equity valuation pdf
DESCRIPTION
This slide set is a work in progress and is embedded in my Principles of Finance course that I teach to computer scientists and engineers. http://awesome.weebly.com/TRANSCRIPT
Equity Valua+on
Objec&ves
¨ Firm and equity fair valua&on methods ¤ Present value DCF methods ¤ Approximate valua&on methods
¨ Understand drivers of equity value ¨ Understand cri&cal growth rates
2
Book Value and Fair Value
¨ Book Values ¤ IC = EB + DB ¤ Basis: Balance sheet
¨ Fair Values ¤ D: Fair Value of Debt ¤ E: Fair Value of Equity ¤ V: Value of Firm is Fair Value of Invested Capital
n V = E + D n At Yahoo:
n V: Enterprise value n E: Market cap
¤ Opera&ng assets: V + NOA ¤ Basis: Discounted cash flows
3
4
NIBCLOWC = OCA -‐ NIBCLC = EB + DB NIBCLIC = OWC + N = C -‐ NOA V = PV(FCF) = value of IC = value of OWC + N
NIBCL CE AP ITP NIBCLAR
NIBCL
NOA NOA
Value of OA
D
E
-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ Fair Values -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐
STDNOA
OA
NOA
DB
EB
N
OCA
EB
LTD
IBCL
IS
N
INV
V
-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ Book Values -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐
OWC
N
LTD
EB
IS
Firm Valua&on
NIBCL: non-interest bearing current liabilities
Market Value or Price
¨ Market Value ¤ In an efficient market the market value will fluctuate randomly from the fair value
¤ Basis of Market Value n Amount an “arm length” buyer is willing to pay today for the firm’s future free cash flow
n There is a control premium if buying controlling interest n For a publically traded firm we know the market price of its equity and debt
n Financial newspapers publish the market value of a share of common stock
n E = ns ·∙ p
5
Google’s market value to book value ratio
Cost of Capital
¨ A firm’s cost of capital is equal to the capital provider’s expected return on the market value of her investment ¤ k = weighted average cost of capital ¤ kE = cost of equity ¤ kD = cost of debt
6
VE k +
VD ) -‐ (1 k = k ED ⋅⋅τ
Dividend Discount Model
¨ Method is most applicable to firms that have a high dividend payout ra&o
¨ Assume final equity value paid out as a dividend (sale of firm)
i = 0 1 2 3 4 5 N
DIV
DIV1
7
000
N
1ii
E
i0
DEV
)k(1DIV
E
+=
+=∑
=
Free Cash Flow to the Firm Method
¨ FCFF is the cash flow available to capital providers ¤ Cash flow not affected by dividend policy or capital structure
¨ The congruent discount rate is the weighted average cost of capital, k, which does include the effect of capital structure and tax shield
$-‐
$20
$40
$60
$80
$100
$120
$140
$160
Book Value
and
Fair V
alue
[$M]
D
IC
DB
EB
E
V
0
N
1ii
i0 D
k)(1FCFE −+
=∑=
∑= +
=+=N
1ii
i000 k)(1
FCFDEV
8
¨ FCFE is free cash flow that is available to equity providers ¨ And is discounted at the cost of equity, kE.
¨ FCFEi = FCFi – IXi·∙(1-‐τ) + (DBi – DBi-‐1)
¨ FCFEi+1 = FCFi+1 – kD·∙Di·∙(1-‐τ) + (DBi+1 – DBi)
Free Cash Flow to Equity Method
∑= +
=N
1ii
E
i0 )k1(
FCFEE i-‐1 i i+1
ti-‐1 ti ti+1
DBi-‐1 DBi DBi+1
9
IXi kD·∙Di
FCFi FCFi+1
FCFEi FCFEi+1
The DBi and Di corresponding to the target D/E is a be_er value than the current value
$-‐
$20
$40
$60
$80
$100
$120
$140
$160
Fair Va
lue [$M]
D
V
MVA
ICE
Economic Profit Method
¨ Economic profit can be used as the cash flow with the weighted average cost of capital as the discount rate
∑= +
+=N
1ii
i00 )k1(
EPICV ∑= +
=
+=
+=
N
1ii
i0
000
000
k)(1EPMVA
MVAICVBE BDIC
EPi = $NOPATi $)$k$+$ICi)1
10
APV Method
11
∑=
⎥⎦
⎤⎢⎣
⎡
++
+=
N
1ii
TS
ii
U
i0 )k1(
TS)k1(
FCFV
( ) ( )∑∑
∑
=
−
=
=
+
⋅⋅=
+=
+=
N
1ii
TS
1iDN
1ii
TS
iTS
N
1ii
U
iU
ii
0
0
k1Dkτ
k1TSV
)k(1FCFV
i=0 i=1 i=2
t0 t1 t2
D0 D1 D2
TS1 TS2 FCF1 FCF2
Split cash flow into the two sources of value Business opera&ons: FCF Financing: Tax Shield, TS
TSi = τ ·∙ kD ·∙ Di-‐1 TSi = τ ·∙ IXi kTS = rate cost of the tax shield kU is the cost of capital assuming that the firm has no tax shield ( no taxes or no debt ) VU = value of the unleveraged firm VTS = value due to the present value of a firm’s tax shield
Some Debt Policy / Tax Shield Alterna&ves
12
gk)g1(DτkV
TS
DTS −
+⋅⋅⋅=
Dτk
DτkVD
DTS ⋅=
⋅⋅=
gk)g1(DkV
U
DTS −
+⋅⋅τ⋅=
Du
UD
DTS
DTS
k11
gk)k1(Dτk
k11
gk)g1(DτkV
+⋅
−
+⋅⋅⋅=
+⋅
−
+⋅⋅⋅=
Modigliani & Miller
Harris & Pringle
Miles & Ezzell
Tax shield, TS, and debt, D, are constant
over time Tax shield has same
risk as debt kTS = kD
Tax shield, TS, and debt, D, have same risk
as assets kTS = kU
D increases with FCF, Leverage (D/V) is
constant
Leverage (D/V) is constant 1st year TS risk is that of debt
Thereafter TS risk is that of assets
Constant Growth Value
¨ In the case where a cash flow is growing at a constant rate, g, a simple formula is found from series convergence
¨ Example for DDM
DIVE0 gk
DIVE−
=
13
∑= +
=N
1ii
E
i0 )k(1
DIVE
∑∞
=
−
+
+=
1ii
E
1iDIV
10 )k(1)g(1DIVE
⎥⎦
⎤⎢⎣
⎡
+
+++
+
++
+
++
+=
∞
−∞
)k(1)g(1...
)k(1)g(1
)k(1)g(1
k11DIVE
E
1DIV
3E
2DIV
2E
DIV
E10
)g1(DIVDIV DIV1i-‐i +⋅=
Constant Growth Value Formulas
¤ Dividend Discount Method
¤ Free Cash Flow To the Firm Method
DIVE
10 gk
DIVE−
=
FCF
10 gk
FCFV−
=
14
APV Valua&on with Constant FCF Growth
0
20
40
60
80
100
120
140
160
Fair Va
lue [$M]
VU
VTS
D
ETS
FCFU
1
TSU
FCF
1
Vgk
FCF
VVVAPVM
gkFCF
EDVFCFM
+−
=
+=
−=
+=
15
No assumption yet on growth of debt, D, tax shield, TS, or present value of tax shield, VTS
Constant Growth Value
¨ As the spread between the rate cost and cash flow growth narrows, convergence slows considerably
¨ As cash flow growth rate approaches the rate cost, the series does not converge
0
10
20
30
40
50
60
70
80
90
100
0 50 100 150 200 250 300
s: number of terms in summation
Discount Factor
g=7%
g=8%
g=9%
g=10%g=11%
k=10% gk
CFV 10 −=
16
No Growth Value Formulas
¨ Dividend Discount Method
¨ Free Cash Flow To the Firm Method
E
10 k
DIVE =
kFCFV 1
0 =
17
The numerator (cash flow) is a perpetuity
Variable Growth Value: FCFFM
0HFCF
1HH
1ii
i0 D
)k1(1
)gk(FCF
)k1(FCF
E −⎥⎦
⎤⎢⎣
⎡
+⋅
−+⎥⎦
⎤⎢⎣
⎡+
= +
=∑
18
0 1 H H+1 N
gFCF
Step 2 Step 3
Step 1
Variable Growth Value: FCFFM
1 2 3 4 5 6 7 8 9 10 11 12 13 14
FCF
Years H
010FCF
1110
1ii
i0 D
k)(11
)g(kFCF
k)(1FCF
E −⎥⎦
⎤⎢⎣
⎡
+⋅
−+⎥⎦
⎤⎢⎣
⎡+
= ∑=
19
Equity Value Management
¨ Explore the rela&onships between ¤ Earnings growth ¤ Dividend payouts ¤ Cost of equity ¤ Fair value of equity
¨ Based on the Dividend Growth Model with constant dividend growth assump&on
20
DDM w/ constant dividend growth rate
i=-1 Previous period i=0 Next period i=1
NP0 NP1 DIV0 DIV1
EB-1 EB0 EB1 E-1 E0 E1
DIVE
10 gk
DIVE−
=
DIV1 = (1+gDIV)·∙DIV0
21
Equity Value Per Share
d0
1EEE g
pdkr]r[E +=≡≡
d0
1E g
pdk +=
)gk(dp
dE
10 −=
pvgo pvcy pkd
)gk(d
kd p
0
E
1
dE
1
E
10
+=
⎥⎦
⎤⎢⎣
⎡−
−+=ns
Ep
nsDIVd
00
11
=
=
22
perpetuity a as dividend firstof value presentkd
yield dividendpd
gg
E
1
0
1
DIVd
≡
≡
≡
Share price v. Dividend Growth Rate
d1 = $0.50, kE = 10%
p0 = pvcy + pvgo
23
$-‐
$10
$20
$30
$40
$50
0% 1% 2% 3% 4% 5% 6% 7% 8% 9%
Share price, p0
dividend growth rate, gd
p0
pvgo
pvdy
Price/Earnings Ra&o: pe 24
ΔIC = ΔEB + ΔDB
= ΔRE + ΔPAR + ΔAPC + ΔDB ΔIC = addi&onal invested capital ΔRE = addi&onal retained earnings (=NP1 – DIV1) ΔPAR = addi&onal common equity at par ΔAPC = addi&onal paid in common equity ΔDB = addi&onal debt
i=-1 Previous period i=0 Next period i=1
Price/Earnings Ra&o, pe
i=-1 i=0 i=1 e0 e1
d0 d1 eb-1 eb 0 eb1
)gk(e)b1(p
e)b1(d
dE
10
11
−
⋅−=
⋅−=
)gk()b1(
ep
peeE1
0
−
−=≡
b = plowback ra&o (assume constant) thus ge = gd
(1-‐b) = dividend payout ra&o
25
NPDIV b1
NPREb
=−
Δ=
ΔRE = NP – DIV = NP·∙ b RE
NP
ΔRE
DIV
Price/Earnings Ra&o, pe 26
d1 = $0.50, kE = 10%, b = 0.6
0510152025303540
0% 1% 2% 3% 4% 5% 6% 7% 8% 9%
pe
earnings growth rate, ge
Price/Earnings Ra&o: pe
¨ In the case of no addi&onal investor financing ¤ ΔDB = 0, ΔAPC = ΔPAR = 0 ¤ ΔIC = ΔEB = ΔRE
¨ And a scalable firm with a constant plowback, b
roebg
ebeb
ebroebebebeberoe
eb0
01
0
1
⋅==Δ
⋅⋅=⋅=Δ
=
)roebk()b1(
eppe
E ⋅−
−==
27
b = plowback ra&o
reinvestment of earnings
(1-‐b) = dividend payout ra&o
Long run assump&on ge=geb
Price/Earnings Ra&o: pe 28
eb0 100$
ge 15%b 0.8e1 2.00$
Note: With this input, amer ~40 years geb -‐> ge
Price/Earnings Ra&o, pe
05
1015202530354045
0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15%
roe
pe
kE=10% , b=.6
Increasing expected return on equity increases forward pe
29
Price/Book Ra&o, pb 30
b = 0.6, kE = 10%
0123456
0% 2% 4% 6% 8% 10% 12% 14%
pb
roe
roebkroe)b1(
ebp
pb
roebkebroe)b1(
p
gke)b1(p
E0
0
E
00
dE
10
⋅−
⋅−=≡
⋅−
⋅⋅−=
−
⋅−=
Historic pe ra&os 31
Source: http://www.multpl.com/shiller-pe/
PEG Ra&o
¨ The peg is a price measure normalized for earnings (e1) and earnings growth (ge)
¨ Typical heuris&c ¤ > 1 rela&vely high valua&on ¤ < 1 rela&vely low valua&on
( )eEee gkg100)b1(
g100pepeg
−⋅⋅
−=
⋅≡
32
Valua&on Ra&os 33
Tobin’s Q 34
Source: http://www.vectorgrader.com/indicators/tobins-q
Cri&cal Growth Rates
¨ Internal growth rate, gint: the maximum growth rate that does not require addi&onal external financing
¨ Sustainable growth rate, gsus: the maximum growth rate that maintains the current capital structure, , with addi&onal investor contributed debt EB
DB
35
NA-‐1 NA0 NA1
IC-‐1 IC0 IC1
i=-‐1 i=0 i=1
DIV0 = NP0·∙(1-‐b) DIV1= NP0·∙(1-‐b)·∙(1+g)
ΔRE0 = NP0·∙b ΔRE1=NP0·∙b·∙(1+g)
Cri&cal growth rate deriva&ons for core business opera&ons So use • NA not TA and • IC not C or LE • NA≡IC • roa is return on net book assets • roe is return on book equity
Cri&cal Growth Rates 36
ΔNA = ΔIC = IC1 – IC0
= ΔDB + ΔEB
= ΔDB + ΔAPC + ΔPAR + ΔRE
ΔNA = g·∙NA0 ΔNA = ΔRE + ΔDB
= NP0·∙b·∙(1+g) + ΔDB
NA-‐1 NA0 NA1
i=-‐1 i=0 i=1
ΔRE0 = NP0·∙b ΔRE=NP0·∙b·∙(1+g)
ΔNA = ΔRE + ΔDB
Internal Growth Rate, gint 37
bNP)g1(RE
0DB
DBRENAgNA
int
int
⋅⋅+=Δ
=Δ
Δ+Δ=⋅=Δ
b·∙NP )g(1 NA g intint ⋅+=⋅
b·∙NP b·∙NP) (NA g
b·∙NP b·∙NP g -‐ NA g
int
intint
=−⋅
=⋅⋅
)roab1(roabg
roab )roab -‐ (1 g
NANP roa
int
int
⋅−
⋅=
⋅=⋅
=
NA-‐1 NA0 NA1
i=-‐1 i=0 i=1
ΔRE0 = NP0·∙b ΔRE1=NP0·∙b·∙(1+g)
ΔNA1 = ΔRE1 + ΔDB1
Sustainable Growth Rate, gsus
38
EBDBbNP)g1(bNP)g1(NAg sussussus ⋅⋅⋅++⋅⋅+=⋅
)EBDB
1(bNP)g1(NAg sussus +⋅⋅⋅+=⋅
EBNA
EBEBDB
EBDB1 =
+=+
EBNAbNP)g1(NAg sussus ⋅⋅⋅+=⋅
EBNPb)g1(g sussus ⋅⋅+=
)roeb1(roebg
roeb)g1(g
EBNProe
sus
sussus
⋅−
⋅=
⋅⋅+=
=
NA-‐1 NA0 NA1
i=-‐1 i=0 i=1
ΔRE0 = NP0·∙b ΔRE1=NP0·∙b·∙(1+g)
ΔNA1 = ΔRE1 + ΔDB1
bNP)g1(RE
EBDBREDB
DBRENAgNA
sus
sus
⋅⋅+=Δ
⋅Δ=Δ
Δ+Δ=⋅=Δ
Cri&cal Growth Rates For Fairway Corp 39
NA 2,448.92$ b 70.00%IC 2,448.92$ roa 8.17%EB 2,007.00$ roe 9.97%NP 200.00$ gint 6.06%
gsus 7.50%
Essen&al Points
¨ Equity valua&on via discount cash flow formulas ¤ Dividend discount method ¤ Free cash flow to the firm method ¤ Free cash flow to equity method ¤ Economic profit method ¤ (Adjusted present value method)
¨ Constant growth and no growth discount methods ¨ Equity valua&on by constant growth dividend method
¨ Drivers of equity value ¨ Equivalence of expected return on equity, rE and cost of equity capital, kE
¨ Plowback and payout ra&os
¨ Price/earnings and price/book ra&os ¨ Internal and sustainable growth rates
40