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Corporate Finance Cheat Sheet

Financial Management (University of Technology Sydney)

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Perpetuity t Dividend Growth Model Ratios / Perpetuities Plowback Ratio Calculating Share Value Taxes and NOPAT Accounting Statement
C V2.2 - Licence / Copyright
PV = ∑
(1 + r )t
Cashflow AKA the Gordon Growth Model or Ratios can be equivalent to a b = plowback ratio To value shares, divide dividends and If actual taxes are known then we Revenues
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C 1 Potential problem: RoI = Book Income constant growth model. Assumes perpetuity resulting in Dividends = E(1-b) repurchases by number of shares can use - Costs
PV = multiple IRRs constant growth, ok for mature or Ratio = r – g RoE > r : positive growth opportunities outstanding EBIT – Tax Expense = EBITDA (operating income)
Attribution-ShareAlike 3.0
r−g Growth NPV
Book Assets
stable industries => beware same assumptions as RoE < r : value being destroyed Instead of NOPAT - Depreciation
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Discount rate rate r such that Accounting -sa/3.0/
DGM = EBIT (operating profit)
1 NPV = 0 Rate of Return
DFt = - Interest Expense
Annuity (1 + rt )t IRR
D0 ⋅ (1 + g ) Note: VA = Free Cash Flows of the company
= Pretax Income

V=
- Taxes
P (1 − b ) (1 − b )
discount Created © Matt McNeill 2007

(RE − g )
Funds that would be available to equity holders if D = 0: = Net Income
C C (1 + g)t factor V / EBITDA
= = mmcneill.semba2008@london.edu
PV = − E RE − g RE − RoE ⋅ b
Funds from company free cash flows - Dividends (& share buy-backs)
(r − g) (r − g ) (1 + r)t = Addition to Retained Earnings Contributions: Mike Rizzo, Mark Carroll
Payback = NOPAT
Equivalent to
equivalent Dividend + Depreciation
Project Valuation annual cost RoE = Net Income - Change in NWC ( = current assets – current liabilities)
perpetuity at time 1 – perpetuity at time t Growth Model
PV (COSTS ) Market Value of Equity Stockholders Equity
+ New investments NPV (All Equity) Notes on FCF
EAC =
EBIT (1 − T )
Ratios Book Value of Equity
Interest Rates AnnuityFactor
also known as Use a ratio for a given VE = Essentially cash generated before

(1 + r )(1 + π ) = (1 + i )
break-even rental industry or similar firms
Operating FCF [NOPAT = EBIT (1 − T )] ( RE − g ) payment is made to debt holders
and apply. •Sunk costs – ignore, but market value if
real inflation nominal RoI
(FCF)
FCF = NOPAT + DEPREC − CAPX − ΔNWC for all equity firm : sold is relevant.
Firm Value
VA − VD = VE
r +π ≈ i (rate of return) Comprises of value of all
FCF [WACC = RA = RE ] •Opportunity costs – (incremental) should
be included (not allocated). Excess
V=
its projects - The present

(WACC − g )
CashOut capacity is not free.
T RoI = −1 discounted value of all its
Equity FCF EFCF = NetIncome + Depreciation − CAPX − ΔNWC + NetDebt
⎛ APR ⎞ InitialInvestment cashflows. •Inflation – cashflows need to be matched
r = EAR = ⎜1 + ⎟ EFCF = FCF − Interest (1 − T ) + NetDebtIssues
(EFCF) to rates of return (nominal usually)
effective ⎝ T ⎠ C1 + L + Ct Adjusted Present Value (APV)
RoI = −1 VE + VD = VA •Financing costs – taken into account in
WACC (e.g. dividends and interest)
annual rate C0 Corporate Value project as if all equity financed – use
Valuation Note: VE = Free Cash Flows available to equity holders Operating FCF, discount at RA = RE all equity
•Depreciation is not inflated in
firm. Add PV(TS) generated by new project
Free Cash Funds available in company after: nominal/real calculations.
Market Value Flows -Building up NWC
Mergers & Acquisitions -New investments
APV = NPV ( AllEquity) + PV (TS )
Market Value (MV) could be a
combination of PV and expectation -Paying off old debt / Issuing new debt Note: APV assumes D constant over time,
Overall / Economic Gain
(P) of takeover premium (C): Funds available in form of dividends or share iterative WACC assumes D/V ratio constant, so Modigliani-Miller
MV = PV + P*C
Gain = PV ( AB ) − [PV ( A) + PV (B )] repurchases
values may be slightly different.
• MMI – Capital Structure Irrelevant
• Perfect Capital Markets:
Terminal Value Bankruptcy Costs (BC) P(ExpectedCost ) • Individuals can borrow at the same
Stock Acquisitions Cost of CASH Acquisition / Premium (A buying B) PV( BC ) = rate as corporations.
Cost = Cash − PV (B )
• FCF insufficient to meet RD.D (interest) RBC • No bankruptcy costs / distress costs
Note: that the cost to firm A cannot Based on the PV of a constant FCF (as in • Direct Costs – Legal, Accounting, • No agency problems
be calculated from the stock price Company Value
Gain − Cost = PV ( AB ) − PV ( A) − Cash
last period) with constant growth Trustee, Management fees etc • Symmetric information

FCFT ⋅ (1 + g )
ratio. •Indirect Costs – Production inefficiencies V PV(TS) •NO TAXES
FCF1 FCF2 FCFT 1 (e.g. supplier terms), lost investment

V = FCF0 + + + L+ ×
The economic Gain is required to opportunities, talent loss etc PV(TS)-PV(BCFD)-PV(AC) This allows us to make RA = WACC

(1+ WACC) (1+ WACC)2 (1 + WACC )T (WACC − g )

Cost of STOCK Acquisition / Premium (A buying B)

(1 + WACC)T
calculate true cost, since share price •Typically 1-20%, μ=3-4%, Ç young firms
may change with merger.
Cost = x ⋅ PV ( AB ) − PV (B ) Financial Distress Costs (FD) VU Thus RA does not change due to capital

Gain − Cost = PV ( AB ) − PV ( A) − x ⋅ PV ( AB )
structure – but this does not hold in the
True cost can also be calculated •Reduced financing capacity (D & E)
Note: Perpetuities bring back 1 period (T = last real world of taxes etc.
from computing gain to shareholders •Higher cost of capital
period of FCF model)
of company B. x = fraction of combined firm stock going to
shareholders of B Tax Shields R A ≤ RTS ≤ RD •Loss of customers / suppliers / talent Optimum Leverage D/E
Optimum Leverage

Tax = T ⋅ (EBIT − Interest )

Valid Motives
Does the Market Value of the firm reflect ⎛ R D⎞ VL = VU + PV(TS ) − PV(BCFD) − PV(AC)
PV( BCFD ) << PV(TS )
WACC = R A ⎜⎜1 − T D ⎟
Shareholders are better off

Cost of capital
VU = VL − PV (TS )
RA

RTS V ⎟⎠
•Value Creation takeover premium?
= T ⋅ EBIT − T ⋅ Interest Unlevered
PV( AC ) << PV(TS )
•Operating synergies – horiz:
market power and vert: market Cost = [Cash − MV (B )] + [MV (B ) − PV (B )] [Interest = RD ⋅ D] ⎝ Agency Costs (AC) wacc

RAVU + T ⋅ RD D = RD D + RE E
foreclosure.
•Complimentary resource
Premium paid Difference between = T ⋅ EBIT − T ⋅ RD ⋅ D When RTS = RD • Debt Overhang • Risk Shifting D/V
over market value MV and value as
synergies •New E raised goes to D shortfall if project •2 +ve NPV projects with different risk Risk of bankruptcy due to debt
separate entity (PV) Thus annual tax savings are:
•Cheaper external financing Real additional successful. E insures D. •D fear funds will be allocated to hi-risk payments makes debt more risk
•Correct management failure
•Wealth Transfers Dubious Motives TS = T ⋅ RD ⋅ D When T=0
cashflows from TS RE = R A +
D
(RA − RD )(1 − T ) •Soln: Issue more D, use E to buy back D,
convertibles
(ltd liability of E means D loses)
•D thus require higher RD and no
E
•Bondholders to shareholders •Agency – empire building, larger T ⋅ RD ⋅ D D E • Overinvestment projects now have +ve NPV Leverage
•Employees to shareholders companies, prestige, perks, compen. PV (TS ) = R A = RD + RE When RTS = RA •FCF which should go to D is risked by E on •Soln: Debt covenants etc
Gearing = Leverage = D/V
(wage concessions)
•Customers to shareholders
•Diversification – declining cash rich
industry. Funds should be returned to
RTS V V RE = RA +
D
( R A − RD ) risky project.
•Downside goes to D, upside to E (ltd liability)
(market power) shareholders.
RTS approximates to RD when risk of E Asset Beta = unlevered
•Taxes to shareholders (unused NOT using tax shields is minimal
•Increase EPS – number of shares Equity Beta = levered
RA = RF + β A (RM − RF ) (β A − β D )
taxshield)
R A ≤ RTS ≤ RD D
traded may not be equal.
βE = βA +
E
Leverage
Interest Rates Covered Interest Parity Expected Divisional Leverage
Estimating
D E
WACC = RD (1 − T )
•S$£ : $/£ spot exchange rate ($x:£1) future
D E β A = βD + βE
+ RE
To UK +1 year Back to US spot rate future
•F$£ :$/£ forward exchange rate No riskless arbitrage
forward
1 1
(1 + r£ ) → 1 (1 + r£ )F$£ (1 + r$ ) = F$£ (1 + r$ ) S
•r£ : nominal interest rate £
$1 → →
rates
V V CAPM V V Company
F$£ = E(S$£
′ ) ⇒ E(S$£
′ )≈
•r$ : nominal interest rate $

(1 + r£ ) S$£ (1 + r£ ) $£ RE = RF + β E (RM − RF )
•i£ : UK inflation rate S$£ S$£ S$£ D1 , E1 D2 , E2
(1 + r$ )
•i$ : the US inflation rate. RD = YTM on the Can be assumed to
[S$£ x S£$ = 1] $1 → debt of the company be 0 if debt is risk-free β E1, β D1, β A1 β E 2 , β D2 , β A2
P$
Purchasing
P S $£ ≈ P ⇒ S $£ ≈ £
£ $
D1 D
Bonds P Risk Free Rate Equity Beta L= L= 2
E (1 + i$ ) E (S$£
′ )
Power Parity Market Risk Premium
Given by short term
V1 w % V2 w2 %
Price = P(C,T) coupon face ≈ Given by the covariance of 1

E (1 + i£ )
treasury bills (up to 1 year
P = ∑ PV (C ) + PV ( F )
The difference between the the stock with a give index
coupon terminal S$£ DC
% period r2
maturity) in the US, or gilts
in the UK.
return expected from
investing in shares and the
(usually via regression DC , EC , β EC , β DC , L =
analysis) VC
T risk free rate.
C F
P=∑ r3 Tax Rate Debt Equity
+ Forward
ZCB
β AC = w1β A1 + w2 β A2
(1 + rt )t (1 + rT )T
Zero-Coupon Bonds
Use ZCBs to get r-values for each t =1 Rates (1 + r3 )3 Only consider
The market value of the
equity of the company
Typically ~ 5%

year (spot values) when Expected interest Interest bearing

2T C F
PSEMI = ∑ × (1+ 2 r3 )
rates in the future $1 debt
(1+ r2 )2
calculating bond prices if there is 2
+ E = share price * number of
RP = w1 R1 + w2 R2
Beta
(1 + ) (1 + )
non-flat term structure. t 2T shares outstanding Actual Returns:
(could use annuity only when t =1
rt r2 T Taxes Paid Portfolio Theory A measure of how much a stock
E (RP ) = w1 E (R1 ) + w2 E (R2 )
2 2
term-structure is flat) EBT Expected Returns: contributes to portfolio risk, i.e. how much
D = LT Debt βI x Rm Major Part the stock moves when the market moves.
B(0,t) is equivalent to Pricing t (RP ) = w12V (R1 ) + w2 2V (R2 ) + 2w1w2 ⋅ COV (R1 , R2 ) Market Specific

(1+2 r3 ) = (1 + r3 )2 = DF2
3 Variance: V Risk of 1 = same as market
Earnings + ST Debt = risk of + risk of
$1 ZCB for t years share 0 = unrelated to the market
before tax Efficient Market share share
(1 + r2 ) DF3 σ P = w1 σ 1 + w2 σ 2 + 2w1w2σ 1, 2
(if ST debt is not Standard Deviation: 2 2 2 2 2
-1 = inverse to the market
1 Hypothesis
B(0, t ) =
[σ = ρ1, 2σ 1σ 2 ] corr(mkt, stk ) ⋅σ stk
related to workng Risk of Market Specific
(1 + rt )t T captial) [w1 + w2 = 1] [ρ ≡ rho] portfoli = risk of + risk of
βi =
D = ∑ t ⋅ wt
Abnormal Returns 1, 2
σ mkt
[V (R ) = σ 2 ]
Yield to o share share
αi = Ri − [RF + βi (RM − RF )]
Bonds & - Cash Correlation
Discount Factor Maturity t =1 βp x Rm Negligible
Fixed Income cashflow (if cash is not between two
1 Ct at time t stocks Portfolio Terms
What value of r gives wt = ⋅ used
P (1 + rt )t
Interest Rate Term Structure
Graph of YTM for the market price P for working capital Risk = covariance / correlation
ZCBs over time equal to the discounted
Duration it could be used to
r Abnormal Returns Portfolio Risk and Diversity Portfolio Performance
ΔV Δr pay off debt 1 T
∑ rt
cash flows for the bond? The weighted average of the Correlation
yield
Market
price T time taken to get payments = −D ⋅ holders) Abnormal returns: αi Risk Idiosyncratic Risk RP RP rho = -1 (max benefits from
μ = mean return =
C F 1+ r T t =1
P=∑
curve V Specific Risk diversification)
+ But if capital markets are (Diversifiable Risk)

t =1 (1 + YTM ) (1 + YTM )T
t
ratio of change ratio of change Tax Debt efficient then 1 T
∑ (rt − μ )
-1 < rho < 1 (some benefits
t in value in interest rate from diversification) VAR = 2
Market
Ri = RF + β i (RM − RF )
The tax rate to be used In principle the market
may not be the value of the debt, but in Risk Market Risk
(Systematic Risk) rho = 1 (no benefits from
T t =1
⇒ E ( ARi ) = 0
ZCB Duration Interest Rate Sensitivity Treasury Securities Forward Rates corporate tax rate. practice this hard to diversification)
Strictly speaking it find. Book value is a 20 # Stocks
The duration of a ZCB is the same Interest rates are more sensitive: 1yr <= T-Bills Nomenclature: 100% w1:w2 StdDev = SQRT(VAR)
0% Risk
as its time to maturity - when maturity is longer
- when the coupon is lower
10yr <= T-Notes
10yr > T-Bonds r ≡ f (0,2,3) Downloaded by Ph??ng V? Tr?n Lan (050610220479@st.buh.edu.vn)
should be the effective
tax rate
valid proxy unless
A portfolio of about 20 stocks can diversify
company is in distress.
almost all specific risk
(Mix) (StdDev)
2 3
 lOMoARcPSD|35863263

Terminology Call Option Put Option Replicating Portfolio 2 Period Binomial Model C2U = max{0, S2U − K} Warrants Convertible Bonds n = number of existing shares
V2.2 - Licence / Copyright
m = number of bonds
Long = Buy the right to… S>K = In the money S<K = In the money Use arbitrage principle. For European Call Option = S2U ⋅ Δ′ + (1 + RF ) B′ Equiv. To Call option except: Equivalent to a package of a:
t
r = conversion ratio: number of shares per bond Creative Commons
Short = Sell the right to… S=K = at the money S=K = at the money Δ = proportion of stock = S1U ⋅ Δ′ + B′ • Issued by company so company gets straight bond + warrant FB = face value of each bond
S<K = out of the money S>K = out of the money Attribution-ShareAlike 3.0
Call = … buy at given price
Put = … sell at given price
Options (aka hedge ratio / option delta)
B = value of risk free Bonds C1U = S1U ⋅ Δ + (1 + RF ) B
t
= S2M ⋅ Δ′ + (1 + RF ) B′
t
purchasing price
• On exercise company issues new shares
•Mitigate agency problems of debt
•Mitigate signalling problems
FB/r
KB
= conversion price
= conversion value: market price of bond
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-sa/3.0/
Call: Δ > 0, B < 0 (long S, short B) C0 = S0 ⋅ Δ + B C1M = max{0, S2M − K} and gets exercise price •Can obtain debt at lower current cost (coupon divided by r (strike price of each share).
Strike = Exercise = K
Put: Δ < 0, B > 0 (short S, long B) = S2M ⋅ Δ′′ + (1 + RF ) B′′
Long Call Short Call • Delayed equity issue (mitigates signalling discount related to value of warrant)
C1D = S1D ⋅ Δ + (1 + RF ) B
t
Premium = Cost = P, C $ t Usually calculations worked out with complete
Stock Price = S $ problem) company values:
C = S1D ⋅ Δ′′ + B′′ • Exec stock options are warrants
C = Max{0, S - K}
Created © Matt McNeill 2007
K value of
V = S ⋅Δ + B = S2 D ⋅ Δ′′ + (1 + RF ) B′′ convertible = warrant + straight FD = Face value of debt (#bonds * FB)
t
K St Note: that Δ,B in each period will • Equity rights issues are “special mmcneill.semba2008@london.edu
option bond bond KD = Exercise (strike) price of debt
C2D = max{0, S2D − K}
CB = W + B(C , T )
C St Change depending on outcome of warrants”. Contributions: Mike Rizzo
E0 = Value of initial equity
previous period (Dynamic Replication) E0* = Adjusted value of initial equity
Need to solve ET * = Adjusted value of equity at maturity
Option Binomial Model Treat same as Options for pricing but need to
C1U = max{0, S1U − K } = S1U ⋅ Δ + (1 + RF )B
Long Put Short Put recursively
$ $ Pricing adjust for share increases and purchase price
X [where F’ = CB See bond pricing [
CB = max λ ⋅ ET − FD ,0
*
]

Convertible (CB)
P = Max{0, K - S}
Option types P
P% n = number of existing shares ???] on other side
K St m = number of warrants ⎡ * F ⎤

Value of
European K P not known, thus cannot Using replicating portfolio, = λ ⋅ max ⎢ ET − D ,0⎥
Can exercise only on 0
St
P C0 = S 0 ⋅ Δ + B use weighted average for C0 solve simultaneously for Δ, B
r = number of shares per warrant FD ⎣ λ ⎦
(conversion ratio)
given maturity date -X
European Call 1-P% K = exercise price
C1D = max{0, S1D − K } = S1D ⋅ Δ + (1 + RF )B
( )
option λ = dilution factor (% fraction of E that goes to
American Payoff
W = λ ⋅ C BS E0 , K D , T , R f , σ
Profit new stockholders) *
Can exercise any time up FD FD/λ Value of firm (ET*)

V0 = E0 + m ⋅ (price of warrants)
to (and on) the given
default holds converts
maturity date. Black-Scholes Normal
Value of all
Combining options requires bonds to shares
European Call option
Derived from cumulative
equity firm VT = ET + mrK
C = S ⋅ N(d1 ) − PV(K ) ⋅ N(d 2 ) λ ⋅ ET ∗ > F
maturity = expiration going long / short on options
WT = λ ⋅ max[ET − nK ,0]
binomial with Conversion exercised if:
( )
with different strike prices. density
E0 = PV ET
infinitely small distribution * *
Value of all
W0 = λ ⋅ C BS (E0 , nK , T , R f , σ )
F
Arbitrage Principle Long Call = +45˚ (L Æ R)
periods (and Incorporating warrants ⇒ KD =
assumptions) ⎛ coupons before ⎞ λ
⎟⎟ − PV (dividends)
Short Call = -45˚ (L Æ R) dividends into BS
E0 = E0 − PV⎜⎜
*
If two combinations of mr
C = (S − PV(D )) ⋅ N(d1 ) − PV(K ) ⋅ N(d 2 )
Long Put = +45˚ (L Å R) μ d2 d1 λ=
assets have same ⎝ maturity ⎠
Short Put = -45˚ (L Å R) n + mr
E0 = (n ⋅ S0 ) + (m ⋅ FB )
cashflows in every period
ln⎛⎜ S ⎟⎞
⎝ PV(K )⎠ + σ T
and every outcome, then e.g. Straddle e.g. Butterfly
$ $
they must have the same C(X) European Put option d1 = existing monies raised
+ σ T 2 equity by convertible
P = − S ⋅ N(− d1 ) + PV(K ) ⋅ N(− d 2 )
price.
P(X)
X issue
This can be used to = Long C(X) d 2 = d1 − σ T
calculate replicating St
X Y Z St + 2 x Short C(Y)
Incorporating
PV(K ) =
portfolio for use in pricing + Long C(Z) K
options
dividends into BS
P = −(S − PV(D )) ⋅ N(− d1 ) + PV(K ) ⋅ N(− d 2 )
(1 + R ) f
T
Forward & Future Contracts Assuming both strategies of
buying now and storing (at
Futures Swaps
Forward Contract is commitment to deliver • Extremely liquid due to use of exchange A swap is an agreement by which 2 parties exchange
zero cost) and buying a F
predetermined asset at a future time for a S0 = • Firms can quickly rebalance risk cash-flows of 2 securities (without changing their
Put-Call Parity American Options Black-Scholes Shorthand Black-Scholes Assumptions predetermined price.
forward contract on the
asset are both 100% (1 + r )T management portfolios at low cost ownership)
PV(K ) =
B(0, K ) • BUT: we do not know counterparty and
C = C BS (S , K , T , R f , σ )
•Stock variance σ2 is constant Futures Contract is a standardised forward riskless then: Interest Rate Swap is an exchange of interest
(1 + RF )T
F = S0 ⋅ (1 + r )
•Can be exercised before maturity date default risk.
P(K ) + S = C(K ) + PV(K ) •Call options – Effect on CBS if the given •Rf is constant contract traded on an organised exchange. (risk of underlying asset T payments on debt (most commonly the coupon swap:
• THUS: exchanges require collateral and
P(K ) = − C(K ) - No dividends = European Call variable increases in value: •No dividends S0 = current spot price (t=0) already incorporated in S0) fixed rate with floating rate)
typically daily settlements (potentially
- Price: calc euro call options maturing + S = Stock price at time 0 •Frictionless trading (no transaction F = cost of T-period forward contract requiring some cash now) Currency Swap is an exchange of payments in
And now accounting for the costs of
at all dividend paying & expiry dates - K = Strike price / exercise price costs) Cost of carry: different currencies.
storage and income from the asset:
and choose largest + T = Time to maturity (years) Note: σ is not an observed quantity F – S0 > 0 Market is in Contango
$ + $ = $ = $ +$ •Put options – + Rf = Risk free rate Interest Rate Swap Example
F = [S0 − PV(income) + PV(storage costs)]⋅ (1 + r )T
K K K K in market, and BS is often used to F – S0 < 0 Market is in Backwardation
S K S S S S - no dividends: may still exercise early + σ = volatility find implied volatility. •Assume that the floating coupon is 8% in first
- value larger than euro put semester and increases 1% every period
•The net payments from X to firm Y are

Equity Issues Advantages of IPO Rights Issue Hedging Real Options Payout Policy S1 S2 S3 S4
Floating rate 8% 9% 10% 11%
•IPO = Initial Public Offering, a • Obtain cash – bank finance, venture capital not • Rights = short warrants (~3 weeks) issued at zero price • Hedging is obtaining insurance against some exogenous risk by These are options as applied to business Real Options This is how a firm distributes cash to the X’s payment $5 $5 $5 $5
company’s first offering of shares to the enough • UK ~60% equity issues, US <5% taking an offsetting risk. decisions: shareholders in one of two ways: Y’s payment $4 $4.5 $5 $5.5
general public. • Cheaper financing – higher liquidity and lower • Rights issued are proportional to shares owned • Risk Management is defining an optimal set of hedges Y pays to X $1.0 $0.5 $0.0 -$0.5
Dividends – firm distributes cash (or stocks) to
•Primary Shares – new shares info asymmetry (disclosure reqs.) • Shares trade “cum rights”, but later can be split and We usually want to hedge: Follow-on investment (Call option / BS) shareholders in proportion to number of
issued by company where money • Other financing cheaper – (as above) traded separately. Timing options (American calls / Binomial) By entering the rate swap, Y borrows at floating rate
•Interest rate risk (inflation / real rate changes) shares held. (to which it has access) but eliminates interest rate
raised is invested in the firm • Insiders can cash out • Exercise price drivers: •Currency risk Abandonment Options (Put option / binomial) •DPS – dividends per share
•Secondary Shares – insiders selling • Easy future access to equity markets risk.
• low as possible to ensure that always in money •Fluctuation of commodity prices (inputs / complementary •Dividend Yield: DPS / share price
stake in company where money
C = C BS (S , K , T , R f , σ )
Disadvantages of IPO and all rights are exercised (income) products) Follow-On Investment •Payout Ratio: DPS / EPS
raised goes to the previous owners • not so low as to signal the market that the Share repurchases – firm buys shares from
•SEO = Secondary/Seasoned Equity • Costly – admin fees (4%) & underwriters fees Value of hedging usually depends on the need for a stable •Although a project may not
• Loss of control managers think the share price will drop a lot in the cashflow to take on other projects. shareholders (US = treasury shares / UK Signalling Methods
Offering, an equity issue by a firm that is next 3 weeks look as if it will payoff at t=0, the eliminated, unless reserved to balance stock
already public. • Legal reqs. – disclosure rules etc •If the hedge will provide the capital for the stable project it is a volatility and upside risk profile S = NPV of FCFs (at t=0) • Dividends: most effective since they set future
• Value of firm subject to external perception • shareholders not bothered, since right value will good thing to do. Risk is bad. K = PV(expected investment) t=0 options etc.)
•Pecking Order: (1) Internal Funds, may still make the option very commitment.
• Easier target for hostile takeovers always balance dilution of current share price. •If the hedge eliminates the chance of raising the capital for a T = Time of inventment (years) •Open market repurchases
(2) Debt, (3) Equity valuable. • Shares repurchases with auction: very effective, if the
project it is a bad thing to do. Risk is good. Rf = Risk free rate •Fixed Price Tender Offer
•The risk downside is not shares are bought at a premium and management
E0 = value of pre-rights company (all equity) σ = volatility (comparable stocks) •Dutch Auction Tender Offer
Underwriters n = number of existing shares relevant since option would not precommits not to tender (i.e. not selling own stock at
ET = value of pos-rights company (all equity) Share repurchases should only be used to a premium).
i = issue ratio (rights issued per share) be exercised in that case.
•Investment banks which advise the firm S0 = value of each pre-rights stock Discount at RF distribute extraordinary surplus cash-flow, but • Open-market share repurchases: weakest signal.
m = number of rights (m = i.n) Assume firm value V, depends on asset price S: Discount at RP
and provide independent monitoring of ST = value of each post-rights stock since mid 1980s US firms now redistribute – Shares are bought at their current market price.
r = number of shares per right (r = 1) PV0(FCF) FCFT+1 FCFT+2 …
quality of firm to the market. FUW = underwriter’s fees S1U Return on asset S for 1 period upside of 50%. Europe is 20%. – 50% of announcements do not follow through, and
(conversion ratio) P%
•Also handles: investment
•Roadshows – for signalling
K = exercise price V0 = value of exercising a right immediately P%⋅ (S1U − S0 ) + (1− P%) ⋅ (S1D − S0 ) PV0(inv) InvT 10% repurchase less than 5% of the value announced.

considerations and demand

λ = dilution factor (% fraction of E that goes to W0 = value of the option of exercising a right at maturity
S0 RS = 0 T
evaluation
new stockholders) S0 t Payout Policy Irrelevance Signalling and Dividends
1-P% S1D PV(FCF) PV(Inv)
•Bookbuilding – bids during BB In perfect capital markets and dividends and • Investors react sharply to changes in dividends
period (~2 weeks) can be revised E0 = S 0 ⋅ n Find expected return cap gains tax are zero or the same, payout – Omission: -9.5%
Value of exercising
Value of option of No Hedge Timing Options
and cancelled. ET = E0 + nK a right now Valuing Rights policy is irrelevant. – Reduction of more than 25%: -6.4%
V (S1U )
•Price and Allocation – following BB exercising a right at Current value of the firm •Cashflows equivalent to S1U S = Value of project Dividends: shareholders could use dividends – Reduction: -1.2%
maturity dividends from a stock. When a P%
period. ET P%
P%⋅V (S1U ) + (1− P%) ⋅V (S1D )
D = cashflows from project – Increase: 0.7%
ST = to buy more shares, or could sell shares for
•Alternatives to BB might be allocations by
auctions, but no discretion to underwriter (n + mr ) V0 V0 =
project’s forecasted cashflows
are sufficiently large the
S0 during period 1 cash to simulate dividend. – Increase of more than 25%: 1.0%

on final price and allocations (Google)

1+ RS investment is made right away 1-P%
Rf = Risk free rate Share repurchase: shareholders total wealth – Initiation: 3.9%
S1D P% = chance of going high • A superior firm has higher payouts to signal wealthy
V (S1D )
1-P% unchanged whether they sell shares or not.
•UW formally buy shares from firm and sell (option is called) and confident. Less profitable firm cannot sustain large
Also equal to dividend distributions. If shares

W0 = ⋅ λ ⋅ C BS (E0 − FUW , nK , T , R f , σ )
to public at higher price. 1 ⎡ (S + D1U ) ⎤ ⎡ (S + D ) ⎤ dividends over long run.
•Various sales models: V0 = ST − K If C0 > S0-K then the option to RP = P%⎢ 1U −1⎥ + (1 − P%)⎢ 1D 1D −1⎥
repurchased at premium there is no wealth
• A less profitable firm will eventually have to cut
F = S0 ⋅ (1 + r )
T transfer between shareholders unless some
•Firm commitment – all shares (see
m Full Hedge r = risk free rate defer the project and miss ⎣ S0 ⎦ ⎣ S0 ⎦ fail to participate in bid. dividends, miss investments, issue equity or debt to
Underwriter’s put) V0 < W0 possible cash-flows is more finance dividends (inefficient!)
V (S1U ) −V (S1U − F ) = V (F )
•Best Efforts – sale and return valuable. i.e. Wait and see. To find P%, set RP = RF (for example) Payout Policy Relevance
•All-or-none
S 0 = ST + V0 ⋅ i Options increase Implications – select conservative ratios, and avoid
V (F ) C = P% ⋅ max{0, S1U - K}
P% When dividends and capital gains are taxed raising dividends if risk of having to reverse it.
•Price premium covers UW responsibility: value of the rights
Payoff

Shareholders are Rights issues where K is closer to

V0 V0 = differently, payout policy is not irrelevant. Dividend change should be smaller than change
1+ r + (1 − P%) ⋅ max{0, S1D - K}
•Market maker – liquidity in first not bothered ST have higher (W0) option values
Dividends: pay taxes on full cash distribution. implied by earnings (smoothing). Avoid dividend cuts if
trading days since the downside is more limited
V (S1D ) −V (S1D − F ) = V (F )
1-P% Share repurchases: cost is small.
•Research coverage after IPO (value of a call option decreases
•Price premium covers UW risks: as K is further from S) Abandonment Options •Pay cap gains tax rate only (typically lower)
•Stabilising prices – if they fall below •Only pay tax on part of distribution (the gain)
Hedging Instruments •Exercised when value
•Only pay tax if chose to sell
Stock Splits
offer price
K K* ST recovered from project’s assets
•Buying unallocated stock C – right owner
Payoff structure should cancel underlying risk as much as possible • Stock Splits: Increasing the number of the
P – firm si greater than the PV of Depends on investors tax bracket, e.g.
•Mitigated by green shoe option outstanding shares by reducing its nominal value.
UP Forwards Futures Swaps Options continuing the project for at pension funds are indifferent (but may like
(option to purchase additional ~15% • Example: In a 2:1 split, investors receive two new
Cunstomised Yes No Yes No* least 1 more period. predictability of dividends)

UP = λ ⋅ PBS (E0 − FUW , nK , T , R f , σ )

shares from company at offer price if Upfront Payment No No** No Yes shares in exchange for each old one. The stock price
demand high within ~30 days of Liquidity Low High High*** High drops by 50% (no money ever changes hands!).
IPO) K S Default Risk High Low High Low Tax Clienteles • A rationale for a stock split is that it makes stocks
•IPO Fees usually a fixed % of the issue (*) Unless traded OTC, but then they are (much) less liquid. cheaper for small investors.
Investors with different dividend tax treatment • However, this “liquidity effect” is not well supported
(~7% in US, ~5% in UK, ~3.5% in Europe) (**) However they do require a margin account.
P – underwriter will hold shares of firms with different by the existing empirical evidence: there is no
•SEO fees about half IPO – very varied (***) Huge demand for swaps makes them extremely liquid. dividend-payout ratios. significant price response to a stock split.
•Rights fees usually ~2%
•Underpricing IPOs (-12% UK, -15.8% US) Different investors might pay different tax
•UW favour current / potential clients Underwriter’s Put Preferred Stocks Optimal hedging rates on dividend income and capital gains:
•Signalling/Reputation (future SEO) When firm’s get a firm commitment from the • Shares with fixed dividend (like debt) Optimal hedging depends of structure of costs associated with low • In most countries individual investors pay Tax Cost of Excess Cash
•Dispersion/Liquidity on lower prices underwriters, then it is equivalent to the firm • Junior claim to debt, but senior to ordinary stocks cash flow. higher tax rates on dividends than on capital
gains. • Excess cash is effectively generating a negative tax
•Attract less informed investors putting a put option on the rights it is selling • Dividend may not be paid, but only if ordinary stock dividend not paid • Inability to service interest payments, increasing costs of financial
• Pension funds are tax exempt. saving for the investors.
(mitigating winners curse problem) • Limited voting rights (usually become normal voting rights if dividend not distress and decreasing debt capacity (tax savings) of the firm.
• Corporations typically pay lower tax rates on • If firms have more cash than what they actually need
UP is typically a very small part of the fee. paid) •Inability to take advantage of profitable investment opportunities
dividends than individuals. to finance their business and have financial flexibility,
Advice and monitoring is usually much more • Often viewed as flexible leverage (classified as equity, limited control, •Inability to perform dividend smoothing. then they should distribute it to shareholders.
significant. cashflow flexibility if dividends not paid) This creates different tax clienteles for • Important caveat: “cash required to finance the
(income tax < cap gains tax)
Downloaded•Note:
• Often bought by institutions, corporations or low income tax bracket byThese
financing.
Ph??ng
are only validV? Tr?n
of there is a cost Lan (050610220479@st.buh.edu.vn)
of obtaining outside dividends: e.g. attracting institutional
investors.
business” and “cash required for financial flexibility” are
not exactly well-defined quantities!