Equity Asset valuation
Kevin C.H. Chiang
Free cash flow valuation
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EAV, Chapter 4
Intrinsic value
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A major task of fundamental analysis is about
finding the present values of future expected
(deterministic) cash flow streams.
Present values are also called intrinsic
values, fundamental values, or economic
values.
Intrinsic values of stocks
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This topic is about finding intrinsic values of stocks.
This task is more challenging than calculating
intrinsic values of bonds.
The main reason for this is that (1) future, expected
cash flows of stocks are highly uncertain; thus, when
we use deterministic methods, we are making strong
assumptions; (2) there are many ways of defining
cash flows for stocks; and (3) firms (and thus their
stocks) can potentially have a infinite life.
Uncertain cash flows
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When deterministic methods are used, the
cash flow estimates are treated as if they are
certain.
We know this is not true.
We usually rely on a sensitivity analysis to
address this unrealistic assumption; we will
talk about sensitivity analysis later.
That is, a “range” of fundamental values.
What cash flows?
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After-tax (corporate tax) cash flows.
There are three (popular) different measures
of cash flows used by practitioners: (1)
expected cash dividends, (2) expected free
cash flows to the firm (FCFF), and (3)
expected free cash flows to equity (FCFE).
Potential infinite life
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A potential infinite life means an infinite
series of cash flows.
It is impossible to individually discounting an
infinite series of cash flows; there is no end
of it.
We need some assumptions to make the
calculation doable. The usual assumption is
to assume there is a constant growth rate in
cash flows.
Dividends as cash flows
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Dividends are the cash flows actually paid to
equity investors.
Expected dividends should be discounted by
the required rate of return on equity (cost of
equity).
The required rate of return on equity can be
estimated by the CAPM (or other asset
pricing models): E(Ri) = Rf + i * (E(Rm) – Rf).
FCFFs as cash flows
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FCFFs are cash flows available for distribution to
debtholders and equityholders.
Thus, the appropriate discount rate is the required
rate of return on debt and equity.
The discount rate is the WACC.
WACC = (D / (D+E))*YTM*(1-Tax rate) + (E /
(D+E))*E(Ri) if bonds are used to finance 100% of
(long-term) debt.
D is the market value of debt; E is the market value
of equity.
FCFEs as cash flows
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FCFEs are the cash flows available for
distribution to equityholders.
FCFEs can be lower or higher than
dividends, depending on the firm’s cash
generating capacity and the firm’s dividend
policy.
Like dividends, FCFEs should be discounted
by the required rate of return on equity (cost
of equity).
Make infinite calculations possible
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The usual strategy is to assume a constant
growth rate, g, in cash flows beyond certain
year t, i.e., growing perpetuity.
PVt = CFt+1 / (r – g).
r is the appropriate discount rate.
An example
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Suppose that we expect IBM will pay $2 per
share as dividends in 3 years, and the
dividends afterwards are able to grow at 5%.
The required rate of return on equity is 10%.
What is the price that we expected in 2
years?
PV2 = CF3 / (r – g) = $2 / (10% – 5%) = $40.
Calculating FCFF from net income, I
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FCFF is the after-tax cash flow available to
debtholders and equityholders after all operating
expenses and operating investments have been
accounted for.
FCFF = NI + net noncash charges + interest
expense * (1 – tax rate) – net investment in fixed
capital for the year – net investment in working
capital for the year (eq. 4-7, p. 151).
Noncash charges include depreciation expense,
intangible-asset amortization expense, etc.
Calculating FCFF from net income, II
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Net noncash charges must be added back because
they reduce NI, but they are not cash outflows.
After-tax interest expense must be added back
because interest expense net of the related tax
shield was deducted in arriving at NI and because
interest expense is a cash flow available to
debtholders, i.e., part of FCFF.
Extra: note that if the firm issues preferred stocks,
preferred stock dividends must be added back as
well.
Calculating FCFF from net income, III
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Net investment in fixed capital (long-term
assets) is the cash outflow needed to sustain
the firm’s current and future operations.
For stock valuation, working capital is
defined as: accounts receivable + Inventory –
accounts payable.
Another method for computing FCFF
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The benchmark method for computing FCFF
is based on NI.
FCFF can be computed from the statement
of cash flows as well.
FCFF = cash flow from operations + interest
expense * (1 – tax rate) – net investment in
fixed capital for the year
See pp. 156-157.
VTwares, I
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We have
VTwares’ income
statement and
balance sheet for
Year 0 and pro
forma income
statements and
balance sheets
for Year 1, Year
2, and Year 3.
D: depreciation;
A: Amortization.
EBITDA
Dep.
Interest
Taxable Income
Taxes (30%)
Net Income
Year 0
Year 1
Year 2
Year 3
100
110
120
135
30
35
40
45
20
20
22
21
50
55
58
69
15
16.5
17.4
20.7
35
38.5
40.6
48.3
Cash
A/R
Inventory
Fixed Assets
Less: Acc. Dep.
30
40
40
400
60
A/P
N/P
L-T Debt
Common Stock
R/E
40
0
150
150
110
33
44
44
470
95
70
44
0
153.5
150
148.5
4
36
48
48
560
135
90
46
0
171.9
150
189.1
6
40
50
50
630
180
70 Net Capital
48
0
154.6
150
237.4
2 Net WC
VTwares, II (calculating FCFF from NI)
Year 1
Year 2
Year 3
NI
38.5
40.6
48.3
Plus: noncash
35
40
45
Plus: interest*(1-tax rate)
14
15.4
14.7
Less: fixed capital
70
90
70
Less: working capital
4
6
2
FCFF
13.5
0
36
VTwares, III
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The appropriate discount rate for FCFF is WACC.
WACC may change over time.
Analysts usually use target capital structure weights
instead of current weights when calculating WACC.
Nowadays, there are a number of information
providers posting their WACC estimates on the
internet, e.g., valuepro.net.
Suppose that you find the WACC of VTwares to be
10%.
VTwares, IV
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Suppose that your research show that the FCFFs of
VTwares will grow at a constant rate of 5% after
Year 3. That is, the FCFF for Year 4 is
36*(1+5%)=37.8.
This means we can use: PV3 = CF4 / (r – g).
Suppose that the market value of debt is 160. Note
that the market value is different from the book value
of debt, 150.
Suppose that the number of shares outstanding is
15.
VTwares, V
Year
Year
Year
Year
1
2
3
4
W ACC
g
FCFF
PV(3)
PV
13.5
12.2727
0
0
36
27.0473
37.8
756 567.994
607.314
160
0.1
447.314
0.05
29.8209
V(Firm)
V(Debt)
V(Equity)
PV per share
Calculating FCFE from FCFF
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FCFE is cash flow available to equityholders only.
We need to reduce FCFF by interest paid to
debtholders and to add net borrowing (debt issued
less debt repayments) over the year.
FCFE = FCFF – interest expense * (1 – tax rate) +
net borrowing (eq. 4-9, p. 163).
Net borrowing: the sum of net change in notes
payable and long term debt.
Alternative ways of computing FCFE
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FCFE = net income + net noncash charges –
net investment in fixed capital – investment in
working capital + net borrowing
FCFE = cash flow from operations – net
investment in fixed capital + net borrowing
P. 164
VTwares, VI
EBITDA
Dep.
Interest
Taxable Income
Taxes (30%)
Net Income
Cash
A/R
Inventory
Fixed Assets
Less: Acc. Dep.
A/P
N/P
L-T Debt
Common Stock
R/E
Year 0 Year 1 Year 2 Year 3
100
110
120
135
30
35
40
45
20
20
22
21
50
55
58
69
15
16.5
17.4
20.7
35
38.5
40.6
48.3
30
33
36
40
40
44
48
50
40
44
48
50
400
470
560
630
60
95
135
180
40
44
46
48
0
0
0
0
150
153.5 171.9
154.6
150
150
150
150
110
148.5 189.1
237.4
3.5
18.4
-17.3 Net Borrowing
VTwares, VII (calculating FCFE
from FCFF)
Year 1
FCFF
Less: interest*(1-tax rate)
Plus: net borrowing
FCFE
Year 2
13.5
14
3.5
3
FCFE
0
15.4
18.4
3
PV(3)
Year 1
Year 2
Year 3
Year 4
3
3
4
4.44
E(Ri)
g
0.12
0.11
Year 3
36
14.7
-17.3
4
PV
2.678571
2.391582
2.847121
444 316.0304
323.9477 V(Equity)
21.59651 PV per share
Dividends vs. FCFs
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About ½ of U.S. publicly traded firms do not pay
dividends.
This make the use of dividend discount models
difficult.
Practitioners tend to like FCF-based discount models
better when (1) the firm does not pay dividends, (2)
the firm pay relatively small amount of dividends
relative to its capacity, and (3) outside investors may
takeover the firm.
FCFF vs. FCFE
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Practitioners tend to work with FCFFs for
levered firms with negative FCFEs.
Working with FCFEs tend to be more
straightforward if firms’ capital structures are
relatively stable over time.
End-of-chapter
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EAV, Chapter 4: Problems 2, 5, 6, 7, 8, 9, 12,
14, and 16.
Residual income valuation
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EAV, Chapter 5
Residual income
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Residual income (RI): net income less an
equity charge (deduction) for common
shareholders’ opportunity cost in generating
net income.
Residual income is a measure of valueadded.
Equity charge = beginning (of the period)
book value of equity * cost of equity
Residual income for year T
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AXCI has a book value of equity $1 million at
the end of year T-1. For year T, the net
income is $91,000. The cost of equity based
on the CAPM is 12%. What is the residual
income for year T?
RI = NI – equity charge = $91,000 $1,000,000 * 12% = -$29,000.
AXCI does not earn enough to cover the cost
of equity capital; there is a loss in value in
year T.
The residual income model
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V0 = B0 + RI1 / (1 + r) + RI2 / (1 + r)2 + RI3 / (1
+ r)3 + ……
where V0 is the value of a share today, B0 is
current per-share book value of equity, and r
is the cost of equity.
RI valuation, I
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PUP’s expected EPS is $2.0, $2.5, and $4.0,
for the next three years. BUP will pay
dividends of $1.0, $1.25, and $1.5 for the
three years. BUP’s current book value is
$6.0 per share. The cost of equity based on
the CAPM is 10%. The residual income
beyond year 3 is expected to grow at 5%
forever.
RI valuation, II
Year
Beginning book value
NI
Dividends
Add. to R/E
Ending book value
Cost of equity
Equity charge
RI
Growth rate for RI
1
6
2
1
1
7
0.1
0.6
1.4
2
7
2.5
1.25
1.25
8.25
0.1
0.7
1.8
3
8.25
3
1.5
1.5
9.75
0.1
0.825
2.175
0.05
PV(3)
45.675
V(0)
44.7107438
4
2.28375
The clean surplus relation
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The validity of the RI model is based on the clean
surplus relation.
That is, the following equation hold: ending book
value = beginning book value + period earning –
period dividends.
The assumption of the clean surplus relation may not
be true when an accounting event bypasses the
income statement and affect book value of equity
directly; e.g., gains and losses on re-measuring
available-for-sale financial assets. When the
assumption is violated, adjustments need to be done
(see pp. 234-249).
End-of-chapter
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Problems 1, 2, 3, 4, 5, 8, 9, 11, 13, 14, and
15