FIN 300 Session

FIN 300 Session Ryerson SOSAgendaRecap Time Value of Money (TVM)BondsShares and DividendsCapital BudgetingPortfolio Theory

Time Value of Money TVMAPR Interest rate as if it was compounded once a yearDoes not consider compoundingAlso known as the Nominal RateTime Value of Money TVMEffective Annual Rate (EAR) Adjusted annualized interest rate that considers compounding. EAR = (1+APR/n)n 1 N = Number of compounding per year.

4Time Value of Money TVMEffective Periodic Rate (EPR) Interest rate that considers compounding and the number of payments per year. EPR = (1+EAR)t - 1 T = (1 / Number of payments per year)

5Using the P/Y & C/Y Calculator Function If we use the P/Y & C/Y function, there is no need to convert the annual rate into EPR.P/Y Payments per yearC/Y Compounding per yearExample: TVM If SOS invests $100 per month for 2 years at 10% compounded semiannually, how much will it have at the end of 2 years?EAR = 10.25 EPR = .8165N=24 I/Y=.8165 C/Y P/Y=1 PV=0 PMT=100 FV= 2,639Example: TVM If SOS invests $100 Per month for 2 years at 10% compounded semiannually, how much will it have at the end of 2 years?N=24 I/Y=10 C/Y = 2 P/Y=12 PV=0 PMT=100 FV= 2,639Valuing PerpetuitiesPerpetuity Annuity in which the cash flows continue forever. Formula:

Valuing Growing PerpetuitiesFormulaExample:Homer promises to give you $100 every year forever. Homer promises to pay you a 10% return compounded annually. Homer also states that the $100 will grow at a rate of 4%. What is the present value of Homers offer? = (100) / (.10-.04) --> $1666.67

MortgagesMortgages = AnnuitiesExample: You get a $200,000, 30 Year mortgage. SOS Bank offers you a 10% loan compounded weekly. You agreed to make weekly payments. How much are the mortgage payments? Mortgage ExampleN= (30 X 52) 1,560 I/Y= 10% P/Y = 52 C/Y= 52 PV = $200,000 FV = 0 Payment = $404.83ORN = 1,560 I/Y= .19231% P/Y = 1 C/Y= 1 PV = $200,000 FV = 0 Payment = $404.83

Mortgage ExampleHow much do you owe SOS Bank after 2 years (104 payments)?N= (28 X 52) 1,456 I/Y= 10% P/Y = 52 C/Y= 52 FV = $0 PMT= 404.83 Present Value = $197,674ORN = 1,456 I/Y= .19231% P/Y = 1 C/Y= 1 FV = 0 PMT= 404.83 Present Value = $197,674

BondsWhat is a bond? A bond is an IOU issued by a corporation, government, or governmental agency.As a bondholder, you are a creditor.BondsKey Terms:Coupon Rate Stated interest payments made on a bond.Yield to Maturity (YTM) Also known as the market rate.This is the rate we use to discount the coupons and the face value of the bond. Bond Valuation Example 1You purchased a SOS 9% bond with 10 years to maturity. The bond makes semiannual payments and it has a YTM of 9%. What is the value of the bond today?N= (10x2) 20 I/Y= 9% P/Y = 2 C/Y=2 FV = $1,000 PMT= 45 (9% x $1,000 / 2) Present Value = $1,000

Bond Valuation Example 2You purchased a SOS 9% bond with 10 years to maturity for $1060. The bond makes semiannual payments. What is the YTM of the bond? N= (10x2) 20 P/Y = 2 C/Y=2 FV = $1,000 PMT= 45 (9% x $1,000 / 2) PV= ($1,060) APR (I/Y) = 8.11%

Bond Valuation Example 3You purchased a SOS bond with 10 years to maturity for $920. The bond makes semiannual payments and it has a YTM of 10%. Compute your semiannual coupon payments N= (10x2) 20 I/Y = 10% P/Y = 2 C/Y=2 FV = $1,000 PV= ($920) Payments = 43.58 or 8.72%

Remember When the coupon rate is HIGHER than the YTM, the bond will sell at a premium. (above par).When the coupon rate is EQUAL to the YTM, the bond will sell at par.When the coupon rate is LOWER than the YTM, the bond will sell at a discount (bellow par).

Zero Coupon BondsAlso called stripped BondA bond that makes no coupon paymentsSells at a deep discountThis type of bonds sell at a deep discountZero Coupon Bonds ExampleSuppose SOS issues a $1000 face value, 10 year strip bond. What is the price of the bond today if the YTM is 10%?N= 10 I/Y= 10% P/Y = 1 C/Y=1 FV = $1,000 PMT= 0 Present Value = $653.32The bond sell at a deep discount because there is no coupon payments.

Chapter 8Stock ValuationTVM is used in the dividend discount modelRequired rate of returnTypes of dividendsConstantGrowingSupernormal growthChapter 8Stock ValuationRequired rate of returnreturn the market requires from this investmentDifferent than risk-free rate because equity investment is more riskyConsider this the same as r in TVM formulas

Chapter 8Stock ValuationYou should have a solid grasp of TVM and cash flows by now, so focus on how to apply this knowledge to stock valuation

Zero Growth DividendDividend does not changeThink of this as a perpetuity with D being the cash flow and r being the rate of interest

Zero Growth DividendDividend does not changeThink of this as a perpetuity

Zero Growth DividendExample: SOS Common will be paying a dividend of $3 forever. The rate of return required for SOS Common stock is 12%. What should you pay for SOS?

Zero Growth DividendExample: The price of RSOS common stock is $30 and the required rate of return is 10%. What constant dividend is RSOS paying?

Constant Growth DividendThe dividend keeps growing at a constant rate foreverThis is the same as a constant growth perpetuity: D is the cash flow, r is the rate and g is the growth rateNote the difference between D0 and D1_

Constant Growth DividendAlso called dividend growth modelP0 is the current stock priceD0 is the current dividendD1 is the next dividendg is the growth rate of the dividendr is the required return from the equity

Constant Growth DividendYou may also see the formula in the form belowPt is the price at time tDt is the dividend at time t

Constant Growth DividendExample: SOS common stock will pay a dividend of $2 next year. The dividend will increase by 5% a year after that. Required rate of return is 15%. What is the value of SOS today? What is the value of the stock in five years?D1 = $2, g=.05, r=.15 P0=???, P5=???Constant Growth DividendD1 = $2, g=.05, r=.15 P0=???

We now have to find the price in five years

Constant Growth DividendD1 = $2, D5 = ???, g=.05, r=.15 P5=???What will the dividend be in five years?

We now have to find the price in five years

Non-Constant Growth DividendIn real life dividends often vary from quarter to quarter and year to yearNeed a way to price these equities with non-constant growth dividendsThe solution: use TVM and the dividend pricing formulasAlready know how to discount cash flows back to PV and that is what this process does

Non-Constant Growth DividendThe best way to show this process is to do an exampleSOS common stocks dividend has been growing at 50% and will continue to grow at this rate for the next five years. After five years the dividend will only grow at the rate of 5% per year. What is the price of the stock now?

Non-Constant Growth DividendSOS common stocks dividend has been growing at 50% and will continue to grow at this rate for the next two years. After two years the dividend will only grow at the rate of 5% per year forever. Required return for this stock is 10%. If they just paid a dividend of $1, what is the price of the stock now?D0 = $1, g1=50%, g2=5%, r=10%P0=???

Non-Constant Growth DividendD0 = $1, g1=.50, g2=5%, r=.10 P0=???Find first two dividends (1+g1)=1.50D1=($1*1.50)=$1.50D2=($1.50*1.50)=$2.25Now we have to find price for the constant growth period

Non-Constant Growth DividendD2 = $2.25, g1=.50, g2=5%, r=.10

Discount all cash flows to t0 to find price of stock

Common and Preferred StockCommon StockRight to share proportionally in dividendsRight to share assets after liabilities have been paid i.e. bond and debt holdersRight to vote on matters of great importance e.g. mergerSometimes have preemptive right to by new stock sold first

Common and Preferred StockPreferred StockPreference over dividend paymentMust receive dividend before common shareholdersPreference over division of assets if company gets liquidatedUsually have no voting privileges

DividendsSome legal stuff about themNot a liability unless declared by the board of directorsNot a business expenseNot tax deductible for corporationPaid out of after tax profitsDividends are sheltered in Canada by a tax credit

Chapter 8Stock ValuationTricks: Prof may ask an over or under questionGive a stock price and information to find price and ask if stock is over or undervaluedRemember to discount cash flows properly with supernormal growth dividendsPay attention to which dividend you are given or required to solve for i.e. D0 or D1Pay attention to which price you are given or required to solve for i.e. P0 or Pt Know the difference between required rate of return and risk free rate

Chapter 8Stock ValuationStudy tips: Do supernormal growth questions in text bookCapital BudgetingThe process of planning and managing a firms investment in long term assets. Methods:Net Present Value (NPV)Internal Rate of Return (IRR)Payback PeriodProfitability IndexNPV and IRRNPV and IRR use the discounted cash flow methods to make a decision and rank projects.IRR is the discount rate that makes the NPV of an investment ZERO If the NPV > 0, Then accept project.If IRR is > required rate return, then accept project.Capital Budgeting Example:YearCash Flows0($100,000)1$60,0002$70,0003$50,000Compute the NPV and IRR of the above cash flows. Assume a 15% required rate of return.

NPV = $37,980 IRR= 37.42%

Capital Budgeting ContUse only incremental cash flows only. Sunk costs (Costs that have already been incurred) are not considered in an investment decision.Cost of old equipment. Net Present ValueThe List ApproachCapital CostPV of SalvageInitial Net Working Capital (NWC)Change in NWCPV of Operating Cash FlowsPVCCATS Loss CCATS due to Salvage ValueList Approach Example:3 Year Project$1,000,000 Initial Investment, with a salvage of $576,000 after 3 years.The project also requires a $100,000 investment in NWC. After Tax incremental income = $240,000Tax rate: 40% Rate of Return (After Tax): 10% CCA Rate: 20%

List Approach Example:($1,000,000)$432,757($100,000)$75,131$596,844$139,144 NPV=$143,876 NPVCost Cutting ProblemABC is considering buying a machine to cut cost and speed up production. The new machine would cost $15,000 with an additional $800 installation cost. The Machine would allow ABC to produce and sell an additional 25 machines per year. The machines are produced at a cost of $1000 and sold for $1,800. The new machine is expected to last 8 years and has a 30%CCA Rate. Its salvage value is estimated to be $3,000 at the end of 8 years. ABCs corporate tax rate is 35%. Assume a 10% discount rate.

NPVCost Cutting Problem($15,000)$1,40000$69,354$3,592NPV = $58,546

NPV Replacement ProblemHomer Sampson owns a bar in downtown Toronto. Two years ago he replaced all his beer dispensers (Kegs) for the newest models available, making an investment of $400,000. However, a month ago a new, technology enhanced model was released onto the market. This model cools and dispenses the beer faster and better than any other model in the market. As a result, Homers old machines are quickly loosing value and are now worth only $35,000. In 10 years they will be only worth $5,000. The new dispensers would have a cost of $700,000 and would increase revenues by 65,000 annually. The new dispensers have a 10-year life and an expected salvage value of $115,000. The tax rate is 39%, CCA rate is 25% and the required rate of return is 14%.

NPV Replacement Problem*Remember to only consider Incremental Cash flows*($665,000)$29,672$0$0$206,819148,624 NPV = (279,885)

Chapter 12Capital Market HistoryTotal dollar return = Dividend income + Capital gain or lossTotal cash if sold = initial investment + total returnCheck your text book for exampleChapter 12Capital Market HistoryRisk premiumEquity is more risky than bonds or t-bills so it carries a risk premiumThis risk premium is the extra return that investors in equity require to purchase equity sharesChapter 12Capital Market HistoryArithmetic Mean

Geometric MeanThe bigger the variance the greater the difference between arithmetic and geometric mean

Chapter 12Capital Market HistoryConsider the following returns: 2%, 8% and 10% n =3Arimethic Mean

Geometric Mean

See the difference?

Chapter 12Capital Market HistoryVariance and Standard DeviationPage 351 in book shows how to do it with your calculatorLearn how to do it with your calculator to save time on exam and get the right answer because these questions can be calculation intensive

Chapter 12Capital Market HistoryQuick example using a table

(1) Returns(2) Average Return(3) Deviation (1)-(2)Sqrd Dev. (4)12%9.75%2.25%0.0005065%9.75%-4.75%0.00225630%9.75%20.25%0.041006-8%9.75%-17.75%0.031506n=40.00%0.07528Var(R)=^2=.07528/(4-1)2.509%SD(R)==.02509^(1/2)15.840%Chapter 12Efficient Market HypothesisWeak FormFuture prices cannot be predictedSemi-Strong FormPrices adjust to new public information quicklyStrong FormPrices reflect all information public and privateChapter 12Weak FormSupported by dataFuture prices do not reflect past pricesTechnical analysis has no valueFundamental analysis may produce returnsRandom walk theory

63*** Technical Analysis & Fundamental Analysis: give an over view while explaining [add slides]Put examples for each type of Form

** create a one page handout on porters 5 forces and what to look for in a company 63Chapter 12Technical Analysis ExamplesMicroeconomic basedSupply and demandCandle sticksOriginally developed for Rice tradingUses patterns to predict price movements or trendsBollinger BandsMiddle band is period moving average, two outer bands are N times standard deviation64*** Technical Analysis & Fundamental Analysis: give an over view while explaining [add slides]Put examples for each type of Form

** create a one page handout on porters 5 forces and what to look for in a company 64Chapter 12Technical Analysis Example

65*** Technical Analysis & Fundamental Analysis: give an over view while explaining [add slides]Put examples for each type of Form

** create a one page handout on porters 5 forces and what to look for in a company 65Chapter 12Semi-Strong FormPrices reflect all public information Fundamental techniques are of no value E.g. Dividend Growth ModelThe market is also weak form efficientChapter 12Fundamental AnalysisDividend Growth ModelPrediction of future dividend growth

Strong FormAll information including public and private is reflected in stock priceMarket is also weak and semi-strong formInsider information could produce very high returns because of laws regulating insider trading

Chapter 12Tips and TricksKnow capital gains has already been covered previous as investment returnKnow how to calculate variance and standard deviationLearn your calculatorIt will come in handy for other courses and professional examsKnow the difference between arithmetic and geometric mean

Chapter 12Tips and TricksKnow the difference between arithmetic and geometric meanEfficient Market HypothesisCommon question: SOS just released its earnings. The stock rose on this news and then fell back down to its previous levels. This is an example of what form of market?

Chapter 13Return Risk and Security Market LineRisk premiumRisk premium = expected return risk-free rateExpected returns

Example: A economy has two states: boom or bust. The probably of each state is 40% and 60% respectively.

Chapter 13Return Risk and Security Market LineExample: A economy has two states: boom or bust. The probably of each state is 60% and 40% respectively. A stock returns 15% during a boom and -5% during a bust. What is the expected return of the stock?

Expected return is 7%

Chapter 13Return Risk and Security Market LineVariance and standard deviation calculationsVariance

Standard Deviation.

Chapter 13Return Risk and Security Market LineExample: A economy has two states: boom or bust. The probably of each state is 60% and 40% respectively. A stock returns 15% during a boom and -5% during a bust. We know expected return is 7% from previous example. What is the variance and standard deviation?

Chapter 13Return Risk and Security Market LineStandard deviation is around 9.8%

(2)(3)(4)(5)(1)ProbabilityReturn Deviation from E(R)Sqr Deviation from expected return(2)*(4)Recession0.4-0.1200.01440.00576Boom0.60.0800.00640.00384Variance0.0096Standard Deviation0.09798Chapter 13Return Risk and Security Market LinePortfolio Expected Returns example: SOS holds a portfolio that consists of two assets: A and B. A has an E(R) of 5% and B an E(R) of 15%. SOS has invested 30% of its capital in asset A. What is the expected return of the portfolio?

Chapter 13Return Risk and Security Market LinePortfolio VarianceCalculate expected return of the portfolio for its statesTreat the portfolio like a single asset in this matterVariance (j is the state of the economy)

Standard Deviation

Chapter 13Return Risk and Security Market LineSOS has a portfolio that during a boom that returns 15% and during a bust returns 5%. The probability of each state is 40% and 60% respectively. What is the standard variation of the portfolio?

(2)(3)(4)(1)ProbabilityReturnProduct 2*3Recession0.40.050.020Boom0.60.150.090E(R)=0.110Chapter 13Return Risk and Security Market LineSOS has a portfolio that during a boom that returns 15% and during a bust returns 5%. The probability of each state is 40% and 60% respectively. What is the standard variation of the portfolio?

(2)(3)(4)(5)(1)ProbabilityReturn Deviation from E(R)Sqr Deviation from expected return(2)*(4)Recession0.4-0.0600.00360.00144Boom0.60.0400.00160.00096Variance0.0024Standard Deviation0.04899Chapter 13Return Risk and Security Market LineCorrelation: The way a series of assets move togetherIf two assets move in the same direction at the same time Corr = 1If two assets move in the opposite direction at the same time Corr = -1If two assets do not appear to have related movement then Corr = 0See page 377 for graph examples

Chapter 13Return Risk and Security Market LineWhy is correlation important?It can help mitigate risk or reduce risk in a balanced portfolioZero-variance portfolio: Using a mix of portfolio weights find a portfolio that always returns the same no matter the condition of the economy

Chapter 13Return Risk and Security Market LineExample: A two stock portfolio consisting of SOS and RSOS stock with standard deviations of .25 and .1 respectively. The Ryerson SOS has invested 35% of this portfolio in the SOS stock. The correlation between the two stocks is .5. What is the standard deviation of the portfolio?

Standard deviation is 13.3%

Chapter 13Return Risk and Security Market LineExpected and Unexpected returnsTotal return = expected return + unexpected returnUnexpected return is the risky part, and the reward that investors receive for bearing the risk of equity investmentsSystematic and Unsystematic RiskR= E(R)+ systematic portion+ unsystematic portionSections 13.3 and 13.4 are easy know the definitions in these sections

Chapter 13Return Risk and Security Market LineSystematic and Unsystematic RiskR= E(R)+ systematic portion+ unsystematic portion

Sections 13.3 and 13.4 are easy know the definitions in these sections

Chapter 13Return Risk and Security Market LineSection 13.5 Diversification and Portfolio RiskSystematic Risk or nondiversifiable riskCannot be diversifiedUnsystematic Risk or diversifiable riskAsset specific risk or unique riskCan be diversified by portfolio management techniquesTotal risk = systematic risk + unsystematic risk

Chapter 13Return Risk and Security Market LineSystematic Risk PrincipleThe expected return on an asset depends only on that assets systematic riskBeta () measures the amount of systematic risk an investment carries

In this example A has more total risk but less systematic risk because of its lower betaB has a higher risk premium and therefore higher expected return

Std DevBetaA20%0.75B10%1.75Chapter 13Return Risk and Security Market LinePortfolio BetasWeighted averages again...

Seen weighted averages before and theyre calculated the same way here

Chapter 13Return Risk and Security Market LineSecurity Market Line

This equation tells us the reward to risk ratio of an investmentThink of it as amount of reward per unit of risk borne by the investorThe reward-to-risk ratio must be the same for all assets in the market

Chapter 13Return Risk and Security Market LineExample: An asset has a beta of .6 and an expected return of 11%. The risk free rate is 3%. Find the slope of the reward-to-risk ratio for this asset?

15% is the reward-to-risk ratio for this asset

Chapter 13 Capital Asset Pricing Model (CAPM)Capital Asset Pricing Model (CAPM)E(R)=rf+*[E(Rm)-Rf]Market Risk PremiumThis is the difference between the expected return from the market and the risk free rateE(Rm)-Rf=E(Rmp)E(R)=rf+*E(Rmp)The theory behind this is difficult, but the applications in this course are easy

Chapter 13 Capital Asset Pricing Model (CAPM)Arbitrage Pricing TheoryCAPM is limitedAPT adds more factors to the pricing of assetsThe more factors the more complex the equations getQuants exploit APTProbably will only have to know the above for the exam

Chapter 13 Tricks, Traps and Tips Know risk premium, expected return and risk-free rate definitionsKnow how to calculate all related portfolio calculations including return, standard deviation, and betaUnderstand correlation and how it is applied to portfolio theorySML is important to know theory and how to calculate, but probably wont be a calculation on the exam

Chapter 13 Tricks, Traps and Tips CAPM this will be important in your later courses if you are a finance major LEARN IT NOW!!!I have never seen a question on APT on any review exam, but there is always a first timeAPT is usually for upper level FIN coursesLearn how to use your calculatorUse memory and stats functionsDo not rush through calculations, write down intermediate steps to check answers