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FINANCE 363 FINAL STUDY GUIDE

History of Finance

∙ Finance: the field that deals with the study of investments

∙ Finance is a technology that enables the allocation of resources over time ∙ Emerged in Mesopotamia around 3,000 BCE

∙ Babylonia 2000 BCE

o Temples collected deposits/made loans

o Emergence of banking

∙ Code of Hammurabi – 1754 BCE

o Law 88: a merchant may collect interest of 33 and 1/3 percent on a loan of grain and 20% interest may be charged on a loan of silver o Law 48: if a person is in debt and loses a crop because of a natural disaster the contract shall be changed so that person will not owe the creditor any interest for the year If you want to learn more check out What are the differences between civil and criminal cases?

o Emergence of central banking and financial regulation

∙ Ancient Greece – 4th century BCE

o Athens had population in 100,000s and had outgrown its local agricultural capacity

o Long/risky voyages to import crops

o Wealthy citizens invested in voyages

o Emergence of partnerships

∙ Renaissance Europe- birth of modern financial system

o In 1172 Venice issued 1st government bond

o In 1300s beginning of bond market in Venice

o Honor del Bazacle- 1372

World’s first modern corporation

o Amsterdam Bourse- 1602

First modern stock market

What does finance do?

We also discuss several other topics like How to identify cash inflows and outflows?

1. It reallocates capital

2. It reallocates risk

3. It reallocates economic value through time

The Financial System

∙ Purpose: to efficiently move funds from those with a surplus (suppliers) to those with a need (users)

Financial Markets

∙ Transfer money from the suppliers to users of capital through trading of securities

∙ Security: a transferable instrument representing rights to debt or ownership interest

o Debt securities that represent money that is borrowed and must be repaid or with terms that define the amount borrowed, interest rate, and maturity date

o Equity securities (or stock or share) that represent ownership interest held by shareholders in a corporation

FINANCE 363 FINAL STUDY GUIDE

Profits from increases in the value of their ownership interest (capital gains)

No maturity date

∙ 2 types of markets by the maturity of securities Don't forget about the age old question of Who is armstrong williams?

o Money markets: the market for short-term securities

Maturity ranging between overnight and 1 year

Typically debt instruments

Very liquid and low cost source of short-term funds

Issued by companies, banks, and governments in need of short term financing

o Capital markets: the market for long-term securities

Original maturity of more than a year

Long-term bonds and equity

Issued by companies, banks, and governments for long-term capital needs

∙ 2 types of markets by the identity of the seller: If you want to learn more check out Who is gavrilo princip?

o Primary markets

For securities offered for sale by the issuer for the 1st time

Issuer (corporation or government) receives the funds

Important source of external capital for businesses

Intermediated by investment banks due to severe information asymmetry problems between issuers and investors

IPO (initial public offering): when a firm 1st offers shares to the public and becomes a public company

SEO (seasoned equity offering): when an already public Don't forget about the age old question of Who is thomas hobbes?

Don't forget about the age old question of How did eratosthenes measure the size of the earth?

company sells more shares to the public to raise more capital

o Secondary markets

For securities traded among investors after their initial sale

Proceeds from the sale go to the selling investor, not issuer

Provide the means for investors to tailor their investment

horizons

Investors may want to sell to other investors

Efficiency: Accurate pricing of securities

Liquidity: easy to buy/sell without affecting the price too much ∙ 2 Types of Markets by whether Trading is centralized

o Auction markets: Centralized

All trading funnels through one location

Trading managed by a single “specialist” for each security

Only 1 best price for a given security at a given time

Example: New York Stock Exchange

o Dealer Markets: Decentralized

Trading takes place in a variety of places

Managed by a number of dealers (“market makers”) in each security

Brokers’ responsibility to find the best deal

Example: NASDAQ (National Association of Securities Dealers Automated Quotation)

FINANCE 363 FINAL STUDY GUIDE

Financial Intermediaries

∙ Suppliers and users of capital usually transact through a variety of “financial intermediaries”

∙ Mutual Funds: buy a large number of publicly traded stocks and bonds on behalf of their investors

∙ Hedge Funds: invest in any kind of investment to maximize returns ∙ Pension Funds: manage retirement savings

∙ Endowments: manage funds donated to the university to support the university’s budget

∙ Venture capital funds: buy stock of private high-tech start-up entrepreneurial firms

∙ Private equity funds: purchase a whole company using large amounts of debt

Summary

∙ Finance isn’t all good or bad

∙ Good

o Engine of economic growth and innovation by allocating society’s savings into their most efficient use

o Democratizes entrepreneurship and investing

o Reduces household economic risk

∙ Bad

o Excessive debt

o Market bubbles resulting in financial crises and crashes

o Financial fraud, Ponzi schemes, etc

Formulas to know:

Simple interest = PV x i

Future value with compounded interest: FVn = PV0 x FVIFi,n where FVIFi,n = (1+i)n FVn = PV0 x (1+i)n

Total interest earned (or owed): Interest = FVn – PV0

Solving for the interest rate: i = [FVn / PV0]1/n – 1

Solving for the number of years: n = ln(FVn/PV0) / ln(1+i)

FV with non-annual compounding: FVn=PV0 x [1+ (i/m)]nxm

Effective interest rate: EIR = [1 + (i/m)]m – 1

Present value of a single sum: PV0 = FVn x PVIFi,n where PVIFi,n = 1/(1+i)n PV0 = FVn / (1+i)n

PV with non-annual compounding: PV0=FVn/[1+(i/m)]nxm

FINANCE 363 FINAL STUDY GUIDE

Capital Budgeting

∙ Firms must allocate limited funds in a way that maximizes firm value ∙ Process of deciding which investments and projects a firm should acquire in pursuit of that goal

FINANCE 363 FINAL STUDY GUIDE

∙ Good investments increase firm value, bad investments destroy value Techniques for Analyzing Projects

Method

Description

Equation

Decision Criteria

Payback Period

Number of years required to

recapture initial investment

initial investment

annual cash flow

None

Net Present Value

Present value of all cash flows

PV (cashinflows)−PV

Accept if greater ( cashoutflows) than or equal to 0

Profitability Index

The ratio of the present value of the cash inflows to outflows

PV (inflows)

PV ( outflows)

Accept if greater than or equal to 1

Internal Rate of Return

The interest rate that sets the

present value of the cash inflows equal to the

present value of the outflows

Calculator or

spreadsheet

Accept if greater than or equal to cost of capital

Modified Internal Rate of Return

The interest rate that sets the

present values of the outflows equal to the future

values of the

inflows, computed at the firm’s cost of capital

Calculator or

spreadsheet

Accept if greater than or equal to cost of capital

The appropriate Discount Rate

∙ Risk-free rate: we need to be compensated for inflation

∙ Risk premium: risk-averse people require extra compensation for taking on risk

∙ Discount rates increase (and present value decreases with)

o Higher expected inflation

o Greater risk

o Greater risk aversion

The Risk-Return Relationship

∙ Investors estimate an asset’s risk, based on the uncertainty of future cash flows

∙ Use the appropriate discount rate to establish a price that compensates for holding an asset with that level of risk

FINANCE 363 FINAL STUDY GUIDE

∙ Higher risk higher required returns higher discount rate lower price today greater expected return

∙ Too low a discount rate valuation too high returns too low ∙ Too high a discount rate valuation too low you turn down or miss out on too many profitable opportunities

∙ Different labels for discount rate

o Bonds – bond yield

o Stocks – investors’ required return

o Capital budgeting – hurdle rate or firm’s cost of capital

Holding Period Return

∙HPRi=ending price−beginning price+dividends

beginning price

∙ HPR = capital gains + dividend yield

Multi-period returns

∙HPRtotal=(1+HPR1) (1+HPR2)…(1+HPRn )−1

∙ HPRtotal=(adjusted ending value

adjusted beginnning value)-1

Average Returns

∙ Arithmetic Average Return: average return ignoring compounding

1

nk1+k 2+…+k n

o

n∑i=1

n

∙ Geometric (compound) average return: Average return incorporating compounding

o(HPRtotal+1)1/ n−1

1

o (ending value

beginning value )

n−1

Computing Expected Returns

∙ Expected returns: Investors’ evaluation of the probable yield of an investment ∙ Historical Analysis: Expected return = arithmetic average return observed in the past

oE( k )=(k1+k2+…+k n)/ n

∙ Scenario Analysis: expected return = weighted average of possible future outcomes

oExpected Return=E (k )=Pr 1k1+Pr2k2+…+Pr nkn

FINANCE 363 FINAL STUDY GUIDE

Computing Standard Deviation

∙standard deviation=√∑i=1n(ki−E (k ))2∗Pri

∙ Historical analysis

n−1∑i=1n(ki−E (k ))2

o standard deviation=√1

o Computing the standard deviation using historical analysis is equivalent to conducting a scenario analysis with each historical data point treated as a potential future outcome with a probability of 1/(n-1)

Computing the Expected Return for a Portfolio of Assets

∙ Portfolio is a collection of assets

∙portfolioweight=wi=amountinvested∈i

total amount invested

∙expected return on portfolio=E ( k p)=w1 E( k1)+w2 E( k2)+…+wnE ( kn )

Evaluating Risk of a Portfolio of Assets

∙ Portfolio returns=weighted sum of individual asset returns

∙ If one asset is moving up while the other is moving down, these two assets will at least partially offset each other

∙ Measuring how closely assets are correlated becomes important in constructing a portfolio

Diversification

∙ The act of giving something variety

Portfolio Risk

∙ We need to know

o Risk of the component stocks

o Weights of the component stocks

o Degree to which they move together

∙ Correlation

o A relationship between observations, in which the movement over time of one item is related to the movement of another

Correlation

∙ Measures the degree to which assets’ returns share common risks ∙ The correlation coefficient varies between -1 (perfectly negative correlation) and +1 (perfectly positive correlation)

FINANCE 363 FINAL STUDY GUIDE

oPX ,Y=σX ,Y

σXσY

Volatility of a portfolio with two assets

∙ Portfolio return is the weighted average of the returns of component securities

ok p=wk1+(1−w) k 2

∙ Portfolio standard deviation is typically not the weighted average standard deviations of component securities

o σp=√w2σ12+(1−w)2σ22+2w(1−w)ρ1,2σ1σ2

Volatility and Returns

∙ Portfolio volatility is lower than individual assets’ volatilities ∙ Strong positive relation between portfolio volatility and returns ∙ Weak/no relation between individual volatility and returns

Types of Risk

∙ Diversifiable risk

o Risk that can be eliminated through diversification

o Caused by events that affect 1 or few firms

o Also called unsystematic or firm-specific risk

∙ Non-diversifiable risk

o Risk that cannot be eliminated through diversification

o Caused by events that affect all assets to some extent

o Measured by beta

o Also called market risk or systematic risk

Total risk=non-diversifiable risk + diversifiable risk

o Diversification is “free”

Investors should not expect to earn higher returns for bearing diversifiable risk they can diversify away

The only way to get higher returns is by bearing non

diversifiable risk

Risk-averse investors’ optimal portfolios will be fully diversified o Reflects vulnerability to events that affect aggregate outcomes Recession

o Good way to evaluate an asset’s systematic risk is to measure its movements with the broad stock market (market portfolio)

Beta

Beta

∙ Graph the asset’s returns against the returns on the market portfolio ∙ Slope of the line of best fit (characteristic line) is the asset’s beta

FINANCE 363 FINAL STUDY GUIDE

k i, k M

¿

o

Cov ¿ βi=¿

oβi=ρi , M σi

σM

∙ Many points don’t fall on the characteristic line due to the asset’s diversifiable risk

∙ Properties

∙ Captures the change in an asset’s return for each 1% change in the market return

∙ The market’s beta is 1

∙ The risk free asset’s beta is 0

Addition of borrowing to portfolio

∙ Buying on margin

o Borrowing to buy more assets than you can afford with your own money

o Typically from a broker

Treynor Index

∙ Slope of the portfolio-possibility line can be used as a performance metric for evaluating risky investments

∙ “How much risk premium (excess return) am I earning for the amount of risk I am bearing?”

o Treynor Index=E (k i)−kF

βi

∙ Market equilibrium: the treynor indexes of all assets are equal ∙ Market Treynor Index=E ( k M)−kF

o Market risk premium

CAPM

k

k¿

(¿ M ¿)−k F

∙

E¿

E(¿¿ i)=k F+βi∗¿ ¿

∙ Implies a linear relation between expected return and β for all capital assets ∙ If markets are efficient, meaning that all assets are correctly priced, the 2 are the same and the asset is on the SML

FINANCE 363 FINAL STUDY GUIDE

∙ If an asset is mispriced

o Expected return > CAPM required return asset is above the SML buy the asset until expected return falls

o Expected return < CAPM required return asset is below the SML sell (or short-sell) the asset until expected return goes up

Introduction to bonds and interest rates

∙ Bond: a type of debt security issued in connection with a borrowing arrangement

∙ Similar to a loan except:

o Loan: the lender typically holds loan until maturity

Often 1 lender or a small group of lenders participate in a loan o Bond: the lender can sell the bond to other investors before maturity Often a large number of bondholders participate in a bond

issuance

∙ Typical coupon bond: issuer (borrower) makes semi-annual interest payments (coupon) to the bondholder for the life of the bond plus a lump-sum payment (par value or face value) at maturity

o Zero coupon bonds: no interest payment until maturity

Debt Markets

∙ Money markets

o Market for bonds with short maturities

1 year or less

o Very liquid, relatively safe debt instruments

o US Treasury bills

o Commercial paper

∙ Bond markets

o Market for debt instruments with long maturity

More than 1 year

o Coupon or zero-coupon

o US treasury notes and bonds

Zero-Coupon Bonds

∙ Promises holder a fixed sum of money (face value or par value of the bond) at a fixed date in the future (bond maturity)

∙ Typically sell at a discount to their face value

∙ Return

1

ok=(FV

Price )

n−1

o Yield to maturity or yield

∙ Yield curve: term structure graphed against respective maturities o Expectations theory:

Long term spot rates reflect market’s expectations about future short term rates

o Liquidity preference:

FINANCE 363 FINAL STUDY GUIDE

Issuers prefer to borrow for long maturities, investors prefer to lend for short maturities

∙ Lower rates in the short term, higher rates in the long

term

o Normal yield curve: upward sloping with maturity

steep yield curve implies higher expected short term rates in the future

this is a positive signal since higher future rates indicate

increasing productivity of capital

Steep yield curves have historically preceded economic upturns o Flat yield curve: spot rates don’t vary much with maturity

Flat curve despite liquidity preference

Implies declining short term rates in the future

∙ Negative signal

Signals economic slowdown

o Inverted yield curve: downward sloping

Significantly lower rates in the future

∙ Very negative signal

12-18 months before recession

∙Price=FV

(1+k n)n

Coupon Bond

∙ Debt instrument which pays periodic interest payments to the holder and pays the final lump sum (face value) at maturity

∙ Convertible bond

o A corporate bond which allows the holder the right to convert the bond into a fixed number of shares in the company

∙ Callable bond

o The issuer has the right to force early redemption of the bond o When called the holder must return the bond in exchange for the FV of the bond and possibly a premium

∙ Foreign bond

o Bonds issued by an entity in a foreign country and in that country’s currency

∙ Floating rate bonds

o Coupon rate fluctuates with some benchmark rate

∙ Coupon bond cash flows

o Coupon rate

The annual dollar value of the coupons divided by the FV of the bond

Annual coupon amount = coupon rate x face value

Each coupon amount = coupon rate x face value / number of coupons per year

∙ Coupon bond price

FINANCE 363 FINAL STUDY GUIDE n Ct

oPbond=∑t=1

Yield to Maturity

(1+k t)t+FV (1+k n)n

∙ What return will the bond holder earn if she holds the bond until maturity? ∙ Single rate which discounts the bond’s cash flows such that PV=Pbond ∙ Common rate for all maturities

n Ct

∙Pbond=∑t=1

(1+k d)t+FV (1+k d)n

∙Pbond=C∗PVIFAn ,k d+FV (1+k d)n

1−1

o PVIFAn ,k d=

(1+kd)n k d

Non-annual Coupon Bonds

∙Pbond=C/m∗PVIFAn∗m, k d/m+FV (1+k d/m)m∗n

C/m∗1−1

(1+kd/m)m∗n

∙ Pbond=

kd/m+FV (1+k d/ m)m∗n

Coupon Bond Price Properties

∙ Par value bond: bond price=FV

o Coupon rate = YTM

o All bonds trade at par right before they mature

∙ Discount bond: bond price < FV

o YTM > coupon rate

o Discount bonds’ price goes up to FV as bond approaches maturity ∙ Premium bond: Bond price > FV

o YTM < coupon rate

o Bonds price goes down to FV as bond approaches maturity

Bond Price Changes over Time

∙ HPR = (End price-Beg Price + Earnings paid)/ Beg Price

o Earnings paid = coupon payments

∙ If YTM stays the same, we earn the YTM despite selling early ∙ If YTM goes up before we sell the ending price is lower

∙ If YTM goes down before we sell the price is higher

FINANCE 363 FINAL STUDY GUIDE

Bond Duration

∙ Macaulay Duration

o Weighted average maturity of cash flows n

∑

t∗Ct

o

MacD=

( 1+k d)t+n∗FV

t=1

(1+k d)n

Pbond

o Useful to estimate bond price sensitivity to yield changes

o Used to ensure that the firm’s assets and liabilities have similar duration and similar interest rate risk

∙ Modified Duration

o Bond price sensitivity to yield changes

oModD=MacD

(1+k d)

o∆ Price=(−1)∗Price∗∆ kd∗ModD

Stock Valuation & Market Efficiency Definitions

∙ Equity

o Ownership interest in an entity

o Equity value goes up if the entity becomes more valuable, vice versa ∙ Stock

o A company can raise equity capital by selling a portion of its ownership to investors by issuing stock

∙ Share

o A company’s stock is divided into shares

Two Types of Equity Securities vs. Debt

CASH FLOWS PRIORITY (SENIORITY)

TIME

HORIZON

VOTING RIGHTS

DEBT Coupons (guaranteed)

Highest Finite maturity No

PREFERRED STOCK

Dividends (typically guaranteed)

Middle Perpetual (typically)

No

COMMON STOCK

Dividends (not guaranteed)

Lowest Perpetual Yes

Valuation of Preferred Stock

∙ Simple preferred stock that pays fixed dividends in perpetuity oPPreferred=Dk

FINANCE 363 FINAL STUDY GUIDE

Valuation of Common Stock

∙ DCF valuation

o Based on the idea that every asset has an intrinsic value driven by its fundamentals (cash flows)

o Discount forecasted dividends using firm’s cost of equity

o Discount forecasted FCFE using cost of equity

o Discount forecasted FCFF using firm’s cost of capital, then subtract the value of debt and preferred stock

oP0=D1

1+k+P1

1+k

∙ Relative valuation

o Based on how the market prices similar assets

Generalized Dividend Valuation

∙ Based on the idea that stock price is the present value of all future dividend payments

∞ Dt

∙P0=∑t=1

(1+k )t

∙ Constant Growth Model

o Based on the assumption that dividends grow at a constant rate forever

o P0=D0∗(1+g)

k−g=D1

k−g

og=(D0 D−n)

1/ n

−1

Free Cash Flow Valuation

∙ Ideal cash flow measure: FCFE

∙ FCFE = Net Income + Cash-flow adjustments

∙P0=FCFE1

1+k+FCFE2

(1+k )2 …

Valuation Multiples

∙ When CF projections are unreliable, we need an alternative methodrelative valuation

∙ Price-to-Earnings Ratio

oPE=P0

EPS

o P0=EPS1

k−g

FINANCE 363 FINAL STUDY GUIDE

Efficient Market Hypothesis

∙ Efficient market

o Market where securities are priced fairly at all times and new info is rapidly reflected in the price

o “Fair” price: reflecting firms’ intrinsic value without systematic bias o Many competitive, informed investors

o Investors with the same goal of locating securities offering the highest risk-adjusted returns

o Investors that are reacting rapidly and accurately to new information ∙ Inefficient market

o Price adjustments are slow

o Price movements are unpredictable based on past information o Similar securities have different prices

∙ Implications

o Keep trading to a minimum

Lower trading commissions

Lower taxes

Lower likelihood of making a mistake

Weighted Average Cost of Capital

∙ Firms can issue debt (bank loan, bonds) or stock (preferred, common) ∙ Cost of capital is the required return of the investors’ providing that capital ∙ WACC

o Captures the average cost of funds for firm’s projects

o Computed as weighted average cost of debt and stock financing, using the long-term target weights from the balance sheet

After-tax Cost of Debt

∙ Interest on debt is a tax deductible expense for firms

∙ After-tax cost of debt = (1-T)kd

Cost of Preferred Stock

∙k p=Dp/ Ppreferred

Cost of Common Stock

∙ Often the most expensive source of financing due to increased risks faced by outside investors

∙ Cost of equity comes from having to sell ownership interest at a relatively low price

∙ Three methods to find cost of equity

k

o CAPM:

(¿¿ i)=k F+β[E ( k M )−kF] ke=E ¿

Challenging to forecast the expected market risk premium

FINANCE 363 FINAL STUDY GUIDE

o Constant growth model: k e=D1

P0+g

Works for firms paying steadily growing dividends

o Premium over Bond Yield: k e=k d+θ

Usually for firms with bonds outstanding

Computing the WACC

∙ WACC=wdk d(1−T )+wpk p+weke

∙ Total firm value: V = D + P + E

FCFF Valuation

∙ Very similar to D and FCFE valuation except

o FCFF is the cash flow measure

o WACC is the discount rate

o Measures entire firm value, so the market value of debt must be subtracted at the end

∙P0=FCFF1

1+WACC+FCFF2

(1+WACC)2 …−MV of Debt−MV of Preferred

FINANCE 363 FINAL STUDY GUIDE

Chapter 3 (TVM)

∙ Future and present values of sums and mixed streams

∙ Solving for the interest rate

∙ Solving for the number of periods

∙ Non-annual compounding and the Effective interest rate (EIR)

Chapter 4 (Annuities and Loans)

∙ Future and present values of annuities

∙ Present value of perpetuities

∙ Solving for payment (PMT)

∙ Solving for the number of payments

∙ Imbedded annuities

∙ Balloon and amortized loans

Chapter 9 (Capital budgeting)

∙ Payback period

∙ Net present value

∙ Profitability index

∙ Modified internal rate of return (MIRR)

Chapter 5 (Risk and return)

∙ Holding period return (HPR), capital gains yield, dividend yield ∙ Multi-period HPR, arithmetic and compound average returns ∙ Expected return of a single asset (Historical and scenario analysis) ∙ Standard deviation of returns of a single asset (Historical and scenario analysis)

∙ Portfolio weights and portfolio returns

Chapter 6 (Portfolio theory)

∙ Portfolio standard deviation

∙ Correlation coefficient

∙ Estimating beta

∙ Treynor index and the capital asset pricing model (CAPM) ∙ Portfolio beta

∙ Buying on margin

Chapter 7 (Interest rates and bonds)

∙ Zero coupon bond pricing

o Find yield given price

o Find price given yield

∙ Coupon bond pricing

o Find price given the term structure

o Find price given the yield-to-maturity

o Find price for coupon bond with non-annual coupons

∙ HPR of bond holdings

∙ Bond duration

FINANCE 363 FINAL STUDY GUIDE

o Macaulay Duration (MacD)

o Estimate the change in bond price given MacD

Chapter 8 (Stock valuation and market efficiency) ∙ Valuation of preferred stock

∙ Stock valuation using DCF methods

o Methods: One-period, constant-growth, non-constant growth o Cash flows: Dividends and free cash flow to equity (FCFE) ∙ Valuation multiples and relative valuation

Chapter 11 (Cost of capital)

∙ Computing the weighted average cost of capital (WACC) ∙ Stock valuation using FCFF discounting

Typical numerical question distribution in past final exams ∙ Chapters 3 and 4 (TVM): 2 questions

∙ Chapter 9 (Capital budgeting): 2 questions

∙ Chapter 5 (Risk & Return): 4 questions

∙ Chapter 6 (Portfolio theory): 4 questions

∙ Chapter 7 (Bond valuation): 4 questions

∙ Chapter 8 (Stock valuation): 4 questions

∙ Chapter 11 (Cost of capital): 2 questions