Chapter 3 Free Cash Flow Valuation

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Chapter 3 Free Cash Flow Valuation

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Title: Chapter 3 Free Cash Flow Valuation


1
Chapter 3Free Cash Flow Valuation
2
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).

3
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).

4
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.

5
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.

6
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.

7
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.

8
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

9
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.

10
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.

11
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.

12
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.

13
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.

14
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.

15
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

16
Computing FCFF from Net Income
  • This equation can be written more compactly as
  • FCFF NI NCC Int(1 Tax rate) Inv(FC)
    Inv(WC)

17
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

18
Computing FCFF from CFO
  • Or you can write the equation as
  • FCFF CFO Int(1 Tax rate) Inv(FC)

19
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

20
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.

21
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.

22
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

23
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

24
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)

25
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.

26
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)

27
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

28
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.

29
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.

30
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.

31
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.

32
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.

33
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.
34
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.
35
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.

36
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.

37
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.

38
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.

39
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.

40
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.

41
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.

42
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.

43
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.

44
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.

45
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.

46
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.

47
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.

48
Cash Equivalents / Market value
  • Cash and Equivalents
  • December 2001

49
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?

50
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.

51
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?

52
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.

53
Taiwan Semiconductor solution
54
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.

55
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

56
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

57
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.

58
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.

59
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.

60
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.

61
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.

62
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.

63
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.

64
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.

65
Bron solution
  • FCFE is shown in this table

66
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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