Transcript Chapter 3 Free Cash Flow Valuation

Chapter 3
Free 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 firm’s 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 firm’s 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 firm’s 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 firm’s 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 firm’s 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 firm’s 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)



FCFFt
Firm Value 
t total value of all of
Discounting FCFF at the WACC
gives the
(1

WACC)
t 1
the firm’s capital. The value of equity is the value of the firm
minus the market value of the firm’s 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.
WACC 
MV (debt)
MV (equity)
rd (1  Tax rate) 
re
MV (debt)  MV (equity)
MV (debt)  MV (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):
Equity Value 


t 1
FCFEt
(1  r )t
 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 firm’s 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 = FCFFt–1 (1 + g).
 The value of the firm if FCFF is growing
at a constant rate is
FCFF0 (1  g )
FCFF1
Firm Value 

WACC  g
WACC  g
 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 = FCFEt–1 (1 + g).
 The value of equity if FCFE is growing at a constant
rate is
FCFE1 FCFE 0 (1  g )
Equity Value 

rg
rg
 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 firm’s suppliers of capital after all operating expenses
(including taxes) have been paid and operating investments
have been made. The firm’s 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 firm’s statement of cash flows.
 Some common non-cash charges and the adjustments
to net income to get cash flow are:
Non-Cash Item
Depreciation
Amortization of intangibles
Restructuring Charges (expense)
Restructuring Charges (income resulting
from reversal)
Losses
Gains
Amortization of long-term bond discounts
Amortization of long-term bond premium
Deferred taxes
Adjustment to NI to arrive at CF
Added Back
Added Back
Added Back
Subtracted
Added Back
Subtracted
Added Back
Subtracted
Warrants special attention
Non-cash charges
 Deferred taxes result from a difference in
timing of reporting income and expenses
on the company’s 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 analyst’s 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)
– Tax rate)
– Int(1
 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
n

FCFFt
FCFFn1
1
+
t
n
(WACCg
)
(1+WACC)
(1+WACC)
t 1
 The summation gives the present value of the first n
years’ FCFF. The terminal value of the FCFF from year
n+1 onward is FCFFn+1 / (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.
Firm Value=
Two-stage FCF models
 The general expression for the two-stage FCFE valuation
model is
Equity 
n

t 1
FCFEt FCFE n 1 1

t
r  g (1  r )n
(1  r )
 The summation is the present value of the first n years’
FCFE, and the terminal value of FCFEn+1 / (r – g) is
discounted at the required rate of return 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 company’s 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 firm’s
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
firm’s 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 firm’s 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
Value(Operating) 
FCFF0 (1  g )
22(1.05)
23.1


 CD 385
WACC  g
0.11  0.05 0.06
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
Stock
Royal PTT Nederland NV (NYSE: KPN)
Fiat S.p.A. (NYSE: FIA)
Solectron Corp. (NYSE: SLR)
Wal-Mart Stores (NYSE: WMT)
Intel Corp. (Nasdaq NMS: INTC)
Nokia Corp. (NYSE: NOK)
Cash and
Equivalents
($ millions)
3,374
2,157
2,553
2,033
10,326
1,327
Total Market
Value of Equity
($ millions)
4,462
5,077
7,314
263,637
217,819
103,415
Cash and
Equivalents as a
Percentage of
Market Value
75.6%
42.5%
29.5%
0.7%
4.7%
1.3%
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. Proust’s 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 Proust’s equity using
the FCFF valuation approach?
B. What is the total value of Proust’s 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
FCFF0 (1  g ) 1.7(1.07) 1.819
FCFF1



 45.475
WACC
 g value
WACC
 g is the
0.11
 0.of
07the 0firm
.04minus the
The
market
of equity
value
Firm 
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
FCFE
) 1this
FCFE
.3(1.075
) 1.3975
The value
of equity
using
approach
is $25.409 billion.
0 (1  g
1
PV 



 25.409
rg
rg
0.13  0.075 0.055
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.
TSM’s 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 + bi[E(RM) – RF] = 6.4% + 2.1 (5.0%) = 16.9%.
The table below shows the values of Sales, Net income, Capital expenditures less
Depreciation, and Investments in working capital. 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
All data in $ billions
Sales (growing at 28%)
2002
5.500
2003
7.040
2004
9.011
2005
11.534
2006
14.764
Net Income = 32% of sales
1.760
2.253
2.884
3.691
4.724
Capex – Dep = (35% – 9%) × Sales
Inv(WC) = (6% of Sales)
1.430
0.330
1.830
0.422
2.343
0.541
2.999
0.692
3.839
0.886
0.80 × [Capex – Dep + Inv(WC)]
1.408
1.802
2.307
2.953
3.780
FCFE = NI–0.80×[Capex–Dep+Inv(WC)]
0.352
0.451
0.577
0.738
0.945
PV of FCFE discounted at 16.9%
0.301
0.330
0.361
0.395
0.433
Terminal stock value
PV of Terminal value discounted at 16.9%
Total PV of first five years’ FCFE
Total value of firm
85.040
38.954
1.820
40.774
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 Dunn’s 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 + bi[E(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 Alcan’s 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.
Alcan’s 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 + bi[E(RM) – RF] = 7% + 1.3(4%) = 12.2%.
To estimate FCFE, use the relation
FCFE = Net income – (1 – DR)(Capex – Depreciation)
– (1 – DR)(Invest in WC)
The table below shows net income, which grows at 20 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:
P3 
FCFE4
918.19

 $21,861.67
rg
0.122 0.08
 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.
Year
1
2
3
4
Net income
720.00 864.00 1,036.80 1,119.74
Investment in operating assets
1,150.00 1,322.50 1,520.88 335.92
New debt financing
460.00 529.00 608.35 134.37
Free cash flow to equity
30.00
70.50 124.28 918.19
PV of FCFE discounted at 12.2%
26.74
56.00
87.98
Alcan, Inc. solution
The planner’s 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 company’s cash flow and
should be taken out. These cash flows are not available to
equity holders.
Second, EBITDA does not account for the company’s
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 firm’s 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 firm’s 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:
Year
Growth rate for earnings per share
Earnings per share
Capital expenditure per share
Investment in WC per share
New debt financing = 40% of
[Capex + Inv(WC)]
FCFE = NI – Capex – Inv(WC) +
New debt financing
PV of FCFE discounted at 12%
2003
21%
3.630
5.000
1.250
2004
18%
4.283
5.000
1.250
2005
15%
4.926
4.500
1.125
2006
12%
5.517
4.000
1.000
2007
9%
6.014
3.500
0.875
2008
6%
6.374
1.500
0.375
2.500
2.500
2.250
2.000
1.750
0.750
–0.120
–0.107
0.533
0.425
1.551
1.104
2.517
1.600
3.389
1.923
5.249
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.
P2007
FCFE2008
5.249


 $87.483
rg
0.12  0.06
 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.