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.