) fromhighest to lowest.

At the same time, the cumulative investment required is listed.

Example:Consider a firm that has six different capital investment proposals thisyear. Each project has its own IRR and capital cost.

(see the next slide)



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A Detailed Example

Example:Consider a firm that has six different capital investmentproposals this year. Each project has its own IRR and capital

cost. Each project has the same risk as the firm as a whole.

Capital

Project Initial Cost

Annual ATCF

Benefits

Useful

Life NPV IRR

A $1,500,000 $290,000 7 -$88,159 8.19%

B $2,300,000 $529,000 6 $3,933 10.06%

C $3,750,000 $940,000 6 $343,945 13.07%

D $180,000 $40,000 7 $14,737 12.45%

E $985,000 $318,540 5 $222,517 18.50%

F $2,154,000 $421,500 8 $94,671 11.20%

Project A can beeliminated at this

point because it hasa negative NPV.

Investment Opportunity ScheduleA Detailed Example


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A Detailed Example

Example:The first step in developing an IOS is to order the projectsfrom highest IRR to lowest, and then to calculate thecumulative capital cost of the projects.

Capital

Project Initial Cost

Cumulative Cost

of the Projects IRR

E $985,000 $985,000 18.50%

C $3,750,000 $4,735,000 13.07%

D $180,000 $4,915,000 12.45%

F $2,154,000 $7,069,000 11.20%B $2,300,000 $9,369,000 10.06%

A $1,500,000 $10,869,000 8.19%

Investment Opportunity ScheduleA Detailed Example Continued


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A Detailed Example Continued

Example:It was clear at the start that project A was unacceptableit had a

negative NPV.

The remaining projects certainly meet the first investment screen (theyhave positive NPVs that is, they offer rates of return in excess ofthe firms WACC).

Now we can prepare a graphical representation of the IOS by plottingthe projects IRR against the cumulative dollars of capital to be raised.

Investment Opportunity Schedule (IOS)A Detailed Example Continued


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0 $2,000,000 $4,000,000 $6,000,000 $8,000,000 $10,000,000


IRR

(%)

15

10

5

EIRR =

18.5%

CIRR = 13.07%

FIRR = 11.2% B

IRR = 10.06%

DIRR = 12.45%

The height of each cylinder is equal to the projects IRR; the width is equal to the initial

investment for the project.The upper surface of

the columns is theIOS

Investment Opportunity Schedule (IOS)A Detailed Example Continued


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0 $2,000,000 $4,000,000 $6,000,000 $8,000,000 $10,000,000


IRR

(%)

15

10

5

EIRR =

18.5%

CIRR = 13.07%

FIRR = 11.2%

BIRR = 10.06%

DIRR = 12.45%

IOS

MCC Superimposed on the IOSA Detailed Example Continued


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0 $2,000,000 $4,000,000 $6,000,000 $8,000,000 $10,000,000


IRR

(%)

15

10

5

EIRR =

18.5%

CIRR = 13.07%

FIRR = 11.2%

BIRR = 10.06%

DIRR = 12.45%

MCC1=WACC= 9.44%MCC2= 10.64%

The break in the MCC is causedby the exhaustion of low cost

retained earnings and the need tofinance project F through external

offering of equity, incurringfloatation costs.

IRRB

< MCC2

so this projectis rejected. It

will notincrease thevalue of the

firm.

The Break In the IOSA Detailed Example Continued


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The break in the IOS curve (the amount of capital investment thatexhausts retained earnings) can be estimated as:

Assuming the firm has $3.3 million in internal capital to invest andequity represents 60% of the firms capital structure the break point

occurs at:

StructureCapitalin theUpMakesEquitythatPercentage

InvestmentforAvailableEarningsRetainedof$MCCinBreak

$5,500,00060%

$3,300,000MCCinBreak

MCC and IOS


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The foregoing is consistent with economic theorythat states a firm will operate where marginal cost

equals marginal revenue.

Now the rationale for this must be clear. The valueof the firm will fall if it undertakes projects that offer arate of return that is less than the marginal cost of

capital used to finance them.

Divisional Costs of Capital


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An overall cost of capital developed for a highly diversifiedconglomerate may not be appropriate for decisions made withinspecific divisions of the company.

High-risk divisions (with high return possibilities) would have adisproportionate share of their investment proposals accepted if they

use an overall WACC.

The solution to this is to develop risk-adjusted discount rates thatreflect the unique risk characteristics of each division.

Developing these estimates can sometimes be accomplished bylooking at other firms in that industry that are not highly diversified intheir operations this is called the pure play approach.

Summary and Conclusions


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In this chapter you have learned: How types of equity differ in their degree of equityness andtherefore have different costs of capital

WACC is the market value weighted average of the after-taxcosts of all securities used to finance the firm.

If a firm earns more than its WACC, the value of the firm will

rise. Common shareholders are residual claimants hence they hold

the riskiest securities issued by the firm. The most difficult estimate in WACC is the cost of common

equity. DCF approaches to estimating the cost of equity is particularly

prone to errors for high growth firms. CAPM can be used to minimize estimation errors, however,

estimation of beta can be affected by recent stock marketperformance.


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Concept Review Questions

Cost of Capital

Concept Review Question 1Earnings Yield


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Earnings Yield

Why is the earnings yield not usually an adequatemeasure of the required rate of return by equityinvestors?


139/151

Appendix 1Steep Hill Mines 1

An Exercise in Cost of Capital

Steep Hill Mines # 1The Question


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The Question

Steep Hill Mines Ltd. shares are publicly traded on the TorontoStock Exchange. The shares currently trade at a price of $30.00 pershare. Security analysts that follow the stock have estimated it's betacoefficient to be 0.9. Steep Hill paid a dividend on its common stocklast year that totaled $1.50 per share. Dividends have been growing ata 4% compound rate for the past six years and the expectation is thatthis growth can continue into the foreseeable future.

Steep Hill also has it's long-term bonds trading on public markets.The bonds are currently trading at a discount from their par value of96.54%. These 5.75% bonds have ten years left until they mature.

Steep Hill Mines Ltd. has an important capital project to consider.

Project A is expected to produce annual cash flows after tax of$100,000 for the next eight years. It is considered to be of similar riskto the risk of the firm itself. It will cost Steep Hill $400,000 this year toget this project up and running.



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e Quest o

Cathy Jones, Steep Hill's manager of finance has collected currentdata from the firm's underwriters.

Government of Canada 91-day Treasury bills are currently yielding 4.25%. The expected return on the TSE 300 composite index is forecast to be 10% in

the next year

New equity capital could be raised by the firm at the current market price, butfloatation costs would amount of 4% of the value of the issue. New bonds could be sold into the market, but the floatation cost percentage

would be 6%. The firm faces a corporate tax rate of 40%. The company will seek to sustain the current capital structure based on existing

market value weights.

If the firm goes ahead with the capital project, it will have to seek externalfinancing since there is no internal cash flow available for reinvestment.

The firm's most recent financial statements are found below:



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Q

Steep Hill Mines Ltd.

Balance SheetAs at December 31, 20XX

In $ '000sAssets: Liabilities:Cash 100 Accruals 30Accounts Receivable 220 Accounts Payable 312Inventories 450 ____

Total Current Assets 770 Total Current Liabilities 342Gross Fixed Assets 4,000 5.75% bonds 1,000Accumulated Depreciation 1,500 Common stock

(100,000 outstanding) 1,000Net Fixed Assets 2,500 Retained earnings 928TOTAL ASSETS 3,270 TOTAL CLAIMS 3,270

Required:Find the WACC using book value weights, market value weights and target capital structure

weights. Using the target capital structure weights, is the proposed project viable?

Steep Hill Mines # 1The SolutionThe Equity Investors Required Return


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q y q

Investor's Required Return on Equity Capital:DDM Approach:

CAPM Approach:

%2.904.052.004.30$

56.1$04.

30$

)04.1(50.1$)1(

0

0

gP

gDKS

%425.9%175.5%25.4%]25.4%10[9.0%25.4][

S

MsS

KRFERBRFK

Steep Hill Mines # 1The Solution The Cost of Equity


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q y

Investor's Required Return on Equity CapitalThe average of our two estimates for the cost of retained earningsis: (9.2 + 9.425)/2 = 9.3%

This is the returns our current shareholders are demanding on our

stock.If we raise external capital, we will incur floatation costs(underwriter's fees, legal costs, etc.) This represents 4%.

%7.996.

%3.9.4-1

%3.9

f-1

ReturnRequiredInvestors

EquityNewofCost


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Steep Hill Mines # 1The Solution The Cost of Debt


146/151


Since interest on debt is tax deductible to the firm, the after-tax andafter floatation cost of debt is:

Where:

T = 40%

f = 6%

%97.306.1

)4.1%(22.6

1

)1%(22.6

f

TKd

Steep Hill Mines # 1The Solution Determining Market Value Weights


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Market Value Weights:Market values are always found by multiplyingthe number of outstanding securities timestheir price per unit.

Market Value of LT Debt = 1,000 bonds outstanding times $965.40 = $965,400

Market Value of Equity = 100,000 times $30.00 = 3,000,000

TOTAL MARKET VALUE OF THE FIRM = 3,965,400

Market Value Weight of LT Debt = $965,400/$3,965,400 = 24.35%

Market Value Weight of Equity = (1 - .2435) = 75.65%

g g

Steep Hill Mines # 1The Solution Market Value WACC


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The Cost of Capital Using Market Value Weights:

Source of

Capital

Market

Value

Weight

Specific

Marginal

Cost

Weighted

CostL. T. Debt 24.4% 3.97% 0.97%

Preferred 0.0% 0.00% 0.00%

Common 75.7% 9.70% 7.34%

WACC = 8.30%

Steep Hill Mines # 1The Solution


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Viability of the Capital Project

Since the project has similar risk characteristics to the firm asa whole, we do not have to calculate a risk-adjust discountrateinstead, we can just use the firm's WACC.

Since the market value capital structure weights will be usedby the firm in the long run, let's use that as the WACC, anddiscount the prospective after-tax cash flows on this projectback to the present and compare that with the cost of the

project to see if there is a positive NPV.

Steep Hill Mines # 1The Solution Project NPV


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178,168$

000,400$178,568$

000,400$).681788$100,000(5

000,400$083.

(1.083)

1-1

$100,000

000,400$)VIFA$100,000(P

000,400$)VIFA$100,000(P

)1(

...)1()1()1(

8

8.3%k8,n

WACCk8,n

01

03

3

2

2

1

1

NPV

CFk

CF

CFk

CFk

CFk

CFNPV

t

n

i

t

[ 13-1] Using Equation13 -1 for NPV,and substitutingin the annualcash flow

benefits of$100,000 after-tax, initial cost,useful life of 8years, andWACC of 8.3%

we find theproject offers apositive NPV.

Copyright


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Copyright 2007 John Wiley & SonsCanada, Ltd. All rights reserved.Reproduction or translation of this workbeyond that permitted by AccessCopyright (the Canadian copyrightlicensing agency) is unlawful. Requestsfor further information should beaddressed to the PermissionsDepartment, John Wiley & Sons Canada,Ltd. The purchaser may make back-upcopies for his or her own use only andnot for distribution or resale. The authorand the publisher assume noresponsibility for errors, omissions, ordamages caused by the use of these filesor programs or from the use of theinformation contained herein.

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Chapter 20 - Cost of Capital

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