fcf valuation - business school

7/31/2019 FCF valuation - business school

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Chapter 3

Free Cash Flow Valuation


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Intro to Free Cash Flows

If applied to dividends, the DCF model isthe dividend discount model (DDM) from

Chapter 2.

Chapter 3 extends DCF analysis to valuea firm and the firms equity securities by

valuing its free cash flow to the firm(FCFF) and free cash flow to equity(FCFE).


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Dividends are the cash flows actually paid tostockholders

Free cash flows are the cash flows availablefor distribution.

Applied to dividends, the DCF model is the

discounted dividend approach or dividenddiscount model (DDM). This chapter extendsDCF analysis to value a firm and the firmsequity securities by valuing its free cash flowto the firm (FCFF) and free cash flow toequity (FCFE).


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Analysts like to use free cash flow valuationmodels (FCFF or FCFE) whenever one or

more of the following conditions are present: the firm is not dividend paying,

the firm is dividend paying but dividendsdiffer significantly from the firms capacity to

pay dividends, free cash flows align with profitability within

a reasonable forecast period with which theanalyst is comfortable, or

the investor takes a control perspective.


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Common equity can be valued by either

directly using FCFE or

indirectly by first computing the value ofthe firm using a FCFF model andsubtracting the value of non-commonstock capital (usually debt and preferredstock) to arrive at the value of equity.


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Defining Free Cash Flow

Free cash flow to the firm(FCFF) is the cashflow available to the firms suppliers of capitalafter all operating expenses have been paid and

necessary investments in working capital andfixed capital have been made.

FCFF is the cash flow from operations minus

capital expenditures. To calculate FCFF, differingequations may be used depending on whataccounting information is available. The firmssuppliers of capital include commonstockholders, bondholders, and, sometimes,

preferred stockholders.


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Defining Free Cash Flow

Free cash flow to equity (FCFE) is thecash flow available to the firms commonequity holders after all operating expenses,interest and principal payments have beenpaid, and necessary investments inworking and fixed capital have been made.

FCFE is the cash flow from operations minuscapital expenditures minus payments to (andplus receipts from) debtholders.


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1

FCFFFirm Value

(1 WACC)

t

tt

Valuing FCFF

The FCFF valuation approach estimates thevalue of the firm as the present value of futureFCFF discounted at the weighted average costof capital (WACC)

Discounting FCFF at the WACC gives the totalvalue of all of the firms capital. The value of equityis the value of the firm minus the market value ofthe firms debt


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Valuing FCFF

Equity Value = Firm Value Market Valueof Debt

Dividing the total value of equity by thenumber of outstanding shares gives thevalue per share.


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Calculating a WACC

The cost of capital is the required rate ofreturn that investors should demand for a

cash flow stream like that generated bythe firm. The cost of capital is oftenconsidered the opportunity cost of the

suppliers of capital.


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Calculating a WACC

If the suppliers of capital are creditors andstockholders, the required rates of return for debt andequity are the after-tax required rates of return for the

firm under current market conditions. The weights thatare used are the proportions of the total market value ofthe firm that are from each source, debt and equity.

MV(debt) and MV(equity) are the current market valuesof debt and equity, not their book or accounting values.The weights will sum to 1.0.

ed requityMVdebtMV

equityMVrateTaxr

equityMVdebtMV

debtMVWACC

)()(

)()1(

)()(

)(


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Valuing FCFE

The value of equity can also be found bydiscounting FCFE at the required rate of return onequity (r):

Since FCFE is the cash flow remaining for equity

holders after all other claims have been satisfied,discounting FCFE by r (the required rate of returnon equity) gives the value of the firms equity.

Dividing the total value of equity by the number of

outstanding shares gives the value per share.

1

FCFEEquity Value

(1 )

t

tt r


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Single-stage constant-growth FCFF

valuation modelFCFF in any period is equal to FCFF in the

previous period times (1 + g):

FCFFt = FCFFt1 (1 + g).The value of the firm if FCFF is growing at

a constant rate is

Subtracting the market value of debt fromthe firm value gives the value of equity.

01FCFF (1 )FCFF

Firm Value WACC WACC

g

g g


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Single-stage, constant-growth

FCFE valuation modelFCFE in any period will be equal to FCFE in the

preceding period times (1 + g):

FCFEt = FCFEt1 (1 + g).The value of equity if FCFE is growing at a

constant rate is

The discount rate is r, the required return onequity. The growth rate of FCFF and the growth

rate of FCFE are frequently not equivalent.

01 FCFE (1 )FCFE

Equity Value

g

r g r g


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Computing FCFF from Net Income

Free cash flow to the firm (FCFF) is the cash flowavailable to the firms suppliers of capital after alloperating expenses (including taxes) have been

paid and operating investments have been made.The firms suppliers of capital include creditors andbondholders and common stockholders (andoccasionally preferred stockholders that we willignore until later). Free cash flow to the firm is:

FCFF = Net income available to common shareholdersPlus: Net Non-Cash ChargesPlus: Interest Expense times (1 Tax rate)Less: Investment in Fixed Capital

Less: Investment in Working Capital


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Computing FCFF from Net Income

This equation can be written more compactlyas

FCFF = NI + NCC + Int(1 Tax rate) Inv(FC) Inv(WC)


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Computing FCFF from CFO

To estimate FCFF by starting with cash flowfrom operations (CFO), we must recognize

the treatment of interest paid. If, as the casewith U.S. GAAP, the after-tax interest wastaken out of net income and out of CFO,after-tax interest must be added back in

order to get FCFF. So free cash flow to thefirm, estimated from CFO, is

FCFF = Cash Flow from Operations

Plus: Interest Expense times (1 Tax rate)

Less: Investment in Fixed Capital


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Computing FCFF from CFO

Or you can write the equation as:

FCFF = CFO + Int(1 Tax rate) Inv(FC)


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Non-cash charges

The best place to find historical non-cashcharges is to review the firms statement of cash

flows.Some common non-cash charges and theadjustments to net income to get cash flow are:

Non-Cash Item Adjustment to NI to arrive at CF

Depreciation Added Back

Amortization of intangibles Added BackRestructuring Charges (expense) Added BackRestructuring Charges (income resultingfrom reversal)

Subtracted

Losses Added BackGains SubtractedAmortization of long-term bond discounts Added BackAmortization of long-term bond premium Subtracted

Deferred taxes Warrants special attention


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Non-cash charges

Deferred taxes result from a difference intiming of reporting income and expenseson the companys tax return. The incometax expense deducted in arriving at netincome for financial reporting purposes isnot the same as the amount of cash taxespaid. Over time these differencesbetween book and taxable income shouldoffset each other and have no impact onaggregate cash flows. In this case, noadjustment would be necessary for

deferred taxes.


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Non-cash charges

If the analysts purpose is forecasting and he seeksto identify the persistent components of FCFF, thenit is not appropriate to add back deferred taxchanges that are expected to reverse in the nearfuture. In some circumstances, however, acompany may be able to persistently defer taxesuntil a much later date. If a company is growing

and has the ability to indefinitely defer tax liability,an analyst adjustment (add-back) is warranted. Anacquirer must be aware, however, that these taxesmay be payable at some time in the future.


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Finding FCFE from FCFF

Free cash flow to equity is cash flow available toequity holders only. It is therefore necessary toreduce FCFF by interest paid to debtholders andto add any net increase in borrowing (subtract anynet decrease in borrowing).

FCFE = Free cash flow to the firm

Less: Interest Expense times (1 Tax rate)

Plus: Net Borrowing

Or

FCFE = FCFF Int(1 Tax rate) + Net borrowing


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Finding FCFE from NI or CFO

Subtracting after-tax interest and addingback net borrowing from the FCFF

equations gives us the FCFE from NI orCFO:

FCFE = NI + NCC Inv(FC) Inv(WC)

+ Net borrowing

FCFE = CFO Inv(FC) + Net borrowing


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Finding FCFF from EBIT

FCFF and FCFE are most frequentlycalculated from a starting basis of NI or CFO.Two other starting points are EBIT orEBITDA.

To show the relation between EBIT andFCFF, let us start with the FCFF equation

and assume that the non-cash charge (NCC)is depreciation (Dep):FCFF = NI + Dep + Int(1 Tax rate)

Inv(FC) Inv(WC)


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Finding FCFF from EBIT

Net income (NI) can be expressed asNI = (EBIT Int)(1 Tax rate) = EBIT(1 Tax rate)

Int(1 Tax rate)

If this equation for NI is substituted for NI inEquation 3-7, we haveFCFF = EBIT (1 Tax rate) + Dep Inv(FC)

Inv(WC)To get FCFF from EBIT, multiply EBIT times

(1 Tax rate), add back depreciation, andthen subtract the investments in fixed capitaland working capital.


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Finding FCFF from EBITDA

To show the relation between FCFF fromEBITDA (Earnings Before Interest, Taxes,Depreciation and Amortization), use theformula for FCFF:FCFF = NI + Dep + Int(1 Tax rate) Inv(FC)

Inv(WC)

Net income can be expressed asNI = (EBITDA Dep Int)(1 Tax rate)NI = EBITDA(1 Tax rate) Dep(1 Tax rate)

Int(1 Tax rate)


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Finding FCFF from EBITDA

Substituting this for NI in the FCFF equationresults in

FCFF = EBITDA(1 Tax rate) + Dep(Tax rate) Inv(FC) Inv(WC)

To get FCFF from EBITDA, multiply EBITDA

times (1 Tax rate), add back depreciationtimes the tax rate, and then subtract theinvestments in fixed capital and workingcapital


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Forecasting free cash flows

Computing FCFF and FCFE based uponhistorical accounting data is straightforward.Often times, this data is then used directly in a

single-stage DCF valuation model.On other occasions, the analyst desires to

forecast future FCFF or FCFE directly. In thiscase, the analyst must forecast the individual

components of free cash flow. This sectionextends our previous presentation on computingFCFF and FCFE to the more complex task offorecasting FCFF and FCFE. We present FCFF

and FCFE valuation models in the next section.


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Forecasting free cash flows

Given that we have a variety of ways in which toderive free cash flow on a historical basis, itshould come as no surprise that there areseveral methods of forecasting free cash flow.

One approach is to compute historical free cashflow and apply some constant growth rate. This

approach would be appropriate if free cash flowfor the firm tended to grow at a constant rateand if historical relationships between free cashflow and fundamental factors were expected to

be maintained.


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Forecasting FCFF

One approach recognizes that capitalexpenditures have two components; those

expenditures necessary to maintainexisting capacity (fixed capitalreplacement) and those incrementalexpenditures necessary for growth. When

forecasting, the former are likely to berelated to the current level of sales, whilethe latter are likely to be related to theforecast of sales growth.


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Forecasting FCFF

When forecasting FCFE, analysts oftensimplify the estimation of FCFF and FCFE.Equation 3-7 can be restated as

FCFF = NI + Int (1 Tax rate) (Capital spending Depreciation) Inv(WC)

which is equivalent to

FCFF = EBIT (1 Tax rate) (Capital spending Depreciation) Inv(WC)

The components of FCFF in these equationsare often forecasted in relation to sales.


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Forecasting FCFE

If the firm finances a fixed percentage of its capitalspending and investments in working capital withdebt, the calculation of FCFE is simplified. Let DR

be the debt ratio, debt as a percentage of assets. Inthis case, FCFE can be written as

FCFE = NI (1 DR)(Capital Spending Depreciation)

(1 DR)Inv(WC)

When building FCFE valuation models, the logic,that debt financing is used to finance a constantfraction of investments, is very useful. Thisequation is pretty common.


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What about dividends and stock

repurchases?To find FCFF or FCFE, ignore dividends and stockrepurchases. Recall two formulas for FCFF and FCFE,

FCFF = NI + NCC + Int(1 Tax rate) Inv(FC) Inv(WC)FCFE = NI + NCC Inv(FC) Inv(WC) + Net borrowing

Notice that dividends and other stock transactions are absentfrom the formulas. The reason is that FCFF and FCFE arethe cash flows availableto investors or to stockholders, while

dividends and share repurchases are usesof these cashflows. Transactions between the firm and its shareholders(through cash dividends, share repurchases and shareissuances) do not affect free cash flow.


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What about dividends and stock

repurchases?Leverage changes, such as using more debt financing,would have some impact because they would increase theinterest tax shelter (reducing corporate taxes because of the

tax deductibility of interest) and reduce the cash flowavailable to equity. In the longer run, however, investing andfinancing decisions made today will affect future cash flows.


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Preferred stock in the capital

structure Including preferred stock as a third source of capital can

cause the analyst to add terms to the equations forFCFF and FCFE for the dividends paid on preferred

stock and for the issuance or repurchase of preferredshares.

Instead of including those terms in all of the equations,we chose to leave preferred stock out since it exists onlyfor a minority of corporations. For those companies that

do have preferred stock, the effects of preferred stockcan be incorporated with good judgment. For example,when we are calculating FCFF starting with Net incomeavailable to common, Preferred dividends paid wouldhave to be added to the cash flows to obtain FCFF.


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Preferred stock in the capital

structure When we are calculating FCFE starting with Net income

available to common, if Preferred dividends were alreadysubtracted when arriving at Net income available to

common, no further adjustment for Preferred dividends isrequired. However, issuing (redeeming) preferred stockincreases (decreases) the cash flow available tocommon stockholders, so this term would be added in.

In many respects, the existence of preferred stock in the

capital structure has many of the same effects as theexistence of debt, except that preferred stock dividendspaid are not tax deductible unlike interest payments ondebt.


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Two-stage FCF models

FCF models are much more complex than DDMsbecause the analyst usually estimates sales, profitability,investments, financing costs, and new financing to find

FCFF or FCFE. In two-stage FCF models, the growth rate in the second

stage is a long-run sustainable growth rate. For adeclining industry, the second stage growth rate could beslightly below the GDP growth rate. For an industry that

will grow in the future (relative to the overall economy),the second stage growth rate could still be slightlygreater than the GDP growth rate.


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The two most popular versions of the two-stage FCFF and FCFE models are:

the growth rate is constant (or given) instage one, and then it drops to the long-run sustainable rate in stage two.

the growth rates are declining in stage

one, reaching the sustainable rate at thebeginning of stage two. This latter modelis like the H model for dividend valuation.


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The growth rates can be applied to different variables.The growth rate could be the growth rate for FCFF orFCFE, or the growth rate for income (such as net

income), or the growth rate could be the growth rate forsales. If the growth rate were for net income, thechanges in FCFF or FCFE would also depend oninvestments in operating assets and financing of these

investments. When the growth rate in income declines,such as between stage one and stage two, investmentsin operating assets will probably decline at the sametime. If the growth rate is for sales, changes in net profitmargins as well as investments in operating assets and

financing policies will determine FCFF and FCFE.


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A general expression for the two-stage FCFFvaluation model is

The summation gives the present value of thefirst n years FCFF. The terminal value of theFCFF from year n+1 onward is FCFF

n+1

/ (WACC g), which is discounted at the WACC for nperiods. Subtracting the value of outstandingdebt gives the value of equity. The value pershare is then found by dividing the total value

of equity by the number of outstanding shares.

1

1

FCFF FCFF 1

Firm Value= + (WACC- )(1+WACC) (1+WACC)

nt n

t nt g


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The general expression for the two-stage FCFEvaluation model is

The summation is the present value of the first n

years FCFE, and the terminal value of FCFEn+1 / (r g) is discounted at the required rate of return onequity for n years. The value per share is found bydividing the total value of equity by the number ofoutstanding shares.

1

1

FCFE FCFE 1Equity(1 ) (1 )

n

t nt n

t r gr r


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Nonoperating assets and firm value

Analysts usually segregate operating and non-operating assets when they value a firm.

Many non-operating assets are financial assetsthat can be directly valued by observing theirmarket prices. It is unnecessary to use avaluation model when the market value can be

observed reliably. Non-operating assets that are not contributingoperating income to the firm could be sold. Theliquidation value of these non-performing assetscould then be added to the value of theperforming assets.


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Finally, if non-operating assets are not segregated, thecash flows from these assets could be combined withthe cash flows of the operating assets, often making it

difficult to find the cash flows of the operating assets.For example, interest and dividend income and capitalgains from an investment portfolio could mask the factthat the companys operating profitability is poor. The

value of the firm should be the value of its operatingand non-operating assets:Value of firm = Value of operating assets

+ Value of non-operating assets.


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When calculating FCFF or FCFE, investments in workingcapital do not include any investments in cash andmarketable securities. The value of cash and marketable

securities should be added to the value of the firmsoperating assets to find the total firm value.

Some companies have substantial non-currentinvestments in stocks and bonds that are not operating

subsidiaries but financial investments. These should bereflected at their current market value. Based onaccounting conventions, those securities reported atbook values should be revalued to market values.


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Finally, many corporations haveoverfunded or underfunded pension plans.

The excess pension fund assets should beadded to the value of the firms operatingassets. Likewise, an underfunded pension

plan should result in an appropriatesubtraction from the value of operatingassets.


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Nonoperating assets example

Virginia Mak is estimating the value of Charleson Partners, a non-publicly traded Canadian food wholesaler. Mak has assembled thefollowing information for her appraisal.

The firms operating assets generated a FCFF of CD35 million in the

year just ended. A perpetual growth rate of 5% is expected forFCFF. The weighted average cost of capital is 11%. Charleson Partners has non-operating assets of

CD12 million of cash and short-term marketable securities CD105 million in a diversified portfolio of common stocks and

bonds Pension fund assets of CD75 million and pension fund liabilities ofCD58 million.

Charleson has total debts (notes and bonds payable) with anestimated market value of CD 108 million.

There are 8,250,000 outstanding shares.


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Nonoperating assets example

The value of the operating assets (in million CD) is

The value of the non-operating assets is:Cash and short-term investments CD 12 millionStock and bond portfolio CD 105 millionPension fund surplus (75 58) CD 17 millionTotal non-operating assets: CD 134 million

The total value of the firm is Value of operating assets + Value of non-operating assets = 385 + 134 = CD 519 million.The value of equity is the total value of the firm less the market value of

its debt obligations, or 519 108 = CD 411 million.Finally, the value per share is CD 411 million / 8,250,000 shares = CD

49.82.

0FCFF (1 ) 22(1.05) 23.1Value(Operating) CD 385WACC 0.11 0.05 0.06

g

g


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Cash & Equivalents / Market value

Cash and Equivalents

December 2001

StockCash andEquivalents($ millions)

Total MarketValue of Equity($ millions)

Cash andEquivalents as aPercentage ofMarket Value

Royal PTT Nederland NV (NYSE: KPN) 3,374 4,462 75.6%

Fiat S.p.A. (NYSE: FIA) 2,157 5,077 42.5%

Solectron Corp. (NYSE: SLR) 2,553 7,314 29.5%Wal-Mart Stores (NYSE: WMT) 2,033 263,637 0.7%Intel Corp. (Nasdaq NMS: INTC) 10,326 217,819 4.7%Nokia Corp. (NYSE: NOK) 1,327 103,415 1.3%


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Proust Company (#5)

Proust Company has free cash flow to the firm of$1.7 billion and free cash flow to equity of $1.3billion. Prousts weighted average cost of capital

is 11 percent and its required rate of return forequity is 13 percent. FCFF is expected to growforever at 7 percent and FCFE is expected togrow forever at 7.5 percent. Proust has debt

outstanding of $15 billion.A.What is the total value of Prousts equity using

the FCFF valuation approach?

B.What is the total value of Prousts equity using

the FCFE valuation approach?


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Proust Company solution

A. The Firm Value is the present value of FCFF discountedat the weighted average cost of capital (WACC), or

The market value of equity is the value of the firm minusthe value of debt:

Equity = 45.475 15 = $30.475 billion.B. Using the FCFE valuation approach, the present value of

FCFE, discounted at the required rate of return onequity, is

The value of equity using this approach is $25.409 billion.

475.45

04.0

819.1

07.011.0

)07.1(7.1)1(01

gWACC

gFCFF

gWACC

FCFFFirm

409.25055.0

3975.1

075.013.0

)075.1(3.1)1(01

gr

gFCFE

gr

FCFEPV


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Taiwan Semiconductor (#6)

In 2001, Quinton Johnston is evaluating Taiwan SemiconductorManufacturing Co., Ltd, (NYSE: TSM) headquartered in Hsinchu, ROC,Taiwan. In 2001, the company is unprofitable. Furthermore, TSM paysno dividends on common shares. So, Johnston is going to value TSMusing his forecasts of free cash flow to equity. Johnston is going to use

the following assumptions. 17.0 billion outstanding shares Sales will be $5.5 billion in 2002, increasing at 28 percent annually for the next four years

(through 2006). Net income will be 32 percent of sales Investments in fixed assets will be 35 percent of sales, investments in working capital will

be 6 percent of sales, and depreciation will be 9 percent of sales. 20 percent of the investment in assets will be financed with debt. Interest expenses will be only 2 percent of sales. The tax rate will be 10 percent. TSMs beta is 2.1, the risk-free government bond rate is 6.4 percent, and the market risk

premium is 5.0 percent. At the end of 2006, TSM will sell for 18 times earnings.

What is the value of one ordinary share of Taiwan SemiconductorManufacturing Co., Ltd?


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Taiwan Semiconductor solution

The required rate of return found with the CAPM is:

r = E(Ri) = RF+ bi[E(RM)RF] = 6.4% + 2.1 (5.0%) = 16.9%.

The table below shows the values of Sales, Net income, Capital

expenditures less Depreciation, and Investments in working capital. Thefree cash flow to equity is equal to net income less the investmentsfinanced with equity, which is:

FCFE = Net income (1 DR)(Capital expenditures Depreciation) (1 DR)(Investment in working capital)

Since 20 percent of new investments are financed with debt, 80 percent of

the investments are financed with equity, reducing FCFE by 80 percent of(Capital expenditures Depreciation) and 80 percent of the investment inworking capital.


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Taiwan Semiconductor solution

All data in $ billions2002 2003 2004 2005 2006

Sales (growing at 28%) 5.500 7.040 9.011 11.534 14.764

Net Income = 32% of sales 1.760 2.253 2.884 3.691 4.724

Capex Dep = (35% 9%) Sales 1.430 1.830 2.343 2.999 3.839Inv(WC) = (6% of Sales) 0.330 0.422 0.541 0.692 0.886

.80 [Capex Dep + Inv(WC)] 1.408 1.802 2.307 2.953 3.780

FCFE = NI

0.80[Capex

Dep+Inv(WC)] 0.352 0.451 0.577 0.738 0.945

PV of FCFE discounted at 16.9% 0.301 0.330 0.361 0.395 0.433

erminal stock value 85.040PV of Terminal value discounted at 16.9% 38.954

otal PV of first five years FCFE 1.820

otal value of firm 40.774


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BHP Billiton Ltd. (#9)

Watson Dunn is planning to value BHP Billiton Ltd. using asingle-stage free cash flow to the firm approach. BHPBilliton, headquartered in Melbourne Australia, is aprovider of a variety of industrial metals and minerals.

The financial information Dunn has assembled for hisvaluation is:

1,852 million shares outstanding market value of debt is $3.192 billion free cash flow to the firm is currently $1.559 billion

equity beta is 0.90, the market risk premium is 5.5 percent, and therisk-free discount rate is 5.5 percent before-tax cost of debt is 7.0 percent tax rate is 40 percent for purposes of calculating the WACC, assume the firm is financed

25 percent debt

FCFF growth rate is 4 percent


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BHP Billiton Ltd.

Using Dunns information, calculate:

A. The weighted average cost of capital

B. Value of the firm

C. Total market value of equity

D. Value per share


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BHP Billiton Ltd. solution

A. The required return on equity is

r = E(Ri) = RF+ bi[E(RM)RF]

= 5.5% + 0.90(5.5%) = 10.45%

The weighted average cost of capital isWACC = 0.25(7.0%)(1 0.40) + 0.75(10.45%) = 8.89%

B. Firm Value = FCFF0(1 +g) / (WACC g)

Firm Value = 1.1559(1.04) / (0.0889 0.04) = $24.583

billionC. Equity Value = Firm Value Market Value of Debt

Equity Value = 24.583 3.192 = $21.391 billion

D. Value per share = Equity Value / Number of Shares

Value per share = 21.391 / 1.852 = $11.55.


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Alcan, Inc (#11)

An aggressive financial planner who claims to have a superiormethod for picking undervalued stocks is courting one of yourclients. The planner claims that the best way to find the value

of a stock is to divide EBITDA by the risk-free bond rate. Theplanner is urging your client to invest in Alcan, Inc. (NYSE:AL). Alcan is the parent of a group of companies engaged inall aspects of the aluminum business. The planner says that

Alcans EBITDA of $1,580 million divided by the long-term

government bond rate of 7 percent gives a total value of$22,571 million. Since there are 318 million outstandingshares, this gives a value per share of $70.98. Shares of

Alcan, Inc. are currently trading for $36.50, and the plannerwants your client to make a large investment in Alcan through

him.


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Alcan, Inc. (#11)

A. Provide your client with an alternative valuation of Alcan based on a two-stage FCFE valuation approach. Use the following assumptions:

Net income is currently $600 million. Net income will grow by 20 percent annually forthe next three years.

The net investment in operating assets (capital expenditures less depreciation plusinvestment in working capital) will be $1,150 million next year and grow at 15 percentfor the following two years.

Forty percent of the net investment in operating assets will be financed with net newdebt financing.

Alcans beta is 1.3, the risk-free bond rate is 7 percent, and the market risk premiumis 4 percent.

After three years, the growth rate of net income will be 8 percent and the netinvestment in operating assets (Capital expenditures minus Depreciation plusIncrease in working capital) each year will drop to 30 percent of net income. Debtfinancing will continue to fund 40 percent of the net investment in operating assets.

There are 318 million outstanding shares.

Find the value per share of Alcan.B. Criticize the valuation approach that the aggressive financial planner used.


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Alcan, Inc. solution

A. Using the CAPM, the required rate of return for Alcan is:r = E(Ri) = RF+ bi[E(RM)RF] = 7% + 1.3(4%) = 12.2%.

To estimate FCFE, use the relation

FCFE = Net income (1 DR)(Capex Depreciation) (1 DR)(Invest in WC)

The table below shows net income, which grows at 20 percentannually for years 1, 2, and 3, and then at 8 percent for year 4.

Investments (Capex Depreciation + Investment in WC) are1,150 in year 1 and grow at 15 percent annually for years 2and 3. Debt financing is 40 percent of this investment. FCFE isNI investments + financing. Finally, the present value ofFCFE for years 1, 2, and 3 is found by discounting at 12.2percent.


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The value of FCFE after year 3 is found using the constantgrowth model:

The present value of P3 discounted at 12.2 percent is $15,477.64million. The total value of equity, the present value of the firstthree years FCFE plus the present value of P3, is $15,648.36million. Dividing by the number of outstanding shares (318million) gives a price per share of $49.21. For the first threeyears, Alcan has a small FCFE because of the high investments itis making during the high growth phase.

Year 1 2 3 4Net income 720.00 864.00 1,036.80 1,119.74Investment in operating assets 1,150.00 1,322.50 1,520.88 335.92New debt financing 460.00 529.00 608.35 134.37Free cash flow to equity 30.00 70.50 124.28 918.19

PV of FCFE discounted at 12.2% 26.74 56.00 87.98

21,861.67$08.0122.0

19.91843

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FCFEP


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The planners estimate of the share value of $70.98 ismuch higher than the FCFE model estimate of $49.21.There are several reasons for the differing estimates.

First, taxes and interest expenses, which were $254 and$78 million, have a prior claim to the companys cash flowand should be taken out. These cash flows are notavailable to equity holders.

Second, EBITDA does not account for the companysreinvestments in operating assets. By distributingdepreciation charges (which were $561 million), theplanner is essentially liquidating the firm over time, muchless accounting for the net investments that the firm is

making over time.


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Third, EBITDA does not account for the firms capital structure.Using EBITDA to represent a benefit to stockholders (asopposed to stockholders and bondholders combined) is a

mistake.Finally, dividing EBITDA by the bond rate commits majorerrors, as well. The risk-free bond rate is an inappropriatediscount rate for risky equity cash flows. The required rate ofreturn on the firms equity should be used. Dividing by a fixed

rate also assumes erroneously that the cash flow stream is afixed perpetuity. EBITDA cannot be a perpetual streambecause, if it were distributed, the stream would eventuallydecline to zero (because of no capital investments). Alcan isactually a growing company, so assuming it to be a non-

growing perpetuity is a mistake.


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Bron (#12)

Bron has earnings per share of $3.00 in 2002 and expects earnings per share toincrease by 21 percent in 2003. Earnings per share are going to grow at adecreasing rate for the following five years, as shown in the table below. In 2008,the growth rate will be 6 percent and is expected to stay at that rate thereafter. Netcapital expenditures (Capital expenditures minus depreciation) will be $5.00 per

share in 2002, and then follow the pattern predicted in the table. In 2008, net capitalexpenditures are expected to be $1.50, and then to grow at 6 percent annually afterthat. The investment in working capital parallels the increase in net capitalexpenditures and is predicted to equal 25 percent of net capital expenditures eachyear. In 2008, investment in working capital will be $0.375 and is predicted to growat 6 percent thereafter. Bron will use debt financing to fund 40 percent of net capitalexpenditures and 40 percent of the investment in working capital.Year 2003 2004 2005 2006 2007 2008Growth rate eps 21% 18% 15% 12% 9% 6%Net capex per share 5.00 5.00 4.50 4.00 3.50 1.50

The required rate of return for Bron is 12 percent. Find the value per share using atwo-stage FCFE valuation approach.


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Bron solution

FCFE is shown in this table:

Year 2003 2004 2005 2006 2007 2008Growth rate for earnings per share 21% 18% 15% 12% 9% 6%

arnings per share 3.630 4.283 4.926 5.517 6.014 6.374Capital expenditure per share 5.000 5.000 4.500 4.000 3.500 1.500nvestment in WC per share 1.250 1.250 1.125 1.000 0.875 0.375ew debt financing = 40% of

[Capex + Inv(WC)] 2.500 2.500 2.250 2.000 1.750 0.750CFE = NI Capex Inv(WC) +

New debt financing

0.120 0.533 1.551 2.517 3.389 5.249V of FCFE discounted at 12% 0.107 0.425 1.104 1.600 1.923


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Bron solution

The present values of FCFE from 2003 through 2007 aregiven in the bottom row of the table. The sum of thesefive present values is $4.944. Since the FCFE from 2008

onward will be growing at a constant 6 percent, theconstant growth model can be used to value these cashflows.

The present value of this stream is $87.483 / (1.12)5 =$49.640.

The value per share is the value of the first five FCFE(2003 through 2007) plus the present value of the FCFE

483.87$06.012.0

249.520082007

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FCFEP

fcf valuation - business school

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