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Chapter 3Free Cash Flow Valuation

Intro to Free Cash Flows

- If applied to dividends, the DCF model is the

dividend discount model (DDM) from Chapter 2. - Chapter 3 extends DCF analysis to value a firm

and the firms equity securities by valuing its

free cash flow to the firm (FCFF) and free cash

flow to equity (FCFE).

Intro to Free Cash Flows

- Dividends are the cash flows actually paid to

stockholders - Free cash flows are the cash flows available for

distribution. - Applied to dividends, the DCF model is the

discounted dividend approach or dividend discount

model (DDM). This chapter extends DCF analysis to

value a firm and the firms equity securities by

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

free cash flow to equity (FCFE).

Intro to Free Cash Flows

- Analysts like to use free cash flow valuation

models (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 dividends differ

significantly from the firms capacity to pay

dividends, - free cash flows align with profitability within a

reasonable forecast period with which the analyst

is comfortable, or - the investor takes a control perspective.

Intro to Free Cash Flows

- Common equity can be valued by either
- directly using FCFE or
- indirectly by first computing the value of the

firm using a FCFF model and subtracting the value

of non-common stock capital (usually debt and

preferred stock) to arrive at the value of

equity.

Defining Free Cash Flow

- Free cash flow to the firm (FCFF) is the cash

flow available to the firms suppliers of capital

after all operating expenses have been paid and

necessary investments in working capital and

fixed capital have been made. - FCFF is the cash flow from operations minus

capital expenditures. To calculate FCFF,

differing equations may be used depending on what

accounting information is available. The firms

suppliers of capital include common stockholders,

bondholders, and, sometimes, preferred

stockholders.

Defining Free Cash Flow

- Free cash flow to equity (FCFE) is the cash flow

available to the firms common equity holders

after all operating expenses, interest and

principal payments have been paid, and necessary

investments in working and fixed capital have

been made. - FCFE is the cash flow from operations minus

capital expenditures minus payments to (and plus

receipts from) debtholders.

Valuing FCFF

- The FCFF valuation approach estimates the value

of the firm as the present value of future FCFF

discounted at the weighted average cost of

capital (WACC) - Discounting FCFF at the WACC gives the total

value of all of the firms capital. The value of

equity is the value of the firm minus the market

value of the firms debt

Valuing FCFF

- Equity Value Firm Value Market Value of Debt
- Dividing the total value of equity by the number

of outstanding shares gives the value per share.

Calculating a WACC

- The cost of capital is the required rate of

return that investors should demand for a cash

flow stream like that generated by the firm. The

cost of capital is often considered the

opportunity cost of the suppliers of capital.

Calculating a WACC

- If the suppliers of capital are creditors and

stockholders, the required rates of return for

debt and equity are the after-tax required rates

of return for the firm under current market

conditions. The weights that are used are the

proportions of the total market value of the firm

that are from each source, debt and equity. - MV(debt) and MV(equity) are the current market

values of debt and equity, not their book or

accounting values. The weights will sum to 1.0.

Valuing FCFE

- The value of equity can also be found by

discounting FCFE at the required rate of return

on equity (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 return on 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.

Single-stage constant-growth FCFF valuation model

- FCFF 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 from the

firm value gives the value of equity.

Single-stage, constant-growth FCFE valuation model

- FCFE 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 on

equity. The growth rate of FCFF and the growth

rate of FCFE are frequently not equivalent.

Computing FCFF from Net Income

- Free cash flow to the firm (FCFF) is the cash

flow available to the firms suppliers of capital

after all operating expenses (including taxes)

have been paid and operating investments have

been made. The firms suppliers of capital

include creditors and bondholders and common

stockholders (and occasionally preferred

stockholders that we will ignore until later).

Free cash flow to the firm is - FCFF Net income available to common

shareholders - Plus Net Non-Cash Charges
- Plus Interest Expense times (1 Tax rate)
- Less Investment in Fixed Capital
- Less Investment in Working Capital

Computing FCFF from Net Income

- This equation can be written more compactly as
- FCFF NI NCC Int(1 Tax rate) Inv(FC)

Inv(WC)

Computing FCFF from CFO

- To estimate FCFF by starting with cash flow from

operations (CFO), we must recognize the treatment

of interest paid. If, as the case with U.S.

GAAP, the after-tax interest was taken 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 the firm, estimated from CFO, is - FCFF Cash Flow from Operations
- Plus Interest Expense times (1 Tax rate)
- Less Investment in Fixed Capital

Computing FCFF from CFO

- Or you can write the equation as
- FCFF CFO Int(1 Tax rate) Inv(FC)

Non-cash charges

- The best place to find historical non-cash

charges is to review the firms statement of cash

flows. - Some common non-cash charges and the adjustments

to net income to get cash flow are

Non-cash charges

- Deferred taxes result from a difference in timing

of reporting income and expenses on the companys

tax return. The income tax expense deducted in

arriving at net income for financial reporting

purposes is not the same as the amount of cash

taxes paid. Over time these differences between

book and taxable income should offset each other

and have no impact on aggregate cash flows. In

this case, no adjustment would be necessary for

deferred taxes.

Non-cash charges

- If the analysts purpose is forecasting and he

seeks to identify the persistent components of

FCFF, then it is not appropriate to add back

deferred tax changes that are expected to reverse

in the near future. In some circumstances,

however, a company may be able to persistently

defer taxes until 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. An acquirer

must be aware, however, that these taxes may be

payable at some time in the future.

Finding FCFE from FCFF

- Free cash flow to equity is cash flow available

to equity holders only. It is therefore necessary

to reduce FCFF by interest paid to debtholders

and to add any net increase in borrowing

(subtract any net 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

Finding FCFE from NI or CFO

- Subtracting after-tax interest and adding back

net borrowing from the FCFF equations gives us

the FCFE from NI or CFO - FCFE NI NCC Inv(FC) Inv(WC)
- Net borrowing
- FCFE CFO Inv(FC) Net borrowing

Finding FCFF from EBIT

- FCFF and FCFE are most frequently calculated from

a starting basis of NI or CFO. Two other starting

points are EBIT or EBITDA. - To show the relation between EBIT and FCFF, 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)

Finding FCFF from EBIT

- Net income (NI) can be expressed as
- NI (EBIT Int)(1 Tax rate) EBIT(1

Tax rate) Int(1 Tax rate) - If this equation for NI is substituted for NI in

Equation 3-7, we have - FCFF EBIT (1 Tax rate) Dep Inv(FC)

Inv(WC) - To get FCFF from EBIT, multiply EBIT times (1

Tax rate), add back depreciation, and then

subtract the investments in fixed capital and

working capital.

Finding FCFF from EBITDA

- To show the relation between FCFF from EBITDA

(Earnings Before Interest, Taxes, Depreciation

and Amortization), use the formula for FCFF - FCFF NI Dep Int(1 Tax rate) Inv(FC)

Inv(WC) - Net income can be expressed as
- NI (EBITDA Dep Int)(1 Tax rate)
- NI EBITDA(1 Tax rate) Dep(1 Tax rate)

Int(1 Tax rate)

Finding FCFF from EBITDA

- Substituting this for NI in the FCFF equation

results 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 depreciation times the

tax rate, and then subtract the investments in

fixed capital and working capital

Forecasting free cash flows

- Computing FCFF and FCFE based upon historical

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 this

case, the analyst must forecast the individual

components of free cash flow. This section

extends our previous presentation on computing

FCFF and FCFE to the more complex task of

forecasting FCFF and FCFE. We present FCFF and

FCFE valuation models in the next section.

Forecasting free cash flows

- Given that we have a variety of ways in which to

derive free cash flow on a historical basis, it

should come as no surprise that there are several

methods of forecasting free cash flow. - One approach is to compute historical free cash

flow and apply some constant growth rate. This

approach would be appropriate if free cash flow

for the firm tended to grow at a constant rate

and if historical relationships between free cash

flow and fundamental factors were expected to be

maintained.

Forecasting FCFF

- One approach recognizes that capital expenditures

have two components those expenditures necessary

to maintain existing capacity (fixed capital

replacement) and those incremental expenditures

necessary for growth. When forecasting, the

former are likely to be related to the current

level of sales, while the latter are likely to be

related to the forecast of sales growth.

Forecasting FCFF

- When forecasting FCFE, analysts often simplify

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 equations are

often forecasted in relation to sales.

Forecasting FCFE

- If the firm finances a fixed percentage of its

capital spending and investments in working

capital with debt, the calculation of FCFE is

simplified. Let DR be the debt ratio, debt as a

percentage of assets. In this 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 constant

fraction of investments, is very useful. This

equation is pretty common.

What about dividends and stock repurchases?

To find FCFF or FCFE, ignore dividends and stock

repurchases. 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 absent from the

formulas. The reason is that FCFF and FCFE are

the cash flows available to investors or to

stockholders, while dividends and share

repurchases are uses of these cash flows.

Transactions between the firm and its

shareholders (through cash dividends, share

repurchases and share issuances) do not affect

free cash flow.

What about dividends and stock repurchases?

Leverage changes, such as using more debt

financing, would have some impact because they

would increase the interest tax shelter (reducing

corporate taxes because of the tax deductibility

of interest) and reduce the cash flow available

to equity. In the longer run, however, investing

and financing decisions made today will affect

future cash flows.

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 for FCFF and FCFE for the dividends

paid on preferred stock and for the issuance or

repurchase of preferred shares. - Instead of including those terms in all of the

equations, we chose to leave preferred stock out

since it exists only for a minority of

corporations. For those companies that do have

preferred stock, the effects of preferred stock

can be incorporated with good judgment. For

example, when we are calculating FCFF starting

with Net income available to common, Preferred

dividends paid would have to be added to the cash

flows to obtain FCFF.

Preferred stock in the capital structure

- When we are calculating FCFE starting with Net

income available to common, if Preferred

dividends were already subtracted when arriving

at Net income available to common, no further

adjustment for Preferred dividends is required.

However, issuing (redeeming) preferred stock

increases (decreases) the cash flow available to

common 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 the existence of debt, except

that preferred stock dividends paid are not tax

deductible unlike interest payments on debt.

Two-stage FCF models

- FCF models are much more complex than DDMs

because 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 a declining industry, the second stage

growth rate could be slightly 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 slightly

greater than the GDP growth rate.

Two-stage FCF models

- The two most popular versions of the two-stage

FCFF and FCFE models are - the growth rate is constant (or given) in stage

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 the beginning of

stage two. This latter model is like the H model

for dividend valuation.

Two-stage FCF models

- The growth rates can be applied to different

variables. The growth rate could be the growth

rate for FCFF or FCFE, or the growth rate for

income (such as net income), or the growth rate

could be the growth rate for sales. If the growth

rate were for net income, the changes in FCFF or

FCFE would also depend on investments in

operating assets and financing of these

investments. When the growth rate in income

declines, such as between stage one and stage

two, investments in operating assets will

probably decline at the same time. If the growth

rate is for sales, changes in net profit margins

as well as investments in operating assets and

financing policies will determine FCFF and FCFE.

Two-stage FCF models

- A general expression for the two-stage FCFF

valuation model is - The summation gives the present value of the

first n years FCFF. The terminal value of the

FCFF from year n1 onward is FCFFn1 / (WACC

g), which is discounted at the WACC for n

periods. Subtracting the value of outstanding

debt gives the value of equity. The value per

share is then found by dividing the total value

of equity by the number of outstanding shares.

Two-stage FCF models

- The general expression for the two-stage FCFE

valuation model is - The summation is the present value of the first n

years FCFE, and the terminal value of FCFEn1 /

(r g) is discounted at the required rate of

return on equity for n years. The value per share

is found by dividing the total value of equity by

the number of outstanding shares.

Nonoperating assets and firm value

- Analysts usually segregate operating and

non-operating assets when they value a firm. - Many non-operating assets are financial assets

that can be directly valued by observing their

market prices. It is unnecessary to use a

valuation model when the market value can be

observed reliably. - Non-operating assets that are not contributing

operating income to the firm could be sold. The

liquidation value of these non-performing assets

could then be added to the value of the

performing assets.

Nonoperating assets and firm value

- Finally, if non-operating assets are not

segregated, the cash flows from these assets

could be combined with the 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 capital

gains from an investment portfolio could mask the

fact that the companys operating profitability

is poor. The value of the firm should be the

value of its operating and non-operating assets - Value of firm Value of operating assets
- Value of non-operating assets.

Nonoperating assets and firm value

- When calculating FCFF or FCFE, investments in

working capital do not include any investments in

cash and marketable securities. The value of cash

and marketable securities should be added to the

value of the firms operating assets to find the

total firm value. - Some companies have substantial non-current

investments in stocks and bonds that are not

operating subsidiaries but financial investments.

These should be reflected at their current market

value. Based on accounting conventions, those

securities reported at book values should be

revalued to market values.

Nonoperating assets and firm value

- Finally, many corporations have overfunded or

underfunded pension plans. The excess pension

fund assets should be added to the value of the

firms operating assets. Likewise, an underfunded

pension plan should result in an appropriate

subtraction from the value of operating assets.

Nonoperating assets example

- Virginia Mak is estimating the value of Charleson

Partners, a non-publicly traded Canadian food

wholesaler. Mak has assembled the following

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 for FCFF. - 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 of CD58 million. - Charleson has total debts (notes and bonds

payable) with an estimated market value of CD 108

million. - There are 8,250,000 outstanding shares.

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 million
- Stock and bond portfolio CD 105 million
- Pension fund surplus (75 58) CD 17 million
- Total 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.

Cash Equivalents / Market value

- Cash and Equivalents
- December 2001

Proust Company (5)

- Proust Company has free cash flow to the firm of

1.7 billion and free cash flow to equity of 1.3

billion. Prousts weighted average cost of

capital is 11 percent and its required rate of

return for equity is 13 percent. FCFF is expected

to grow forever at 7 percent and FCFE is expected

to grow 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?

Proust Company solution

- A. The Firm Value is the present value of FCFF

discounted at the weighted average cost of

capital (WACC), or - The market value of equity is the value of the

firm minus the 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 on equity, is - The value of equity using this approach is

25.409 billion.

Taiwan Semiconductor (6)

- In 2001, Quinton Johnston is evaluating Taiwan

Semiconductor Manufacturing Co., Ltd, (NYSE TSM)

headquartered in Hsinchu, ROC, Taiwan. In 2001,

the company is unprofitable. Furthermore, TSM

pays no dividends on common shares. So, Johnston

is going to value TSM using 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

Semiconductor Manufacturing Co., Ltd?

Taiwan Semiconductor solution

- The required rate of return found with the CAPM

is - r E(Ri) RF biE(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. The free cash

flow to equity is equal to net income less the

investments financed 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 in working capital.

Taiwan Semiconductor solution

Taiwan Semiconductor solution

- The terminal stock value is 18.0 times the

earnings in year 2006, or 18 4.724 85.04

billion. - The present value of the terminal value (38.95

billion) plus the present value of the first five

years FCFE (1.82 billion) is 40.77 billion. - Since there are 17 billion outstanding shares,

the value per share is 2.398.

BHP Billiton Ltd. (9)

- Watson Dunn is planning to value BHP Billiton

Ltd. using a single-stage free cash flow to the

firm approach. BHP Billiton, headquartered in

Melbourne Australia, is a provider of a variety

of industrial metals and minerals. The financial

information Dunn has assembled for his valuation

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 the risk-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

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

BHP Billiton Ltd. solution

- A. The required return on equity is
- r E(Ri) RF biE(RM) RF
- 5.5 0.90(5.5) 10.45
- The weighted average cost of capital is
- WACC 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 billion - C. 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.

Alcan, Inc (11)

- An aggressive financial planner who claims to

have a superior method for picking undervalued

stocks is courting one of your clients. The

planner claims that the best way to find the

value of a stock is to divide EBITDA by the

risk-free bond rate. The planner is urging your

client to invest in Alcan, Inc. (NYSE AL). Alcan

is the parent of a group of companies engaged in

all 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 outstanding shares,

this gives a value per share of 70.98. Shares of

Alcan, Inc. are currently trading for 36.50, and

the planner wants your client to make a large

investment in Alcan through him.

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 for the next

three years. - The net investment in operating assets (capital

expenditures less depreciation plus investment in

working capital) will be 1,150 million next year

and grow at 15 percent for the following two

years. - Forty percent of the net investment in operating

assets will be financed with net new debt

financing. - Alcans beta is 1.3, the risk-free bond rate is 7

percent, and the market risk premium is 4

percent. - After three years, the growth rate of net income

will be 8 percent and the net investment in

operating assets (Capital expenditures minus

Depreciation plus Increase in working capital)

each year will drop to 30 percent of net income.

Debt financing 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.

Alcan, Inc. solution

- A. Using the CAPM, the required rate of return

for Alcan is - r E(Ri) RF biE(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 percent annually for years 1, 2, and 3, and

then at 8 percent for year 4. Investments (Capex

Depreciation Investment in WC) are 1,150 in

year 1 and grow at 15 percent annually for years

2 and 3. Debt financing is 40 percent of this

investment. FCFE is NI investments financing.

Finally, the present value of FCFE for years 1,

2, and 3 is found by discounting at 12.2 percent.

Alcan, Inc. solution

- The value of FCFE after year 3 is found using the

constant growth model - The present value of P3 discounted at 12.2

percent is 15,477.64 million. The total value of

equity, the present value of the first three

years FCFE plus the present value of P3, is

15,648.36 million. Dividing by the number of

outstanding shares (318 million) gives a price

per share of 49.21. For the first three years,

Alcan has a small FCFE because of the high

investments it is making during the high growth

phase.

Alcan, Inc. solution

- The planners estimate of the share value of

70.98 is much 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 flow and should be taken out.

These cash flows are not available to equity

holders. - Second, EBITDA does not account for the companys

reinvestments in operating assets. By

distributing depreciation charges (which were

561 million), the planner is essentially

liquidating the firm over time, much less

accounting for the net investments that the firm

is making over time.

Alcan, Inc. solution

- Third, EBITDA does not account for the firms

capital structure. Using EBITDA to represent a

benefit to stockholders (as opposed to

stockholders and bondholders combined) is a

mistake. - Finally, dividing EBITDA by the bond rate commits

major errors, as well. The risk-free bond rate is

an inappropriate discount rate for risky equity

cash flows. The required rate of return on the

firms equity should be used. Dividing by a fixed

rate also assumes erroneously that the cash flow

stream is a fixed perpetuity. EBITDA cannot be a

perpetual stream because, if it were distributed,

the stream would eventually decline to zero

(because of no capital investments). Alcan is

actually a growing company, so assuming it to be

a non-growing perpetuity is a mistake.

Bron (12)

- Bron has earnings per share of 3.00 in 2002 and

expects earnings per share to increase by 21

percent in 2003. Earnings per share are going to

grow at a decreasing 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. Net capital

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 capital expenditures are

expected to be 1.50, and then to grow at 6

percent annually after that. The investment in

working capital parallels the increase in net

capital expenditures and is predicted to equal 25

percent of net capital expenditures each year. In

2008, investment in working capital will be

0.375 and is predicted to grow at 6 percent

thereafter. Bron will use debt financing to fund

40 percent of net capital expenditures and 40

percent of the investment in working capital. - Year 2003 2004 2005 2006 2007 2008
- Growth 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 a

two-stage FCFE valuation approach.

Bron solution

- FCFE is shown in this table

Bron solution

- The present values of FCFE from 2003 through 2007

are given in the bottom row of the table. The sum

of these five present values is 4.944. Since the

FCFE from 2008 onward will be growing at a

constant 6 percent, the constant growth model can

be used to value these cash flows. - 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 after 2007, or 4.944 49.640

54.58.

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