Foundations of Finance 1 Flashcards
to move a CF foward in time
we compound it to account for anticipated growth
future value formula
FV0 = C0(1+r)^n
to move a CF backward in time
we discount it to account for the fact we have to wait for it
present value formula
PV0 = Cn / (1+r)^n
if discount rate > 0
0 < DF < 1
if discount rate < 0
DF > 1
total present value formula
C0 + C1/(1+r) + C2/(1+r)^2 + C3/(1+r)^3
NPV formula
= PV(inflows) - PV(outflows)
if NPV > 0
accept project
perpetuity
stream of equal cash flows that occur at regular intervals and last forever
perpetuity formula
PV = C/r
growing perpetuity
stream of cash flows that occur at regular intervals which grows at a constant rate forever
growing perpetuity formula
PV = C / r-g
constant annuity
stream of N equal cash flows paid at regular intervals, number of payments is fixed, start at t=1
constant annuity PV and FV formulas
PV = C/r x [1 - 1/(1+r)^N],
FV = C/r x [(1+r)^N - 1]
growing annuity
fixed number of N growing cash flows paid at regular intervals
growing annuity formula
PV = (C / r-g) x [1 - (1+g / 1+r)^N]
things to include in any NPV/IRR calculation
any CFs that arise directly from project, any cash outflows in future directly from project, any forgone income which might otherwise have been earned, any future purchases which will be reduced as result of project, effect of project on existing projects
things to exclude from any NPV/IRR calculation
any sunk or fixed costs that are independent of investment decision and cannot be recovered
cannibalisation
new investment project decreases sales of existing business
IRR
discount rate for which NPV = 0
IRR decision rule
if IRR > r accept project
cases where NPV and IRR disagree
delayed investments, non existent IRR, multiple IRRs
payback period
only accept a project if its CFs repay initial investment within a pre specified period
problems with payback period
ignores cost of capital, ignores time value of money, ignores CFs after payback period, relies on ad-hoc decision criterion
multiple IRRs
there are as many IRRs as sign changes in CF stream
mutually exclusive projects
investing in one project necessarily excudes the toher
3 differences in projects that IRR ignores but NPV doesnt
differences in scale, differences in timing, differences in risk
incremental cash flows
a CF that takes place in one project but doesn’t happen at the same time in another project
incremental IRR
IRR of differences between projects. When discount rate = IRR one project stops being optimal and the other starts
problems with incremental IRR
difficult to interpret, don’t know which project is optimal when; doesn’t say if NPV > 0; doesn’t adjust projects for different amounts of risk
calculating NPV steps
1 - find unlevered income (before interest), 2 - use to find tax payable, 3 - convert accounting profits into annual CFs by making changes for non-cash items, 4 - discount CFs to present value, 5 - sum to find NPV
non-cash items
items in a profit and loss statement that relate to accounting entries instead of actual CFs - depreciation and amortisation, capital expenditure
capital expenditures
paid immediately while they’re subtracted from earnings over the lifetime of the project through depreciation
Net Working Capital
NWC = Cash + Inventory + Receivables - Payables
Free Cash Flow
FCF = (Revenues - Costs - Depreciation)(1 - Corporate Tax Rate) + Depreciation - Capital Expenditure - (Change in NWC)
NPV: Break-even analysis
how bad would one input have to go to make NPV = 0
NPV: sensitivity analysis
calculate how much NPV varies due to change in an input parameter, holding all others constant
NPV: scenario analysis
calculate effect of simultaneously changing more than one input parameter on NPV
Profitability Index formula
PI = PV of future cash flows / initial investment
Profitability index decision rule
PV > 1, accept
Annual percentage interest rate
doesn’t take into account effects of compound interest
effective annual percentage interest rate
reflects actual returns of investing
EAR formula
EAR = (1 + APR/k)^k - 1, where interest is paid k times a year
If r is the EAR in annualised terms…
equivalent n-month rate = (1+r)^(n/12) - 1
bond
debt instrument which is marketed in the form of securities of a fixed denomination
bond buyers
investors who want stable, predictable, low risk investments; pension funds; risk averse private investors
life cycle of a bond
1) bond issued by issuer: have a prospectus which defines t&c of bond. 2) initial bondholders buy bonds and give cash. 3) if its a coupon bonds, issuer pays interest payments called coupons to bondholder, if its a zero coupon bonds, no payment. 4) End of life of bond: issuer repays face value (specified at start), face value usually = denomination. If bond is a coupon bond, final coupon payment made at same time
fixed coupons
specified at outset
floating coupons
tied to variable rate
denomination relates to
traded units of bonds
face value relates to
cash flows
tenor
remaining length of life of bonds
coupon formula
[Coupon Rate x Face Value] / N.o. of coupon payments a year
default
when issuer fails to make coupon payments or face value payment on time
collateral
issuer’s assets which prospectus states can be seized by bondholders in event of default
unsecured bond
bond with no collateral
yield to maturity
overall profit of bond considering current price and future CFs - helps ot compare to other investments
2 ways to define YTM
1) discount rate at which: PV of all future cash flows = bond current price, 2) IRR of bond given current price
Bonds: if current price > face value
bond trading at premium - pay more now than receive later
Bonds: if current price = face value
bond trading at par - pay same now as receive later
Bonds: if current price <. face value
bond trading at a discount - pay less now than receive later, YTM > Coupon Rate
Bonds risks
default (but collateral is insurance), interest rates affect bond prices
shares risk
future dividends and company cost of equity are uncertain
Bonds vs. shares
bonds have lower risk and lower return than shares
Zero coupon bonds usually
trade at a discount
PV of zero coupon bonds
PV = Cn / (1+r)^n
YTM of zero coupon bonds
YTM = (FV/P)^(1/n) - 1
usually, a higher bond tenor =
higher yield to maturity
zero coupon yield curve
plots YTM against time to maturity - specifies discount rates for risk free CFs and acts as a potential indicator for future economic activity
bond prices and interest rate/YTM move
in opposite directions
zero coupon bonds issues by governments in developed markets…
yield a risk free rate of return as government cannot in theory default on domestic currency debt obligations
coupon bonds
pay face value at maturity and regular coupon payments
current market price is
sum of present value of all future CFs
Coupon Bond: PV(constant annuity)
= C/YTM [1 - (1/(1+YTM)^N)]
Coupon Bond: PV(face value at N)
= FV / (1+YTM)^N
price of coupon bonds in words
= PV(constant annuity) +PV(face value at N)
price of coupon bond formula
P = Coupon/YTM [1 - (1/(1+YTM)^N)] + [FV / (1+YTM)^N]
if we have semi annual coupon payments
need to express YTM is semi annual rate and ensure N is in 6 month periods
expectations
have major effects on investors willingness to lend or borrow for long term
steep yield curve indicates
short term interest rates expected to rise in future
inverted/decreasing yield curve indicates
expected decline in interest rates
nominal interest rate
not adjusted for inflation
real interest rate
adjusted for inflation
if inflation > 0
nominal rate > real rate
real interest rate equation
r_r = (1+r)/(1+i) - 1
fisher equation
(r-i)/(1+i) = r - i
3 main things that affect bond prices
changes in market interest rates (creates changes in YTM), time, bond paying a coupon
as interest rate/bond yields rise
bond prices fall
as interest rate/bond yields fall
bond prices rise
high coupon bonds vs. low coupon bonds
high coupon rates are less sensitive to YTM/IR changes. CFs of high coupon bonds arrive earlier so if YTM increases, the PV of CFs in near future decline a little but CFs in distant future decline a lot
short term bonds vs. long term bonds
bonds with shorter maturity rates less sensitive to YTM/IR changes
Maturity: a bond trading at discount
will increase in price as approach maturity
maturity: a bond trading at par
will stay the same price as approach maturity
maturity: a bond trading at premium
will decrease in price as approach maturity
dirty price
includes accrued interest rate for next coupon
clean price
adjusts for effect of receiving next coupon
to receive coupon, bondholder must buy bond before
ex-coupon date. on that date, bond price falls by coupon payment amount
the presence of default risk leads to…
increased required YTM
credit ratings
debtholders rely on Credit Rating Agencys to evaluate creditworthiness of issuers.
low bond rating =
higher risk and thus higher YTM
gordon growth model def
dividends grow at a constant rate forver
gordon growth model formula
P0 = Div1/(rE - g) or = [Div0 x (1+g)] / (rE - g)
r_E
equity cost of capital - discount rate used to discount future dividends - reflects riskiness of dividends - the return we expect for holding firm equity
rE formula
r_E = (Div1/P0) + g
dividend payout ratio
fraction of earning paid out as dividends
Dividend worded formula
= (Earnings / Shares Outstanding) x Dividend Payout Ratio
dividends can be increased by
increasing earnings or payout ratio
new investments formula
earnings x retention rate
change in earnings
New investments x return on new investments
earnings growth rate
change in earnings / earnings, OR, retention rate x return on new investments, OR (1 - dividend payout ratio) x return on new investments
retention rate
1 - dividend payout ratio
Simple dividend discount model: 1-year horizon. Price and rE formula
P0 = (Div1 + P1) / (1 + rE), rE = [(Div1 + P1) / P0] - 1 = Div1/P0 + (P1 - P0)/P0
Simple dividend discount model: n-year horizon. Price formula
P0 = Div1/(1+rE) + Div2/(1+rE)^2 + … + (Divn + Pn)/(1+rE)^n
two stage dividend discount model: First Stage
first stage until time t=N we predict each dividend individually by modelling company’s performance in detail -> High Growth Stage
two stage dividend discount model: Second Stage
from time t=N assume constant dividend growth which is usually low. Use gordon growth model to value share price at t=N -> Low/Terminal Growth Stage
two stage dividend discount model: Price formula
P0 = Div1/(1+rE) + Div2/(1+rE)^2 + … + DivN/(1+rE)^N + [1/(1+rE)^N] x [(1+g)DivN/(rE-g)]
total payout valuation model- words
firms can repurchase their shares rather than/in addition to paying out dividends.
total payout valuation model: Price Formula
P0 = PV(Future total dividends and repurchases) / Current shares outstanding
Enterprise Value, EV
present value of whole company
market value of equity
= price per share x number of shares = EV - debt value + cash
EV formula
market value of equity + debt value - cash
value of firms net debt
total debt - cash
Free Cash Flow
= EBIT(1 - Corporate Tax Rate) + Depreciation - Capital Expenditure - Change in NWC
FCF Waterfall
firm generate FCF; some FCF used on debt repayments; remaining FCF belongs to shareholders; some paid out in dividends; any leftover FCF reinvested in firm
when calculating PV of FCF we discount it with
Weighted average cost of capital (WACC)
discounted FCF model method
calculate EV of firm (PV of all future FCF); calculate equity value; divide market value of equity by number of shares to get predicted current share price
discounted FCF model: EV formula
= FCF1/(1+rWACC) + FCF2/(1+ rWACC)^2 + … + FCFN/(1+rWACC)^N + [1/(1+rWACC)^N x (1+g)FCFN/(rWACC - g)]
discounted FCF model: Price formula (EV)
EV0 + Cash - Debt / Shares Outstanding
price earnings ratio
used to compare firms: P/E ratio = share price / earnings per share
other multiples to compute firm value
enterprise value multiple (EV/EBIT(DA)); sales multiples (EV/Sales); price-to-book value of equity (P/BV)
EBITDA
earnings before interest, tax, depreciations, amortisation
EBIT
earnings before interest, tax
limitations of using valuation multiples
no clear guidance on how to adjust for differences across firms; provides info about firm relative to another but no info about overall mispricing
ESG Investing: environmental
climate change, environmental sustainability
ESG Investing: social
diversity and inclusion; human rights
ESG Investing: governance
corporate structure (Chair and CEO different?); executive and employee compensation structure
challenges to divestment strategy
difficulty and controversy in identifying firms; underperformance because divestment restricts investment universe, excluding potential high performenrs
comparison conducted based on key ESG factors
environment; community and society; employees and supply chain; customer; government and ethics
methods for applying ESG criteria
exclusion screen (excluding sin stocks); including only top ESG (in each industry); combination of methods - ratings often based on old info so asset managers do own research
dirty industry example
oil
clean industry example
pharmaceuticals
advantages of ESG investing
helps reduce cost of capital and thus cost of equity; reduces downside and overall risk so lower stock volatility
disadvantages of ESG investing
restricts investment universe and efficient frontier so may reduce maximum sharpe ratio - not able to access asset pricing factors that yield as much profit
ESG investings: financial motivation
lower risk - particulalry from regulatory uncertainties
ESG investings: non-financial motivation
ethical and environmental values; impact
green bonds
debt securities issued for specific projects designed to achieve environmental goals. issuer can be firms, banks, governments
green bonds features
usually have same credit rating as conventional bonds; YTM is lower - Green Premium - cheaper way for firm to borrow money. forego some returns and accept lower yields to pursue non-financial objectives
green vs. brown stocks
interest rate of green is lower - Carbon Risk Premium - firms face higher climate and regulatory risks so investors are compensated with higher expected return
green vs. brown portfolios
green portfolios outperform brown in realised returns over long term
return
increase in the value of an investment expressed in a percentage
probability distribution
assigns a probability that each possible return will orccur
return equation with prices
(Pt+1 - Pt)/Pt
expected (mean) returns
calculated as a weighted average of the possible returns where weights correspond to possibilities
Expected return formula
E[R] = ∑_RxP_R ×R
variance
expected squared deviation from the mean - measure of how spread out the distribution is
variance formula
var(R) = E[(R - E[R])^2] = ∑_RxP_R ×(R - E[R])^2
standard deviation
square root of the variance - the volatility of a return
variance and standard deviation do not differentiate between
upside and downside risk
realized return
return that actually occurred over a particular time period
realized return formula
Rt+1 = (Divt+1 + Pt+1)/(Pt) - 1 = Divt+1/Pt + (Divt+1 - Pt)/Pt
annual total realized return
1 + Rannual = (1+RQ1) (1+RQ2)(1+RQ3)(1+RQ4)
how can we estimates the underlying proability distribution
by counting the number of times a realized return falls within a particular range
empirical distribution is obtained when
the probability distribution is plotted against historical data
average annual return
R (bar) =1/T (R1+R2+⋯+ RT) = 1/T ∑R_t
variance of realized returns
Var(R) = 1/T-1∑(Rt - R(bar))^2
two problems with looking at historical data and realized return
we dont know what investors expected in the past, the average return is just an estimate of the expected return so we need to take into account an estimation error
standard error
statistical measure of the degree of estimation error
SD(Average of Independent, Identical Risks) =
SD(Individual Risk) / sqrt(Number of Observations)
the higher the standard deviation
the higher the standard error
the lower the number of observations
the higher the standard error
excess return (or equity risk premium)
difference between the average return for an investmenet and the average return for T-Bills (government bonds)
common risk
risk that is perfectly correlated and affects all securities
independent risk
risk that is uncorrelated and affects a particular security
diversification
the averaging out of independent risks in a large portfolio
firm specific news
good or bad news about and invidivual company
market wide news
news that affects all stocks, such as news about the economy
systematic risk
will affect all firms and not be diversified
risk premium for diversifiable risk
is zero so investors are not compensated for holding firm specific risk because they can diversify to eliminated it
risk premium of a security is determined by
systematic risk
how to determine how sensitive a stock is to systematic risk
look at the average chagne in return for each 1% change in the return of a portfolio that fluctuates solely due to systematic risk
efficient portfolio
portfolio that contains only systematic risk - no way to reduce volatility without lowering expected turn
a market portfolio is assumed to be
efficeint
Beta
is the sensitivity of the security’s return to the return of the overall market - the expected percentage change in the excess return of a security for a 1% change in the excess return of the market portfolio
volatility measures
total risk - systematic and unsystematic
beta is measure of
only systematic risk
market risk premium
the reward investors expect to earn for holding a portfolio with a beta of 1
risk premium formula
risk premium = beta x market risk premium
Capital Asset Pricing Model formula
E[R] = Risk Free Interest Rate + Risk Premium = rf + beta x (E[Rmkt] - rf)
portfolio weights formula
xi = Value of intestments / total value of portfolio
return on the portoflio
weighted average of the returns on the single stocks included in the portfolio, and the weights correspond to the portfolio weights
return on the portfolio formula
Rp = X1R1 + X2R2 + … + XnRn
expected return of a portfolio
E[Rp] = ∑ Xi E[Ri]
covariance
expected product of the deviation of two returns from their means
covariance formula
Cov(R1, R2) = E[(R1 - E[R1])(R2 - E[R2])]
covariance from historical data formula
= 1/T-1 ∑ (R1 - R(bar)1)(R2 - R(bar)2)
if covariance is positive
the two returns move together
if covariance is negative
the two return move in opposite directions
correlation
Corr(R1, R2) = Cov(R1, R2) / SD(R1)SD(R2)
variance of return of portfolio
x_1^2Var(R1) + x_2^2Var(R2) + 2x_1x_2Cov(R1, R2)
inefficeint portfolio
its possible to find another portfolio that is better in terms of both expected reutrn and volatility
lower correlation means
lower volatility - shown graphically by a bend to the left of a greater degree
short sale
investors sell a stock that they do not own then buy that stock back in the future
short position
there is a negative investment in a security
long position
positive investment in a security
portfolio risk premium formula
E[Rp] - rf
Sharpe ratio equation
Portfolio Excess Return / Portfolio Volatility = E[Rp] - rf / SD(Rp)
the higher the sharpe
the better the risk-return combination
the portfolio with the hgihest sharpe ratio
is the portfolio where the line from the risk-free investment is tangent to the efficeint frontier of risky investments - efficeint portfolio is portfolio with highest sharpe ratio
Beta formula
SD(R1) x Corr(R1, Rp) / SD(Rp) = Cov(R1, Rp) / Var(Rp)
increasing the amount invested in 1 will increase the Sharpe ratio of portfolio P if
expected returns exceeds the required return - E[R1] > rf + beta x (E[Rp] - rf)
required retuns
expected return that is necessary to compensate for risk
CAPM assumptions
1) investors can buy and sell all securities at competitive market prices (without taxes or transaction costs) and can borrow and lend at the risk free rate, 2) investors are rational so only hold efficeint portfolios, 3) investors have homogenous expectations
when CAPM assumptions hold an optimal portfolio is…
combination of the risk free investment and the market portfolio
capital market line
when the tangent line goes through the market portfolio
expected return of a capital market line portfolio
E[Rxcml] = (1-x)rf + xE[Rmkt] = rf + x(E[Rmkt] - rf)
under CAPM assumptions the best portfolios
are a combination of risk free investment and market portfolios
beta < 1
less volatile than market
beta > 1
more volatile than the market
beta < 0
negatively correlated to market
CAPM is a
single factor model, just one varibale (beta) explains differences in returns across securities
security market line
all individual stocks with beta-expected return combinations must lie on this line
an asset that offered an expected return above the SML
is unpriced and investors would immediately buy it driving up its price and driving down its expected return until it reached the SML
stocks alpha
difference between stocks expected return and reuqired return
portfolio beta
weighted average beta of all the securities in teh portfolio = ∑x_i β_i
value weighted portfolio
portfolio in which each security is held in proportion to its market capitaliztion
market capitalization (MV)
= number of shares outstanding x price per share
value weighted portfolio weight formula
x = market value / total market value of all securities
price weighted portfolio
portfolio that holds an equal number of shares of each stock, independent of their size
risk-free rate
yield on US treasury securities
linear regression that identifies the best-fitting line through a set of points is
(Ri - rf) = alpha + beta(Rmkt - rf) + e
E[Ri] with alpha
= rf + beta(E[Rmkt] - rf) + alpha
if alpha is positive
the stock has performed better than predicted by CAPM - above the SML
if alpha is negative
the stock has performed worse than predicted by CAPM - below the SML
alpha formula
alpha = E[Rs] - rs
what does CAPM predict
investors would immediatley buy (sell) a positive (negative) alpha stock, driving up (down) their price and driving down (up) their expected returns until they reach teh SML
portfolios consisting of small stocks
had higher average excess return than those consisting of large stock
low B/M ratio
growth stocks - low or negative alpha
high B/M ratio
value stocks
market value
= dividend stream / cost of capital
alpha formula with percentages
alpha = cost of capital - required return
momentum strategy
buying stocks that have had past high returns and shorting stocks that have had past low returns
reasons for persistent positive alphas
CAPM correctly computes the risk premium - positive alpha = positive NPV, but investors ignore either because theyre unaware or costs > NPV; CAPM does not correctly compute the risk premium - positive alpha are returns for bearing risk that CAPM does nto capture
arbitrage pricing model
we can identify a collection of well-diversified portfolios from which the efficient portfolio can be constructed
factor portfolios
portfolios that can be combined to form an efficeint portfolio
arbitrage pricing model: risk premium formula
E[Rs] = rf + beta^F1(E[Rf1] - rf) + beta^F2(E[Rf2] - rf) + … + beta^FN(E[Rfn] - rf)
self-financing portfolio
portfolio where we borrow funds at rf to invest in factor portfolio
SMB portfolio
each year buys a portfolio of small stocks and finances this position by short selling a portfolio of big stocks has histroically produced positive risk-adjusted returns (+ alphas) - small-minus-big portfolio
HML portfolio
each year buys equally weighted portfolio of stocks with high book-to-market ratio and finances this position by short selling an equally weighted portfolio of stocks with low book-to-market ratio, produced positive risk-adjusted return - high-minus-low portfolio
PR1YR portfolio
each year, after ranking stocks by their return over the last year, buy high past returns stock (top 30%) and finances this by short selling low past return stocks (bottom 30%), produced positive risk-adjusted returns, prior one-year momentum portfolio
E[Rs] with different portfolio types
= rf + beta^mkt(E[Rmkt] - rf) + beta^SMB(E[Rsmb]) + beta^HML(E[Rhml]) + beta^PR1YR(E[Rpr1yr])
FFC model
SMB portfolio, HML portfolio, PR1YR portfolio
limitations of FFC
according to FFC, a firm with low B/M ratio is less risky and will offer lower returns than firm with high ratio - e.g. new firms, are they low-risk?
capital budgeting
process used to analyse alternative investments to decide which to accept
role of financial manager
investment decisions, financing decisions, working capital management: ensure availability of cash
current value of assets (V0)
= present value of expected future cash flow discounted at appropriate cost of capital k
current value of assets formula
V0 = E(CF1)/(1+k) + E(CF2)/(1+k)^2 + … + E(CFt)/(1+k)^t
cost of capital
return offered in financial markets on investments of equivalent risk - also called required (and expected) return
r_WACC
= (E/E+D)rE + (D/E+D)rD - (D/E+D)rDtC
why is the cost of debt reduced by corporate tax?
tax shield effect of debt: interest payments on debt are tax deductible, while dividend payments on equity arent. financing through debt saves the company paying taxes
how to find cost of equity
construct market portfolio, obtain risk free rate for market risk premium, estimate beta, calculate (yearly) cost of equity capital
how to find cost of debt
if firm has bonds: take YTM on long-term bond, if no bonds: add rating default-spread to risk free rate, if neither available: find interest rate from recent long-term bank loans of firm and/or calculate synthetic rating using credit rating agency’c capital ratio to proxy default spead
unlevered cost of capital
WACC without tax-shield: rU = (E/E+D)rE + (D/E+D)rF
required rate of return for an asset (firm) financed with equity and debt
r_WACC = (E/E+D)rE + (D/E+D)rD x (1- τ_C)
WACC estimation in words
determine permanent sources of capital, estimate cost of each capital source, weight each component to determine WACC
project evaluation in words
determine the free cash flows of the investment, compute WACC including tax benefit of leverage, compute value of investment by discounting free cash flows of investment using WACC
using company WACC for new project assumes that
risk of new project is equivalent to risk of existing projects, new projects won’t cause the company’s optimal or target capital structure to change
alternative method for calculating the division’s WACC
(d=D/V): rWACC = rU - dτCrD
derivatives def
securities that derive their value from the price of other assets
most prevalent used derivatives
options, futures, forwards
call option
gives its holder the right but not the obligation to buy an asset: at the exercise or strike price; on or before expiration date
exercise option to buy the underlying asset if
market value of asset > strike price
call option payoff
Max [ 0, S_T - K]
put option
gives the holder the right but not the obligation to sell an asset: at the exercise or strike price; on or before the expiration date
exercise option to sell the underlying asset it
market value of asset < strike price
put option payoff
Max [ 0, K - S_T]
option premium
purchase price of the option
exercise/strike price (K)
price at which you buy or sell the security
in-the-money option
exercise of option produces positive cash flow: call: exercise price < asset price (K<S_T); put: exercise price > asset price (K>S_T)
at-the-money option
exercise price and asset price are equal (K=S_T)
out-of-the-money option
exercise of the option would not be profitable - call: exercise price > asset price (K>S_T); put: exercise price < asset price (K<S_T)
expiration date
last date on which the option can be exercised
american option
can be exercised at any time before expiration
european option
can only be exercised on expiration date
call - long
the right but not obligation to buy 100 shares of the underlying asset at a certain strike price –> hope stock price will rise
call - short
the potential obligation to sell 100 shares of the asset upon demand
put - long
the right not obligation to sell 100 shares of the underlying asset at a certain strike price
put - short
the potential obligation to buy 100 shares of the asset upon demand
on expiry date, option price equals
intrinsic value
intrinsic value
option payoff if option expired immediately
if the long call purchaser is gaining
the short call writer is losing
option value =
stock price - exercise price
valuation at expiration =
exercise price - stock price
derivative markets
allow market participants to trade/reallocate different types of risk in the economy
hedging (insurance)
reducing riskiness of cash flows
speculation
betting
protective put
long position in put held on stock you already own
portfolio insurance
protective put written on portfolio rather than single stock
straddles
put and call have same strike price
strangles
call has higher strike price
law of one price
in efficient market, identical securities (same PV of cashflows) must sell for the same price
synthetic replication
invest in zero-coupon risk-free bond and European call option on same stock as in Protective put
2 ways to construct portfolio insurance
purchase the stock and a put, purchase a bond and call
law of one price equation
S (stock) + P (put) = PV(K) + C
expression for price of a European call option for a non-dividend-paying stock
C = P + S - PV(K)
price of call option for dividend-paying stock
C = P + S - PV(K) - PV(Div)
put-call-parity
relationship between the value of the stock, the bond, and call and put options
how factors affect European Call
+: stock price, risk-free rate, volatility. -: exercise price, dividends. ?: time to maturity
how factors affect European Put
+: exercise price, volatility, dividends. -: stock price, risk-free rate. ?: time to maturity
how factors affect American Call
+: stock price, time to maturity, risk-free rate, volatility. -: exercise price, dividends
how factors affect American Put
+: exercise price, time to maturity, volatility, dividends. -: stock price, risk-free rate
time value
difference between option’s price and intrinsic value
what will always have a positive time value
any call option on non-dividend paying stock
C =
S - K + dis(K) + P where dis(K) = amount of discount from face value of zero-coupon bond K
binomial option pricing model assumption
each period, stock’s return can only take on two values
replicating portfolio technique
option payoff in one period can be replicated by a portfolio consisting of a stock and a risk-free bonds
binomial pricing tree: payoffs of replicating portfolios formula
Su∆ + (1+rf)B = Cu and Sd∆ + (1+rf)B = Cd where u is the up state and d is the down state
binomial pricing tree: formula for ∆
∆ = (Cu - Cd) / (Su - Sd)
binomial pricing tree: formula for B
B = (Cd - Sd)∆ / (1+rf)
binomial pricing tree: value of the option formula
C = S∆ + B
black-scholes option pricing model
technique for pricing european-style options when stock can be traded continuously, can be derived from binomial option pricing model by allowing the length of each period to shrink to zero and letting the number of period grow infinitely large
black-scholes pricing model: example for finding N(d)
When d <= 0:
N(-0.1234) = N(-0.12) - 0.34[N(-0.12) – N(-0.13)] = 0.4505
When d >= 0:
N(0.6278) = N(0.62) + 0.78[N(0.63) – N(0.62)] = 0.7350
black-scholes pricing model: N(d1) meaning
number of shares in tracking portfolio = delta
black-scholes pricing model: -Ke^(-rT) N(d_2) meaning
risk-free borrowing = B
5 inputs needed for black-scholes formula
stock price, strike price, exercise price, risk-free rate, volatility of the stock
two strategies to find volatility
historical data, implied volatility
implied volatility
the volatility of an asset’s returns that is consistent with the quoted price of an option on the asset
capital structure
mix of securities which serves to divide cash flows between different classes of investors
Modigliani-Miller model assumptions
capital markets are perfect, companies and individuals borrow at same rate, no taxes, no transaction costs, no issuance costs, no costs associated with company liquidation, companies have fixed investment policy
M&M proposition 1
Capital structure does not impact firm value.
M&M proposition 1 formula stuff
in perfect capital market, total value of firm equals market value of total cash flows generated by its assets and it not affected by choice of capital structure -> E + D = U = A where: E is market value of equity of levered firm; D is market value of debt of levered firm; U is market value of equity of unlevered firm; A is market value of firm’s assets
digression
with perfect capital markets, financial transactions neither add or destroy value, but instead represent a repackaging of risk (and return) -> implies that any financial transaction that appears to be a good deal may be exploiting type of market imperfection
M&M proposition 2
Equity risk increases with leverage, but overall firm risk (WACC) stays constant.
M&M proposition 2 formula stuff
cost of capital of levered equity: rE = rU + (D/E)(rU - rD) where rU is expected asset cost of capital/compensation for business risk and the other component is compensation for financial risk
if firm is unlevered…
all free cash flows generated by its assets are paid out to its equity holders. therefore, rWACC = rU = rA
unlevered beta
market risk of firm’s underlying assets: βU = (E/E+D)βE + (D/E+D)βD
two costs associated with the introduction of debt
direct cost of debt (explicit) - interest. indirect cost of debt (implicit) - increase rate of return required by shareholders
interest tax shield =
corporate tax rate x interest payments
M&M proposition 1 with taxes formula stuff
value of levered firm = value of unlevered firm of same risk class plus PV of tax saving. V_L = V_U + τ_c(D) where τ_c is the PV of the tax shield associated with interest payments
M&M theory with taxes shows
firm value increases with leverage because of the tax shield of debt (WACC decreases)
WACC with taxes
rWACC = (E/E+D)rE + (D/E+D)rD(1-τ_c)
to receive full tax benefits of leverage…
firms need not use 100% debt financing. companies can use non-debt related tax shields - depreciation. Firm needs to have taxable earnings - no corporate tax benefit arises from interest payments about EBIT
financial distress
when firm has difficulty meeting its debt obligations
default
when firm fails to make required interest of principal payments on it debt
bankruptcy
if asset value < liabilities. debt holders take legal ownership of firm’s assets
leverage saves taxes but…
increases default risk
2 types of bankruptcy costs
direct costs - fees to accountants, lawyers etc. indirect costs - lost sales, damage to reputation and management time spent attempting to avert bankruptcy
trade-off theory of capital structure formula
V_L = V_U + τcD - PV(Financial Distress Costs)
announcement of new equity interpreted as
signal that equity is overpriced - share price would decrease on day of announcement
issuing debt involves
issuance costs and restricts firm flexibility through covenants
pecking order theory assumptions
sticky dividend policy, a preference for internal funds, an aversion to issuing equity
asset substitution problem
shareholders in company with outstanding debt own call option on assets of the company. managers have incentive to accept negative NPV projects with large risks if firm close to bankruptcy. call option values increase with increasing volatility. transfer of wealth from bondholders to shareholders.
underinvestment problem
equity holders dont invest in positive NPV projects because firm is in financial distress and the value of undertaking the investment will accrue to bondholders rather than themselves. existing shareholders won’t contribute equity as first gains from investing in positive NPV projects accrue to debtholders. new shareholders won’t buy equity at existing price but require a substantial discount. existing shareholders reject this as their interests are diluted.
debt overhang problem
too highly levered firm may not always choose positive NPV projects
debt overhang problem extreme case: cashing out
when firm faces financial distress, shareholders have incentive to withdraw money from firm if possible - eg. sell assets below market value and pay dividend. potential solution - debt restructuring
free cash flow problem
if FCF is not paid to out investors, managers more likely to abuse the funds for their own benefit - invest in negative NPV projects for growth, increase consumption of perquisites (corporate jet)
free cash flow problem solution
increase leverage or pay higher dividends, aligns goals of management and shareholders through compensation
value of the levered firm equation
V^L = V^U + PV(Interest Tax Shield) - PV(Financial Distress Costs) - PV(Agency Costs of Debt) + PV(Agency Benefits of Debt)
tangible assets facts
in case of default value of tangible assets is easier to realise than that of intangible assets, debtholder’s risk is lower if company’s value is largely attribute to its tangible assets, companies with more tangible assets can borrow more
general-use assets fact
general-use assets are easier to realise than that of firm-specific assets, debtholder’s risk is lower if company’s value is largely attribute to its general-use assets, companies with more general-use assets can borrow more
payout policy
the way a firm chooses between alternative ways to distribute free cash flow to equity holders
firms options of what to do with its free cash flow
retain: invest in new projects, increase cash reserves. pay out: repurchase shares, pay dividends
two main types of dividend:
cash dividend: paid either quarterly or yearly. stock dividend: less common and resemble stock split
declaration date
date on which the board of directors authorise the payment of the dividend
record date
when a firm pays a dividend, only shareholders on record on this date receive the dividend
ex-dividend date
a date, two days prior to a dividend’s record date on or after which anyone buying stock will not be eligible for the dividend
payable date (distribution date)
a date, generally within a month after the record date, on which a firm mails dividend checks to registered stockholders.
dividend timeline
declaration date -> ex-dividend date -> record date -> payable date
what is a share repurchase
an alternative way to pay cash to investors is through share repurchase - the firm uses cash to buy shares of its own outstanding stock
share repurchase: open market repurchase
when a firm repurchases shares by buying shares in the open market. 95% of all repurchase transactions
share repurchase: tender offer
a public announcement of an offer to all existing security holders to buy back a specified amount of outstanding securities at a pre-specified price
share repurchase: dutch action
firm lists different price at which it is prepared to buy shares, and shareholders in turn indicate how many shares they are willing to sell at each price
share repurchase: targeted repurchase
when a firm purchases shares directly from a specific shareholder at a discounted or premium price
share repurchase: greenmail
when a firm avoid a threat of takeover and removal of its management by a major shareholder by buying out the shareholder often at a large premium over the current market price
signalling power of dividends
firms may use dividend increases to send positive signals to the market and dividend cuts can be seen as negative signals. share repurchases may be used to send positive signals since firms are likely to buy back own stock when it is undervalued.
the dividend controversy
does the decision to pay a dividend change the value of the stock or is it just a signal to the markets?
the dividend controversy: the neutral perspective overview
dividend policy doesn’t affect firm value.
the dividend controversy: the neutral perspective detail
assumptions: perfect capital markets, no agency costs, individual investors borrow at same rate as firms, cash flows are perpetuities, two types of claim: debt (risk-free) and equity (risky), all firms same risk class, no bankruptcy costs. V0 = ∑_(t=1)^∞((E_t - I_t)/(1+K_e )^t ) - value of firm = PV of future cash inflows minus the PV of future cash outflows discounted at risk-adjusted discount. any change in dividend payment will lead to an equal and opposite change in the amount of funds raised from new shares. investors dont need dividends to get cash in hands, they can sell stocks, so investors wont increase their demand for stocks with higher dividends so market value of firm wont change because of increase in dividend paid
perfect market view equations
P0 = (D1 + P1/1 + Ke), Ke = (D1/P0) + (P1 - P0/P0)
the dividend controversy: the conservative perspective overview
an increase in the dividend payout increases firm value
the dividend controversy: the conservative perspective detail
stock market in favour of liberal dividends. standard practice to evaluate common stock by applying one multiplier to that proportion of the earning paid out in dividends and a much smaller multiplier to the undistributed balance. these investors increase the price of the stock through their demand for a dividend paying stock
the dividend controversy: the radical perspective overview
an increase in the dividend payout reduces firm value
the dividend controversy: the radical perspective detail
income tax > capital gains tax, because dividends are taxed at income companies should pay the lowest dividend. effective dividend tax rate is: τd = (τd - τg / 1 - τg) where τg is capital gains tax. this measures additional tax paid by investor per dollar of after-tax capital gains income received as a dividend.
the radical perspective investors preferences
INDIVIDUAL INVESTOR: tax disadvantage for dividends, generally prefer share repurchase (52%). INSTITUTIONS, PENSION FUNDS: no tax preference, prefer dividend policy that matches income needs (47%). CORPORATIONS: tax advantage for dividends (1%)
if the radical perspective is correct, then why do firms bother paying dividends?
according to radicals, if companies regularly repurchase shares, then the authorities will tax these payments by income tax. so whenever companies repurchase shares, they try to find a good excuse to do so
retain cash or pay it out as dividends?
in perfect capital markets (no taxes) it doesnt matter as long as excess cash is invested in zero NPV projects. corporate taxes make it costly to retain cash. firms can build cash holdings to pursue positive NPV projects without issuance costs. cash holdings reduce the likelihood of financial distress but agency costs
put-call parity equation
P + S = C + Xe^(-rt) where P = value of put option, S = share price, C = value of call option, X = exercise price, t = time to maturity, r = risk free rate
categories of real options
the timing option, the abandonment option, the expansion option
the timing option
if no uncertainty, calculate NPVs for several dates in future and select date with highest NPV. with uncertainty, need to see whether its better to wait. Delay the project? - better conditions in the future (Lower interest rates), calculate value of option to delay and see whether value is > current NPV. Trade off: if you exercise now you lose the value of option to wait. if you keep option (wait) you lose possible positive cash flows of project today
the abandonment option
if actual CFs are low, you have option to abandon project. option to abandon is equivalent to put option. Adjusted Present Value (APV) = NPV (assuming no abandon) + value of abandonment put option
the expansion option
many investments have follow-on opportunities to expand at a later date. these add value to project even if the future expansion doesnt seem attractive today. the option to expand is equivalent to an out-of-the money call option. APV = NPV(assuming no expansion) + the value of the expansion call option
profitability index rule
PI = NPV/Initial Investment. invest when index is at least 1
the hurdle rate rule
raises the discount rate by using a higher discount rate than the cost of capital to compute NPV but then applied normal NPV rule. if project can jump the hurdle with positive NPV then it should be undertaken. Hurdle Rate = Cost of Capital x (Callable Annuity Rate / Risk-Free Rate) where callable annuity rate is the rate on a risk-free annuity that can be repaid at any time.
sources of funding
angel investors, private equity firms, institutional investors, corporate investors
angel investors
individual investors offering capital for a significant portion of equity
private equity firms
limited partnerships, raising money to invest in private firms. often appoint their managers to boards of firms they invest in
institutional investors
invest in private firms either directly or indirectly through VCs
corporate investors
corporations invest in other firms for the returns and/or to achieve strategic objectives
how do you exit from an investment in a private firm?
corporate acquisition - large firms could acquire the outstanding shares of the private firm. public offering - marking the firm public through an IPO
advantages of going public
greater liquidity, better access to capital
disadvantages of going public
less monitory therefore less control, costly and time-consuming information disclosure
types of IPOs: types of shares
primary offering - new shares, company gets the money. secondary offerings - insiders selling their shares
types of IPOs: mechanism used for listing
best efforts - underwriters do their upmost to list the company but they’re not contractually obliged to list the company. firm commitment - underwriter lists the company whatever the conditions. auction IPO
mechanics of an IPO
find an underwriter, provide info to authorities (prospectus), value the firm (set up initial price range), build a book (road shows), price the deal and manage risk
IPO puzzles
under-pricing - marked price always turns out to be higher than offer price, if you are allocated shares you make a gain on first day of trading. cyclicality - IPOs come in waves -> cost of underwriters -> firms do well in short run as offer price is below market price -> in long run IPOs tend to underperform. cost of issuing IPO. long-run underperfrmance
mechanics of an SEO - Seasoned Equity Offerings
companies listed on market and been trading for years sometimes go to market to raise additional capital. many IPO steps still apply but no need for price setting. usually offered at a price below market price
SEO kinds
cash offer - new shares to investors at large. rights offer - new shares to existing investors
debt financing
interest on debt is tax deductible. debtholders face lower risk than equity holder thus cost of debt is lower than cost of capital. higher the debt on balance sheet, higher the probability of future default
types of public debt
bearer bonds - cannot be traced. registered bonds - every owner is registered and all transactions are electronic
types of corporate debt
notes - unsecured short term debt. debentures - unsecured long term debt. mortgage bonds - secured by real property, don’t own property until you pay mortgage off. asset-backed bonds - secured by any kind of asset. senior debt - priority in claiming assets when in default junior debt - in default, holders receive what’s left after senior debt
types of bond markets
domestic bonds - issued and traded locally, open to foreign investors. foreign bonds - issued by foreign firm in local market and purchased by local investors. eurobonds - international bonds not in local currency. global bonds - combination of domestic, foreign and eurobonds.
default risk facts
bond prices go down and promised interest rates go up when probability of default increases. in default, actual rates < promised rates
junk bonds
bonds with high probability of default and therefore high yields.
types of private debt
term loans - a loan that lasts a specific term and is funded by either one bank or a group of banks. private placements - a bond issue sold directly to a small group of investors, less costly to issue since its not registered
types of debt other than corporate debt
sovereign debt - government debt, depending on maturity you can have bills, notes and bonds. asset-backed securities - the securities’ CFs are backed by CFs from other assets. municipal bonds - issued by local govs, several kinds including serial, general obligation, double-barrelled, revenue bonds.
restrictive covenants
rules that prevent firm from increasing probability of going into default -> rules in order not to increase value of option to default. apply to dividends and new issues to debt: senior debt, secured debt
repayment provisions
sinking funds - when part of the issue is repaid before maturity (firms makes regular payments to fund). callable bonds - call option that allows firm to pay back debt early. puttable bonds - put option that allows bondholder to demand early repayments
convertible bonds
the right to convert (exchange) a bond for equity at a predetermined price. resembles a bond-warrant portfolio. Conversion Ratio - number of shares into which each bond can be converted. Conversion Price - bond’s face value over the conversion ratio
exchange rate
amount of one currency needed to purchase one unit of another currency
spot rate of exchange
exchange rate for an immediate transaction
forward exchange rate
exchange rate for a forward transaction
direct quotation
the exchange rate is given in number of units of the home currency per unit of the foreign currency
indirect quotation
exchange rate is given in number of units of foreign currency per unit of home currency
factors that affect exchange rates equations
e = f(∆INF, ∆INT, ∆INC, ∆GC, ∆EXP) where e is % change in spot rate
∆INF
change in relative inflation rate
∆INT
change in relative interest rate
∆INC
change in relative income levels
∆GC
change in government controls
∆EXP
change in expectation of future exchange rates
factors affecting exchange rates diagram
difference in interest rates (1+ £ interest rate / 1 + $ interest rate) === expected difference in inflation rates (1 + expected £ inflation rate / 1 + expected $ inflation rate) === expected change in spot rate (expected £ spot rate / currency £ spot rate) === difference between forward and spot rates (forward £ exchange rate / current £ spot rate)
interest rate parity
as a result of market forces, forward rate differs from spot rate by an amount that offsets the interest rate differential between two currencies. Then, covered interest arbitrage is no longer feasible and the equilibrium state achieved is referred to as IRP
IRP relationship equation
[F - S] / S = [S(1+p) - S] / S = p = (1+iH)/(1+iF) - 1 = (iH - iF)/(1 + iF). The approximated form p = iH - iF provides reasonable estimate when interest rate differential is small
purchasing power parity
dollar price of goods in US = peso price of goods in ruritania / number of pesos per dollar. when a country’s inflation rate increases relative to that of another country, decreased exports and increased imports depress the high-inflation country’s currency
absolute form of PPP
extension of the law of one price. suggests that the prices of the same products in different countries should be equal when measured in a common currency
relative form of PPP
accounts for market imperfections like transportation costs, tariffs and quotas. states that the rate of price changes should be similar
rationale of PPP theory
suppose UK inflation > US inflation. Higher UK imports from US and lower UK exports to US. Upwards pressure placed on $. This shift in consumption and the $’s appreciation continue against £ until: price of US goods >= price of UK goods in both countries
PPP does not hold consistently due to
- Confounding effects - exchange rates are also affected by differences in expected inflation, interest rates, income levels, government controls. 2. Lack of substitutes for some traded goods
relative nominal interest rates facts
relatively high interest rate may indicated expectations of relatively high inflation which may discourage foriegn investment. so, its important to consider the real interest rate which adjust nominal for expected inflation
effects on exchange rates: relative interest rates equations - Fisher Effect
(1+R) = [(1+r)(1+E(i))] -> R = [(1+r)(1+E(i))] - 1 -> r = [(1+R)/(1+E(i))] - 1 where r = cost of capital in real terms, E(i) = expected annual inflation, R = cost of capital in nominal terms
expectations theory
the forward premium/discounts are supposed to be unbiased predictors of the future spot rates (changes in spot rates)
international fisher effect
since all investors require the same real return, differentials in nominal interest rates may be due to differentials in expected inflation. IFE suggests that currencies with higher interest rates will depreciate because the higher nominal interest rates reflect higher expected inflation. so, investors hoping to capitalise on a higher foreign exchange rate should earn a return no higher than what they would have earned domestically
derivation of IFE
E(r_f), the expected effective return on a foreign money market investment should be equal to r_h, the effective return on a domestic investment. r_f = (1+i_f)(1+e_f) - 1. when the interest rate differential is small the IFE is e_f = i_h - i_f
when does IFE not hold
since it is based on PPP, it will not hold when PPP doesn’t. if there are factors other than expected inflation that affect exchange rates, exchange rates may not adjust in accordance with the expected inflation differential
fluctuations in exchange rates: importer-exporter dilemma
Consider a US firm that imports parts from Italy. if the supplier sets the price in euros, the US firm faces the risk that the dollar may fall, making euros and parts more expensive. if the supplier sets the price in dollar, the supplier faces the risk that the dollar may fall and it will receive fewer euros
hedging with forward contracts
by entering into a currency forward contract, a firm can lock in an exchange rate in advance and reduce or eliminate its exposure to fluctuations in currency value. contract specifies: exchange rate, amount of currency to exchange, a delivery date
potential problem with forward exchange rate contracts
the forward contract locks in the exchange rate and eliminates the risk whether the movement of the exchange rate is favourable or unfavourable.
cash-and-carry strategy
strategy used to lock in the future cost of an asset by buying the asset for cash today and carrying it until a future date - eliminates exchange rate risk. Trades: borrow euros today using a one-year loan with interest rate r€ -> exchange the euros for dollars today at the spot exchange rate S -> invest the dollars today for one year at interest rate r$ -> in a years time the investor will owe euros and receive dollars
covered interest parity
states that the difference between the forward and spot exchange rates is related to the interest rate differential between currencies. F = S x (1+r$ / 1+r€) -> ($ in a year / € in a year) = ($ today / € today) x [($ in a year/$ today) / (€ in a year/€ today)]. For no arbitrage forward exchange rate put both parts of last fraction to the power of T
advantages of forward contracts over cash-and-carry strategy
simpler requiring one transaction rather than 3. many firms not able to borrow easily in different currencies and may pay higher interest if credit quality is poor
hedging with options
say a one year forward exchange rate is $1.20 per euro. firm will need euros in one year can buy a call option on the euro giving it the right to buy euros at max price. if the spot exchange rate is < $1.20 per euro the firm will exercise the option and convert at spot rate. if the spot rate is > $1.20 per euro firm will exercise the option and convert $ to euro at $1.20 per euro. if the firm doesnt hedge, its cost for euros is the spot rate. if they hedge a forward contract it locks in the cost of euros and cost is fixed. if it hedges with option, it caps potential cost but will benefit if euro depreciates
when would a firm use options instead of a forward contract
the firm can benefit if the exchange rate moves in their favour and not be stuck paying above market rate. the transaction they are hedging may not take place
horizontal merger
target and acquirer are in same industry - volkswagen purchase of porsche
vertical merger
target’s industry buy from or sells two acquirer’s industry - google acquired android
conglomerate merger
target and acquirer are in unrelated industries
acquisition premium
paid by an acquirer in a taken, the % difference between the acquisition price and the pre-merger price of target firms
reasons to acquire - 13
LARGE SYNERGIES: cost reduction and revenue-enhancement - ECONOMIES OF SCALE: savings made from producing goods in high volume - ECONOMIES OF SCOPE: savings from combining the marketing and distribution - VERTICAL INTEGRATION: coordination - EXPERTISE: more efficient to purchase the talent as a functioning unit - TAX ADVANTAGE: losses in one division can offset profits in another - RISK REDUCTION: larger firms bear less unsystematic risk - DEBT CAPACITY AND BORROWING COSTS: large firms have lower probability of bankruptcy - ASSET ALLOCATION - LIQUIDITY - EARNINGS PER SHARE OF MERGED EXCEED THAT OF PRE-MERGER: even when merger itself creates no economic value - CONFLICTS OF INTEREST: managers prefer to run large company due to additional pay and prestige - OVERCONFIDENCE
vertical integration
merger of two companies in same industry that maker products required at different stages of production
takeover synergies
additional value created due to a merger
mergers: the offer
once valuation is complete, make a tender offer. bidder can use two methods to pay for target: cash or stock. in cash, bidder pays for target in cash. with stock-swap transaction, bidder pays for target by issuing new stock and giving it to target shareholders - bidder offers to swap target stock for acquirer stock
mergers: exchange ratio
number of bidder shares received in exchange for each target share
mergers: board and shareholder approval
both target and acquiring board of directors must approve the deal and put the question to a vote of the shareholders of the target
friendly takeover
when a target’s board of directors supports the merger, negotiates with acquirers and agrees on price that’s put to shareholder vote
hostile takeover
situation in which an individual or organisation purchases a large fraction of target company’s stock and in doing so, gets enough votes to replace the target’s board of directors and CEO
corporate raider
the acquirer in a hostile takeover
takeover defences
PROXY FIGHT: acquirer attempts to convince target shareholder to unseat board by using proxy votes - POSION PILLS: a right offering that gives target shareholders the right to buy shares in either target or acquirer at deeply discounted price - STAGGERED BOARD (CLASSIFIED BOARD): board of directors have three year terms that are staggered so only 1/3 of directors are up for election each year - WHITE KNIGHT: target company looks for another company to acquire it - GOLDEN PARACHUTE: lucrative severance package that is guaranteed to a firm’s senior management in the event that the firm is taken over and managers let go - RECAPITALISATION: a company changes its capital structure to make itself less attractive as a target
the leveraged buyout
corporate raider announces tender offer for half outstanding shares of a firm. instead of using cash to pay, the raider borrows money and puts the shares as collateral. if the offer succeeds, raider has control of company. law allows the raider to attach the loans directly to the firm. at the end, raider owns half the shares but the firm is responsible for repaying the loan
why do acquirers choose to pay so large a premium?
competition. once an acquirer starts bidding on a firm it becomes clear that significant gains exist and other potential acquirers may submit their own bids. result is like an auction and target is sold to highest bidder
interest rate risk
firms that borrow must pay interest on the debt. increase in interest rates raises the cost of borrowing and reduces profitability. many firms have long-term future liabilities - a fall in interest rate increases the PV of these liabilities and lowers PV of the firm.
interest rate swap
contract in which 2 parties agree to exchange the coupons (interest payments) from two different types of loans. one party agrees to pay coupon based on a fixed interest rate in exchange for receiving coupons based on prevailing market interest rate during each coupon period. parties exchange a fixed-rate coupon for a floating-rate coupon. can reduce cost of borrowing and eliminate interest rate risk
floating rate
interest rate that adjusts to current market conditions
interest rate swap example
5 year, $100 million interest rate swap with 7.8% fixed rate. standard swaps have semi annual coupons so fixed coupon amounts would be 1/2 x 7.8% x $100 million = $3.9 million every six months
interest rate swap facts
floating rate coupons based on the six month LIBOUR - calculated based on six month interest rate that prevailed in market six months prior to coupon payment date. each payment of the swap is the difference between the fixed and floating rate coupons.
combining swaps with standard loans
interest rate a firm pays on its loans can fluctuate for 2 reasons: the risk-free interest rate in market may change, firm’s credit quality can vary. by combining swaps with loans, firms can choose which of these sources of interest rate risk they will tolerate and which they will eliminate
swap and standard loan: net borrowing cost for firm
Net Borrowing Cost = Short Term Loan Rate + Fixed Rate Due on Swap - Floating Rate Received from Swap
trade offs of long term vs short term borrowing
borrow long term at fixed rate: pro = lock in current low interest rate, con = lock in currency high spread given low initial credit rating. borrow short term: pro = get benefit of spread falling as credit improves, con: risk of an increase in interest rate
incremental IRR rule technique
find the incremental cash flows - minus the two inflows and outflows from one another. find the IRR from the incremental cash flows. if the IRR > cost of capital, accept project with the higher initial investment
