Financial & Capital Markets Flashcards
Time Value of Money
the difference in money today and at a future time
Net Present Value
PV(Benefits)-PV(Costs)
Risk Free Interest rate (rf)
The interest rate at which money can be borrowed or lent without risk over that period
Interest rate factor
(1+rf) - the exchange rate across time
Discount factor
1/1+r
Positive NPV
means it is probably best to take up the project
NPV Decision rule
When making an investment decision, take the alternative with the highest NPV.Choosing this alternative is equivalent to receiving its NPV today.
If it down to a choice between projects we should always aim to chose the project with the highest NPV
Arbitrage
The practice of buying and selling equivalent a goods in different markets of take advantage of a price difference
Arbitrage opportunity
making a profit without taking any risk or making any investment
normal market
A competitive market where no arbitrage opportunities exist.
Law of One Price
If equivalent investment opportunities trade in different competitive markets, then they must trade for the same price in both markets.
financial security (security)
An investment opportunity that trades in a financial market
A bond
A security sold by governments and corporations to raise money from investors today with the promise of payment in the future.
No arbitrage price of a security
=PV(All cash flows paid by the security)
Return
Percentage gain you earn from investing in a bond.
Gain at the end of the year/Initial Cost
Portfolio
Combination of securities
Risk Aversion
preference to safe investments rather than those that carry risk
risk premium
is the difference between the expected return on an investment - the risk free interest rate of the investment
Compounding
The process of moving a value of money from one point in time to another.
Compound interest
“Earning interest on interest”.
Discounting
Finding the equivalent value today of a future cash flow
Perpetuity
Stream of Cash Flows that occur at regular intervals and last forever.
in arrreas
When the first payment of a perpetuity occurs at the end of the first period.
Present Value of a Perpetuity
C/r
Annuity
Stream of N cash flows paid at regular intervals
Present Value of an annuity
PV(annuity of C for N periods with interest rate r=
C/r(1-1/(1+r)^N)
Future Value of an Annuity
PV x (1+r)^N
C x 1/r((1+r)^N - 1)
Growing Perpetuity
Stream of cash flows that occur at regular intervals and grow at a constant rate forever.
Present Value of a growing perpetuity
= C/r-g where r is the interest rate and g is the amount we withdraw each year.
Internal Rate of Return
The interest rate that sets the NPV of cash flows to zero
Growing annuity
a cash flow that grows at a constant rate g. The cash flow stops after a finite number of years
Present value of a growing annuity
PV = c/r-g * (1 - (1+g)^N/(1+r)^N)
Effective Annual Rate (EAR)
The total amount of interest that will be earned at the end of the year. It considers the effect of compounding
Annual Percentage Rate (APR)
Simple interest without the effect of compounding. It is typically less than the EAR. It cannot be used as a discount rate and thus must be converted to an EAR
APR —> EAR formula
1+EAR = (1+APR/k)^k where k is the compounding periods
The fisher effect
Is the relation between the nominal interest rate, real interest rate and inflation. Given by 1+real = 1+nominal/1+inflation
An increase in interest rates will typically reduce the NPV of an investment
Term structure
The relationship between the investment term and the interest rate
Can be used to compute the present and future values of risk free investments over different investment horizons
A steep yield curve indicates…
that interest rates are expected to rise. It is common on short interest rates and inflation is low or an economy is emerging from a recession
An inverted yield curve indicates….
the interest rates are expected to decline in the future
A flat yield curve indicates…
occurs when interest rates are transitioning
A humped yield curve…
occurs when rates are transitioning or market participants are attracted to a particular maturity segment of the market
What risk do treasury securities hold?
None. They are risk free
After tax interest interest rate
the amount of interest an investor can keep once the earnings have been taxed.
r~ = r * (1- t) where t is the tax rate
Opportunity cost of capital
The best available expected return offered in the market on an investment of comparable risk and term to the cash flow being discounted
What choice should be made when rules of investment conflict?
Follow the NPV
Internal rate of return investment rule?
Take any investment where the IRR exceeds the cost of capital and turn down an investment where it does not exceed the cost of capital
When will the IRR work?
for standalone projects when all negative cash flows precede the positive cash flows
What situations would the IRR conflict with the NPV
Delayed investments.
Non-existent IRR
Multiple IRR
What could the reason be for IRR not working for delayed investment?
The IRR may appear to be greater than the cost of capital however when the NPV is calculated the NPV could be negative indicating the investment should not be undertaken
What could be the issue with a non-existent IRR?
Here it would see there is no clear cut way of deciding on the project using the IRR rule but in this situation it could be that the NPV will always be positive (or negative)
What could be the issue with multiple IRRS?
Wouldn’t know when IRR to make and there is also bound and so it can make the decision difficult. To rectify this rely on the NPV
What is the advantage of the IRR?
It can measure the average return of the investment and the sensitivity of the NPV to any estimation error in the cost of capital
The Payback Rule
If the payback period is less than a prespecified time you accept the project .
Payback period
is the amount of time it take to recover or payback the initial investment
Disadvantages to the payback rule method
Ignores projects cost of capital and time value of money
Ignores cash flows after the payback period
Relies on ad hoc decision criterion about the cut off period
Project chosen based on this may not have a positive NPV
Advantages to the payback rule method
Easy to understand and apply
focuses on the liquidity of an investment project
commonly used when the capital investment is small and the horizon is short
The discounted payback period
Involves considering the time value of money by taking the discount rate into consideration. However, by the time you have calculated this you might as well work out the NPV
When using the IRR rule what must we take into consideration in order to avoid mistakes?
Projects differ in:
Scale of investment
timing of cash flows
riskiness
What effect does the scale have when comparing projects?
If a size doubles the NPV will double. However, the IRR does not
What effect does the timings of cash flow have when comparing projects?
The IRR can change as a result of differences in timings and so can change the rankings of the IRR. The NPV isnt affected
What effect does the risk have when comparing projects?
An IRR that is safe for a safe project need not be attractive for a riskier project
Incremental IRR rule
Apply the IRR rule to the difference between the cash flows of the mutually exclusive alternatives. It tells us the discount rate at which it becomes profitable to switch from one project to another
Shortcomings of the IRR
incremental irr may not exist
multiple irrs
The fact the the IRR exceeds the cost of capital does not mean the NPV is positive
when there are different costs of capital for projects it is not obvious which one to use.
Profitability index
The value created in terms of NPV for the amount of resource consumed. Starting with the highest ranking and move down the ranking until all the resource is consumed
NPV/resource consumed
Shortcomings of the profitability index
the set of projects taken following the profitability index ranking exhausts all available resources
with multiple resource constraints the index could break down completely
Bond certificate
states the terms of the bond
maturity date
the final repayment date
term
the time remaining until repayment date
Coupon
promised interest payments
Fave value
notional amount used to compute the interest payments
coupon rate
amount of each coupon payment (express as apr)
Coupon payment
CPN = coupon rate*facevalue/ no. of coupon payments per year
Yield to maturity
discount rate that sets the present value of the promised bond equal to the market price of the bond
Zero-coupon bond
a bond which does not make coupon payments
Always sells at a discount
Yield to maturity of a Zero-Coupon bond
P= facevalue/(1+YTM)^n
Law of one price guarantees what?
That the risk free interest rate equals the yield to maturity on a zero-coupon bond
Risk free interest rate with maturity n equals…
rn=YTMn
Zero coupon yield curve
a plot of the risk free zero coupon bonds as a function of the bonds maturity date
Coupon bonds
regular coupon interest payments and pays face value at maturity
Yield to maturity of a zero-coupon bond
P = CPN *1/y(1-1/1+y)^N) + facevalue/(1+y)^N
A bond is selling at a discount when…
its price is less than its face value and coupon rate is greater than YTM
A bond is selling at par when….
its price is equal to the face value and the coupon rate is equal to the YTM
A bond is selling at premium when…
its price is greater than the face value and the coupon rate is less than the yield to maturity
If a bond’s yield to maturity has not changed…
the IRR of an investment in the bond equals its yield to maturity even if you sell the bond early
Duration
measures the sensitivity of a bond’s price to change in the interest rate
As interest rates rise what happens to bond prices?
Bond prices fall
As interest rate fall what happens to bond prices?
Bond prices increase
Bond with high duration….
are more sensitive to changes in the interest rate
Price of a coupon bond
P=CPN/(1+ytm) +CPN/(1+ytm)^2……CPN+facevalue/(1+ytm)^N
Corporate bonds
bonds issued by corporations
credit risk
risk of default
yields of corporate bonds with high credit risk…
will be higher than they would be for identical default free bonds
Dividend discount model
potential cash flows…. Dividend + Sale of stock
Equity cost of capital…
the expected return of other investments available in the market rE
P0= Div1+P1/1+rE
Price of a stock today when using the equity cost of capital
If the actual stock price is found to be less than what is found to be true
there is a positive NPV
Solving for total return rE
Div1+P1/P0 which can be split into divided yield and capital gain rate
Dividend yield
the percentage return the investor expects to earn from the dividend paid
Capital gain rate
expresses the capital gain as a percentage return
Price of a Share for two years
P0 = Div1/1+rE + Div2+P2/(1+rE)^2
Total return of a stock
sum of dividend yield and capital gain rate
Dividend discount model
Initial price of a stock where the horizon N is arbitrary
P0 = Div1/1+rE + Div2/(1+rE)^2…+DivN/(1+rE)^N + PN/(1+rE)^N
What is the price of a stock if it is held forever?
Is equal to the present value of the expected future dividends it will pay
Constant dividend growth model
models dividends which grow at a constant rate
P0=Div1/rE-g where g is the growth rate
Total return of a growing dividend
rE=Div/p0 +g where g is capital gain
Implied return
Pn=P0(1+IR)^n
What is the dilemma faced when a company wants to increase its share price?
There has to be a trade off between paying out dividends and instigating growth. In order to facilitate growth some of the company earnings will have to go on investment rather than be paid out as dividends
Dividend payout rate
fraction of the company’s earnings which is used for paying dividends
Divt= earnings/shares outstanding * dividend payout rate
What two things can a company do with its earnings?
Payout to investors
retain it and reinvest
Change in earnings =
new investment * return on new investment
new investment =
earnings * retention rate
retention rate
the fraction of earnings that the company retains
earnings from growth
retention rate * return on new investment
If a firm keeps its retention rate constant…
then the growth rate in dividends will equal the growth rate of earnings
What does cutting the firms dividend depend on?
the rate of return on the new investment
Limitations to the dividend discount model
uncertainty with forecasting a firm’s dividend growth rate and future dividends
small changes in the assumed growth rate can affect the stock price greatly
Share repurchase
firm uses excess cash to buy back shares but….
the more cash firms use to rebuy stocks the less it has to pay dividends
EPS increases
Dividend discount model
PV0=PV(Future dividends per share)
Total payout model
Value of all the firms equity per share
PV0= PV(future total dividend + repurchases)/shares outstanding
Discount free cash flow model
determines the total value of a firm to all investors
Enterprise value V0=PV(future free cash flows of firm)
Free cash flow
cash flow available to pay both debt holders and equity holders
Enterprise value
market value of equity+debt - cash
value of owning the unlevered business
Share price
P0=V0+cash0-debt0/Shares outstanding
Present value of dividends payments can determine…
Stock price
Present value of total payments can determine…
equity value
Present value of free cash flow can determine
enterprise value
Valuation based on comparable firms
can estimate the value of a firm based on the value of comparable firms or investments with similar cash flows
Valuation multiple
ratio of the value to some measure of the firms scale
analogous to floor space pricing if confused
Price earnings ratio
Share price/Earnings per share
Trail earnings
earnings over the last 12 months
Forward earnings
expected earnings over the next 12 months
firms with high growth rates should….
have high P/E raitos
Other multiples
Multiples of sale
Price to book value of equity per share
enterprise value per subscriber
Limitations of multiples
When comparing there is no guidance about how to adjust for differences in future growth rates or risk. Only provides information of firm relative to others. Doe not tell us if the whole sector is overvalued
Discount cash flow methods can be…
more accurate than valuation multiples as they can incorporate specific information about the firms cost of capital or future cash flows
Efficient market hypothesis
Securities will be fairly priced, based on their future cash flows, given all information that is available to investors
Securities with same equivalent risk should have same expected return
Public, easily interpretable information means….
All investors can determine the effect of the information on a firms value
Private or difficult to interpret information means…
only a small number of investors may be able to profit by trading on their information (that they will have gathered from their own research). If trade opportunities are large more will devote time to finding alternative resources
The efficient market hypothesis does not hold but as traders trade then the prices will begin to change
Consequences for investors
if stocks are fairly priced, investors who buy stocks can expect future cash flows that fairly compensate them for their investment
average investor can invest with confidence
Implications for the corporate managers
Focus on NPV and future cash flows
avoid accounting illusions and focus on free cash flows
use financial transactions to support investment
Probability distribution
when an investment is risky, there are different returns in may earn and a probability associated with them
Expected return
weighted average of the possible returns
E[R] = Σp * R
Variance
expected square deviation from the mean
Var(R) = Σp * (R-E[R])^2
Standard deviaition
also known as the volatility
square root of variance
Realised returns
return that actually occurs over a particular time period
Rt+1 = (Divt+1 + Pt+1 - Pt)/ Pt
If a stock pays dividends at the end of each quarter what is the realised annual return?
1+Rannual = (1+RQ1)(1+RQ2)(1+RQ3)(1+RQ4)
Average annual Return
If Rt is the realised return of a security in year t, then for the years 1 through T the average return is….
Rbar = 1/T ΣRt
Variance estimate using realised returns
1/T-1 Σ(Rt-Rbar)^2
standard error
statistical measure of degree of estimator error
SD/root(no. of obs)
95% confidence interval
historical average return + or - 2 SE
Excess returns
Difference between the average return for an investment and the average return for t-bills
Independent risks
related to firm specific news. Diversified, unsystematic
Common risk
market wide news related risk/ Also known as undiversified or systematic
When stocks are combined in a portfolio what happens to the risk of the stock
the risks will average out and be diversified. Systematic risk will affect all firms and not be diversified. Therefore, volatility will decline until all that remains is systematic risk
The risk premium for diversifiable risk is….
Zero. investors are not compensated for holding stocks with firm-specific risk. The can eliminate this for free by diversifying their portfolio
Risk premium for a security is determined by…
the systematic risk
Why is volatility not a good way of determining a risk premium?
It includes diversifiable risk in the value. We need to determine how much of the volatility is down to systematic risk
An efficient portfolio
A portfolio that contains only systematic risk. The only way to reduce the risk of this portfolio is by decreasing the expected returns
Market portfolio
An efficient portfolio that contains all shares and securities in the market
What is β?
Measure the sensitivity to systematic risk. It is the expected percentage change in the excess return of a security for a 1% change in the excess return in the market portfolio
Market risk premium
difference between the expected return of the market portfolio and the risk free interest rate
Market risk premium = E[Rmkt)-rf
Cost of capital
also known as the Capital Asset Pricing Model
E[RI] = rf + β(E[Rmkt] - rf)
Portfolio weights
the fraction of total investment held in each individual investment
xi = value of investment/total value of portfolio
Return of a portfolio
weighted average of returns on the investment in the portfolio where weights correspond to portfolio weights
ΣxiRi
Expected return of portfolio
Σxi * E[Ri]
Volatility of a two stock portfolio
by combining the stocks we diversify the risk
the amount at which the risk is eliminated is depends on the extent at which they share common risks and prices move together
Covariance
the expected product of to returns from their means
positive = they move together negative = they move in opposite direction
Correlation
measures the common risk shared by stocks that doesnt depend on it volatility
= cov(Ri,Rj)/SD(Ri)SD(Rj)
Variance of a two stock portfolio
x1^2Var(R1)+x2^2Var(R2)+2x1x2cov(R1,R2)
volatility of a large portfolio
the variance of a large portfolio is equal to the weighted average covariance of each stock with the portfolio
A positive investment in a security is called
long position
Investing a negative amount in a stock…
Short position. sell a stock you dont own and buy it back later
Efficient frontier
the combination of efficient portfolio combinations.
how can risk be reduced in a portfolio?
By investing a proportion in risk free investments such as T-Bills. This will, however, also reduced the expected return of the portfolio
Levered portfolio
the action of an aggressive investor who borrows money to be able to invest more
Expected return on a portfolio which is a mixture of risky and risk free investment
E[Rxp]= (1-x)rf +xE[Rp] = rf + x(E[Rp] - rf)
The standard deviation of a mix portfolio
xSD(Rp)
How do we find the highest possible expected return for any level of volatility
Find the portfolio that generates the steepest possible line when combined with the risk free investment
Sharpe Ratio
measures the ratio of reward to volatility provided by a portolio
E[Rp]-rf/SD(Rp)
Tangent Portfolio
the portfolio with the highest sharpe ratio, where the line with the risk free investment is tangent to the efficient frontier of risky investments.
Combination of the risk free asset and the tangent portfolio provide the best risk and return trade off.
The tangent portfolio is efficient
conservative investors
will invest a small amount in the tangent portfolio
aggressive investors
will invest more in the tangent portfolio
What does the Capital asset pricing model allow us to do?
identify the efficient portfolio of risky assets
What is the first assumption of CAPM?
Investors can buy and sell all securities at competitive market prices and can borrow and lend at the risk free interest rate
What is the second assumption of the CAPM?
Investors only hold efficient portfolios of trade securities (portfolios that yield the maximum return for a given level of volatility)
What is the third assumption of the CAPM?
Investors have homogeneous expectations regarding the volatilities, and expected returns of securities
What does the demand of the market portfolio equal?
the supply of market portfolio
When CAPM assumptions hold, what is the optimal portfolio?
Is a combination of the risk free investment and market portfolio
What is the line called when the tangent line goes through the market portfolio?
the capital market line
CAPM expected return
E[Ri] = rf + βmkt(E[Rmkt] - rf)
CAPM beta
β = Cov(Ri,Rmkt)/Var(Rmkt)
CAPM: Beta of a portfolio
weighted average of securities in the portfolio
βp=Σxiβi
Market capitalisation
total market value of a firms outstanding shares
MV = (no. of shares outstanding)(price per share)
= Ni x Pi
Value weighted portfolio
A portfolio in which each security is held in proportion to its market capitalisation
xi = market value of i/ total market value of all securities
MV/ΣMV
Market indexes
particular portfolios of securities.
examples:
S&P 500
Wilshire 500
Dow Jones
Drawbacks of using historical data
Standard errors of the estimates are large
backward looking may not reflect current expectations
Beta corresponds to…
the best fitting line in the securities excess returns vs the market excess return
what is the purpose of the linear regression?
identifies the best fitting line
Ri-Rf = αi + βi(Rmkt - rf) + ei
What does the alpha represent in the linear regression?
it is the intercept of the regression and is the distance from the security market line : risk - adjusted permance measure for historical returns
When α > 0 what does this indicate?
the stock has performed better than predicted by the CAPM
When α<o what does this indicate?
the stock’s historical return is below the security market line
Stocks Alpha
difference between expected and required return according to the security market line
αs = E[Rs] - rs
When the market portfolio is efficient….
all stocks are on the SML
All stocks have α = 0
If the market portfolio is inefficient how can investors improve the market portfolio
buying stocks with positive α and selling stocks with negative α
Rational expectations
all investors can correctly interpret and use their own information as well as information inferred from market prices or trades of others
What is the average portfolio of all investors?
is the market portfolio and therefore average α = 0
When can the market portfolio be inefficient?
if investors misinterpret information and believe they are earning a positive alpha when it is negative
in investors are willing to hold inefficient portfolios
Familiarity bias
investors favour investments in companies that they are familiar with
relative wealth concerns
care more about portfolios relative to their peers
excessive trading
a tremendous amount of trading occurs each day while according to investors CAPM investors should hold
Overconfidence bias
investors believe they can pick winners when in fact they cannot
Sensation seeking
An individuals desire for novel and intense risk taking experience
If individuals depart from CAPM what happens
the departures tend to cancel out, individuals will hold Market portfolio in aggregate will be no effect on market price or returns
Disposition effect
when an investor holds on to stocks that have lost their value and sell stocks that have risen in value since time of purchase
Investor attention as a systematic trading bias
individuals are more likely to invest in stocks that have been subject to media attention, experienced high trading volume or have more extreme returns
effect of mood on trade of stocks
if it is sunny more likely to be happy and thus stock returns are higher
experience as a systematic trading bia
investors consider own experience rather than historical evidence
Herd behviour
when investors make similar trading errors because they are actively trying to follow each others behavious
informational cascade effects
when investors ignore own information hoping to profit from others
Implications of behavioural bias
engaging in strategies that earn a negative α
superior past performance is not a good predictor of a funds future ability to outperform the market
size effect
small market stocks earned higher average returns than the market portfolio even after accounting for their betas
stocks have historically earned higher average returns than low book to market stocks
momentum strategy
buying stocks that have had past high returns and selling stocks that have had past low returns
Implication of positive α trading strategy
only way positive α strategies can persist in a market is if some barrier to entry restrict competition
proxy error
true market portfolio may be efficient but proxy used for it may be inaccurate
Expected return of marketable security
E[R] = rf +βeff (E[Reff] - rf)
Self financing portfolio
constructed by going long in some projects and short in other stocks with equal market value
the weights sum to zero
E[Rs] = rf + Σβ E[Rf]
Market capitalisation strategy
small minus big portfolio SMB
Book-to-market ratio strategy
high- minus-low portfolio HML
Past returns strategy :
the prior one year momentum PR1YR
Fama-French-Cahart factor specifications
E[Rs] = rf + βmkt (E[Rmkt]-rf) + βsmb(E[Rsmb - rf) + βhml(E[R] - rf) + βpr1yr(E[Rpr1yr - rf)
The FFC compared to CAPM
it does no better at measuring risk of actively managed mutual funds
Balance sheet
list of firms assets and liabilities providing a snapshot of financial position of the firm
Assets
Liabilities +equity
networking capital
current assets - current liabilities
Book Value of equity
BV of assets - BV of liabilities
Liquidation Value
value once all assets sold and liabilities paid
Debt to Equity ratio
Total debt/total equity
Capital struture
mixture of debt and equity
traits of debt
Not an ownership interest
creditors do not have voting rights
Interest considered cost of doing business and tax is deductible
creditors have legal recourse if payments are missed
excess debt can lead to financial distress and bankruptcy
Equity
ownership interest
common stockholders vote for the board of directors and other issues
Dividends are not a cost of doing business and are not tax deductible
Dividends are not a liability and stockholders have no recourse if dividends are not paid
An all equity firm cannot go bankrupt
Perfect capital markets
Investors can trade the same set of securities at competitive market prices
No taxes
No transaction costs
No issuance cost
Financing decisions do not change cash flows or reveal new information
Modigliani-Miller Proposition 1
In a perfect capital market the total value of a firm is equal to the market value of the total cash flows generated by its assets and is not affected by its choice of capital structure
Unlevered equity
is equity in a firm with no debt outstanding
Levered equity
is equity in a firm with debt
market value balance sheet
a balance sheet where
all assets and liabilities of the firm are included (even intangible assets such as reputation, brand name, or human capital which are missing from standard accounting)
all values are current market values rather than historical costs
MV Equity + MV Debt = MV assets = MV unlevered equity
What effect does leverage have?
Will not affect total value of the firm but changes allocation of cash flows between debt and equity without altering total cash flows
What effect does debt have on equity?
Debt increase the risk of equity
Homemade leverage
If investors prefer an alternative capital structure to the one the firm has chosen, investors can borrow or lend their own and achieve the same result
How can holding unlevered equity be replicated
by holding a portfolio or firms equity and debt
Leveraged recapitalisation
When a firm borrows funds to pay a large special dividend or repurchase a significant amount of outstanding shares
The return on unlevered equity
ru is related to the returns of levered equity rE and debt rD
E/E+D *rE + D/E+D *rD = rU
rE = rU + D/E(rU - rD)
Modigliani- Miller proposition 2
The cost of capital of levered equity is equal to the cost of capital of unlevered equity plus a premium that is proportional to the market value debt-equity ratio
As D/E changes
rA (return of assets) is constant
the equity cost of capital changes
If a firm is unlevered….
all free cash flows generated by its assets are paid out to its equity holders
ru = rA
If a firm is levered
the free cash flows generated by its assets are paid out in to its debt and equity holders in proportions equal to the fraction of the firms value financed
ru = rwacc = E/E+D *rE + D/E+D *rD
if the firms structure is made up of multiple securities then the WACC is calculated by computing the weighted average cost of capital of all the firm’s securities
Unlevered beta
measure of the risk of a firm as if it did not have leverage which is equivalent to the beta of the firms asset
βu = E/E+D*βE + D/E+D * βD
Leverage amplifies the market risks of a firms assets βu by raising the market risk of equity
Conservation of value principle
With perfect capital markets transactions neither add nor destroy value but would instead represent a repackaging of risk
value only created by real assets
Any market transaction the appears to e a good deal may be exploiting some type of market imperfection
What is the reality of the market and capital structure?
Capital structure matters
the irrelevance result serves as a bench mark
Often investors cannot undertake the same financial transactions as firms due to transaction costs, taxes and information asymmetry
When do corporations pay taxes on profits?
The pay them after interest payments are deducted
Interest expenses reduce the amount of corporate taxes made
Interest tax shield
reduction in tax paid due to the tax deductibility of interest
The cash flows a levered firm pays to investors will be higher than they would be without leverage by the amount of the interest tax shield
Modigliani proposition 1 with taxes
The total value of a levered firm exceeds the value of the firm without leverage due to the present value of tax savings from debt
VL = VU + PV(Interest tax shield)
If firms borrow a debt and keeps it permanently how can we treat the tax shield?
As a perpetuity
PV(Tax shield) = (tax rate * Interest)/rf
With tax deductible interest what is the effect after tax borrowing rate?
rD(1-taxrate)
What happens to WACC in the presence of tax
WACC will decline with tax
rWACC = E/E+D *rE +D/E+D *rD (1-taxrate)
by expanding the brackets on the last term we then get
pre-tax WACC - D/E+D rDtaxrate
Modigliani miller proposition 2 with taxes
The equity cost of caital in the presence of corporation taxes is
rE = rU + (D(1-taxrate)/E)(rU-rD)
When are cash flows to investors taxed?
They are taxed twice. First at the corporate level and again when they receive the interest payment or dividend.
Personal taxes
Interest payments received from debt are taxed as income
equity investors also must pay taxes on dividends and capital gains
There are however different types of investors Personal, Institutional, tax exempt, internation
When will a firm be indifferent between issuing equity or debt?
If
1-taxratei) = (1-taxratec)(1-taxrateE
Effective tax advantage of debt
taxrate* = 1 - [(1-taxratec)(1-taxrateE)/(1-taxratei)]
The value of a levered firm with tax
VL = Vu + taxrate* D
If taxrate* >0 what does this indicate?
Tax advantage of debt
If taxrate* < taxratec
benefits of leverage reduced due to personal taxes
Determining actual tax advantage of tax
capital gains taxes are only paid once investor sells stock and realises the gain and loss can be used to offset gains
Income tax rates vary for individuals
Many investors pay no personal taxes
When corporate taxes are introduced what happens to the the firms value?
It increases with the D/E ratio
What do personal taxes and cost of financial distress favour?
Equity
Limits to the tax benefits of debt
to receive the full tax benefits of leverage, the firm does need to have high taxable earnings
What is the optimal level of leverage from a tax saving perspective?
the level such that interest equal EBIT
Financial distress
when a firm has difficulty meeting its debt obligation
Default
when a firm fails to make the required interest or principle payments on its debt, or violates a debt covenant
Equity financing
does not carry default risk - not legally obligated
The risk of bankruptcy
is an important consequence of leverage. A firm does not default as long as market value of its assets exceeds its liabilities
How does bankruptcy shift ownership?
from the firms equity holders to debt holders without changing the total value available to investors
Bankruptcy in reality
never simple or straightforward!
Prepackage Bankruptcy (Prepack)
method for avoiding many direct costs of bankruptcy in which a firm first develops a reorganisation agreement with its main creditors and then files for Chapter 11 to implement the plan
- this is handled quickly and with minimal cost
Indirect costs of financial distress
Other costs that can arise among financially distressed firms which may never actually go bankrupt They are difficult to measure but are greater than direct costs -loss of customers -loss of suppliers -loss of employees -loss of receivables -Fire sale of assets -Delayed Liquidation -Cost to creditors
What two important things should we consider when estimating indirect costs?
Loss to firms value
incremental losses due to firms economic distress
Who bares the brunt of bankruptcy costs?
equity holders
Trade off theory
Firms pick a capital structure by trading off the benefits of the tax shield against costs of financial distress
Modigliani Miller proposition 1 with taxes and bankruptcy
Total value of a levered firm
VL = VU + PV(Interest tax shield) - PV(financial distress)
US bankruptcy code
creditors treated fairly and value of assets not needlessly destroyed
2 forms of bankruptcy protection
Chapter 7
Chapter 11
Chapter 7 bankruptcy
Liquidation
A trustee is appointed to oversee the liquidation of the firms assets through an auction
proceeds from the sale of the assets goes to pay firms creditors. The firm then ceases to exist
Chapter 11 Bankruptcy
All pending collection attempts are suspended
The firms management can propose a reorganisation plan which specifies the treatment of each creditor of the firm
Creditors must vote for to accept the plan and must be approved by bankruptcy court
If an acceptable plan is not reached the court can force chapter 7
Direct costs of bankruptcy
They are related to the legal process involed in reorganising the bankrupt firm
- legal expenses
- advisory fees
- time that management and creditors spend working out the situation and negotiating
Average direct cost of bankruptcy
3-4% of the firms pre-bankruptcy market value of total assets
Given these costs firms may avoid filing for bankruptcy by first negotiation with creditors
Workout
method for avoiding bankruptcy in which a firm in financial distress negotiates with creditors to reorganise
Three factors that determine the present value of financial distress
- the probability of financial distress
- the magnitude of the cost after a firm is in financial distress
- Discount rate for the distress costs
Probability of financial distress
Increases with the amount of liabilities
Increases with the volatility cash flows and assets
Magnitude of the costs after a firm is in financial distress
depends on the industry….
tech firms will have high costs due to the potential for loss of customers and key personnel, lack of tangible assets that can be easily liquidated
real estate firms likely to have low costs due to their assets being sold easily
Discount rate for distress costs
depends on the firms market risk
the beta of distress cost has the opposite sign to that of the firms
the higher the firm’s beta, the more negative the beta of its distress cost will be
Agency costs
costs that arise when there are conflicts of interest between the firms stakeholders
Overinvestment problem
when a firm faces financial distress, shareholders can gain at the expense of the debt holders by taking a negative NPV project if it is sufficiently risky
Underinvestment problem
When equity holders choose not to invest in a positive NPV project because the firm is in financial distress and then value of undertaking the investment opportunity will accrue to bond holders rather than themselves
Cashing out
When a firm faces financial distress shareholders have an incentive to withdraw money from a firm
Leverage can encourage managers and shareholders to act in ways that reduce firm value
Two effects of adding leverage to captial structure on share price
- The share price benefits from the equity holders’ ability to exploit debt holders in times of distress
- Debt holders recognise this probability and pay less for the debt when it is issued, reducing the amount the firm can issue to shareholders
Debt holders lose more than shareholders gain from these activities and the net effect is a reduction in the share price
Debt covenanats
conditions of making a loan in which creditors place restriction on actions a firm can take
- the help reduce costs
- hinder management flexibility and have potential to prevent investment in positive NPV opportunities and can have a cost of their own
Management intrenchment
A situation arising as the result of the separation of ownership and control in which managers may make decisions that benefit themselves at investors expenses
- not in best interest of shareholders rather that of the manager
Advantage of leverage
- Concentration of ownership - allows original owners to maintain an equity stake
- Reduction of wasteful investment - avoid the effect of managers empire building. When cash is tight managers run the firm as efficiently as possible. Managers more likely to be fired in financial distress. Creditors provide an additional level of management oversight
- Commitment. - cannot risk the possibility of bankruptcy
The value of a levered firm with addition of agency costs
VL = VU + PV(interest tax shield) - PV(financial distress costs) - PV(Agency costs of debt) +PV(Agency costs of debt)
Managemnt entrenchment theory
managers choose a capital structure to avoid the discipline of debt and maintain their own job security
Asymmetric information
when parties have different information
credibility principle
action speak louder than words
signalling theory of debt
use of leverage as a way to signal to investors
Adverse selection
When buyers and sellers have different information
Implications for equity issuance
the stock price declines on the announcement of equity issue
the stock price rises prior to the announcement of equity issue
firms tend to issue equity when informational asymmetry is minimised
Implication for equity structure in info asymmetry
managers who perceive the firms equity is underpriced will have a preference to fund investment with retained earnings or debt rather than equity
Payout policy
The way a firm chooses between alternative way to distribute free cash flow to equity holders
Part of payout
pay dividend or repurchase share
Part of retained earnings
increase in cash reserves or invest in new projects
Declaration date
date on which the board authorises a dividend to be paid
record date
when a firm pays a dividend, only shareholders on record on this date will receive the dividend
Ex-dividend date
date, two days prior to record date, on or after anyone buying the stock will not be eligible to receive the dividend
Payable date
date, generally a month after the record date or which the company sends cheques to it registered shareholders
Special dividend
one time dividend payment which a firm makes. - larger than a regular dividend
Stock split
when company issues a dividend in shares of stock rather than cash to its shareholders
Open market share repurchase
buying shares in the open market
- represents about 95% of repurchase transactions
Tender offer
Offer to buy back a specified amount of outstanding securities at a prespecified price over a prespecified period of time
- if shareholders dont tender enough shares the company will cancel the transaction
Dutch Auction
firm lists different prices and the shareholders indicate how many shares they are willing to sell at each price. The firm then pays the lowest price at which they can buy back a desired number of shares
Targeted repurchase
purchases from a specific shareholder
Greenmail
when a firm avoids a threat of takeover by buying out the shareholder, often at a large premium over the current market price
Cum-Dividend
When a stock trades before the ex-dividend date entitling anyone to the dividend
Pcum = current dividend +PV(future dividend)
Ex-dividend
After the ex-dividend date, new buyers will not receive the current dividend
In a perfect capital market what is the investors preference for distribution of funds?
they are indifferent between paying a dividend or share repurchase. If the investor wanted cash then he can raise it by selling shares. and vice versa by using cash to buy shares
Modigliani - Miller Dividend policy irrelevance
In perfect capital markets, holding fixed the investment policy of a firm, the dividend policy is irrelevant and does not effect the initial share price.
The firms free cash flows determines the level of payouts that it can make to its investors
Dividends and tax
dividends are typically taxed at a higher rate than capital gains.
Shareholders pay lower taxes if a firm uses share repurchase rather than dividends
This repurchase will increase the value of the firm
Optimal dividend policy with taxes
Pay no dividends at all
Dividend puzzle
when firms continue to issue dividends despite their tax disadvantage
Effective dividend tax rate
taxrated* = (taxrated - taxrateg)/(1-taxrateg)
What does the effect dividend tax rate measure
the additional tax paid by the investor per dollar of after tax capital gains income received as dividend instead
Clientele effect
when dividend policy reflect the tax preferences of its investor clientele
Individuals in high tax bands prefer low dividend paying stocks
Dividend capture theory
Absent transaction cost, investors can trade shares at the time of dividend so that non taxed investors receive the dividend
Modigliani miller payout irrelevance
In perfect capital markets, if a firm invests excess cash flows in financial securities , the firm’s choice of payout versus retention is irrelevant and does not effect initial share price
Consequences of retaining cash
- Reduces cost of raising capital in the future
- Increases taxes - retained earnings are taxed twice
- Increases agency costs - managers may use the funds inefficiently and increase financial distress costs
Dividend smoothing
practice of maintaining relatively constant dividends
when will firms raise dividends?
When they perceive a long term sustainable increase in the expected level of future earnings and only cut them as a last resort
Dividend signalling hypothesis
Dividned changes reflect the manager’s view about a firms future earning prospects.
Signals when a firm increases the dividend
positive signal to investors for the foreseeable future
or
signal lack of investment opportnities
Signals when a firm decreases the dividend
signal management has given up hope that earning will rebound in the near term
or
signal of new positive NPV investment opportunities
Signal of a share repurchase
the shares are underpriced because if they were overpriced a share repurchase would be costly to shareholders
Characteristics of a stock dividend.
a firm does not pay out cash to shareholders
total market value of the firm is unchanged
the stock price will fall as same price over a larger number of shares…
not taxed
Characteristics of a stock dividend
keeps share price within a range
if share prices are too high would be hard for small investors to invest
keeping the price low increases the demand and liquidity and thus boosting the price
reverse split
when the price of a company’s stock falls too low so company reduces the number of outstanding shares
Spin off
When a firm sells off a subsidiary by selling shares in that alone
it avoids transaction costs associated with a subsidiary sale
Financial option
contract that gives the owner the right (but not obligation) to purchase or sell an asset at a fixed price at some future date
Call option
Gives owner the right to buy an asset
Put option
Gives the owner a right to sell an asset
Exercising option
when an option holder buys or sells a share of stock at the agreed upon price
Strike price/exercise price
price at which an option holder buys or sells a share of stock when the option is exercised
Expiration date
last date at which an option holder has the right to exercise the option
American option: allow holders to exercise on any day up to and including the expiration date
European Option: can only exercise on the expiration date
The option buyer (holder)
holds right to option
has a long position in the contract
The option seller(writer)
sells the option
has a short position in the contract
Open interest
total number of contracts of a particular option that have been written
At-the-money
an option whose exercise price is equal to the stock price
In-the-money
an option whose value if immediately exercised would be positive
Out-of-the-money
an option whose value if immediately exercised would be negative
Deep-in-the-money
an option which is in the money and the strike price and stock price are far apart
similar with deep-out-of-the-money
Long position on a call option
The value of a call option at expiration
C = max(S-K,0) s eing the stock price, K is the strike price
Long position on a put option
The value of a put option at expiration
P = max(K-S,0)
Short position in an option contact
An investor that sells an option has an obligation
The seller takes the opposite side to the investor who bought the option
The seller’s cash flows are negative of that of the buyer’s
Profits for holding an option until expiration
Payouts on a long position in an option contract are never negative. The profit from purchasing an option and holding it to expiration could be negative because of the payout at expiration might be less than the initial cost of the option
Characteristics of a call option
the maximum loss is 100%
out-of-the-money call options are more likely to expire worthless but if it goes up then it is more likely to have a higher return
Characteristics of a put option
the maximum loss is 100%
put options will have higher returns in states with low stock prices
put options are not generally held as an investment but as insurance to hedge other risk in a portfolio
How can portfolio insurance be achieved/
Purchase a stock and a put
or
Purchase a bond and a call
Put call parity
by the law of one price the payoffs of both combinations of stock and put and call and bond must be the same and they have the same price
S+P=PV(K)+C
Price of a european call option for a non-dividend paying stock
C = P+S-PV(K)
If the strike price K goes up what happens to the price of the call and put?
Call goes down Put goes up
If the stock price S goes up what happens to the price of the call and put?
call goes up put goes down
A put option cannot be worth more than…
its strike price
A call option cannot be worth more than..
the stock itself
An american option cannot be worth less than…
its intrinsic value
An american option cannot have a….
neegative time value
Intrinsic value
amount by which an option in in-the-money or zero if it is out-of-the-money
Time value
difference between an option’s price and its intrinsic value
The value of an option increases with what?
the volatility of the stock
The price of any call option on a non-dividend paying stock….
always exceeds the intrinsic value
It is never optimal to exercise a call option on a non-div stock early
It may however be optimal to do this for a put
Call option with a dividend paying stock
C=S-K+dis(K)+P-PV(div)
Put option with a dividend paying stock
P= K-S+C-dis(K) +PV(div)
Debt as an option portfolio
Debt owners can be viewed as owners of the firm having sold a call option with a strike price equal to the required debt payment
Debt can also be viewed as a portfolio of riskless debt and a short position in a put option on the firm’s assets with a strike price equal to the required debt payment
Credit default swap
Implies we can eliminate a bonds credit risk by buying the very same put option to protect or insure it
Risky debt = Risk-free debt - put options on a firms assets
(rearrange to get risk free debt)
The buyer pays a premium to the seller and receives a payment from the seller to make up for the loss if the bond defaults
Agency conflicts
Equity is like a call option so equity holders will benefit from risky investments
Debt is a short put option so debt holders will be hurt by an increase in risk
potentially leading to an asset substitution problem
If value of assets increases…
value of put option will decline
Binomial option pricing model
A technique used for pricing options based on the assumption that each period the stock return can only take two values
Binomial tree
A time line with two branches at every date representing the possible events the could happen at those times
Replicating portfolio
A portfolio consisting of a stock, and a risk free bond that has the same value and payoffs as an option written on the same stock
Replicating portfolio in the binomial model
Δ = Cu-Cd/Su-Sd
B= Cd-SdΔ/(1+rf)
Option price in the binomial model
C=SΔ+B
Dynamic trading strategy
A replication strategy based on the idea that an option can be replicated by dynamically trading in a portfolio of the underlying stock
The Black-Scholes option pricing model
A technique for pricing european options. when the stock can be trade continuously can be derived from the binomial option pricing model by allowing the length of each period to shrink to zero and letting the number of periods increase infinitely
Only 5 inputs are needed for the Black Scholes formula
Stock Price Strike Price Exercise date risk free rate volatility of the stock
