20 - Cost of Capital

8/8/2019 20 - Cost of Capital

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CHAPTER 20CHAPTER 20Cost of CapitalCost of Capital


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The Short Story of WACCThe Short Story of WACC

Thus far, we have been given the discount rateThus far, we have been given the discount ratewith which to evaluate projects; now wewith which to evaluate projects; now weconsider where it comes from.consider where it comes from.

Recall that we do not include dividends orRecall that we do not include dividends orinterest payments in our DCF analysis becauseinterest payments in our DCF analysis becausethey are included inthey are included in K K..

The WACC considers the cost and weight of The WACC considers the cost and weight of individual components in the capital structure.individual components in the capital structure.

CHAPTER 20 Cost of Capital 20 - 2


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

Costs associated with financing the firmsCosts associated with financing the firmsinvested capital including:invested capital including: Debt Costs:Debt Costs:

Bank loansBank loansLongLong--term debtterm debt bonds/debenturesbonds/debentures

Equity Costs:Eq uity Costs:Preferred e quity costsPreferred e quity costsCommon e quity costsCommon e quity costs


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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 orWhat capital cost the firm 5 months, 5 years or

5 decades ago is irrelevant.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 todays economiccapital will cost in todays economicenvironment for this particular firm.environment for this particular firm.


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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 of Estimate the market values for the sources of capital and determine the market valuecapital and determine the market valueweights.weights.

3.3. Estimate the marginal, afterEstimate the marginal, after- -tax, and aftertax, 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.


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

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 theIn 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 + DThroughout the course, you will see me use the notationThroughout the course, you will see me use the notation

WWdd for the weight of debt instead of (D/V) for the weight of debt instead of (D/V) likewise withlikewise withWWee andand WWpp (weight of common and preferred equity(weight of common and preferred equityrespectively)respectively)

1V D-T)( K

V P K

V S K WACC d pe![ 20-9]


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

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

Type of Capital

SpecificMarginal Costafter tax and

floatationcosts

MarketValue

Weights

WeightedSpecificMarginal

Costo -Ter De t 5.5% 43.0% 0.02365referred Stoc 11.4% 11.0% 0.01254

Co o Stoc 12.9% 46.0% 0.05934WACC = . %

WACC is the su of the wei htedspecific ar i al costs of each source of capital.


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Market Values!Market Values!

Always remember when calculating the weightsAlways remember when calculating the weightsof various capital sources to use theof various capital sources to use the TOTALTOTALMARKET VALUEMARKET VALUE of these instruments, not theof these instruments, not the

book values listed on the balance sheet.book values listed on the balance sheet. Recall that market capitalization is the total value of COMMON EQUITY! Recall that market capitalization is the total value of COMMON EQUITY!

This can be tricky for debt if required yieldsThis can be tricky for debt if required yieldshave changed substantially from when the debt have changed substantially from when the debt was issuedwas issued we have to look up (or recalculate)we have to look up (or recalculate)the market price of bonds rather than their parthe market price of bonds rather than their parvalue.value.



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Estimating Market ValuesEstimating Market ValuesMarket Value of BondsMarket Value of Bonds

As per Chapter 6, knowing the term to maturity, the couponAs per Chapter 6, knowing the term to maturity, the couponrate and the bondholders required return we can determinerate and the bondholders required return we can determinethe market value of bonds with equation 20the market value of bonds with equation 20 1 21 2Then simply multiply the price by the number of bondsThen simply multiply the price by the number of bonds

outstanding.outstanding.

1

111

1

n

bb

n

b

)k ( F

k

)k ( I B v

-

v![ 20-12]


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Costs of Existing CapitalCosts of Existing Capital

Cost of Debt = Cost of Debt = K K dd = Y (1= Y (1 --T)T)

Cost of Preferred Shares = Cost of Preferred Shares = K K pp = D/P = D/P 00

Cost of Equity = Cost of Equity = K K ee = (D= (D11 /P /P 00)+ g)+ g



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Cost of Eq uityCost of Eq uityConstant Growth Model CautionConstant Growth Model Caution

The constant growth model can only be used inThe constant growth model can only be used incases where it is reasonable to assume that thecases where it is reasonable to assume that thegrowth rate can be sustained in the very longgrowth rate can be sustained in the very longterm.term. This usually means, using it only for large, mature blueThis usually means, using it only for large, mature blue- -chipchip

companies that already pay a significant dividendcompanies that already pay a significant dividend

The Gordon model SHOULD NOT be used onThe Gordon model SHOULD NOT be used onsmaller, more rapidly growing firms where highsmaller, more rapidly growing firms where highcurrent growth rates are experienced, but current growth rates are experienced, but cannot be sustained in the long term.cannot be sustained in the long term.


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Alternate Model for the Cost of Eq uity Alternate Model for the Cost of Eq uityUsing the CAPM to estimateUsing the CAPM to estimate K Kee

CAPM can be used to estimate the required returnCAPM can be used to estimate the required returnby common shareholders in situations where DCFby common shareholders in situations where DCFmethods will perform poorlymethods will perform poorly

CAPM estimate is a market determined estimate:CAPM estimate is a market determined estimate: The RF (riskThe RF (risk--free) rate is the benchmark return and is measuredfree) rate is the benchmark return and is measured

directly, today as the yield ondirectly, today as the yield on - -day Tday T--billsbills

The market risk premium (MRP) is taken from current marketThe market risk premium (MRP) is taken from current marketestimates of the overall return in the market, less RF ( ERestimates of the overall return in the market, less RF ( ERMM RF)RF)

Using this model re quires us toUsing this model re quires us to thinkthink about the inputs however about the inputs however as they can have a significant impact on project evaluationas they can have a significant impact on project evaluation


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RiskRisk--Based Models & the Cost of Eq uityBased Models & the Cost of Eq uityUsing the CAPM to estimate the cost of common e quityUsing the CAPM to estimate the cost of common e quity

As a singleAs a single- -factor model, we estimate the common factor model, we estimate the commonshareholders required return based on an estimate of theshareholders required return based on an estimate of thesystematic risk of the firm (measured by the firms betasystematic risk of the firm (measured by the firms betacoefficient)coefficient)

Where:Where:

K K ee = investors re quired rate of return= investors re quired rate of return ee = the stocks beta coefficient= the stocks beta coefficientR R f f = the risk= the risk--free rate of returnfree rate of returnMRP MRP = the market risk premium ( ER= the market risk premium ( ERMM -- RRf f ))

MR P R K e F e Fv![ 20-26]


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RiskRisk--Based Models & the Cost of Eq uityBased Models & the Cost of Eq uityEstimating the Market Risk PremiumEstimating the Market Risk Premium

RR f f is observable (yield on 9 1is observable (yield on 9 1 --day Tday T--bills)bills)Getting an estimate of the market risk premium is one of theGetting an estimate of the market risk premium is one of the

more difficult challenges in using this model.more difficult challenges in using this model. We really need a forward looking of MRP or a forward lookingWe really need a forward looking of MRP or a forward looking

estimate of the ERestimate of the ERMMOne approach is to use an estimate of the current, expectedOne approach is to use an estimate of the current, expected

MRP by examining a longMRP by examining a long- -run average that prevailed in therun average that prevailed in thepast.past.Table 20Table 20 - -1 2 illustrates the % returns on S&P/TSX Composite1 2 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.

MR P R K e F e Fv![ 20-26]


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RiskRisk--Based Models & the Cost of Eq uityBased Models & the Cost of Eq uityUsing the CAPM to Estimate the Cost of Common Eq uityUsing the CAPM to Estimate the Cost of Common Eq uity

R t s

7 7- 7

- 8

7

8

7

Tabl 20-12 R t s o t &P/T X Composit I Investors areunlikely to e xpectnegative returns

on the stock

market If theydid, no one wouldhold shares!

Who would haveguessed before

hand, there wouldbe two

consecutive yearsof aggregatemarket losses?

Such is the realityof investing since

none of us areclairvoyant

It would bebetter to use

average

realizedreturns over

an entirebusiness/mar

ket cycle


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RiskRisk--Based Models & the Cost of Eq uityBased Models & the Cost of Eq uityEstimating BetasEstimating Betas

After obtaining estimates of the two important After obtaining estimates of the two important

market rates (Rmarket rates (R f f and MRP), an estimate for theand MRP), an estimate for thecompany beta is required.company beta is required.

Figure 20Figure 20 - -3 illustrates that estimated betas for3 illustrates that estimated betas for

major submajor sub- -indexes of the S&P/TSX have variedindexes of the S&P/TSX have variedwidely over time:widely over time:


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RiskRisk--Based Models & the Cost of Eq uityBased Models & the Cost of Eq uityEstimated Betas for Sub Inde xes of the S&P/TSX Composite Inde xEstimated Betas for Sub Inde xes of the S&P/TSX Composite Inde x

20 - 3 F URE


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RiskRisk--Based Models & the Cost of Eq uityBased Models & the Cost of Eq uityEstimating BetasEstimating Betas

E r at rials strials Co s is Co s tap H alt i T T l o tiliti s

-

-

- -- -

-our e Data from Fi nan i a

o Co rpo ra e A na er Da aba e

Ta 20-15 TSX Sub Index Be ta Est at e s

ITBubble


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RiskRisk--Based Models & the Cost of Eq uityBased Models & the Cost of Eq uity Adjusting Beta Estimates and Establishing a Range Adjusting Beta Estimates and Establishing a Range

When betas are measured over the period of aWhen betas are measured over the period of asector bubble or crash, it is necessary to adjust sector bubble or crash, it is necessary to adjust

the beta estimates of firms in other sectors.the beta estimates of firms in other 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 andUsing current MRP and R R f f Develop estimates of KDevelop estimates of K ee

using the range of Company betas prior to the bubbleusing the range of Company betas prior to the bubbleor crashor crash


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Costs of Existing CapitalCosts of Existing Capital

Cost of Debt = Cost of Debt = K K dd = Y (1= Y (1 --T)T)

Cost of Preferred Shares = Cost of Preferred Shares = K K pp = D/P = D/P 00

Cost of Equity = Cost of Equity = K K ee = (D= (D11 /P /P 00)+ g)+ g= = RR f f + + ((RRmm RR f f ))



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Cost of Eq uity CapitalCost of Eq uity Capital

It is extremely rare that the Gordon model andIt is extremely rare that the Gordon model andthe CAPM will give you the same cost of equity.the CAPM will give you the same cost of equity.

THIS IS OK!THIS IS OK! Recall that the cost of e quity capitalRecall that the cost of e quity capital is an estimateis an estimatewhich tries to appro ximate what shareholders re quirewhich tries to appro ximate what shareholders re quireas a return compensating them for the risks they faceas a return compensating them for the risks they face

When you have enough information to calculateWhen you have enough information to calculateboth, do so and then use their average as theboth, do so and then use their average as thecost of equity.cost of equity.



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Estimating the Component CostsEstimating the Component CostsFloatation CostsFloatation Costs

Issuing or floatation costs are incurred by a firm when it Issuing or floatation costs are incurred by a firm when it raises new capital through the sale of securities in theraises new capital through the sale of securities in theprimary market.primary market.These costs include:These costs include:

Underwriting discounts paid to the investment dealer Underwriting discounts paid to the investment dealer Direct costs associated with the issue including legal andDirect costs associated with the issue including legal and

accounting costsaccounting costsThe result:The result: Net proceeds on the sale of each security is less than what theNet proceeds on the sale of each security is less than what the

investor invests, andinvestor invests, and The component cost of capital > investors re quired returnThe component cost of capital > investors re quired return

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


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Floatation Cost CalculationFloatation Cost Calculation

There are two approaches to factoring in floatation costs:There are two approaches to factoring in floatation costs: % Floatation Method% Floatation Method Net Proceeds MethodNet Proceeds Method

The % Floatation method uses the initial cost of capitalThe % Floatation method uses the initial cost of capitalestimates we saw earlier, but divides them by ( 1estimates we saw earlier, but divides them by ( 1 --floatation %) to floatation %) toaccount for the financing wedge.account for the financing wedge. KKxx newnew = = KKxx / (/ ( --fl%)fl%)

The Net Proceeds method scales the cost of capital by replacingThe Net Proceeds method scales the cost of capital by replacingthe price in those same equations with the actual amount of the price in those same equations with the actual amount of funds received from the public. funds received from the public.


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Floatation Cost CalculationFloatation Cost Calculation

These two forms give identical results except in theThese two forms give identical results except in thecase of common equity where there is a minorcase of common equity where there is a minordistortion introduced by using % Float.distortion introduced by using % Float.

Since the cost of capital calculation only gives us anSince the cost of capital calculation only gives us anestimate, and real world market frictions introduceestimate, and real world market frictions introducemuch larger errors in estimation, the % float much larger errors in estimation, the % float method can be used equivalently to the net method can be used equivalently to the net

proceeds methodproceeds method % Float estimates are% Float estimates are slightly slightly lower than Net Proceedslower than Net Proceeds

estimates for estimates for KKee If precision is ESS ENTIAL, use the net proceeds method (its notIf precision is ESS ENTIAL, use the net proceeds method (its not

in this course so % float method is fine to use in all cases)in this course so % float method is fine to use in all cases)CHAPTER 20 Cost of Capital 20 - 27


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The Component Cost of DebtThe Component Cost of Debt

%19.697.0%6

.03-10.4)-(1.010%

%fl-1T)-(1ReturnRequiredsInvestor'

K dDnew

!!v!

v!

If you know the debt investors required rate of return K If you know the debt investors required rate of return K dd , the, thecorporate tax rate and the floatation cost percentage for debt, you cancorporate tax rate and the floatation cost percentage for debt, you canestimate the cost of debt in the following manner:estimate the cost of debt in the following manner:

Assume:Assume:K K d d = % (debt investors re quired return)= % (debt investors re quired return)T T = % (corporate ta x rate)= % (corporate ta x rate)f f d d = % (floatation cost percentage)= % (floatation cost percentage)

The after ta x cost of debt is lower than the

investors re quiredreturn because of thetax shield on interest

expense


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Estimating the Component CostsEstimating the Component CostsDebtDebt

Alternatively you can adjust the bond valuation formula for theAlternatively you can adjust the bond valuation formula for thetaxtax--deductibility of interest expense and the net proceeds thedeductibility 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 floatationcosts) and solve for the rate (costs) and solve for the rate (K K ii ) that causes the formula to) that causes the formula tobecome and equality:become and equality:

K K ii = the after= the after- -tax and aftertax and after- -floatation cost of debt. floatation cost of debt.

1

111

1)1( n

Dn ew Dn ew

n

Dn ew

)( )(

I N v

-

vv![ 20-13]

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

Coupon interest times minus corporatetax rate = after ta x cost of interest


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Estimating the Component CostsEstimating the Component CostsPreferred SharesPreferred Shares

If you know the preferred shareIf you know the preferred shareinvestors required rate of investors required rate of return K return K pp , and the floatation, and the floatationcost percentage for preferredcost percentage for preferredshare financing, you canshare financing, you canestimate the cost of preferredestimate the cost of preferredshares in the following manner:shares in the following manner:

Assume:Assume:KKpp = % (preferred investors= % (preferred investors

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

%74.1495.0

%14

.05-1

14%

%fl-1ReturnRequiredsInvestor'

K p

Pnew

!!!

!

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

Floatationcosts cause

the componentcost to be

greater thanthe investors

requiredreturn


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Estimating the Component CostsEstimating the Component CostsPreferred SharesPreferred Shares

Alternatively, the component cost of preferredAlternatively, the component cost of preferredshares can be found using equation 20shares can be found using equation 20 - -1 4, where1 4, whereNP is the selling price per preferred share less theNP is the selling price per preferred share less the floatation costs per share. floatation costs per share.

N

D K p

n ew ![ 20-14]


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Constant Growth ModelConstant Growth ModelThe Cost of New Eq uityThe Cost of New Eq uity

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

floatation costs) floatation costs)

1 g N

D K

En ew ![ 20-17]


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RiskRisk--Based Models and the Cost of CommonBased Models and the Cost of CommonEq uityEq uity

Using CAPM to Estimate KUsing CAPM to Estimate Knene

We can scale our estimate of the equity holdersWe can scale our estimate of the equity holdersrequired return when accessing new equity andrequired return when accessing new equity andincurring floatation costs.incurring floatation costs.

)%1( e E n e

fl

K K

E ![ 20-27]


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A note of new vs e xisting capital A note of new vs e xisting capital

UNDER NO CIRCUMSTANCES UNDER NO CIRCUMSTANCES can a firm usecan a firm useexisting debt or existing preferred shares toexisting debt or existing preferred shares to finance a project! finance a project!

There is no such thing as KThere is no such thing as K DD or Kor KPP except when usingexcept when usingit to calculateit to calculate KKDnewDnew andand KKPnewPnew Money raised from these sources but not spent endMoney raised from these sources but not spent end

up as common e quityup as common e quity

OnlyOnly in the case of existing common equity canin the case of existing common equity canwe use K we use K EE otherwise we useotherwise we use K K EnewEnew .. example after the break example after the break



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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 weightedThe Marginal Cost of Capital (MCC) is the weightedaverage cost of the next dollar of financing to beaverage cost of the next dollar of financing to beraised.raised.

At low levels of financing the WACC = MCCAt low levels of financing the WACC = MCCAs a firm raises more and more capital in a givenAs a firm raises more and more capital in a given

year, it will exhaust the supply of lower cost year, it will exhaust the supply of lower cost sources, and then have to access marginally highersources, and then have to access marginally highercost sources.cost sources. Therefore MCC increases with the amount of capitalTherefore MCC increases with the amount of capital

to be raisedto be raised

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


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0 $ ,000 ,000 $ ,000 ,000 $ ,000 ,000 $ ,000 ,000 $ 0 ,000 ,000

(%)

olla rs of C a pital to be aised

15

10

5

The Marginal Cost of Capital MCCThe Marginal Cost of Capital MCC

MCC 1=WACC= 9.44%MCC 2= 10.64%

There is o n ly on e b reak in t he

CC cu rve. I t occu r s a t $5,500,000 . At t his poin t t he f irm ha sexhaust ed its i n t er n al equit y and to ra ise more equit ycap it al will mea n acce ssin g ext er n al

equit yusin g t he serv ice s o f a

nu

nd erwr it er.

%64.10%24.2%4.8

)4%(.6.5)6%(.1410040

)3.1%(810060

%14

)1(2

!!

!

!

!V

Dt K

V

S K M CC Dn ew En ew

%44.9%24.2%2.7

)4%(.6.5)6%(.1210040

)3.1%(810060

%12

)1(1

!!

!

!

!V

Dt K

V

S K M CC Dn ewe

2.24 %Each dollar of capital invested is financed 4 0 % by debt . (4 0 % after-ta x cost = 2.24 %)

Each dollar of capital invested up to$5 .5 million is financed 0 % byinternal e quity (R/E). ( 0 % cost

of retained earnings = .2 %)

Each dollar of capital investedbeyond $ 5 .5 million is financed

0 % by new e quity. ( 0 % cost of new e quity = .4 %)


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Investment Opportunity ScheduleInvestment Opportunity Schedule A Detailed Example A Detailed Example

An investment opportunity schedule is a prioritizedAn investment opportunity schedule is a prioritizedlist of capital projects, listed by IRR from highest tolist of capital projects, listed by IRR from highest tolowest.lowest.Consider the 6 projects below:Consider the 6 projects below:

CapitalProject Initial Cost

Annual ATCFBenefits

UsefulLife 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 beeliminate d at t hispoint because it has

a ne gative NPV.


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Investment Opportunity ScheduleInvestment Opportunity Schedule A Detailed Example A Detailed Example

The first step in developing an I OS is to order the projectsThe first step in developing an I OS is to order the projectsfrom highest IRR to lowest, and then to calculate thefrom highest IRR to lowest, and then to calculate thecumulative capital cost of the projects .cumulative capital cost of the projects .

CapitalP oject itial Cost

C lati e Costof t e P ojects RR

E $9 5,000 $9 5,000 1 . 50C $3, 50,000 $4, 35,000 13 .07%

D $1 0 ,000 $4,915, 000 12 . 45%F $2,154, 000 $7 ,0 69, 000 11 . 20%B $2,3 00 ,000 $9,369, 000 10.0 6%

A $1,5 00 ,000 $10 , 69, 000 8. 19%


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Investment Opportunity ScheduleInvestment Opportunity Schedule A Detailed Example Continued A Detailed Example Continued

The remaining projects certainly meet the firstThe remaining projects certainly meet the firstinvestment screeninvestment screen - - that is, they offer rates of return inthat is, they offer rates of return inexcess of the firms WACC (they have a positive NPV) .excess of the firms WACC (they have a positive NPV) .

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

Then we overlay the MCC graph we just saw toThen we overlay the MCC graph we just saw todetermine which projects provide sufficient returnsdetermine which projects provide sufficient returns


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Investment Opportunity Schedule (I OS)Investment Opportunity Schedule (I OS) A Detailed Example Continued A Detailed Example Continued

0 $2 ,000 ,000 $4 ,000 ,000 $ ,000 ,000 $ ,000 ,000 $10 ,000 ,000

D olla rs of C a pital to be aised

I

(%)

15

10

5

EI =18.5%

CI = 13.07% F

I = 11.2%B

I = 10.06%

D

I = 12.45%

The hei ght o f ea ch c yl ind er is equal to t he pr ojects IRR; t he wid t h is equal to t he in itial in ve st men t f or t he pr oject .

The upper surface of the columns is the

IOS


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Investment Opportunity Schedule (I OS)Investment Opportunity Schedule (I OS) A Detailed Example Continued A Detailed Example Continued

0 $2 ,000 ,000 $4 ,000 ,000 $ ,000 ,000 $ ,000 ,000 $10 ,000 ,000


I

(%)

15

10

5

EI =18.5%

CI = 13.07%

FI = 11.2%

BI = 10.06%

D

I = 12.45%IOS


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MCC Superimposed on the I OSMCC Superimposed on the I OS A Detailed Example Continued A Detailed Example Continued

0 $2 ,000 ,000 $4 ,000 ,000 $ ,000 ,000 $ ,000 ,000 $10 ,000 ,000


I

(%)

15

10

5

EI =18.5%

CI = 13.07%

FI = 11.2%

BI = 10.06%

D

I = 12.45%

MCC 1=WACC= 9.44%

MCC 2= 10.64%

The break in the MCC is causedby the e xhaustion of low cost

retained earnings and the need tofinance project F through e xternal

offering of e quity, incurringfloatation costs .

IRRB < MCC 2so this projectis rejected . It

will notincrease thevalue of the

firm.


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Appendi x 1 Appendi x 1

Steep Hill Mines 1Steep Hill Mines 1

An Exercise in Cost of CapitalAn Exercise in Cost of Capital


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

Steep Hill Mines Ltd . shares are publicly traded on the TorontoSteep Hill Mines Ltd . shares are publicly traded on the TorontoStock Exchange . The shares currently trade at a price of $ 0 .00 per Stock Exchange . The shares currently trade at a price of $ 0 .00 per share . Security analysts that follow the stock have estimated it's betashare . Security analysts that follow the stock have estimated it's betacoefficient to be 0 .9. Steep Hill paid a dividend on its common stockcoefficient to be 0 .9. Steep Hill paid a dividend on its common stocklast year that totaled $ 1 .50 per share . Dividends have been growing atlast year that totaled $ 1 .50 per share . Dividends have been growing ata 4 % compound rate for the past si x years and the e xpectation is thata 4 % compound rate for the past si x years and the e xpectation is thatthis growth can continue into the foreseeable future .this growth can continue into the foreseeable future .

Steep Hill also has it's longSteep Hill also has it's long- -term bonds trading on public markets . term bonds trading on public markets . The bonds are currently trading at a discount from their par value of The bonds are currently trading at a discount from their par value of 96. 5 4 % . These 5 . 5 % bonds have ten years left until they mature .96. 5 4 % . These 5 . 5 % bonds have ten years left until they mature .

Steep Hill Mines Ltd . has an important capital project to consider . Steep Hill Mines Ltd . has an important capital project to consider . Project A is e xpected to produce annual cash flows after ta x of Project A is e xpected to produce annual cash flows after ta x of $100 ,000 for the ne xt eight years . It is considered to be of similar risk$100 ,000 for the ne xt eight years . It is considered to be of similar riskto the risk of the firm itself . It will cost Steep Hill $ 4 00 ,000 this year toto the risk of the firm itself . It will cost Steep Hill $ 4 00 ,000 this year toget this project up and running .get this project up and running .


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

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

Government of Canada 9 1Government of Canada 9 1 --day Treasury bills are currently yielding 4.2 5 % . day Treasury bills are currently yielding 4.2 5 % . The e xpected return on the TS E 00 composite inde x is forecast to be 10 % inThe e xpected return on the TS E 00 composite inde x is forecast to be 10 % in

the ne xt year the ne xt year New e quity capital could be raised by the firm at the current market price, butNew e quity 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 percentageNew bonds could be sold into the market, but the floatation cost percentage

would be 6 % . would be 6 % . The firm faces a corporate ta x rate of 4 0 % . The firm faces a corporate ta x rate of 4 0 % . The company will seek to sustain the current capital structure based on e xistingThe company will seek to sustain the current capital structure based on e xisting

market value weights . market value weights . If the firm goes ahead with the capital project, it will have to seek e xternalIf the firm goes ahead with the capital project, it will have to seek e xternalfinancing 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:


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

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

As at December 3 1 , 20XXAs at December 3 1 , 20XXIn $ '000sIn $ '000s

Assets:Assets: Liabilities:Liabilities:CashCash 1 001 00 AccrualsAccruals 3030

Accounts ReceivableAccounts Receivable 220220 Accounts PayableAccounts Payable 31

231

2InventoriesInventories 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 stockCommon stock

(1 00,000 outstanding)(1 00,000 outstanding) 1 ,0001 ,000Net Fixed AssetsNet Fixed Assets 2,5002,500 Retained earningsRetained earnings 928928TOTAL ASSETS TOTAL ASSETS 3,2703,270 TOTAL CLAIMS TOTAL CLAIMS 3,2703,270

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

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


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Steep Hill Mines # 1Steep Hill Mines # 1The SolutionThe Solution The Eq uity Investors Re quired ReturnThe Eq uity Investors Re quired 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 !!!!! g P

g D K S

%425.9%175.5%25.4

%]25.4%10[9.0%25.4][!!

!!

S

M sS

K

R F E R B R F K


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Steep Hill Mines # 1Steep Hill Mines # 1The SolutionThe Solution The Cost of Eq uityThe Cost of Eq uity

Investor's Required Return on Equity CapitalInvestor's Required Return on Equity CapitalThe average of our two estimates for the cost of retained earningsThe average of our two estimates for the cost of retained earningsis: (9.2 + 9.42 5 )/2 = is: (9.2 + 9.42 5 )/2 = 9 39 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 e xternal capital, we will incur floatation costsIf we raise e xternal 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 -1eturnequiredInvestorsEquity Neof Cost

!!!

!


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

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

%22.62%11.3k

%11.3k

111

11

$28.75$965.40

111

11

b

b

20

20

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v

-

!

v

-

v!

ly se ia nn ua l

)k ( F

k )k (

)k ( F k )k (

I B

bb

b

n

bb

n

b

[ 20-12]


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

i e i tere st o e t is ta x e c ti le to t he firm, the aft er i ce i tere st o e t is ta x e c ti le to t he firm, the aft er --ta x ata x aaft er floatatio c ost of e t is:aft er floatatio c ost of e t is:

here :here :TT 4040f f 66

%97.306.1

)4.1%(22.61

)1%(22.6 !!! f T K d


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The Cost of Capital Usi a rke t al e e i h ts:The Cost of Capital Usi a rke t al e e i h ts:

Steep Hill Mines # 1Steep Hill Mines # 1The SolutionThe Solution Market Value WACCMarket Value WACC

Sour e oCapital

MarketValue

W ei ht

Spe i iM ar inal

CostWei hte

CostT e t

re erreCo on

WACC 30


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ia ilit of t he Capital P r o ec tia ilit of t he Capital P r o ec t

Since the project has similar risk characteristics to theSince the project has similar risk characteristics to the

firm as a whole, we do not have to calculate a riskfirm as a whole, we do not have to calculate a risk- -adjust discount rateinstead, we can just use the firm'sadjust discount rateinstead, we can just use the firm'sWACC .WACC .

Since the market value capital structure weights will beSince the market value capital structure weights will beused by the firm in the long run, let's use that in theused by the firm in the long run, let's use that in theWACC, and calculate the projects NPV .WACC, and calculate the projects NPV .

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


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Steep Hill Mines # 1Steep Hill Mines # 1The SolutionThe Solution Project NPVProject 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(

000,400$)VIFA$100,000( )1(

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

8

8.3%k 8,n

WACCk 8,n

01

033

22

11

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!

!

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!

N V

CF k

CF

CF k

CF k

CF k

CF N V

t

n

it

[ 13-1] Using Eq uation13 -1 for NPV,and substitutingin the annual

cash flowbenefits of $100 ,000 after-tax, initial cost,useful life of years, and

WACC of .3 % we find theproject offers apositive NPV.

Documents

20 - Cost of Capital