Notes Fin203 FORMULA SHEET PDF

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Basic Areas of Finance 1. Investments 2. Financial institutions 3. Corporate finance = Business Finance Investments - Work with financial assets such as stocks and bonds - Value of financial assets, risk versus return, and asset allocation Job opportunities - Stockbroker or financial advisor - Portfolio manager - Security analyst Financial Institutions Companies that specialize in financial matters - Banks – commercial and investment, credit unions, savings, and loans - Insurance companies - Brokerage firms Job opportunities Financial Management Decisions Capital budgeting - What long-term investments or projects should the business take on? Capital structure - How should we pay for our assets? - Should we use debt or equity? Working capital management - How do we manage the day-to-day finances of the firm?

Forms of Business Organization Three major forms in the United States 1) Sole proprietorship (Business owned by one person) Advantages Easiest to start Least regulated Single owner keeps all the profits Taxed once as personal

Disadvantages Limited to life of owner Equity capital limited to owner’s personal wealth Unlimited liability Difficult to sell

2) Partnership (Business owned by two or more persons) Advantages Two or more owners

More capital available Relatively easy to start Income taxed once as

Disadvantages Unlimited liability - General partnership - Limited partnership Partnership dissolves when one partner dies or wishes to sell Difficult to transfer ownership

3) Corporation (A legal “person” distinct from owners and a resident of a state) Advantages Limited liability Unlimited life

Disadvantages Separation of ownership and management (agency problem) Double taxation (income taxed at the corporate rate and then dividends taxed at personal rate, while dividends paid are not tax deductible)

Separation of ownership and management Transfer of ownership is easy Easier to raise capital Goal of Financial Management What should be the goal of a corporation? -Maximize profit? -Minimize costs? -Maximize market share? -Maximize the current value per share of the company’s existing stock -Maximize the market value of the existing owners’ equity Does this mean we should do anything and everything to maximize owner wealth? -Outsourcing?

-Off-shoring? -Corporate support of charities? The Agency Problem Agency relationship -

Principal hires an agent to represent its interests Stockholders (principals) hire managers (agents) to run the company

Agency problem -

Conflict of interest between principal and agent Management goals and agency costs

Do Managers Act in the Shareholders’ Interests? Managerial compensation -

Incentives can be used to align management and stockholder interests Incentives need to be carefully structured to ensure that they achieve their goal

Corporate control -

Threat of a takeover may result in better management

Other stakeholders

The Balance Sheet A snapshot of the firm’s assets and liabilities at a given point in time (“as of …”) Assets -

Left-hand side (or upper portion) In order of decreasing liquidity

Liabilities and Owners’ Equity -

Right-hand side (or lower portion) In ascending order of when due to be paid

Balance Sheet Identity -

Assets = Liabilities + Stockholders’ Equity

The Balance Sheet Net working capital -

Current Assets minus Current Liabilities Usually positive for a healthy firm

Liquidity -

Speed and ease of conversion to cash without significant loss of value Valuable in avoiding financial distress

Debt versus Equity -

Shareholders’ equity = Assets – Liabilities

Market vs. Book Value Book value = the balance sheet value of the assets, liabilities, and equity. Market value = true value; the price at which the assets, liabilities, or equity can be bought or sold. Market value and book value are often very different. Income Statement The income statement measures performance over a specified period of time (period, quarter, year). Report revenues first and then deduct any expenses for the period End result = Net Income = “Bottom Line” -

Dividends paid to shareholders Addition to retained earnings

Income Statement Equation: -

Net Income = Revenue – Expenses

Financial Statements GAAP Matching Principle: -

Recognize revenue when it is fully earned

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Match expenses required to generate revenue to the period of recognition

Noncash Items -

Expenses charged against revenue that do not affect cash flow Depreciation = most important

The Concept of Cash Flow Cash flow = one of the most important pieces of information that can be derived from financial statements The accounting Statement of Cash Flows does not provide the same information that we are interested in here Our focus: how cash is generated from utilizing assets and how it is paid to those who finance the asset purchase. Cash Flow From Assets Cash Flow From Assets (CFFA) = Operating Cash Flow (OCF) – Net Capital Spending (NCS) – Changes in NWC (ΔNWC) Cash Flow From Assets (CFFA) = Cash Flow to Creditors (CF/CR) + Cash Flow to Stockholders (CF/SH) Operating Cash Flow (OCF) = Earnings before interest and taxes (EBIT) + depreciation – taxes Net Capital Spending (NCS) = ending net Fixed Assets – beginning net Fixed Assets + depreciation Net working capital (ΔNWC) = ending NWC – beginning NWC = ending (CA-CL) – beginning (CA-CL)

Cash flow from asset (CFFA) = CF/CR + CF/SH CF/CR = interest paid – net new borrowing CF/SH = dividends paid – net new equity

Time value of money (TMV) Time value of money Fundamental concept in Finance -

Allows us to make sense of and value cash flows that occur at different points in time, e.g. securities like stocks and bonds

The concept -

A dollar in hand today is worth more than a dollar promised at some time in the future

Why? -

The dollar today can be invested to earn a rate of interest, so the final amount is more than one dollar

Implications Same amount of cash flow, e.g. one dollar, at different points in time does not have the same worth -

Need to adjust cash flows at different points in time so they can be compared

Interest rate -

Rate at which we can exchange money today for money in the future

TMV Applications Capital budgeting -

NPV, IRR

Security valuation -

Stocks, Bonds

Personal financial planning

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Calculating mortgage payments Comparing savings schemes Planning for major life events

Present Value (PV) -

The current value of future cash flows discounted at the appropriate discount rate Value at t=0 on a timeline

Future Value (FV) FV t = PV (1 + r) t -

The amount an investment is worth after one or more periods. “Later” money on a timeline

Interest rate (r) -

Discount rate Cost of capital Opportunity cost of capital Required return Terminology depends on usage

Rule of 72 -

Number of years to double amount invested, given a certain interest rate, or Interest rate required for invested sum to double in a certain number of years Rule: Number of years to double money ≈ 72 / interest rate Eg : At 12%, you need 72/12 ≈ 6 years to double your money Double money in 5 years? Need 72/5 ≈ 14.5% return

Compounding periods < 1 year Formula: FV t = PV (1 + r nom / m) mt where t = No. of periods, m = No. of times compounded per period r nom = stated annual rate

Multiple Cash Flows - Future Value Suppose we plan to save $1000 today, and $1000 at the end of each of the next two years. If we can earn a fixed 10% interest rate on our savings, how much will we have three years from today? The timeline would look like this:

Perpetuity -

A stream of equal cash flows each year forever Example: Perpetual bond bond with no maturity PV of perpetuity = Payment / Interest rate = C / r

What is the value of a British consol (a government perpetual bond) that promises to pay £15 each year, forever, if the interest rate is 10%?

PV = £15 / 10% = £150.00 Growing perpetuity - A growing stream of cash flows that lasts forever.

PV = 1.30 / (10% - 5%) = $26.00

Annuity

Amortization A process of finding the payment which when made regularly will repay the loan over the loan period Construct an amortization schedule for a $1,000, 10% annual rate loan with 3 equal payments.

Principal vs Interest - Payments are level. - Interest declines because outstanding balance declines. - Lender earns 10% on loan outstanding, which is falling.

Annuities and Perpetuities Annuity - finite series of equal payments that occur at regular intervals - If the first payment occurs at the end of the period, it is called an ordinary annuity

- If the first payment occurs at the beginning of the period, it is called an annuity due Perpetuity - infinite series of equal payments. Perpetuity: PV = PMT / r Annuities:

Ordinary Annuity - payment comes at end of period Annuity Due - payment comes at beginning of period You can afford $632 per month. Going rate = 1%/month for 48 months. How much can you borrow? You borrow money TODAY so you need to compute the present value.

PV (1%, 48, -632) = $23,999.54

Suppose you win the Publishers Clearinghouse $10 million sweepstakes. The money is paid in equal annual installments of $333,333.33 over 30 years. If the appropriate discount rate is 5%, how much is the sweepstakes worth today?

PV (5%, 30, -333333.33) = $5,124,150.29 You want to receive $5,000 per month in retirement. If you can earn 0.75% per month and you expect to need the income for 25 years, how much do you need to have in your account at retirement? PV (0.75%, (25*12), -5000) = $595,808.11

Interest Rates Effective Annual Rate (EAR) - The interest rate expressed as if it were compounded once per year - Used to compare two alternative investments with different compounding periods Annual Percentage Rate (APR) “Nominal” - The annual rate quoted by law - APR = periodic rate X number of periods per year - Periodic rate = APR / periods per year EAR Formula

APR = the quoted rate m = number of compounds per year APRs Formula APRs = No of compound per yr * rate (%) Which rate should you use to compare alternative investments or loans? Use EAR Which rate do you need to use in the time value of money calculations? Use APR Pure Discount Loans Treasury bills are excellent examples of pure discount loans. - Principal amount is repaid at some future date - No periodic interest payments If a T bill promises to repay $10,000 in 12 months and the market interest rate is 7 percent, how much will the bill sell for in the market? PV (7%, 1, 0, 10000) = $9,345.79

Dollar & Percent Returns Total dollar return = the return on an investment measured in dollars - $ Return = Dividends + Capital Gains - Capital Gains = Price received – Price paid Total percent return = the return on an investment measured as a percentage of the original investment. - % Return = $ Return/$ Invested Dividend Yield

Capital Gains Yield

Historical Average Return = simple, or arithmetic average

Sum the returns for large-company stocks from 1926 through 2011, you get about 10.15/86 years = 11.8%. Your best guess about the size of the return for a year selected at random is 11.8%. Risk Premiums Risk-free rate: - Rate of return on a riskless investment - Treasury Bills are considered risk-free Risk premium: - Excess return on a risky asset over the risk-free rate - Reward for bearing risk Return Variability Review Variance = VAR(R) or σ2 - Common measure of return dispersion - Also call variability Standard deviation = SD(R) or σ - Square root of the variance - Sometimes called volatility - Same "units" as the average

Normal distribution: - A symmetric frequency distribution - The “bell-shaped curve” - Completely described by the mean and variance

Arithmetic vs. Geometric Mean

Arithmetic average: - Return earned in an average period over multiple periods - Answers the question: “What was your return in an average year over a particular period?” Geometric average: - Average compound return per period over multiple periods - Answers the question: “What was your average compound return per year over a particular period?” Geometric average < arithmetic average unless all the returns are equal

Where: Π = Product (like Σ for sum) T = Number of periods in sample Ri = Actual return in each period Arithmetic vs. Geometric Mean. Which is better? The arithmetic average is overly optimistic for long horizons The geometric average is overly pessimistic for short horizons Depends on the planning period under consideration • 15 – 20 years or less: use arithmetic • 20 – 40 years or so: split the difference between them • 40 + years: use the geometric Efficient Capital Markets The Efficient Market Hypothesis: - Stock prices are in equilibrium - Stocks are “fairly” priced - Informational efficiency If true, you should not be able to earn “abnormal” or “excess” returns Efficient markets DO NOT imply that investors cannot earn a positive return in the stock market Forms of Market Efficiency Strong-form Efficient Market: - Information = Public or private - “Inside information” is of little use - Prices reflect all information, including public and private - If true, then investors can not earn abnormal returns regardless of the information they possess - Empirical evidence indicates that markets are NOT strong form efficient - Insiders can earn abnormal returns (may be illegal) Semistrong-form Efficient Market: - Information = publicly available information - Fundamental analysis is of little use - Prices reflect all publicly available information including trading information, annual reports, press releases, etc. - If true, then investors cannot earn abnormal returns by trading on public information

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Implies that fundamental analysis will not lead to abnormal returns

Weak-form Efficient Market: - Information = past prices and volume data - Technical analysis is of little use - Prices reflect all past market information such as price and volume - If true, then investors cannot earn abnormal returns by trading on market information - Implies that technical analysis will not lead to abnormal returns - Empirical evidence indicates that markets are generally weak form efficient

Common Misconceptions about EMH EMH does not mean that you can’t make money EMH does mean that: - On average, you will earn a return appropriate for the risk undertaken - There is no bias in prices that can be exploited to earn excess returns - Market efficiency will not protect you from wrong choices if you do not diversify – you still don’t want to put all your eggs in one basket Expected Returns Expected returns are based on the probabilities of possible outcomes

Where: pi = the probability of state “i” occurring Ri= the expected return on an asset in state i Portfolios Portfolio = collection of assets An asset’s risk and return impact how the stock affects the risk and return of the portfolio The risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets

Portfolio Expected Returns

The expected return of a portfolio is the weighted average of the expected returns for each asset in the portfolio Weights (wj) =% of portfolio invested in each asset

Portfolio Risk Variance & Standard Deviation Portfolio standard deviation is NOT a weighted average of the standard deviation of the component securities’ risk If it were, there would be no benefit to diversification. Portfolio Variance Compute portfolio return for each state: RP,i= w1R1,i+ w2R2,i+ … + wmRm,i Compute the overall expected portfolio return using the same formula as for an individual asset Compute the portfolio variance and standard deviation using the same formulas as for an individual asset

Announcements, News and Efficient markets -

Announcements and news contain both expected and surprise components The surprise component affects stock prices Efficient markets result from investors trading on unexpected news o The easier it is to trade on surprises, the more efficient markets should be Efficient markets involve random price changes because we cannot predict surprises

Returns - Total Return = Expected return + unexpected return R = E(R) + U -

Unexpected return (U) = Systematic portion (m) + Unsystematic portion (ε)

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Total Return = Expected return E(R) + Systematic portion m+ Unsystematic portion = E(R) + m + ε

Systematic Risk - Factors that affect a large number of assets - “Non-diversifiable risk” - “Market risk” - Examples: changes in GDP, inflation, interest rates, etc.

Unsystematic Risk

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= Diversifiable risk Risk factors that affect a limited number of assets Risk that can be eliminated by combining assets into portfolios “Unique risk” “Asset-specific risk” Examples: labor strikes, part shortages, etc.

The Principle of Diversification - Diversification can substantially reduce risk without an equivalent reduction in expected return o Reduces the variability of returns o Caused by the offset of worse-than-expected returns from one asset by better-thanexpected returns from another - Minimum level of risk that cannot be diversified away = systematic portion Portfolio Conclusions - As more stocks are added, each new stock has a smaller risk-reducing impact on the portfolio o σpfalls very slowly after about 40 stocks are included o The lower limit for σp≈20% = σM.  Forming well-diversified portfolios can eliminate about half the risk of owning a single stock. Total Risk = Stand-alone Risk Total risk = Systematic risk + Unsystematic risk - The standard deviation of returns is a measure of total risk - For well-diversified portfolios, unsystematic risk is very small  Total risk for a diversified portfolio is essentially equivalent to the systematic risk Systematic Risk Principle - There is a reward for bearing risk - There is no reward for bearing risk unnecessarily - The expected return (market required return) on an asset depends only on that asset’s systematic or market risk. Market Risk for Individual Securities - The contribution of a security to the overall riskiness of a portfolio (Beta measures systematic risk) - Relevant for stocks held in well-diversified portfolios - Measured by a stock’s beta coefficient, βj - Measures the stock’s volatility relative to the market Interpretation of beta - If β= 1.0, stock has average risk, it suggests the portfolio/stock is uncorrelated with the market return - If β> 1.0, stock is riskier than average, it suggests that the portfolio has a positive correlation with the market, but would have price movements of greater magnitude - If β< 1.0, stock is less risky than average, it suggests the portfolio/stock has an inverse correlation with the market return. - Most stocks have betas in the range of 0.5 to 1.5 - Beta of the market = 1.0 - Beta of a T-Bill = 0 - The higher the beta, the greater the risk premium should be

Portfolio Beta βp= Weighted average of the Betas of the assets in the portfolio Weights (wj)= % of portfolio invested in asset j

Reward-to-Risk Ratio -

Reward-to-Risk Ratio:

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= Slope of line on graph In equilibrium, ratio should be the same fo...