Slides A
● Corporation - Legal entity owning assets
○ Separation of ownership and control
○ Private vs public
○ Corporate taxation
○ Limited liability
● Headers - the most current identifiers
● Historical identifiers - have date ranges in which they are valid
● Permno - identifies securities
● Permco - identifies companies
● CUSIP - USA and Canada (infrequent change, no reuse, 6, 8, or 9 digits)
● SEDOL - UK (7 digits, many non-UK securities also have SEDOL)
● ISIN - International (12 digits, 2 is country of origin, 3-11 are unique characters)
● CIK - US, corp/indiv with the SEC (10 digits, rare change, never reuse)
● GVKEY - public traded US, 6 digits (almost perfect)
● FV
● PV
● NPV
● IRR
○ Pitfall 1 - does not distinguish between lending or borrowing
○ Pitfall 2 - multiple IRRs (Ss many IRRs as there are sign changes)
■ Also possible to have NO IRR, but positive or negative NPV
○ Pitfall 3 - does not consider the magnitude of project
■ IRR of one higher but NPV is lower than other project
○ Pitfall 4 - Assume discount rates are always stable
● Capital Budgeting
○ Rule 1 - Treat inflation consistently
■ Nominal interest rates for nominal CF, real IR for real CF
○ Rule 2 - CHANGE in NWC is a cash flow (don’t forget about it!)
○ Rule 3 - Consider the tax shield of depreciation
● Zero Coupon Bond - Pays NO coupon, pays face value at maturity
● Yield Curve - graph of what yield and price is offered for different time periods
● Discount Rates
○ Spot Rates - "actual interest rate today” (taken directly from yield curve)
○ Forward Rate - "the interest rate you will pay tomorrow” (the rate agreed
upon today for future borrowing)
■ Can be calculated from current spot rates and locked in to hedge
against interest rate risk and bet against bad future rates
○ Future Rate - Expected future spot rates (may differ due to market changes)
● REAL interest rate is ALWAYS less than NOMINAL interest rate
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(1+real) = (1+nominal) / (1+inflation)
Debt securities promises fixed cash flow at fixed times, BUT CREDIT RISK
Bond ratings - provide indications of the likelihood of default by each issuer
Bonds rated triple B or above are investment-grade
Lower-rated bonds are referred to as speculative-grade
Yield Spread = Corporate Bond Yield − Treasury Bond Yield (risk-free)
Yield spread fluctuates due to credit risk and market conditions
Primary markets - Sales of new shares to raise new capital
Secondary markets - Trading of secondhand shares (no new capital raised)
2 types of stock markets
○ Centralized Auction Markets - NYSE (broker between buyer and seller)
○ Decentralized Dealer Markets - NASDAQ (all trades between investor and
dealer)
Types of Stock
○ Common Stock - Control rights (voting in shareholder meetings), cash flow
rights (dividends)
○ Preferred Stock - No control rights (no voting), but cash flow rights
(dividends)
○ Convertible Preferred Stock - Converts to common stock at a fixed
conversion rate after the specified date
○ Stock Warrant - Long-term stock call options
ADRs - represent ownership in the shares of a foreign company trading on US
financial markets (Quoted in USD, pay dividends in USD, and can be traded like the
shares of US-based companies)
Dividend Discount Model - (Next Year Dividend + Next Year Stock Price) / (1 +r)^t
Constant Growth DDM - V0 = D1 / (r - g)
Dividend Yield
Payout Ratio - Fraction of earnings paid out as dividends
Plowback Ratio = 1 – Payout Ratio » Fraction of earnings retained by the firm
Growth rate = ROE * Plowback Ratio
Present Value of Growth Opportunities (PVGO) = Growth - No Growth
Established and profitable firms paying dividends is more precise (low PVGO, and
vice versa)
Two Stage DDM:
Slides B
● Arithmetic average = (x + y + z) / 3
● Geometric average = [(1+x)*(1+y)*(1+z)]^⅓
● Variance (high is not correlated, low is correlated) (average of squared deviations)
○ Calculate average return (a)
○ Subtract average from individual returns (x-a), (y-a), (z-a)
○ Square each deviation (x-a)^2, (y-a)^2, (z-a)^2
○ Sum and divide by periods minus one ((x-a)^2 + (y-a)^2 + (z-a)^2) / 2
● Standard Deviation = square root of variance
● Covariance (positive is the same direction, negative is opposite) (larger absolute
value is stronger relationship, smaller is weaker)
○ Calculated average return for respective assets
○ Subtract average from individual returns
○ Multiply deviations (x1-a1)*(y1-a1)
○ Sum and divide by periods minus one (average of multiplied deviations)
● Correlation = (Covariance (X,Y)) / (Standard Deviation X)*(Standard Deviation Y)
○ Ranges from -1 to +1 (perfect negative to perfect positive relationship)
○ Measures the strength and direction of the linear relationship
● Standard deviation is a good measure of risk when returns are symmetric/normal
● Skew = Standard measure of asymmetry in the probability distribution of returns
○ (Average of cubed deviations) / (Variance)^3/2
● Kurtosis = the likelihood of extreme values on either side of the mean at the
expense of a smaller likelihood of moderate deviations (the degree of fat tails)
○ (Average of 4th power deviations) / (Variance)^2
○ 3 is normal tails / >3 is fatter tails more outliers / <3 thin tail low volatility
● Portfolio Rate of Return = (Weight of A)*(Return of A) + (Weight B)*(Return B)
● Short selling - A loans to B only the shares (price doesn’t matter to A)
● Short positions = negative portfolio weights, long positions = positive weights
● Two-Stock Portfolio Variance = ((Weight A)^2)*(Variance A) +
((Weight B)^2)*(Variance B) + 2*(Weight A)*(Weight B)*(Covariance)
● Unique/Idiosyncratic/Diversifiable Risk - Risk factors affecting only individual firm
● Market/Systematic/Non-diversifiable Risk - Economy-wide, overall stock market
● Mean-Variance Frontier and Minimum-Variance Portfolio
○ Correlation does not reduce risk, just combines linearly (return unaffected)
○ Initially, adding Stock B increases return much faster than it increases risk
because of diversification
○ MVP - lowest risk for highest return
○ Efficient Frontier - invest only above MVP
● More assets = more diversification
● Capital Allocation Line (CAL) = The frontier graphing returns of different weights of
the risk-free asset and the portfolio
○ Tangency portfolio - The single point on the efficient frontier with the highest
Sharpe Ratio and best return for risk (every other EF point is irrelevant now)
○ Any point on CAL is efficient (just depends on risk tolerance)
○ Lending = Below TP / Borrowing = Above TP
○ Moving up the CAL increases return by increasing idiosyncratic risk
● CML = portfolio of all risky assets in the market
● Sharpe Ratio = Portfolio’s expected excess return (risk premium) relative to its risk
○ (Expected Portfolio Return - Risk-Free Rate) / (Portfolio Standard Deviation)
● CAPM - Tangency Portfolio = Market Portfolio
○ Expected Return - RFR = Beta*(market return - risk free rate)
○ Excess return = systematic risk * market risk premium
○ Beta = Covariance (of Stock A and market returns) / (market variance)
● Beta = “Quantity of systematic risk” in stock (sensitivity to the market return)
○ Cyclicality of revenues and dividends (high cyclicality = high beta)
○ High operating leverage = high beta
○ High financial leverage = high beta
● SML = graphical representation of CAPM (above=underpriced / below=overpriced)
● R2 = market risk
● Weak efficiency - Market prices reflect historical information
● Semi-Strong Efficiency - historical info + current publicly available info
● Strong Efficiency - Market prices reflect all information
● Abnormal return = the difference between that proxy and the actual return
○ Expected Return = α + (β*Market Return)
● Cumulative abnormal return (CAR) - Sum of abnormal returns over the time window
(captures firm-specific stock movement for period over when market might respond)
Slides C
● Asset beta = (equity beta)*(E/V) + (debt beta)*(D/V)
○ Debt beta = YTM on bonds
○ Equity beta = CAPM
○ WACC = (equity beta)*(E/V) + (debt beta)*(D/V)*(1-tax rate)
● Uses of FCF
○ Retain = Invest in New Projects / Increase Cash Reserves
○ Payout = Repurchase Shares / Pay Dividends
● Stock purchase
○ Buy share on market
○ Tender offer to shareholders
○ Dutch auction - firms lists different buy prices, shareholders list different
different sell prices (firm then pays the lowest price)
○ Private negotiation (green mail - avoids a threat of takeover and removal of
its management by a major shareholder by buying out the shareholder)
● Paying dividends is a financing decision (shareholders cannot force dividend pay)
● Cannot pay out of capital / cannot pay if insolvent / cannot pay in contravention of
contractual commitments)
● Declaration Date / Ex-Dividend Date / Record Date / Payment Date
● Managers may be reluctant to increase dividends until they are confident that
sufficient cash flows will exist (hard to cheat valuation) (dividend = financial health)
● In perfect financial markets, Payout Ratio does not matter
● When can dividends increase firms value
○ Financing frictions: (risk-adjusted) return on firm assets may exceed that on
other investments
○ Investors may appreciate a steady source of cash flows from
dividend-paying stocks
○ Dividends make it harder for managers to waste money, dividend paying
firms thus create restrictions on overspending by managers
● When can dividends decrease firm value
○ If dividends are taxed more heavily than capital gains
○ Paying dividends immediately can reduce firm value
○ Financial distress (paying dividends can increase default risk)
● Capital gains were often taxed at a lower rate in the U.S. historically
● Capital Structure - The composition of securities issued by the firm to finance its
operations
● Modigliani-Miller: capital structure is irrelevant to firm value if capital markets are
“perfect”
● MM 1: Debt policy does not change the (net present) value of the firm
● MM2: The expected return on common stock increases in proportion to the
debt-equity ratio (get bigger slice of smaller pie)
○ No cost of default
○ No asymmetric information (nor irrational agents)
○ No taxation
○ No borrowing constraints
○ No agency frictions (nor coordination frictions)
○ No trading/transaction cost
● Equity return = asset return - (D/E)*(asset return - debt return)
● Capital structure changes WACC, but not FCFO(unlev)
● Maximizing firm value requires minimizing WACC
● Debt tax shield: For a corporation, interest payments are considered a business
expense, and thus deductible from taxable profits in most places
● If available, use the marginal corporate tax rate, not the average rate
● In the US tax system
○ Interest and dividends are taxed as ordinary income
○ Capital gains are taxed at a lower rate
○ Realization of capital gains can be deferred (dividends and interest cannot)
● For personal taxes, equity dominates debt (low cap gains and deferrals)
● For corporate, debt is typically cheaper than equity (tax shield and deductions)
● Adjusted Present Value - Firm Value=Value of Unlevered Firm+Capital Structure
Modifiers (sum total of benefits and cons of taking on debt)
● Default due to illiquidity - Literally not enough cash for servicing contractual debt
payments
● Insolvency - A state where a firm’s liabilities exceed its assets, meaning the firm’s
net worth is negative
● Illiquidity - A firm is temporarily unable to meet its cash flow obligations due to lack
of liquid assets (e.g., delayed payments)
● Bankruptcy - A legal procedure initiated when a firm seeks protection from creditors
or restructuring under the law
○ Restructuring: Firm reorganizes its debts to continue operations (buys the
firm time and stability to be self-sufficient again)
○ Liquidation: Firm shuts down, and assets are sold
● "Evergreening" - creditors extend deadlines
● Direct costs of default
○ Legal expenses for financial reconciliation between investors
○ Disruptions to business operation (during bankruptcy)
● Indirect costs of default
○ Loss of firm value due to deterioration of business relationships
○ Management time and distraction
● Leverage increases expected default cost
○ More states in which firm defaults
○ Decreases expected debt payoff
○ Creditors require higher interest ex ante
● Agency Frictions
○ Conflicts of interest between two or more agents
○ Imperfect coordination between agents’ actions
● Cash In and Run
○ Conflict of interest: Every dollar paid to creditors cannot be paid to you
○ You pay dividends, and default a couple of years later (cf. claw back
provisions)
○ You sell assets at discount to other firm you have stakes in
● Bait and Switch
○ You issue your first tranche of debt at low cost (low default risk)
○ Then you issue second tranche which is senior to the previous / Again at low
cost (low default risk) / But old creditor now would have liked to actually
require higher interest due to higher risk of default (which they are the first in
line to absorb)
○ Firm artificially reduced cost of debt (Compared to when they would have
issued entire debt in one go)
● Debt can only recoup up to a limit of debt, but they are priority to get it
● Equity can be recouped to max, but they are second in line after debt
○ Higher risk for higher reward
● Debt overhang - a situation where a firm with existing debt (legacy debt) may not
invest in a positive NPV project because the benefits of the project primarily go to
creditors, not equity holders
● Leverage increases agency frictions, which translate into tangible costs:
○ Creditors include covenants and need to constantly monitor the debtor
○ Debtor management may take investment decisions which reduce the value
of after-debt. Creditors anticipate this and pay less for before-debt
● Trade-off theory: Benefit of tax shield vs Con of default and agency costs
● Capital structure modifiers:
○ + PV of tax shield
○ - PV of default costs
○ - PV of agency costs
● Valuation Applications - Investment Advice, Court Litigation, Tax Bases, Policy
● USE MARKET VALUES WHEN COMPUTING WACC
● Can sometimes add preferred stock to WACC
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● Opportunity cost of capital = required rate of return on asset = asset beta = equity
beta when equity is 100% and unlevered
● Investors ultimately care about whether the firm's investments and operations
generate returns greater than the opportunity cost of capital, regardless of the
WACC
● WACC is a tool that helps firms optimize their capital structure to maximize the
present value (PV) of their cash flows, enabling them to achieve a higher rate of
return than the opportunity cost of capital
○ Pay debtholders less than shareholders and tax shield
● APV is a way to value a firm (alternative to WACC), (discount using opportunity cost
of capital)
○ Better than WACC when capital structure changes (flexible)
● LBO - transfers ownership of a (publicly trades) equity of a firm
○ Consolidation of ownership
○ Financed with large amounts of debt and small amounts of equity
○ The debt goes onto the balance sheet of the target
○ The firm is “taken private” in the process
● An LBO is indeed a high-risk, high-reward strategy, with the private equity (PE) firm
essentially betting that the target company can weather the short-term financial
stress of high leverage, use its cash flows to reduce debt over time, and ultimately
achieve sustainable growth and high returns
● APV very good to value LBOs
● Unlevered Firm Value - the value from the company's operating cash flows alone
● PV of Tax Shields - the additional value created through the tax shield from debt