Corporate Finance Exam Flashcards
Current Yield
Annual Coupon Payments/ Price
Future Value
C x (1 + r) ^ n
PV * (1 + r) ^ n
PV (discount)
C / (1 + r) ^ n
Growing Perpetuity
C / (r - g)
Fishers
1 + R = (1 + Rr) * (1 + h)
Nominal = R
Real Return = You would like to earn
CPN
(Coupon Rate * Face Value) / coupon payments per year
YTM
Discount Rate for bonds
Zero Coupon Bonds
Only FV, trades at discount
Pure discount bond / spot interest yield
Treasury Bills
YTM = return you will earn from holding the bond to maturity and receiving promised FV
Price increases as term decreases
IRR = YTM = Yield
Formula Zero Coupon Price
FV/ (1 + YTM)^n
YTM Zero Coupon
(FV/P) ^1/n - 1
Coupon Bonds
Treasury notes/treasury bonds
CPN + FV
Price decreases as term increases due to number of coupon bonds remaining
Yield Treasury
(FV - Price)/Price * (365/days) * 100
This is the same thing as:
FV/P - 1 * (365/days) * 100
Dirty vs. Clean Price
When bond fluctuates according to closeness to bond payment - clean price removes this effect
Discounts and Premium
Coupon Rate > YTM = Premium
Coupon Rate = YTM = Par
Coupon Rate < YTM = Discount
Interest Rate effect
Rises - prices fall (higher discount rate)
Falls - prices rise (lower discount rate)
Sensitivity of bonds
Depends on timing of cash flows due to interest rates
Shorter: less affected
Higher CPN: less affected (higher cash flows up front)
Reinvestment Risk
Uncertainty concerning rates C reinvested
- Short term (more reinvestment risk)
- Higher CPN (more reinvestment risk)
Yield Curve
Relationship between (yield) interest and maturity (term)
Interest rate expectations drive yield curve
Yield is essentially the higher return (higher discount).
Steep yield curve (interest rates expected to rise)
Inverted (interest rates expected to fall) negative forecast
Practice drawing both.
Corporate Bonds
Risk of default = credit risk
Promised is the most you could hope to receive. It’s not equal to expected cash flows due to risk of default.
= investors will pay less.
Corporate Bonds P
Expected/ (1 + YTM)
Expected = probability into account.
Discount rate is the debt cost of capital = expected return
Corporate Bonds YTM
(FV/P) - 1
Discount rate (YTM) = Debt cost of capital Use yields on corporate bond credit rating: YTM gilt + credit spread
Libor vs. LIBID
LIBID is the bid rate for eurocurrency deposited.
LIBOR is rate banks borrow at from each other (offer)
Rights for new shares
Old Shares/ New Shares Issued
Market Value through Equity
Direct Method: DDM - PV of Dividends Payments
Indirect Method: DCF - Forecasted Earnings
DDM - Required Return/Yield
RE = (Div1 + P1) / Po
Or;
RE = (DIV/Po) + g
Same as:
EPS/Share Price (other terminology)
Dividends Volatility
Long run: Driven by Cash Flow
Short run: Discount rates
P can change from news of cash flows (firm) or news on dividends
DDM
Cash flows you receive = PV of dividends
Not very practical, trying to forecast the discretionary
It’s up to management
Value of company is just number of shares * Po
- effective way of measuring performance of market on an aggregate level - preferred model, but not on individual company level.
Discount rate is RE - all cash flows going to equity.
Cash & debt & interest are indirectly incorporated through earnings.
Common Shares
Voting rights, share proportionately in declared dividends & assets under liquidation; preemptive rights (first shot at new stock issue)
Preferred shares
Must be paid before common; cumulative (if div. deferred) must pay outstanding preferred before common; no voting rights, but gets FV before common on liquidation - (hence preferred) - start up, protects investors.
Bid Price/Sell Price
Bid price (sell) - low price Ask Price (buy) - high price
IPO’s
Sells issue to underwriter syndicate (investment bank)
=> resells to public;
=> Money on the spread (often guaranteed)
=> Underwriter bears risk = gross spread 7%
Best effort/Dutch (bids determine market price)
Penalty for IPO’s going badly discourages them. Underpricing leave money on the table, clear evidence of.
Seasoned Equity
Signalling: Stock prices decline when new equity issued
- either going badly or shares overvalued
- this is issue cost
(reduce effect when possible by management)
Rights Offering
Reduces signalling costs of issuing equity. Common stock to existing shareholders to avoid dilution (the fall in value due to newer, cheaper shares).
Interest Rates current effect on stock prices
Gov holding interest rates down (inverted yield curve) is forcing out bond investors into shares => many overvalued.
Capital Gains
(P1 - P0) / P0
IRR
It is important always to use the IRR to test sensitivity to the choice of cost of capital
NPV and IRR
Time value of money - NPV is the correct rule comparing to payback and profitability index
Profitability Index
Value Created/Resource Consumed
NPV/Resource
Resource = Capital or Investment
Project Appraisal
Incremental, FCF, NPV
Incremental Earnings
Sales COGS GP Selling, Gen, Admin (Opportunity cost) R&D (upfront) Depreciation) EBIT Tax NOPLAT \+ Depreciation - Change in NWC = FCF
FCF - Taken from Cash Flow Statement
Cash Flow + Interest * (1 - tax) - Capex
DCF
Theoretically pure but hard to find inputs; unreliable
PV of cash flows where value of share is residual value after all liabilities are paid.
Discount rate is WACC + (takes into account tax shield). Value of debt and equity.
Good for individual companies but complex and lots of assumptions.
DCF Po
(Vo - Net Debt)/Shares Outstanding
Net Debt = Cash - Debt
Value of the Firm
V = E + D
FCF
Are estimated assuming business is 100% equity financed - keeps business separate from financing decision (DCF)
Relative Valuations
Third method apart from DFC & DDM;
Multiples - take into account scale. Can’t help decide if overvalued. Only relative to some key statistic. Simply reflects market interpretation of value. Quick and dirty.
No guidance on adjusting for risk, growth rates or accounting policies
Price Earnings
Share Price/ EPS
Enterprise Multiples
EV/EBIT
EV/Sales
EV/EBITA - this is best as capital expenditure can vary substantially. Subtract debt & divide by shares
Estimate TV of industry * estimate EBIT for your year = EV.
Terminal Value
Stable Growth (DCF) = soundest Multiples Liquidation Value = most useful when assets separable and marketable
DCF Dilemma
Can’t forecast 2-3 years, let alone crisis. Can’t predict cash flows. Especially TV with growth. Discount rates criticised (though band 8-12%).
Discount rates absorb some risk and adjusts accordingly. So understanding how to risk adjust is critical.
Ways to increase dividends
Increase earnings
Increase dividends payout
Decrease shares outstanding
Risk & Return
Higher perceived risk = higher return
Standard deviation fluctuates with riskier investments
Could come from capital appreciation
Strong relationship between volatility (SD) and returns (average)
Normally distributed, but negatively skewed - under predicts probability of bad effect
Risk Premium
Additional risk measured as spread between average return treasury bills + average return of chosen investment
Momentum Strategy
Asset performed well buy, badly sell
Efficient Capital Markets
Imply that stock prices are in equilibrium or fairly priced.
- Testing this you test for risk
- Only way to add extra return is to add extra risk
IF TRUE:
- NOT able to earn abnormal positive returns above and beyond level of risk
- Not imply that you can’t earn positive returns, but that prices are a true refection of expressed returns to assets adjusted to risk.
BUT 300 anomalies found.
Efficient Capital Markets & Information
All about info - priced in immediately. Investors doing research enable this. Were they to stop: inefficient markets.
Idea is that information is priced in immediately.
Weak Market Efficiency
Prices reflect all info in market prices, technical analysis can’t earn excess returns. Can’t devise strategy just looking at prices (good evidence)
Semi-Strong Market Efficiency
Information set includes public info like accounting + weak in prices. Fundamental analysis no excess returns
(some evidence)
Strong Market Efficiency
Prices reflect public and private information as soon as its made available it’s priced in. No investor can earn excess returns. (no evidence).
Return to price
The lower the expected return, the higher the price. With higher risk, investors will pay less.
Capital Market Line/Security Market Line
Shows risk as being proportionate to returns. When you include individual stocks, returns don’t follow the capital market line. It’s as the individual firm carries individual risk.
When you remove risk premium, stocks line up to CAPM.
Realised returns and expected returns
Due to idiosyncratic risk, the realised returns are not equal to the expected returns. However, over time, the average of the unexpected returns = 0. So that on average, on receives the expected (portfolio theory built on)
Market Risk/Systematic Risk
Only mark risk receives returns! This is the risk in the overall aggregate economy
Idiosyncratic Risk
Risk individual to the firm. Change in management, shortages, underlying conditions (unique/firm specific)
Diversification of risk
Always some that can’t be diversified away = remunerated for taking. This is determined by the market learning price (equilibrium price).
Diversification reduces variability of returns (risk) without equivalent reduction in returns = it nets. Want circa 20-25.
Systematic risk is not diversified away = this generates returns.
(Practice drawing)
Portfolio Diversification & Investment
Idiosyncratic risk is diversified away - nets out risk by adding more stocks to portfolio.
Simple Idea is:
- Returns are additive: (Expected of A + B) = Expected return of A + Expected return of B (returns of combo always between return of A & return of B.
- Risk/Volatility is not: riskiness falls and rises with relative % invested in one over the other. Unless perfectly correlated then linear. (Variance A + B) = Var(A) + Var(B) ? 2 Cov(AB)
=> Risk and Return Frontier
(choice dependent on risk aversion, but mid point strictly dominates those below).
The lower the correlation, the greater the risk reduction from diversification.
(Practice drawing this)
What does the Beta Measure?
The sensitivity of a stocks returns to the market return.
B = 1 - same systematic risk as overall market
B < 1 - asset has less systematic risk than overall (retail)
B > 1 - asset has more systematic risk than overall (tech)
You get it by running regression. It’s the covariance between Ri and Rmkt. Scaled by the variance of market returns.
Beta of Market
On average, Beta of market has to be 1
Capital Asset Pricing Model
Relationship between risk premium and Beta used to estimate expected returns.
Risk premium = expected returns - risk free
Higher the B, the higher the systematic risk, the greater the reward, (the lower the price).
Adjusting for Beta and Returns
Once you’ve adjusted for risk, you cannot earn abnormal returns (if we think market is efficient). Explains a lot (lining up the stocks) but there are deviations. Small companies tend to outperform.
Deviations are statistically significant.
Cost of Capital
WACC
Reducing this gives greater PV. Need to earn at least required return to compensate investors.
Tax shield
Calculate value of firm as if 100% equity financed.
Either take into account by adding back to adjusted PV method or in the WACC.
Annual tax shield: Tax rate * interest payments
Change in the value of the firm is the PV of the perpetuity.
Debt vs. Equity
Debt is cheaper - lower required return, but makes equity more expensive (higher required return)
Trade off theory - short run, opportunistic (cheaper capital); long run, optimal gearing
WACC
Formula
Cost of Equity for WACC
Return required by equity investors given risk of cash flows:
- Business risk (underlying cash flow)
- Financial risk (extra risk due to capital structure)
Use SML/CAPM = Re = rf + B * premium
Beta of the leveraged firm:
Have to adjust Beta for leverage to be able to compare to unleveraged Beta’s.
BL = BU * (1 + D/E)
Difference shows risk due to debt
Use CAPM/SML to adjust, BUT: estimating market risk premium & Beta - both vary over time + using past to predict future - not reliable
Cost of Debt for WACC
YTM (adjusted for probability of default)
Either;
- If observed, use adjusted YTM on current debt
- Use average YTM On long term bonds of same credit rating
RD = YTM - (p * loss rate )
Assume loss rate = 50%
P = probability default
WACC for project evaluation
Only appropriate for projects with similar risk as current operations. Otherwise, other discount rate:
- Pure Play (similar companies, estimate B, deleverage the Beta to calculate Bu & average). And then adjust unlevered for capital structure of project.
- Subjective Approach (consider risk relative to overall firm)
Raising Capital in Debt Markets
Debt always the same interest => smaller cash flows.
Debt increases variability in both EPS/Net Income and Returns
Leveraged recapitalization
Repurchasing shares = 0 NPV transaction. No change in shareholder value
The Money Market
Large secondary market in short term, highly liquid securities.
It is an ideal place for a firm, government or financial institution to place any surplus funds until needed. Similarly, source of low-cost short term funds for the these same institutions if required.
• Interbank borrowing (e.g. LIBOR / LIBID) – not tradable
unsecured
• Commercial Paper (CP) – tradable, generally unsecured
• Repo. Sale and repurchase agreement where you agree to sell and asset (usually a bond) and buy it back at pre- agreed prices. The price reflects the implicit interest rate on the loan* – non-tradable, secured
• Treasury- Bills.** Buy T-bill = lend to the government
Capital Structure Question
About maximising shareholder wealth by minimising cost of capital. Changing the amount of leverage without changing the firms assets
How can you change leverage without changing assets
Issuing debt and repurchase outstanding shares;
Decrease leverage by issuing new shares and reducing debt;
Adjust leverage more gradually by financing new projects from retained earnings or issuing equity or by issuing debt
Difference debt and qeuity
Tax
Fixed liability (discipline vs. failure to meet)
Source of capital (debt accessed quicker vs. management more risk prone and lenders less ready to offer credit)
Perfect Capital Markets
Value f the firm does not depend on its capital structure.
Total cash flows are the cash flows from its projects.
Leveraged equity has smaller cash flows than unleveragd. Sells for a lower price, but owner is no worse off,
Leverage and Risk
Increases risk of equity, so investors under leveraged equity demand higher returns (higher directount). Leverage increases risk of equity even when there is no risk
Modigliani Miller 1
No taxes, perfect capital markets, offsets gains one for one as more debt increases the discount rate of the equity. Wacc is unaffected. Financial transaction - no value.
Key assumption: perfect capital markets (cash flows are unaffected by capital structure)
Systematic risk depends on: business risk (Bu) and level of debt (D/E)
Cost of Capital leveraged equity
Re = Ru + D/E (Ru - Rd)
Rises linearly with the D/E ratio
Gain of sourcing more debt is offset by RE
Risk of equity
Be = Bu + D/E(Bu - Bd)
Systematic risk rises linearly too with debt to equity
Modigliani Miller 2
Taxes, still perfect capital markets. If capital structure matters, its due to market imperfections like taxes.
Each additional dollar of debt increases cash flows => financial incentive to gear up. Adding debt reduces taxes. All else equal.
Either take into account in WACC or APV method
Pecking Order
Not sensitive to value of debt, raises debt based on cost of raising it.
Internal Financing
Debt
Equity - avoid due to signalling costs
