[PPT]Introduction to Corporate Finance - John Wiley & Sons · Web viewINTRODUCTION TO CORPORATE...

Prepared byPrepared byKen HartviksenKen Hartviksen

INTRODUCTION TOINTRODUCTION TO CORPORATE FINANCECORPORATE FINANCELaurence Booth Laurence Booth •• W. Sean Cleary W. Sean Cleary

CHAPTER 20CHAPTER 20 Cost of CapitalCost of Capital

CHAPTER 20 – Cost of Capital 20 - 3

Lecture AgendaLecture Agenda

• Learning ObjectivesLearning Objectives• Important TermsImportant Terms• Financing SourcesFinancing Sources• The Cost of CapitalThe Cost of Capital• Estimating the Component CostsEstimating the Component Costs• The Effect of Operating and Financial LeverageThe Effect of Operating and Financial Leverage• Growth Models and the Cost of Common EquityGrowth Models and the Cost of Common Equity• Risk-Based Models and the Cost of Common EquityRisk-Based Models and the Cost of Common Equity• The Cost of Capital and InvestmentThe Cost of Capital and Investment• Summary and ConclusionsSummary and Conclusions

– Concept Review QuestionsConcept Review Questions– Appendix 1 – Steep Hill Mines # 1Appendix 1 – Steep Hill Mines # 1


Learning ObjectivesLearning Objectives

1.1. How ROE and the required return by common equity How ROE and the required return by common equity investors are related to a firm’s growth opportunitiesinvestors are related to a firm’s growth opportunities

2.2. How to apply the steps involved in estimating a firm’s How to apply the steps involved in estimating a firm’s weighted average cost of capital, including how to estimate weighted average cost of capital, including how to estimate the market values of the various components of capital, the market values of the various components of capital, and how to estimate the various costs of these componentsand how to estimate the various costs of these components

3.3. How operating and financial leverage affect firmsHow operating and financial leverage affect firms

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


Important Chapter TermsImportant Chapter Terms

• Asset turnover ratioAsset turnover ratio• Beta coefficientBeta coefficient• Capital asset pricing modelCapital asset pricing model• Capital structureCapital structure• Cash cowCash cow• Cost of capitalCost of capital• Debt-to-equity ratioDebt-to-equity ratio• DogDog• Earnings yieldEarnings yield• Hurdle rateHurdle rate• Investment opportunities Investment opportunities

schedule (IOS)schedule (IOS)

• Issuing (or floatation) costsIssuing (or floatation) costs• Marginal cost of capital Marginal cost of capital

(MCC)(MCC)• Market-to-book (M/B) ratioMarket-to-book (M/B) ratio• Market risk premiumMarket risk premium• Multi-stage growth DDMMulti-stage growth DDM• Operating leverageOperating leverage• Present value of existing Present value of existing

opportunities (PVEO)opportunities (PVEO)• Present value of growth Present value of growth

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

(ROIC)(ROIC)• Return on equity (ROE)Return on equity (ROE)


Important Chapter Terms…Important Chapter Terms…

• Risk-based modelRisk-based model• Risk-free rate of returnRisk-free rate of return• StarStar• TurnaroundTurnaround• Weighted average cost Weighted average cost

of capital (WACC)of capital (WACC)


The Short Story of WACCThe Short Story of WACCPurposes/UsePurposes/Use

• The weighted average cost of capital (WACC) The weighted average cost of capital (WACC) serves three primary purposes:serves three primary purposes:

1.1. To evaluate capital project proposals before-the-fact.To evaluate capital project proposals before-the-fact.2.2. To set performance targets in order for management to To set performance targets in order for management to

sustain or grow market values, and sustain or grow market values, and 3.3. to measure management performance after-the-fact.to measure management performance after-the-fact.


The Short Story of WACCThe Short Story of WACCWhat Costs are Measured?What Costs are Measured?

• Costs associated with financing the firm’s Costs associated with financing the firm’s invested capital including:invested capital including:– Debt Costs:Debt Costs:

• Bank loansBank loans• Long-term debt – bonds/debenturesLong-term debt – bonds/debentures

– Equity Costs:Equity Costs:• Preferred equity costsPreferred equity costs• Common equity costsCommon equity costs


The Short Story of WACCThe Short Story of WACCWhy the Marginal Cost?Why the Marginal Cost?

• What capital cost the firm 5 months, 5 years What capital cost the firm 5 months, 5 years or 5 decades ago is irrelevant.or 5 decades ago is irrelevant.

• What is relevant is what the next dollar of What is relevant is what the next dollar of capital will cost in today’s economic capital will cost in today’s economic environment for this particular firm.environment for this particular firm.


The Short Story of WACCThe Short Story of WACCSteps in Solving for the WACCSteps in Solving for the WACC

1.1. Identify the relevant sources of capital (debt Identify the relevant sources of capital (debt and equity).and equity).

2.2. Estimate the market values for the sources Estimate the market values for the sources of capital and determine the market value of capital and determine the market value weights.weights.

3.3. Estimate the marginal, after-tax, and after-Estimate the marginal, after-tax, and after-floatation cost for each source of capital.floatation cost for each source of capital.

4.4. Calculate the weighted average.Calculate the weighted average.


The Short Story of WACCThe Short Story of WACCThe FormulaThe 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(

VDTK

VSKKWACC dea

The cost of equity times the market value weight of

equity

The cost of debt after tax times the

market value weight of debt


The Short Story of WACCThe Short Story of WACCThe Spreadsheet ApproachThe Spreadsheet Approach

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

Type of Capital

Specific Marginal Cost after tax and

floatation costs

Market Value

Weights

Weighted Specific Marginal

CostLong-Term Debt 5.5% 43.0% 0.02365Preferred Stock 11.4% 11.0% 0.01254Common Stock 12.9% 46.0% 0.05934

WACC = 9.55%

WACC is the sum of the weighted specific marginal costs of each source of capital.


The Short Story of WACCThe Short Story of WACCFrequently Asked QuestionsFrequently Asked Questions

1.1. Why don’t we include the cost of accruals Why don’t we include the cost of accruals and accounts payable in the cost of capital?and accounts payable in the cost of capital?– These are ‘spontaneous’ liabilities that rise and fall These are ‘spontaneous’ liabilities that rise and fall

with the volume of business activity, and are not with the volume of business activity, and are not subject to formal lending arrangements.subject to formal lending arrangements.

– Accruals (wages and taxes), it can be argued, don’t Accruals (wages and taxes), it can be argued, don’t have an explicit cost.have an explicit cost.

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



2.2. Why is the cost of capital an estimate and does this Why is the cost of capital an estimate and does this matter?matter?– WACC is calculated based on a current estimate of what it will cost for 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 hasn’t yet the next dollar of debt and equity. Since that next dollar hasn’t yet been raised, we are attempting for forecast or estimate that cost.been raised, we are attempting for forecast or estimate that cost.

– To estimate the cost of debt we often assume it is equal to the 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 (Of required rate of return on existing debt outstanding in the markets (Of course, when a firm actually goes to the market, conditions may have course, when a firm actually goes to the market, conditions may have changed, underwriting costs may be greater, etc.)changed, underwriting costs may be greater, etc.)

– Forecasting WACC also requires estimating the cost of equity. There Forecasting WACC also requires estimating the cost of equity. There may different approaches to this task, and will result in a range of may different approaches to this task, and will result in a range of estimates.estimates.

– In the end, WACC will still be an estimate. The key thing to ensure is In the end, WACC will still be an estimate. The key thing to ensure is that the NPV of the project be positive over the range of possible that the NPV of the project be positive over the range of possible WACC’s. (Graph an NPV profile and determine the range of WACCs WACC’s. (Graph an NPV profile and determine the range of WACCs that will still produce a positive NPV.)that will still produce a positive NPV.)



3.3. Why is the component cost of capital greater than the Why is the component cost of capital greater than the investor’s required return ?investor’s required return ?

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

Cash and marketable securities

Accounts receivable

Inventory

Investment Dealer

Investor buys one new share in a company and pays the investment dealer $20 for it.

$20.00

Investment dealer gives the issuing firm $18.00 for the share, and pockets $2.00 for providing underwriting services.

Issuing company receives $18.00.

$18.00

Investor requires a 10% return on her investment of $20. This is a $2.00 return on invested capital.

Conclusion: The cost of external capital is greater than the investor’s required return because of floatation costs.

The company must produce $2.00 income on an $18.00 investment to meet the investor’s expectations. This is an 11.1% return.


The Short Story of WACCThe Short Story of WACCSummarySummary

• WACC measures the firm’s cost of financing future growth WACC measures the firm’s cost of financing future growth today, based on current capital market conditions, and today, based on current capital market conditions, and assuming the firm use a long-term average of financing assuming the firm use a long-term average of financing sources.sources.

• WACC is an estimate.WACC is an estimate.• WACC is used to make capital investment decisions.WACC is used to make capital investment decisions.• WACC is used to set performance targets for sales, and WACC is used to set performance targets for sales, and

ROE.ROE.• WACC is used to assess management’s performance, WACC is used to assess management’s performance,

answering the question, “has management added value?”answering the question, “has management added value?”


Financing SourcesFinancing SourcesCapital StructureCapital Structure

• Table 20 - 1 illustrates the basic structure of a firm’s Table 20 - 1 illustrates the basic structure of a firm’s balance sheet:balance sheet:– This is a snapshot of the firm’s financial position at one point in This is a snapshot of the firm’s financial position at one point in

time.time.– Left-hand side of the Balance SheetLeft-hand side of the Balance Sheet

• Assets – the things the firm ownsAssets – the things the firm owns• Note the structure of assets (relative proportions of current assets Note the structure of assets (relative proportions of current assets

and net fixed assets)and net fixed assets)– Right-hand side of the Balance SheetRight-hand side of the Balance Sheet

• Liabilities – the borrowed sources of financingLiabilities – the borrowed sources of financing– Note the structure of liabilities (the relative proportions of current versus Note the structure of liabilities (the relative proportions of current versus

long-term debt)long-term debt)• Shareholders’ equity – owner’s investment in the businessShareholders’ equity – owner’s investment in the business

– Note the amount of capital invested versus the amount of earnings that Note the amount of capital invested versus the amount of earnings that have been reinvested in the businesshave been reinvested in the business



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

Cash and marketable securities

Accounts receivable

Inventory

The Financial Structure

Capital Structure


Important TermsImportant Terms

• Financial StructureFinancial Structure– The whole right-hand side of the balance sheetThe whole right-hand side of the balance sheet– Includes both short-term and long-term sources of financing Includes both short-term and long-term sources of financing

(debt and equity)(debt and equity)• Capital StructureCapital Structure

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

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

– Includes:Includes:• Bank Loans Bank Loans • Long-term debtLong-term debt• Common stock and retained earningsCommon stock and retained earnings

(See Table 20 – 2 for a typical example)(See Table 20 – 2 for a typical example)



$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

Cash and marketable securitiesAccounts receivableInventory

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


Financing SourcesFinancing SourcesInterpreting Balance SheetsInterpreting Balance Sheets

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

decision-making purposes.decision-making purposes.• Analysis of reported data should include ratios such Analysis of reported data should include ratios such

as:as:– Debt – to – Equity:Debt – to – Equity:

• Interest bearing debt to shareholder’s equity plus minority interestInterest bearing debt to shareholder’s equity plus minority interest– Convert book values to market valuesConvert book values to market values

• This is done by multiplying the market-to-book ratio times the book This is done by multiplying the market-to-book ratio times the book value.value.

• Interpret the ratios again.Interpret the ratios again.

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


Financing SourcesFinancing SourcesDebt-to-Equity RatioDebt-to-Equity Ratio

$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



70.0000,1$$650$50 RatioEquity -to-Debt

Debt =

Equity =


Financing SourcesFinancing SourcesConverting Book Value to Market ValuesConverting Book Value to Market Values

Book Values$50 Accruals $100200 Accounts payable 200250 Short-term debt 50

0 Total current liabilities 350Total current assets 500 Long-term debt 650

1,500 Shareholders' equity 1,000Total assets $2,000 Total liabilities and shareholders' equity $2,000

Prepaid expenses

Net fixed assets



Market value of debt will be very close (if not equal) to the book values stated on the balance sheet. This is because these are contractual claims that are not negotiable (traded in secondary markets). The amounts stated are the amounts that are required to satisfy the financial claims of these creditors.

The market value of long-term debt will depend on interest rate changes since the debt was originally issued. As the bonds approach maturity, their market price will move progressively to equal their par (face) value. It is the face value of the debt that is presented here.

Equity =

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


Financing SourcesFinancing SourcesConverting Book Value to Market ValuesConverting Book Value to Market Values

Book Values Market Values$50 Accruals $100 $100200 Accounts payable 200 200250 Short-term debt 50 50

0 Total current liabilities 350 350Total current assets 500 Long-term debt 650 650

1,500 Shareholders' equity 1,000 2,500Total assets $2,000 Total liabilities and shareholders' equity $2,000 $3,500

Prepaid expenses

Net fixed assets



28.0500,2$$650$50 RatioEquity -to-Debt ued"Market val"

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

This confirms the importance of using relevant data when making decisions.


The Most Important Corporate Finance The Most Important Corporate Finance DecisionsDecisions

• It is the managers job to maximize shareholders’ It is the managers job to maximize shareholders’ wealth.wealth.

• In this and the next chapter we will address two of the In this and the next chapter we will address two of the most important ways manager can add value to the most important ways manager can add value to the firm:firm:– Changing the mix of financing used by the firm (changing the Changing the mix of financing used by the firm (changing the

relative proportions of debt and equity), andrelative proportions of debt and equity), and– Determining the minimum rate of return needed to maintain the Determining the minimum rate of return needed to maintain the

current market value.current market value.


Valuation Equation for a PerpetuityValuation Equation for a PerpetuityThree Ways of Using the Valuation EquationThree Ways of Using the Valuation Equation

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

• Where:Where:SS = the present value of the perpetuity = the present value of the perpetuityXX = the forecast annual earnings = the forecast annual earningsKKee = the investor’s required return = the investor’s required return

eK

XS [ 20-1] $20.0010.000.2$

S[ 20-1]

If the annual cash flow is $2.00 and the investor’s required return is 10%, the present value of the perpetuity is $20.



• The equation can be rearranged to solve for the The equation can be rearranged to solve for the required return required return KKe e also known as the also known as the earnings yieldearnings yield::

• The earnings yield is not normally used as the The earnings yield is not normally used as the investor’s required return because it simply measures investor’s required return because it simply measures forecast earnings as a percentage of the market price, forecast earnings as a percentage of the market price, ignoring growth opportunities.ignoring growth opportunities.

SXKe [ 20-2] 10%

$20.00$2.00

SXKe[ 20-2]



• The perpetuity valuation model can be further rearranged The perpetuity valuation model can be further rearranged to solve for the forecast earnings given the current to solve for the forecast earnings given the current market price and investor’s required return.market price and investor’s required return.

• This helps managers determine their earnings target that This helps managers determine their earnings target that must be met to support the current market value.must be met to support the current market value.

• If the manager knows the investor requires a 10% rate of If the manager knows the investor requires a 10% rate of return and the market price is $20.00, she knows the firm return and the market price is $20.00, she knows the firm must generate $2.00 in EPS to sustain the stock price.must generate $2.00 in EPS to sustain the stock price.

SKX e [ 20-3] $2.00 $20.00 0.10 SKX e


Setting Performance TargetsSetting Performance TargetsUsing Required Returns and Market ValuesUsing Required Returns and Market Values

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

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

• Working back from these requirements we can forecast the Working back from these requirements we can forecast the level of sales the firm must earn in order to achieve these level of sales the firm must earn in order to achieve these operating results…thereby setting a sales performance target operating results…thereby setting a sales performance target for management.for management.

(1) (2) (3) =(1)×(2)

Market ValueRequired Return

Earnings Required

Debt (D) $700 6.0% $42Equity (S) 2500 12.0% 300V=D+S = $3,200 $342


Setting Performance TargetsSetting Performance TargetsDeriving the Deriving the RequiredRequired Income Statement Income Statement

Sales ? $1,000Variable costs 300 300Fixed costs 158 158EBIT ? $542Interest 42 42Tax (40%) #VALUE! 200Net Income $300 $300

Table 20-3 A Forecasted Income Statement Given the need to earn $42 to cover interest, and to earn $300 after-tax for shareholders, and given a fixed corporate tax rate and other costs, we can determine the Sales required to achieve these goals.

It is $1,000

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

$300$42

)1(

TIncomeNetInterestEBIT

$1,000 $542 $158 $300 EBIT Costs Fixed Costs Variable

Sales

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

So, the cost of capital drives utility rate increases.


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

• Once you have the sales performance target you can Once you have the sales performance target you can establish other operating targets through the application of establish other operating targets through the application of ratios.ratios.

• Since equity in this case is a perpetuity we can express the Since equity in this case is a perpetuity we can express the price per share as:price per share as:

• Dividing both sides of Equation 20 – 4 by BVPS we get the Dividing both sides of Equation 20 – 4 by BVPS we get the basic relationship that drives the M/B ratio:basic relationship that drives the M/B ratio:

ee KBVPSROE

KEPSP

[ 20-4]


Setting Performance TargetsSetting Performance TargetsThe Relationship Between BVPS and MVPS – How to Increase The Relationship Between BVPS and MVPS – How to Increase

Shareholder ValueShareholder Value

• Equation 20 – 5 tells us:Equation 20 – 5 tells us:– If the ROE exceeds the investors required return (If the ROE exceeds the investors required return (KKee) )

then the price of the stock will rise above book value.then the price of the stock will rise above book value.

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

eK

ROEBVPS

P[ 20-5]


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

• The overall market value of the firm is:The overall market value of the firm is:

V = D + SV = D + S

– In our example V= $3,200In our example V= $3,200– After-tax ROI After-tax ROI = 19.13% = 19.13%

= (EBIT)(1-T) = ($542 (1-.4))= (EBIT)(1-T) = ($542 (1-.4))= $325.20 = $325.20

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



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

• First rewrite EBIT minus taxes as ROI × IC and re-express First rewrite EBIT minus taxes as ROI × IC and re-express the valuation equation as:the valuation equation as:

• Equation 20 – 6 can be rearranged to solve for Equation 20 – 6 can be rearranged to solve for KKaa for an all for an all equity firm:equity firm:

aK

ICROIV [ 20-6]



• Using the numbers from the continuing example the WACC is:Using the numbers from the continuing example the WACC is:

• On the following slide will show how we can now substitute in On the following slide will show how we can now substitute in component costs for both equity and debt to develop the component costs for both equity and debt to develop the general equation for WACC (Kgeneral equation for WACC (Kaa))

V

ICROIKa

[ 20-7]

10.16% $3,200$325.20

V

ICROIKa



11VD-T)(K

VSK

VT)D(KSK

VICROIK de

dea

[ 20-8]

The WACC is simply the weighted average of the component costs.



• The equation for WACC including common equity, The equation for WACC including common equity, preferred share financing and debt is:preferred share financing and debt is:

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

V = S + P + DV = S + P + D

1VD-T)(K

VPK

VSKWACC dpe [ 20-9]


Estimating Market ValuesEstimating Market ValuesMarket Value of EquityMarket Value of Equity

• The total market value of equity (market The total market value of equity (market capitalization) is the price per share times the capitalization) is the price per share times the number of shares outstanding:number of shares outstanding:

n 0 PS[ 20-10]


Estimating Market ValuesEstimating Market ValuesMarket Value of Preferred StockMarket Value of Preferred Stock

• The market price for preferred is simply the annual The market price for preferred is simply the annual preferred dividend divided by the preferred shareholder’s preferred dividend divided by the preferred shareholder’s required return.required return.

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

0p

p

kD

P [ 20-11]

n 0 PS[ 20-10]


Estimating Market ValuesEstimating Market ValuesMarket Value of BondsMarket Value of Bonds

• As previously mentioned, the market value of bonds will As previously mentioned, the market value of bonds will differ from their book value only if required rates of return differ from their book value only if required rates of return in the market have changed since the bonds original issue.in the market have changed since the bonds original issue.

• Knowing the term to maturity, the coupon rate and the Knowing the term to maturity, the coupon rate and the bondholder’s required return we can determine the market bondholder’s required return we can determine the market value of bonds with equation 20 - 12:value of bonds with equation 20 - 12:

1

1111

nbb

nb

)k(F

k)k(IB

[ 20-12]


Estimating Market ValuesEstimating Market ValuesMarket Value of BondsMarket Value of Bonds

• Once you know the market value of the bonds, you multiply Once you know the market value of the bonds, you multiply their price by the number of bonds outstanding to their price by the number of bonds outstanding to determine total market value.determine total market value.

n bPB[ 20-10]


Market Value WeightsMarket Value WeightsAn ExampleAn Example

Given:Given:– Market price for common stock = $21.50Market price for common stock = $21.50– Bonds are trading for 95% of face valueBonds are trading for 95% of face value

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

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

Total Market Capitalization = Price × QuantityTotal Market Capitalization = Price × QuantityThe following balance sheet date, when combined with market price data, will allow you to calculate MV weights.The following balance sheet date, when combined with market price data, will allow you to calculate MV weights.


Market Value WeightsMarket Value WeightsAn ExampleAn Example

XYZ Company LimitedXYZ Company LimitedBalance SheetBalance Sheetas at January 30, 2xxxas at January 30, 2xxx

ASSETSASSETS LIABILITIES:LIABILITIES:Current AssetsCurrent Assets $147,000$147,000Current LiabilitiesCurrent Liabilities $75,250$75,250Net Fixed AssetsNet Fixed Assets 15,000,25015,000,2508.5% 2020 Mortgage Bonds8.5% 2020 Mortgage Bonds 4,000,0004,000,000

Common stock (1,000,000 outstanding)Common stock (1,000,000 outstanding) 7,155,0007,155,000Retained earningsRetained earnings 3,917,0003,917,000

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

Number of common shares outstanding is read from the

balance sheet.

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


Market Value WeightsMarket Value WeightsAn Example Continued…An 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

Market Value

WeightBonds $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.


Bond ValueBond ValueGeneral FormulaGeneral Formula

)k(

Fk

)k(IB nbb

nb

111

11

[ 20-12]

Where:I = interest (or coupon ) paymentskb = the bond discount rate (or market rate)n = the term to maturityF = Face (or par) value of the bond

• In the example, you didn’t have to calculate the bond value In the example, you didn’t have to calculate the bond value because you were given the fact that it was trading at 95% of par.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.In the event that you do, however, simply use equation 20 -12.


Estimating the Component CostsEstimating the Component CostsFloatation CostsFloatation Costs

• Issuing or floatation costs are incurred by a firm when Issuing or floatation costs are incurred by a firm when it raises new capital through the sale of securities in it raises new capital through the sale of securities in the primary market.the primary market.

• These costs include:These costs include:– Underwriting discounts paid to the investment dealerUnderwriting discounts paid to the investment dealer– Direct costs associated with the issue including legal and Direct costs associated with the issue including legal and

accounting costsaccounting costs• The result:The result:

– Net proceeds on the sale of each security is less than what the Net proceeds on the sale of each security is less than what the investor invests, andinvestor invests, and

– The component cost of capital > investor’s required return.The component cost of capital > investor’s required return.

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


Estimating the Component CostsEstimating the Component CostsFloatation Costs and the Marginal Cost of Capital (MCC)Floatation 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 the investor pays and what the firm receives, the difference being the money that is lost to these costs. Issue costs are responsible for the component cost of capital being greater than the investor’s required return.

Floatation costs for debt securities is lowest because debt is normally privately placed with large institutional investors not requiring underwriting costs and because debt is either issued by high quality issuers or sits at the top of the priority of claims list in the case of default.


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

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

• At low levels of financing the WACC = MCCAt low levels of financing the WACC = MCC• As a firm raises more and more capital in a given year, As a firm raises more and more capital in a given year,

it will exhaust the supply of lower cost sources, and it will exhaust the supply of lower cost sources, and then have to access marginally higher cost sources.then have to access marginally higher cost sources.– Therefore MCC increases with the amount of capital to be Therefore MCC increases with the amount of capital to be

raised.raised.

The following figure illustrates the MCC concept.The following figure illustrates the MCC concept.


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 MCCThe 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

10040)3.1%(8

10060%14

)1(2

VDtK

VSKMCC de

%44.9%24.2%2.7)4%(.6.5)6%(.12

10040)3.1%(8

10060%12

)1(1

VDtK

VSKMCC 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% by internal equity (R/E). (60% × cost

of retained earnings = 7.2%)

Each dollar of capital invested beyond $5.5 million is financed 60% by new equity. (60% × cost of new equity = 8.4%)


The Component Cost of DebtThe Component Cost of Debt

• The cost of debt is a function of:The cost of debt is a function of:– The investor’s required rate of returnThe investor’s required rate of return– The tax-deductibility of interest expenseThe tax-deductibility of interest expense– The floatation costs incurred to issue new debtThe floatation costs incurred to issue new debt


The Component Cost of DebtThe Component Cost of Debt

%19.697.0%6

.03-10.4)-(1.010%

f-1

T)-(1Return Required sInvestor' Debt ofCost d

• If you know the debt investor’s required rate of return KIf you know the debt investor’s required rate of return Kdd , the , the corporate tax rate and the floatation cost percentage for debt, you corporate tax rate and the floatation cost percentage for debt, you can estimate the cost of debt in the following manner:can estimate the cost of debt in the following manner:

• Assume:Assume:KKdd = 10% (debt investor’s required return)= 10% (debt investor’s required return)

TT = 40% (corporate tax rate) = 40% (corporate tax rate)ffdd = 3% (floatation cost percentage)= 3% (floatation cost percentage)

The after tax cost of debt is lower than the

investor’s required return because of the tax shield on interest

expense.


Estimating the Component CostsEstimating the Component CostsDebtDebt

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

• KKii = the after-tax and after-floatation cost of debt. = the after-tax and after-floatation cost of debt.

1

1111

)1( nii

ni

)K(F

K)K(TINP

[ 20-13]

Net proceeds on the sale of the bond = Selling price – floatation cost per bond.

Coupon interest times 1 minus corporate tax rate = after tax cost of interest


Estimating the Component CostsEstimating the Component CostsPreferred SharesPreferred Shares

• If you know the preferred If you know the preferred share investor’s required rate share investor’s required rate of return Kof return Kpp , and the , and the floatation cost percentage for floatation cost percentage for preferred share financing, you preferred share financing, you can estimate the cost of can estimate the cost of preferred shares in the preferred shares in the following manner:following manner:

• Assume:Assume:KKpp = 14% (preferred investor’s = 14% (preferred investor’s

required return)required return)F = 5% (floatation cost percentage)F = 5% (floatation cost percentage)

%74.1495.0%14

.05-114%

f-1

Return Required sInvestor' Preferred ofCost p

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

Floatation costs cause

the component cost to be

greater than the investor’s

required return.


Estimating the Component CostsEstimating the Component CostsPreferred SharesPreferred Shares

• Alternatively, the component cost of preferred Alternatively, the component cost of preferred shares can be found using equation 20 -14, where shares can be found using equation 20 -14, where NP is the selling price per preferred share less the NP is the selling price per preferred share less the floatation costs per share.floatation costs per share.

NPD

K pp [ 20-14]


Estimating the Component CostsEstimating the Component CostsCommon SharesCommon Shares

• Estimating the component cost of common stock is Estimating the component cost of common stock is the most difficult because:the most difficult because:– Promised cash flows are uncertainPromised cash flows are uncertain– Growth opportunities, their timing and magnitude will influence Growth opportunities, their timing and magnitude will influence

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

such as the use of leveragesuch as the use of leverage• There are numerous alternative approaches that we There are numerous alternative approaches that we

will present to estimate the component cost of equity.will present to estimate the component cost of equity.• Before doing so, we will first address the effect of Before doing so, we will first address the effect of

leverage on shareholders.leverage on shareholders.


LeverageLeverage

• The increased volatility in operating income The increased volatility in operating income over time, created by the use of fixed costs in over time, created by the use of fixed costs in lieu of variable costs.lieu of variable costs.– Leverage magnifies profits and losses.Leverage magnifies profits and losses.

• There are two types:There are two types:– Operating leverageOperating leverage– Financial leverageFinancial leverage

• Both types of leverage have the same effect Both types of leverage have the same effect on shareholders but are accomplished in very on shareholders but are accomplished in very different ways, for very different purposes different ways, for very different purposes strategically.strategically.


Leverage Effects on Operating IncomeLeverage Effects on Operating Income

Years

When a firm increases the use of fixed costs it increases the volatility of operating income.

Normal volatility of operating income

Operating Income

+

0

-


Operating LeverageOperating LeverageWhat is it? How is it Increased?What is it? How is it Increased?

• Your textbook defines operating leverage as:Your textbook defines operating leverage as:– The increased volatility in operating income caused by fixed The increased volatility in operating income caused by fixed

operating costs.operating costs.• You should understand that managers do make You should understand that managers do make

decisions affecting the cost structure of the firm.decisions affecting the cost structure of the firm.• Managers can, and do, decide to invest in assets that Managers can, and do, decide to invest in assets that

give rise to additional fixed costs and the intent is to give rise to additional fixed costs and the intent is to reduce variable costs.reduce variable costs.– This is commonly accomplished by a firm choosing to become This is commonly accomplished by a firm choosing to become

more capital intensive and less labour intensive, thereby more capital intensive and less labour intensive, thereby increasing operating leverage.increasing operating leverage.


Operating LeverageOperating LeverageAdvantages and DisadvantagesAdvantages and Disadvantages

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

profitable.profitable.– Operating efficiencies (faster production, fewer errors, higher Operating efficiencies (faster production, fewer errors, higher

quality) usually result increasing productivity, reducing quality) usually result increasing productivity, reducing ‘downtime’ etc.‘downtime’ etc.

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

earn enough revenue to cover its costs.earn enough revenue to cover its costs.– Higher break even pointHigher break even point– High capital cost of equipment and the illiquidity of such an High capital cost of equipment and the illiquidity of such an

investment make it:investment make it:• Expensive (more difficult to finance)Expensive (more difficult to finance)• Potentially exposed to technological obsolescence, etc.Potentially exposed to technological obsolescence, etc.


Financial LeverageFinancial LeverageWhat is it? How is it Increased?What is it? How is it Increased?

• Your textbook defines financial leverage as:Your textbook defines financial leverage as:– The increased volatility in operating income caused The increased volatility in operating income caused

by fixed financial costs.by fixed financial costs.• Financial leverage can be increased in the Financial leverage can be increased in the

firm by:firm by:– Selling bonds or preferred stock (taking on financial Selling bonds or preferred stock (taking on financial

obligations with fixed annual claims on cash flow)obligations with fixed annual claims on cash flow)– Using the proceeds from the debt to retire equity (if Using the proceeds from the debt to retire equity (if

the lenders don’t prohibit this through the bond the lenders don’t prohibit this through the bond indenture or loan agreement)indenture or loan agreement)


Financial LeverageFinancial LeverageAdvantages and DisadvantagesAdvantages and Disadvantages

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

profitable.profitable.– Lower cost of capital at low to moderate levels of financial Lower cost of capital at low to moderate levels of financial

leverage because interest expense is tax-deductible.leverage because interest expense is tax-deductible.Disadvantages:Disadvantages:

– Magnification of losses to the shareholders if the firm does not Magnification of losses to the shareholders if the firm does not earn enough revenue to cover its costs.earn enough revenue to cover its costs.

– Higher break even point.Higher break even point.– At higher levels of financial leverage, the low after-tax cost of At higher levels of financial leverage, the low after-tax cost of

debt is offset by other effects such as:debt is offset by other effects such as:• Present value of the rising probability of bankruptcy costsPresent value of the rising probability of bankruptcy costs• Agency costsAgency costs• Lower operating income (EBIT), etc.Lower operating income (EBIT), etc.


Effects of Operating and Financial LeverageEffects of Operating and Financial LeverageSummarySummary

• Equity holders bear the added risks Equity holders bear the added risks associated with the use of leverage.associated with the use of leverage.

• The higher the use of leverage (either The higher the use of leverage (either operating or financial) the higher the risk to operating or financial) the higher the risk to the shareholder.the shareholder.

• Leverage therefore can and does affect Leverage therefore can and does affect shareholders required rate of return, and in shareholders required rate of return, and in turn this influences the cost of capital.turn this influences the cost of capital.

HIGHER LEVERAGE = HIGHER COST OF CAPITALHIGHER LEVERAGE = HIGHER COST OF CAPITAL


The Importance of GrowthThe Importance of Growth

• To this point we have been valuing stock as a To this point we have been valuing stock as a perpetuity:perpetuity:– This means that we are assuming the current dividend will be This means that we are assuming the current dividend will be

paid each year in the future into infinity.paid each year in the future into infinity.• Table 20 – 8 illustrates the importance of growth Table 20 – 8 illustrates the importance of growth

opportunities to the price of dividend paying stocks on opportunities to the price of dividend paying stocks on the TSX.the TSX.

• On average, 62.22% of the market value of this On average, 62.22% of the market value of this sample of firms could be attributed to growth sample of firms could be attributed to growth opportunities and the remaining 37.78% to the opportunities and the remaining 37.78% to the present value of the current dividend (perpetuity present value of the current dividend (perpetuity value)value)


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 26.0CAE 11.50 0.161 1.40 3.22 72.0Dennings 3.50 0.102 2.90 2.04 42.0EL Financial 285 0.570 0.20 11.40 96.0GSW (A) 26.75 0.428 1.60 8.56 68.0Hammersen 14.05 0.197 1.40 3.94 72.0Intrawest 6.95 0.292 4.20 5.84 16.0Jannock 29.60 0.148 0.50 2.96 90.0Average 1.89 62.22

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

Table 20-8 Stock Prices and Growth Prospects

Stock Market Time Horizon

Growth Models and the Cost of Common Growth Models and the Cost of Common EquityEquity

The Importance of Adjusting for GrowthThe Importance of Adjusting for Growth

Current stock price

Perpetuity value of current

dividend

% of Current Market Value explained by

growth opportunities.



The Constant Growth ModelThe Constant Growth Model

• The Gordon model assumes constant growth in the The Gordon model assumes constant growth in the stream of dividends from stream of dividends from t =1t =1 through through ∞∞::

• The price of a share (The price of a share (PP0 0 ) today equals the expected ) today equals the expected dividend at dividend at t =1 t =1 dividend b the required shareholder dividend b the required shareholder return (return (K K e e ) minus the long-run growth rate () minus the long-run growth rate (g)g) . .

• This formula can be rearranged to solve for the This formula can be rearranged to solve for the investor’s required rate of return (investor’s required rate of return (K K e e ):):

10

gKDP

[ 20-15]


Constant Growth ModelConstant Growth ModelThe Cost of Common Equity Using Internal FundsThe Cost of Common Equity Using Internal Funds

• Investor’s required rate of return consists of two Investor’s required rate of return consists of two components:components:

1.1. Expected dividend yieldExpected dividend yield2.2. Expected long-run growth rate (g)Expected long-run growth rate (g)

– This is the cost of internal equity (the cost of retained This is the cost of internal equity (the cost of retained earnings where the firm does not need to incur earnings where the firm does not need to incur floatation costs)floatation costs)

0

1 g PDKe [ 20-16]


Constant Growth ModelConstant Growth ModelThe Cost of New EquityThe Cost of New Equity

• The model can be modified to solve for the The model can be modified to solve for the cost of new equity by using NP (net proceeds cost of new equity by using NP (net proceeds the firm receives for each new share sold the firm receives for each new share sold after floatation costs)after floatation costs)

1 g NPDKne [ 20-17]


Constant Growth ModelConstant Growth ModelCautionCaution

• The constant growth model can only be used The constant growth model can only be used in cases where it is reasonable to assume in cases where it is reasonable to assume that the growth rate can be sustained in the that the growth rate can be sustained in the very long term.very long term.– This usually means, using it only for large, mature This usually means, using it only for large, mature

‘blue-chip’ companies that already pay a significant ‘blue-chip’ companies that already pay a significant dividend.dividend.

• The Gordon model SHOULD NOT be used on The Gordon model SHOULD NOT be used on smaller, more rapidly growing firms where smaller, more rapidly growing firms where high current growth rates are experienced, high current growth rates are experienced, but cannot be sustained in the long term. but cannot be sustained in the long term.



Growth and ROEGrowth and ROE

• One way to estimate growth is the One way to estimate growth is the sustainable growth method:sustainable growth method:– Growth rate is the product of the firm’s retention rate Growth rate is the product of the firm’s retention rate

(b), times the forecast ROE:(b), times the forecast ROE:

– This definition of This definition of gg can be used in the Gordon model: can be used in the Gordon model:

ROE bg [ 20-18]




• Substituting the sustainable growth rate into the Substituting the sustainable growth rate into the Gordon model:Gordon model:

• Now we can recognize that the expected dividend DNow we can recognize that the expected dividend D11 is the expected earnings per share (Xis the expected earnings per share (X11) times the ) times the dividend payout ratio (one minus the retention rate):dividend payout ratio (one minus the retention rate):

10

ROEbKDP

e [ 20-19]




• This equation shows that the price per share is This equation shows that the price per share is determined by:determined by:– The firm’s forecast EPSThe firm’s forecast EPS– Dividend payout (1 – b)Dividend payout (1 – b)– ROEROE– Required return by common shareholders (KRequired return by common shareholders (Kee))

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

)1(10

ROEbKbXP

e

[ 20-20]




• Rearranging Equation 20 – 20 by substituting Rearranging Equation 20 – 20 by substituting alternative expressions for alternative expressions for DD11 and and g g ::

• When this equation is used to estimate the cost of When this equation is used to estimate the cost of equity capital (internal) for three different growth equity capital (internal) for three different growth scenarios (10%, 12% and 14%) we get some unusual scenarios (10%, 12% and 14%) we get some unusual results summarized in Table 20 – 9:results summarized in Table 20 – 9:

1

0

1

0

1 ROE bP

b)(X gPDKe

[ 20-21]




ROE P0 Expected Dividend

Yield

Sustainable Growth Rate

Ke

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 as expected growth rate rises.

Three different sustainable growth rates.

A lower dividend yield. As prices rise, dividends as a percentage of share price,

fall.

The firm’s 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 rate changes under the three scenarios where ROE is 10, 12 and 14%.




b 14.0% 12.0% 10.0%0.40 $18.75 $16.67 $15.000.41 18.85 16.67 14.940.42 18.95 16.67 14.870.43 19.06 16.67 14.810.44 19.18 16.67 14.740.45 19.30 16.67 14.670.46 19.42 16.67 14.590.47 19.56 16.67 14.520.48 19.70 16.67 14.440.49 19.84 16.67 14.370.50 20.00 16.67 14.290.51 20.16 16.67 14.200.52 20.34 16.67 14.120.53 20.52 16.67 14.030.54 20.72 16.67 13.940.55 20.93 16.67 13.850.56 21.15 16.67 13.750.57 21.39 16.67 13.650.58 21.65 16.67 13.550.59 21.93 16.67 13.440.60 22.22 16.67 13.33

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

ROE

Retention rate

increases as you go

south.

When ROE = 10%, share

price decreases as

the firm retains more money.


price remains the same as

the firm increases the retention rate.


price increases as

the firm retains more money.

The shareholder’s required return is 12%.

When a firm retains more earnings and reinvests them at a lower rate than what shareholders require, the value of the firm falls.

Clearly, the key to share price growth is to reinvest earnings at rates greater than the cost of capital.


Hurdle RateHurdle RateThe Cost of CapitalThe Cost of Capital

• Table 20 -10 tells us that the cost of capital is Table 20 -10 tells us that the cost of capital is a hurdle rate.a hurdle rate.

• The HURDLE RATE is the return on an The HURDLE RATE is the return on an investment required to create value; below investment required to create value; below this rate, an investment will destroy value.this rate, an investment will destroy value.


Growing Firms Versus Growth FirmsGrowing Firms Versus Growth Firms

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

capital:capital:

ROE = ROE = KKee

Growth FirmsGrowth Firms– Does something that shareholders cannot do – reinvest Does something that shareholders cannot do – reinvest

earnings at rates higher than the cost of capital.earnings at rates higher than the cost of capital.

ROE > ROE > KKee


Growth FirmsGrowth FirmsImportance of the Reinvestment Rate of ReturnImportance of the Reinvestment Rate of Return

Growth FirmsGrowth Firms– Does something that shareholders cannot do – reinvest earnings Does something that shareholders cannot do – reinvest earnings

at rates higher than the cost of capital.at rates higher than the cost of capital.

ROE > ROE > KKee

This is the reason earnings yield is not an appropriate estimate of the This is the reason earnings yield is not an appropriate estimate of the firm’s cost of capital.firm’s cost of capital.

What is relevant is NOT whether dividends or earnings are growing, What is relevant is NOT whether dividends or earnings are growing, but rather WHETHER THE FIRM IS INVESTING AT RATES OF but rather WHETHER THE FIRM IS INVESTING AT RATES OF RETURN GREATER THAN THE COST OF CAPITAL.RETURN GREATER THAN THE COST OF CAPITAL.

Of course, this means, the firm should be investing in projects with Of course, this means, the firm should be investing in projects with positive NPVs (IRRs > cost of capital)positive NPVs (IRRs > cost of capital)



Multi-Stage Growth ModelsMulti-Stage Growth Models

• Multi-stage DDM is a version of the DDM that Multi-stage DDM is a version of the DDM that accounts for different levels of growth in accounts for different levels of growth in earnings and dividends.earnings and dividends.

• There is no limit to the number of growth There is no limit to the number of growth stages one can forecast for a given company, stages one can forecast for a given company, so this is a very flexible model.so this is a very flexible model.

• See Chapter 7 for detailed pricing model See Chapter 7 for detailed pricing model description.description.


Simple Two-stage Growth ModelSimple Two-stage Growth ModelMulti-Stage Growth ModelsMulti-Stage Growth Models

• Equation 20 – 22 is a simple, two-stage growth Equation 20 – 22 is a simple, two-stage growth model.model.

• It breaks the stock price into two components:It breaks the stock price into two components:1.1. PVEO – present value of existing opportunities (the value of the firms PVEO – present value of existing opportunities (the value of the firms

current operations assuming no new investment) andcurrent operations assuming no new investment) and2.2. PVGO – present value of growth opportunities – the net present value PVGO – present value of growth opportunities – the net present value

today of the firm’s future investments.today of the firm’s future investments.

)()1(

210

e

e

ee KKROE

KInv

KBVPSROEP

[ 20-22]

PVEO PVGO


Simple Two-stage Growth ModelSimple Two-stage Growth ModelPVEO and PVGOPVEO and PVGO

• PVGO is discounted back to the present by one year because PVGO is discounted back to the present by one year because it represents an incremental investment decision today that it represents an incremental investment decision today that won’t result in the first cash flow until one year from now.won’t result in the first cash flow until one year from now.

• PVGO does add a perpetual amount represented by the PVGO does add a perpetual amount represented by the difference between ROEdifference between ROE22 earned on this added investment earned on this added investment and Kand Kee

)()1(

210

e

e

ee KKROE

KInv

KBVPSROEP

[ 20-22]

PVEO PVGO


Simple Two-stage Growth ModelSimple Two-stage Growth ModelPVGO and ROEPVGO and ROE22

IfIf ROEROE22 = K = Kee thenthen the the future investment adds nothing future investment adds nothing to the value of the firmto the value of the firm

IfIf ROEROE22 > K > Kee thenthen the the future investment adds value future investment adds value to the firmto the firm

)()1(

210

e

e

ee KKROE

KInv

KBVPSROEP

[ 20-22]

PVGO


Simple Two-stage Growth Model ScenariosSimple Two-stage Growth Model ScenariosPVEO and PVGOPVEO and PVGO

Four Scenarios:Four Scenarios:High PVEO and High PVGOHigh PVEO and High PVGO - Star- StarHigh PVEO and Low PVGOHigh PVEO and Low PVGO - Cash Cow- Cash CowLow PVEO and High PVGOLow PVEO and High PVGO - Turnaround- TurnaroundLow PVEO and Low PVGOLow PVEO and Low PVGO - Dog- Dog

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

)()1(

210

e

e

ee KKROE

KInv

KBVPSROEP

[ 20-22]

PVGO


Simple Two-stage Growth ModelSimple Two-stage Growth ModelGrowth Opportunities and Firm TypeGrowth Opportunities and Firm Type

20 - 1 FIGURE



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

Turnaround – Growth CompanyTurnaround – Growth Company– Low PVEO and high PVGOLow PVEO and high PVGO– Poor PVEO drags down stock price todayPoor PVEO drags down stock price today– DCF methods of valuation are unreliable due to high growthDCF methods of valuation are unreliable due to high growth

Cash CowCash Cow– High PVEO and low PVGOHigh PVEO and low PVGO– DCF methods of valuation are reliable due to lack of growth – we are valuing a DCF methods of valuation are reliable due to lack of growth – we are valuing a

perpetuityperpetuityDogDog

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

the current share price.the current share price.

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



Earnings Yield (%) Market-to-Book

Star 8.84 2.26Cash cow 12.00 1.67Turnaround 2.63 0.76Dog 114.29 0.02

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



The Fed ModelThe Fed Model

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

should send signals to the market to encourage should send signals to the market to encourage ‘reason’ in the market place (to avoid speculative ‘reason’ in the market place (to avoid speculative bubbles and the inevitable price collapse that follows)bubbles and the inevitable price collapse that follows)

Attempting to avoid “irrational exuberance!”Attempting to avoid “irrational exuberance!”

The Fed Model equation is found on the next slide.The Fed Model equation is found on the next slide.




)%)0.1/()(

TBond

actual

Fed

actual

KEPSExpV

VV

[ 20-23]

Actual value of the U.S. stock a market. (Total market capitalization).

Estimate of the U.S. stock market value from the Fed model.

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

Aggregate valuation across the entire market is easier because unsystematic risk attached to individual securities is eliminated as a factor for the market as a whole.




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

• All of this data is continuously, readily available so this All of this data is continuously, readily available so this estimate of value is easy to produce and to track over time estimate of value is easy to produce and to track over time as illustrated in Figure 20 – 2 on the following slide:as illustrated in Figure 20 – 2 on the following slide:

)%)0.1()(

TBondFed K

EPSExp V[ 20-24]

Aggregate valuation across the entire market is easier because unsystematic risk attached to individual securities is eliminated as a factor for the market as a whole.


The Fed ModelThe Fed ModelFed’s Stock Valuation ModelFed’s Stock Valuation Model

20 - 2 FIGURE




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

% .-K P

XTBond

S&P

01500

[ 20-25]




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

• The earnings yield is the appropriate discount rate for the no-The earnings yield is the appropriate discount rate for the no-growth case. (perpetuities), whereas we would expect the growth case. (perpetuities), whereas we would expect the market as a whole to grow at the nominal GDP growth rate.market as a whole to grow at the nominal GDP growth rate.

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

% .-K P

XTBond

S&P

01500

[ 20-25]




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

The required rate of return on the market as a whole can The required rate of return on the market as a whole can serve as a useful benchmark for financial managers as they serve as a useful benchmark for financial managers as they

attempt to estimate their own firm’s cost of capital.attempt to estimate their own firm’s cost of capital.

% .-K P

XTBond

S&P

01500

[ 20-25]


Risk-Based Models and the Cost of Common Risk-Based Models and the Cost of Common EquityEquity

Using the CAPM to Estimate the Cost of Common EquityUsing the CAPM to Estimate the Cost of Common Equity

• CAPM can be used to estimate the required return CAPM can be used to estimate the required return by common shareholders.by common shareholders.

• It can be used in situations where DCF methods It can be used in situations where DCF methods will perform poorly (growth firms)will perform poorly (growth firms)

• CAPM estimate is a ‘market determined’ CAPM estimate is a ‘market determined’ estimate because:estimate because:– The RF (risk-free) rate is the benchmark return and is measured The RF (risk-free) rate is the benchmark return and is measured

directly, today as the yield on 91-day T-billsdirectly, today as the yield on 91-day T-bills– The market premium for risk (MRP) is taken from current market The market premium for risk (MRP) is taken from current market

estimates of the overall return in the market place less RF (ERestimates of the overall return in the market place less RF (ERMM –RF)–RF)




• As a single-factor model, we estimate the common shareholder’s As a single-factor model, we estimate the common shareholder’s required return based on an estimate of the systematic risk of the required return based on an estimate of the systematic risk of the firm (measured by the firm’s beta coefficient)firm (measured by the firm’s beta coefficient)

• Where:Where:KKee = investor’s required rate of return = investor’s required rate of return

ββee = the stock’s beta coefficient = the stock’s beta coefficient

RRff = the risk-free rate of return = the risk-free rate of return

MRPMRP = the market risk premium (ER = the market risk premium (ERM M - R - Rff ) )

MRPRK eFe [ 20-26]



Estimating the Market Risk PremiumEstimating the Market Risk Premium

• RRff is ‘observable’ (yield on 91-day T-bills) is ‘observable’ (yield on 91-day T-bills)• Getting an estimate of the market risk premium is one of Getting an estimate of the market risk premium is one of

the more difficult challenges in using this model.the more difficult challenges in using this model.– We really need a ‘forward’ looking of MRP or a ‘forward’ looking estimate We really need a ‘forward’ looking of MRP or a ‘forward’ looking estimate

of the ERof the ERMM

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

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

MRPRK eFe [ 20-26]




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 are unlikely to expect negative returns

on the stock market. If they

did, no one would hold shares!

Who would have guessed before

hand, there would be two

consecutive years of aggregate

market losses?

Such is the reality of investing since

none of us are clairvoyant.

It would be better to use

average realized

returns over an entire

business/market cycle.




Annual Arithmetic

Average (%)

Annual Geometric Mean (%)

Standard Deviation of

Annual Returns (%)

Government of Canada Treasury Bills 5.20 5.11 4.32Government of Canada Bonds 6.62 6.24 9.32Canadian Stocks 11.79 10.60 16.22U.S. Stocks 13.15 11.76 17.54

Source: Data from Canadian Institute of Actuaries

Table 20-13 Average Investment Returns and Standard Deviations (1938 to 2005)

Long-run average rates of return are more reliable.

Average risk premium of Canadian stocks over bonds was 5.17%The consensus is that the Canadian MRP over the long-term bond yield (an observable yield) is between 4.0 and 5.5%.




Financial Forecasts Average Annual Percent Return

Bank of Canada Overnight Rate 4.50Cash: 3-Month T-bills 4.40Income: Scotia Universe Bond Index 5.60Canadian Equities: S&P/TSX Composite Index 7.30U.S. Equities: S&P 500 Index 7.80International 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 that contains Canada’s and corporate bonds with default risk. Nevertheless, on a risk-adjusted basis, the TD forecast for MRP is consistent with an arithmetic risk premium of 4.3%



Estimating BetasEstimating Betas

• After obtaining estimates of the two After obtaining estimates of the two important market rates (Rimportant market rates (Rff and MRP), an and MRP), an estimate for the company beta is required.estimate for the company beta is required.

• Figure 20 -3 illustrates that estimated betas Figure 20 -3 illustrates that estimated betas for major sub-indexes of the S&P/TSX have for major sub-indexes of the S&P/TSX have varied widely over time:varied widely over time:



Estimated Betas for Sub Indexes of the S&P/TSX Composite IndexEstimated Betas for Sub Indexes of the S&P/TSX Composite Index20 - 3 FIGURE



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

• Actual data for Figure 20 -3 is presented in Table 20 -Actual data for Figure 20 -3 is presented in Table 20 -15 on the following slide:15 on the following slide:

• You should note:You should note:– IT sub index shows rapidly increasing betasIT sub index shows rapidly increasing betas– Other sub index betas show constand or decreasing trends.Other sub index betas show constand or decreasing trends.

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

the market)the market)– If one sub index is changing…that change alone affects all If one sub index is changing…that change alone affects all

others in the opposite direction.others in the opposite direction.• What Happened in the 1995 – 2005 decade?What Happened in the 1995 – 2005 decade?

– The internet bubble of the late 1990s resulted in rapid growth in The internet bubble of the late 1990s resulted in rapid growth in the IT sector till it burst in the early 2000s.the IT sector till it burst in the early 2000s.



Estimating BetasEstimating 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 -0.01Source: Data from Financial Post Corporate Analyzer Database

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

IT Bubble



Nortel Stock PriceNortel Stock Price

• Nortel’s stock price reflects the IT bubble and Nortel’s stock price reflects the IT bubble and crash.crash.

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



Nortel Stock PriceNortel Stock Price20 - 4 FIGURE



IT Bubble effect on Betas of Other Companies Outside the SectorIT Bubble effect on Betas of Other Companies Outside the Sector

• The bubble in IT stocks has driven down the betas in The bubble in IT stocks has driven down the betas in other sectors.other sectors.

• This is demonstrated in Rothman’s beta over the 1966 This is demonstrated in Rothman’s beta over the 1966 – 2004 period.– 2004 period.

• Remember, Rothman’s is a stable company and it’s Remember, Rothman’s is a stable company and it’s beta should be expected to remain constant.beta should be expected to remain constant.

(See Figure 20 -5 on the following slide for Rothman’s beta history)(See Figure 20 -5 on the following slide for Rothman’s beta history)



Rothman’s Beta EstimatesRothman’s Beta Estimates20 - 5 FIGURE



Adjusting Beta Estimates and Establishing a RangeAdjusting Beta Estimates and Establishing a Range

• When betas are measured over the period of When betas are measured over the period of a sector bubble or crash, it is necessary to a sector bubble or crash, it is necessary to adjust the beta estimates of firms in other adjust the beta estimates of firms in other sectors.sectors.

• Take the industry grouping as a major input, Take the industry grouping as a major input, plus the individual company beta estimate.plus the individual company beta estimate.– Using current MRP and Using current MRP and RRf f Develop estimates of KDevelop estimates of Kee

using the range of Company betas prior to the bubble using the range of Company betas prior to the bubble or crashor crash



Using CAPM to Estimate KUsing CAPM to Estimate Knene

• We can scale our estimate of the equity We can scale our estimate of the equity holder’s required return when accessing new holder’s required return when accessing new equity and incurring floatation costs.equity and incurring floatation costs.

NP PKK ene /0[ 20-27]


The Investment Opportunity ScheduleThe Investment Opportunity Schedule

• The IOS is the ranking of a firm’s investment The IOS is the ranking of a firm’s investment opportunities from highest to lowest profitability opportunities from highest to lowest profitability according to expected IRR.according to expected IRR.

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

• A stylized version of this for Rothmans is found in A stylized version of this for Rothmans is found in Figure 20 – 6.Figure 20 – 6.


Cost of Capital and InvestmentCost of Capital and InvestmentRothman’s Inc.’s IOS Schedule, 2006Rothman’s Inc.’s IOS Schedule, 2006

20 - 6 FIGURE

$11,976 Million

Rate of Return

WACC

Internal Funds Available

OPTIMAL INVESTMENT

IOS

$177,607 Million

Projects expected to increase the value of the

firm.

The break in the MCC at $177,607 million

indicates that the firm has a surplus of

internally-generated funds…more than enough to fund the $11,976 of capital

investments.Projects rejected.


Investment Opportunity ScheduleInvestment Opportunity ScheduleA Detailed ExampleA Detailed Example

• In practice, the IOS is a detailed list, rank In practice, the IOS is a detailed list, rank ordered from highest IRR to lowest of the ordered from highest IRR to lowest of the investment project proposals for one year.investment project proposals for one year.

• As you can see on the following slides:As you can see on the following slides:– The width of the columns indicate the capital The width of the columns indicate the capital

investment each project requires, andinvestment each project requires, and– The height of the columns indicates the forecast IRR The height of the columns indicates the forecast IRR

for the projectfor the project


Investment Opportunity ScheduleInvestment Opportunity ScheduleA Detailed Example …A Detailed Example …

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

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

• There is a limit to the amount of money that can be raised in There is a limit to the amount of money that can be raised in any one year (ie. the capital markets are finite … ie. there is any one year (ie. the capital markets are finite … ie. there is a limit to the number of investors and their investment a limit to the number of investors and their investment dollars that will consider investing in any prospect in any dollars that will consider investing in any prospect in any given year.) …hence it is important that the capital given year.) …hence it is important that the capital budgeting analysis be extended to take this fact into budgeting analysis be extended to take this fact into account.account.



• This Investment opportunity schedule is the prioritized This Investment opportunity schedule is the prioritized list of capital projects, listed by IRR (internal rate of list of capital projects, listed by IRR (internal rate of return) from highest to lowest.return) from highest to lowest.

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

Example:Example:Consider a firm that has six different capital investment proposals this Consider a firm that has six different capital investment proposals this year. Each project has it’s own IRR and capital cost. year. Each project has it’s own IRR and capital cost.

(see the next slide)(see the next slide)



Example:Example:Consider a firm that has six different capital investment Consider a firm that has six different capital investment proposals this year. Each project has it’s own IRR and capital proposals this year. Each project has it’s own IRR and capital cost. Each project has the same risk as the firm as a whole.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 be eliminated at this

point because it has a negative NPV.



Example:Example:The first step in developing an IOS is to order the projects The first step in developing an IOS is to order the projects from highest IRR to lowest, and then to calculate the from highest IRR to lowest, and then to calculate the cumulative capital cost of the projects.cumulative 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 ScheduleInvestment Opportunity ScheduleA Detailed Example Continued …A Detailed Example Continued …

Example:Example:It was clear at the start that project A was unacceptable…it had a It was clear at the start that project A was unacceptable…it had a negative NPV.negative NPV.

The remaining projects certainly meet the first investment screen (they The remaining projects certainly meet the first investment screen (they have positive NPV’s … that is, they offer rates of return in excess of have positive NPV’s … that is, they offer rates of return in excess of the firm’s WACC).the firm’s WACC).

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


Investment Opportunity Schedule (IOS)Investment Opportunity Schedule (IOS)A Detailed Example Continued …A Detailed Example Continued …

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% F

IRR = 11.2% BIRR = 10.06%

DIRR = 12.45%

The height of each cylinder is equal to the project’s IRR; the width is equal to the initial investment for the project.

The upper surface of the columns is the

IOS


Investment Opportunity Schedule (IOS)Investment Opportunity Schedule (IOS)A Detailed Example Continued …A Detailed Example Continued …

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 IOSMCC Superimposed on the IOSA Detailed Example Continued …A Detailed Example Continued …

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 caused by the exhaustion of low cost

retained earnings and the need to finance project F through external

offering of equity, incurring floatation costs.

IRRB < MCC2 so this project is rejected. It

will not increase the value of the

firm.


The Break In the IOSThe Break In the IOSA Detailed Example Continued …A Detailed Example Continued …

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

• Assuming the firm has $3.3 million in internal capital to Assuming the firm has $3.3 million in internal capital to invest and equity represents 60% of the firm’s capital invest and equity represents 60% of the firm’s capital structure the break point occurs at:structure the break point occurs at:

Structure Capital in the UpMakesEquity that Percentage

Investmentfor Available Earnings Retained of $ MCCin Break

$5,500,000 60%

$3,300,000 MCCin Break


MCC and IOSMCC and IOS

• The foregoing is consistent with economic The foregoing is consistent with economic theory that states a firm will operate where theory that states a firm will operate where “marginal cost equals marginal revenue.”“marginal cost equals marginal revenue.”

• Now the rationale for this must be clear. The Now the rationale for this must be clear. The value of the firm will fall if it undertakes value of the firm will fall if it undertakes projects that offer a rate of return that is less projects that offer a rate of return that is less than the marginal cost of capital used to than the marginal cost of capital used to finance them.finance them.


Divisional Costs of CapitalDivisional Costs of Capital

• An overall cost of capital developed for a highly diversified An overall cost of capital developed for a highly diversified conglomerate may not be appropriate for decisions made conglomerate may not be appropriate for decisions made within specific divisions of the company.within specific divisions of the company.

• High-risk divisions (with high return possibilities) would have a High-risk divisions (with high return possibilities) would have a disproportionate share of their investment proposals accepted disproportionate share of their investment proposals accepted if they use an overall WACC.if they use an overall WACC.

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

• Developing these estimates can sometimes be accomplished Developing these estimates can sometimes be accomplished by looking at other firms in that industry that are not highly by looking at other firms in that industry that are not highly diversified in their operations… this is called the pure play diversified in their operations… this is called the pure play approach.approach.


Summary and ConclusionsSummary and Conclusions

In this chapter you have learned:In this chapter you have learned:– How types of equity differ in their degree of “equityness” and How types of equity differ in their degree of “equityness” and

therefore have different costs of capitaltherefore have different costs of capital– WACC is the market value weighted average of the after-tax WACC is the market value weighted average of the after-tax

costs of all securities used to finance the firm.costs of all securities used to finance the firm.– If a firm earns more than its WACC, the value of the firm will If a firm earns more than its WACC, the value of the firm will

rise.rise.– Common shareholders are residual claimants hence they hold Common shareholders are residual claimants hence they hold

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

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

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

estimation of beta can be affected by recent stock market estimation of beta can be affected by recent stock market performance.performance.

Appendix 1Appendix 1Steep Hill Mines 1Steep Hill Mines 1

An Exercise in Cost of CapitalAn Exercise in Cost of Capital


Steep Hill Mines # 1Steep Hill Mines # 1The QuestionThe Question

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

Steep Hill also has it's long-term bonds trading on public markets. The 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 of 96.54%. bonds are currently trading at a discount from their par value of 96.54%. These 5.75% bonds have ten years left until they mature.These 5.75% bonds have ten years left until they mature.

Steep Hill Mines Ltd. has an important capital project to consider. Project 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 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 risk to the risk of the firm next eight years. It is considered to be of similar risk to the risk of the firm itself. It will cost Steep Hill $400,000 this year to get this project up and itself. It will cost Steep Hill $400,000 this year to get this project up and running.running.


Steep Hill Mines # 1Steep Hill Mines # 1The Question …The Question …

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

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

the next yearthe next year– New equity capital could be raised by the firm at the current market price, but New equity capital could be raised by the firm at the current market price, but

floatation costs would amount of 4% of the value of the issue. floatation costs would amount of 4% of the value of the issue. – New bonds could be sold into the market, but the floatation cost percentage New bonds could be sold into the market, but the floatation cost percentage

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

market value weights. market value weights. – If the firm goes ahead with the capital project, it will have to seek external If the firm goes ahead with the capital project, it will have to seek external

financing since there is no internal cash flow available for reinvestment.financing since there is no internal cash flow available for reinvestment.

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


Steep Hill Mines # 1Steep Hill Mines # 1The Question …The Question …

Steep Hill Mines Ltd.Steep Hill Mines Ltd.Balance SheetBalance Sheet

As at December 31, 20XXAs at December 31, 20XXIn $ '000sIn $ '000s

Assets:Assets: Liabilities:Liabilities:CashCash 100100 AccrualsAccruals 3030Accounts ReceivableAccounts Receivable 220220 Accounts PayableAccounts Payable 312312InventoriesInventories 450450 ________Total Current AssetsTotal Current Assets 770770 Total Current LiabilitiesTotal Current Liabilities 342342Gross Fixed AssetsGross Fixed Assets 4,0004,000 5.75% bonds5.75% bonds 1,0001,000Accumulated DepreciationAccumulated Depreciation 1,5001,500 Common stock Common stock

(100,000 outstanding)(100,000 outstanding) 1,0001,000Net Fixed AssetsNet Fixed Assets 2,5002,500 Retained earningsRetained earnings 928 928TOTAL ASSETSTOTAL ASSETS 3,2703,270 TOTAL CLAIMSTOTAL CLAIMS 3,2703,270

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

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


Steep Hill Mines # 1Steep Hill Mines # 1The Solution – The Equity Investor’s Required ReturnThe Solution – The Equity Investor’s Required Return

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

CAPM 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 # 1Steep Hill Mines # 1The Solution – The Cost of EquityThe Solution – The Cost of Equity

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

This is the returns our current shareholders are demanding on our This is the returns our current shareholders are demanding on our stock.stock.

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

%7.996.%3.9

.4-1%3.9

f-1

Return Required InvestorsEquity New ofCost


Steep Hill Mines # 1Steep Hill Mines # 1The SolutionThe Solution

Investor's Required Return on DebtInvestor's Required Return on Debt

%22.62%11.3k %11.3k

111

11$28.75$965.40

111

11

b

b

20

20

lysemiannual

)k(F

k)k(

)k(

Fk

)k(IB

bb

b

nbb

nb[ 20-12]


Steep Hill Mines # 1Steep Hill Mines # 1The Solution – The Cost of DebtThe Solution – The Cost of Debt

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

Where:Where:T = T = 40%40%f =f = 6%6%

%97.306.1

)4.1%(22.61

)1%(22.6

fTKd


Market Value Weights:Market Value Weights:Market values are always found by multiplying the Market values are always found by multiplying the number of outstanding securities times their price number of outstanding securities times their price per unit.per unit.

Market Value of LT Debt = 1,000 bonds outstanding times $965.40 =Market Value of LT Debt = 1,000 bonds outstanding times $965.40 = $965,400 $965,400Market Value of Equity = 100,000 times $30.00 =Market Value of Equity = 100,000 times $30.00 = 3,000,0003,000,000TOTAL MARKET VALUE OF THE FIRM =TOTAL MARKET VALUE OF THE FIRM = 3,965,4003,965,400

Market Value Weight of LT Debt = $965,400/$3,965,400 = 24.35%Market Value Weight of LT Debt = $965,400/$3,965,400 = 24.35%Market Value Weight of Equity = (1 - .2435) = 75.65%Market Value Weight of Equity = (1 - .2435) = 75.65%

Steep Hill Mines # 1Steep Hill Mines # 1The Solution – Determining Market Value WeightsThe Solution – Determining Market Value Weights


The Cost of Capital Using Market Value Weights:The Cost of Capital Using Market Value Weights:

Steep Hill Mines # 1Steep Hill Mines # 1The Solution – Market Value WACCThe Solution – Market Value WACC

Source of Capital

Market Value

Weight

Specific Marginal

CostWeighted

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%


Viability of the Capital ProjectViability of the Capital Project

Since the project has similar risk characteristics to the firm as Since the project has similar risk characteristics to the firm as a whole, we do not have to calculate a risk-adjust discount a whole, we do not have to calculate a risk-adjust discount rate…instead, we can just use the firm's WACC.rate…instead, we can just use the firm's WACC.

Since the market value capital structure weights will be used Since the market value capital structure weights will be used by the firm in the long run, let's use that as the WACC, and by the firm in the long run, let's use that as the WACC, and discount the prospective after-tax cash flows on this project discount the prospective after-tax cash flows on this project back to the present and compare that with the cost of the back to the present and compare that with the cost of the project to see if there is a positive NPV.project to see if there is a positive NPV.

Steep Hill Mines # 1Steep Hill Mines # 1The SolutionThe Solution


Steep Hill Mines # 1Steep Hill Mines # 1The Solution – Project NPVThe Solution – Project NPV

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

033

22

11

NPV

CFk

CF

CFk

CFk

CFk

CFNPV

t

n

it

[ 13-1] Using Equation 13 -1 for NPV, and substituting in the annual cash flow benefits of $100,000 after-tax, initial cost, useful life of 8 years, and WACC of 8.3% we find the project offers a positive NPV.


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