Download as PDF, PPTX
![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
$160
$140
$120
$100
$80
$60
$40
$20
$-‐
Book
Value
and
Fair
Value
[$M]
E FCF −
0 D
D
V E D FCF
IC
DB
EB
E
V
0
N
i 1
i
i
(1 +
k)
=Σ=
Σ=+
= + =
N
i 1
i
i
0 0 0 (1 k)
8](https://image.slidesharecdn.com/equity-20valuation-20pdf-130821170442-phpapp02/75/Equity-valuation-pdf-8-2048.jpg)
![Economic
Profit
Method
¨ Economic
profit
can
be
used
as
the
cash
flow
with
the
weighted
average
cost
of
capital
as
the
discount
rate
IC = DB
+
EB
0 0 0
V = IC +
MVA
0 0 0
MVA EP
EP IC V Σ=
$160
$140
$120
$100
$80
$60
$40
$20
$-‐
Fair
Value
[$M]
D
V
MVA
IC
E
Σ=
+
= +
N
i 1
i
i
0 0 (1 k)
+
=
N
i 1
i
i
0
(1 k)
EPi = $NOPATi $)$k$+$ICi)1
10](https://image.slidesharecdn.com/equity-20valuation-20pdf-130821170442-phpapp02/75/Equity-valuation-pdf-10-2048.jpg)
![APV
Valua&on
with
Constant
FCF
Growth
160
140
120
100
80
60
40
20
0
Fair
Value
[$M]
VU
VTS
D
E
TS
FCFM
V = D +
E
FCF
1
FCF
k g
APVM
V = V +
V
U TS
FCF
1
U FCF
V
k g
+
−
=
−
=
15
No assumption yet on growth of debt, D, tax
shield, TS, or present value of tax shield, VTS](https://image.slidesharecdn.com/equity-20valuation-20pdf-130821170442-phpapp02/75/Equity-valuation-pdf-15-2048.jpg)
![Equity
Value
Per
Share
d
E[r ] r k d ≡ ≡ = +
1
g
E E E 0
p
d DIV
ns
=
p E
0
p d
1
0 −
(k g )
d
k d = +
1
g
E 0
p
E d
=
d
1
1
0
= +
⎡
p
pvcy
pvgo
d
k
(k g )
k
p
d
0
1
E
E d
E
⎤
⎥⎦
⎢⎣
−
−
ns = +
0
1
1
=
22
g ≡
g
d DIV
present
value
of
first
dividend
as
a
perpetuity
d
d
k
dividend
yield
p
1
0
1
E
≡
≡](https://image.slidesharecdn.com/equity-20valuation-20pdf-130821170442-phpapp02/75/Equity-valuation-pdf-22-2048.jpg)
More Related Content
Equity valuation pdf
- 1.
- 2. 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
- 3. 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. 4 -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ Fair Values -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ NIBCL Firm Valua&on OWC = OCA -‐ NIBCL C = EB + DB NIBCL IC = OWC + N = C -‐ NOA V = PV(FCF) = value of IC = value of OWC + N NIBCL CE AP ITP NIBCL AR NIBCL NOA NOA Value of OA D E STD NOA NOA OA DB EB OCA N IBCL LTD EB INV N IS V -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ Book Values -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ OWC N LTD EB IS NIBCL: non-interest bearing current liabilities
- 5. 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
- 6. 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 V D τ ⋅ + k D E ⋅ E V k = k (1 -‐ )
- 7. Dividend Discount Model ¨ Method is most applicable to firms that have a high dividend payout ra&o DIV DIV1 i = 0 1 2 3 4 5 N N E DIV i 1 i (1 k ) ¨ Assume final equity value paid out as a dividend (sale of firm) 7 0 0 0 i E 0 V = E + D + =Σ=
- 8. 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 $160 $140 $120 $100 $80 $60 $40 $20 $-‐ Book Value and Fair Value [$M] E FCF − 0 D D V E D FCF IC DB EB E V 0 N i 1 i i (1 + k) =Σ= Σ=+ = + = N i 1 i i 0 0 0 (1 k) 8
- 9. Free Cash Flow to Equity Method ¨ FCFE is free cash flow that is available to equity providers ¨ And is discounted at the cost of equity, kE. ¨ FCFEi E FCFE 0 (1 k ) = FCFi – IXi·∙(1-‐τ) i + (DBi – DBi-‐1) ¨ FCFEi+1 = FCFi+1 – kD·∙Di·∙(1-‐τ) + (DBi+1 – DBi) Σ= + = N i 1 i E 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
- 10. Economic Profit Method ¨ Economic profit can be used as the cash flow with the weighted average cost of capital as the discount rate IC = DB + EB 0 0 0 V = IC + MVA 0 0 0 MVA EP EP IC V Σ= $160 $140 $120 $100 $80 $60 $40 $20 $-‐ Fair Value [$M] D V MVA IC E Σ= + = + N i 1 i i 0 0 (1 k) + = N i 1 i i 0 (1 k) EPi = $NOPATi $)$k$+$ICi)1 10
- 11. APV Method 11 Σ= ⎤ ⎥⎦ ⎡ ⎢⎣ FCF 0 (1 + k ) + + = N i 1 i i TS i i U TS (1 k ) V V FCF Σ = τ ⋅ k ⋅ D i (1 k ) V TS Σ( ) Σ ( ) = D i − 1 = + = + = + = N i 1 i TS N i 1 i i TS TS N i 1 i U U i i 0 0 1 k 1 k TS1 TS2 FCF1 FCF2 i=0 i=1 i=2 t0 t1 t2 D0 D1 D2 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
- 12. Some Debt Policy / Tax Shield Alterna&ves V k τ D (1 g) 12 V k ⋅ τ ⋅ D ⋅ (1 + g) k g TS D = TS − τ D V k ⋅ τ ⋅ D k D D TS = = ⋅ V k ⋅ τ⋅ D ⋅ (1 + g) k g U D = TS − 1 ⋅ ⋅ ⋅ + TS D k ⋅ τ ⋅ D ⋅ (1 + k ) D U 1 u D D TS 1 k k g 1 k k g + ⋅ − = + ⋅ − = 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
- 13. 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 E DIV ⎡ 1 (1 + g ) ... (1 g ) 2 (1 g ) DIV DIV = ∞ E DIV (1 g ) 0 1 (1 k ) E DIV 0 k − g E DIV = 13 E DIV Σ= 0 (1 + k ) = N i 1 i i E Σ ∞ = i − 1 + + = i 1 DIV i E ⎤ ⎥⎦ ⎢⎣ + + + + + + + + + + ∞− (1 k ) (1 k ) (1 k ) 1 k E 1 DIV 3 E 2 E E 0 1 DIV DIV (1 g ) i = i-‐1 ⋅ + DIV
- 14. Constant Growth Value Formulas ¤ Dividend Discount Method E DIV 1 = 0 k − g E DIV ¤ Free Cash Flow To the Firm Method V FCF 1 FCF 0 k − g = 14
- 15. APV Valua&on with Constant FCF Growth 160 140 120 100 80 60 40 20 0 Fair Value [$M] VU VTS D E TS FCFM V = D + E FCF 1 FCF k g APVM V = V + V U TS FCF 1 U FCF V k g + − = − = 15 No assumption yet on growth of debt, D, tax shield, TS, or present value of tax shield, VTS
- 16. 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 100 90 80 70 60 50 40 30 20 10 0 g=9% g=8% V CF1 0 − 0 50 100 150 200 250 300 s: number of terms in summation Discount Factor g=7% g=11% g=10% k=10% k g = 16
- 17. No Growth Value Formulas ¨ Dividend Discount Method E DIV = E 1 0 k ¨ Free Cash Flow To the Firm Method V FCF1 0 = k 17 The numerator (cash flow) is a perpetuity
- 18. Variable Growth Value: FCFFM 1 FCF FCF ⎡ ⎤ ⎡ E − ⎥⎦ 0 D H 0 H 1 = + FCF H i 1 i i (1 k) (k g ) (1 k) ⎤ ⎢⎣ + ⋅ − + ⎥⎦ ⎢⎣ + = Σ 18 gFCF 0 1 H H+1 N Step 2 Step 1 Step 3
- 19. Variable Growth Value: FCFFM FCF 11 1 FCF ⎡ ⎤ ⎡ E − ⎥⎦ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 FCF Years H 10 0 FCF 10 i 1 i i 0 D (1 k) (k g ) (1 k) ⎤ ⎢⎣ + ⋅ − + ⎥⎦ ⎢⎣ + = Σ= 19
- 20. 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
- 21. 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 E DIV 1 0 k − g E DIV = DIV1 = (1+gDIV)·∙DIV0 21
- 22. Equity Value Per Share d E[r ] r k d ≡ ≡ = + 1 g E E E 0 p d DIV ns = p E 0 p d 1 0 − (k g ) d k d = + 1 g E 0 p E d = d 1 1 0 = + ⎡ p pvcy pvgo d k (k g ) k p d 0 1 E E d E ⎤ ⎥⎦ ⎢⎣ − − ns = + 0 1 1 = 22 g ≡ g d DIV present value of first dividend as a perpetuity d d k dividend yield p 1 0 1 E ≡ ≡
- 23. Share price v. Dividend Growth Rate d1 = $0.50, kE = 10% p0 = pvcy + pvgo 23 $50 $40 p0 $30 $20 $10 $-‐ 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% Share price, dividend growth rate, gd p0 pvgo pvdy
- 24. Price/Earnings Ra&o: pe 24 i=-1 Previous period i=0 Next period i=1 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
- 25. Price/Earnings Ra&o, pe i=-1 i=0 i=1 e0 e1 d0 d1 eb-1 eb 0 eb1 d = (1 − b) ⋅ e 1 1 p (1 − b) ⋅ e (k g ) E d 1 0 − = = NP·∙ b RE (1 − b) (k g ) p ≡ = e pe 0 − 1 E e b = plowback ra&o (assume constant) thus ge = gd (1-‐b) = dividend payout ra&o 25 ΔRE = NP – DIV NP b Δ RE = 1 b DIV NP − = ΔRE NP DIV
- 26. Price/Earnings Ra&o, pe 26 d1 = $0.50, kE = 10%, b = 0.6 40 35 30 25 20 15 10 5 0 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% pe earnings growth rate, ge
- 27. 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 roe e 1 eb b e b roe eb Δ = ⋅ = ⋅ ⋅ g b roe eb eb eb eb 0 1 0 0 = = ⋅ Δ = (1 − b) (k b roe) pe p e E − ⋅ = = 27 b = plowback ra&o reinvestment of earnings (1-‐b) = dividend payout ra&o Long run assump&on ge=geb
- 28. Price/Earnings Ra&o: pe 28 eb0 $ 100 ge 15% b 0.8 e1 $ 2.00 Note: With this input, amer ~40 years geb -‐> ge
- 29. Price/Earnings Ra&o, pe 45 40 35 30 25 20 15 10 5 0 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
- 30. Price/Book Ra&o, pb 30 b = 0.6, kE = 10% 6 5 4 3 2 1 0 0% 2% 4% 6% 8% 10% 12% 14% pb roe p (1 − b) ⋅ e k − g = p (1 − b) ⋅ roe ⋅ eb k − b ⋅ roe (1 − b) ⋅ roe k b roe = pb p 0 eb E 0 E 0 0 E d 1 0 − ⋅ ≡ =
- 31. Historic pe ra&os 31 Source: http://www.multpl.com/shiller-pe/
- 32. PEG Ra&o ¨The peg is a price measure normalized for earnings (e1) and earnings growth (ge) (1 − b) = e e ( E e ) 100 g k g peg pe 100 ⋅ g ≡ ¨ Typical heuris&c ⋅ ⋅ − ¤ > 1 rela&vely high valua&on ¤ < 1 rela&vely low valua&on 32
- 33.
- 34. Tobin’s Q 34 Source: http://www.vectorgrader.com/indicators/tobins-q
- 35. 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 DB that maintains the current capital structure, , with addi&onal investor contributed debt EB 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
- 36. 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
- 37. Internal Growth Rate, gint 37 NA g NA RE DB Δ = ⋅ = Δ + Δ DB 0 Δ = RE (1 g ) NP b int int Δ = + ⋅ ⋅ g NA (1 g ) b·∙NP int ⋅ = + int ⋅ g ⋅ NA -‐ g ⋅ b·∙NP = b·∙NP int int g (NA b·∙NP) b·∙NP int ⋅ − = NA-‐1 NA0 NA1 i=-‐1 i=0 i=1 NA g (1 -‐ b roa) b roa int g b ⋅ roa (1 b roa) roa NP int − ⋅ = ⋅ = ⋅ = ΔRE0 = NP0·∙b ΔRE1=NP0·∙b·∙(1+g) ΔNA1 = ΔRE1 + ΔDB1
- 38. Sustainable Growth Rate, gsus 38 NA-‐1 NA0 NA1 i=-‐1 i=0 i=1 NA g NA RE DB Δ = ⋅ = Δ + Δ DB RE DB EB Δ = Δ ⋅ g NA (1 g ) NP b (1 g ) NP b DB sus ⋅ = + sus ⋅ ⋅ + + sus ⋅ ⋅ ⋅ EB DB ) EB g NA (1 g ) NP b (1 sus ⋅ = + sus ⋅ ⋅ ⋅ + NA EB 1 DB DB EB = EB EB + + = g NA (1 g ) NP b NA sus ⋅ = + sus ⋅ ⋅ ⋅ EB g (1 g ) b NP sus = + sus ⋅ ⋅ EB roe NP EB = g = (1 + g ) ⋅ b ⋅ roe sus sus g b ⋅ roe (1 b roe) sus − ⋅ = ΔRE0 = NP0·∙b ΔRE1=NP0·∙b·∙(1+g) ΔNA1 = ΔRE1 + ΔDB1 RE (1 g ) NP b sus sus Δ = + ⋅ ⋅
- 39. 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%
- 40. 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