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COMM 298 Final Exam Review
Abhishek Makhijani [email protected] +604 (773) 6915
1
Cash Flows
Key Concepts: •  Difference between Simple Interest and Compound Interest •  FV (compounding) & PV (discounAng) Multiple Cash Flows
Key points to remember: •  Timeline •  When the CF occurs ? •  PV or FV ? •  Discount or compound ? Example: You expect to receive $400 in one year, $250 in two years, $900 in three years and $800 in four years. Bank pays you 3% interest per year. Find the PV of this stream of cash flows. Multiple Cash Flows – Example
Interest Rates
•  APRs (nominal interest rates) do not consider effect of compounding •  To compute effecAve periodic rate from APR •  More the compounding frequency, higher the EAR Annuities
•  Annuity is a fixed stream of CFs. •  Annuity Due is when payment starts at t=0 •  ALWAYS use the matching effec1ve interest rate (EAR) •  Example: Use monthly effecAve interest rate for monthly CFs Converting between Effective Rates
Perpetuities
•  Perpetuity is an annuity that has no end •  Fixed CFs with infinite lives •  PV of a perpetuity Bonds
•  Fixed income securiAes •  CF of a bond (I = Interest / coupon, F = principal) •  Basic Bond ValuaAon r = effecAve interest rate (discounAng), n = # periods unAl maturity Perpetual Bonds
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Level stream of interest payments Beginning one period from now Occurring at regular intervals Never mature (Bondholder never receivesFV) Price of perpetual bond: Perpetual Bonds
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Level stream of interest payments Beginning one period from now Occurring at regular intervals Never mature (Bondholder never receivesFV) Price of perpetual bond: •  Coupon rate is quoted in APR terms; Coupons are paid semi-­‐annually •  Coupon Payment: F = Face value of bond CR = coupon rate K = # of coupon payments Bonds – YTM
•  YTM – Bonds yield assuming it is held unAl maturity •  Quoted in APR terms •  YTM and bonds effecAve rate (r) where, k = # of coupon payments per year •  Current Yield tells us correct YTM for a bond Current yield = Annual Coupon ($) / Current Price Bonds – ROR
•  ROR (Holding period return) – actual earned annual rate of return for the Ame the asset is owned •  Expressed in effecAve annual terms •  Bonds ROR: FVRC = FV of reinvested coupons at specified rate n = # of years the bond was owned / held Bonds Continued
•  YTM assumes that 1.  Bond is held unAl maturity 2.  Coupons are reinvested at that YTM •  Bond Yields are affected by 1.  Real rate of interest 2.  Premium for expected future inflaAon 3.  Interest rate risk premium 4.  Default risk premium 5.  Liquidity premium Default free bond yields represent combined effect of 1,2 and 3. Term Structure
•  Term Structure – plot of yields on default free bonds of different maturiAes InVlation and TVM
•  Fisher EquaAon: higher inflaAon may lead to negaAve realized rate •  Nominal Cash flows à Nominal Interest Rate Real Cash flows à Real Interest Rate Compare similar cash flows Law of one price
•  "a good must sell for the same price in all loca1ons” •  What is Arbitrage? Buying and selling (immediate) of equivalent assets for a sure profit to capture the price difference in different markets •  Arbitrage ensures that Law of one price holds Dividends
•  What are earning? Residual CFs •  Dividends are a porAon of earnings paid to Shareholders •  Preference SH have priority over common SH •  Preferred dividends are a perpetuity (fixed periodic dividend) Stock Valuation
•  Dividend Discount Model •  If DIV1 = DIV2 = D (D is constant), then This is Zero Growth Dividend Model Growing Perpetuity
•  Infinite series of periodic payments growing at a constant rate •  PV of a growing perpetuity: where: A is amount of first payment, g is growth rate per period •  Assuming Dividends grow at a constant rate, price of stock is where r is required rate of return This is Constant Growth DDM Stocks
•  PE Ra1o: raAo of price per share to earnings per share • 
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EPS is net income dividend by current # of O/S shares Investor’s view of a firm’s potenAal growth High PE à High growth ROR vs Expected rate of return EXAMPLE
EXAMPLE -­‐ SOLUTION
EXAMPLE – SOLUTION CONTINUED
Market EfViciency
•  Efficient Market Hypothesis: Use all available and relevant informaAon Ø  Proper ForecasAng Ø  “Prices are right” •  Efficient Market: Prices quickly reflect new info 1.  Weak form à reflect past prices EsAmates: Technical Analysis 2.  Semi strong form à reflect all publicly available info EsAmates: Fundamental Analysis 3.  Strong form à reflect all info, public or private Insider trading? Investment Criteria
•  Payback Period (PBP): amount of Ame to generate CFs to recover iniAal cost •  Payback Rule: Accept if PBP is <= cut off period •  NPV: value of the investment today C0 is always negaAve •  NPV Rule: Accept if NPV is + •  IRR: discount rate that makes NPV = 0 •  IRR Rule: Accept if IRR > required return Investment Criteria Continued
•  Capital BudgeAng Steps 1.  Forecast FCFs 2.  EsAmate cost of capital (r) 3.  Discount FCFs using cost of capital 4.  If NPV > 0, accept project •  Use of IRR Ø  If IRR > r, then NPV > 0 Ø  If IRR < r, then NPV < 0 •  IRR and NPV give same decision as long as NPV of a project declines smoothly as the discount rate increases. Capital Investment Decisions
•  Profitability Index is benefit/cost raAo PI = PV of FCFs / iniAal cost •  PI measures value created per dollar •  Discount CFs, not profits •  Incremental CFs consist of all changes in FCFs that are a direct consequence of the project Standalone Principle is based on incremental CFs •  Include all incidental effects à impact on CFs •  Ignore Sunk costs à cost occurs regardless of project Capital Investment Decisions Continued
•  Include Opportunity Cost à most valuable alternaAve that was given up •  Include changes in NWC i.e. (TCA – TCL) increased investment in NWC à Cash Ouulow decreased investment in NWC à Cash Inflow •  Ignore financing decisions as they affect cost of capital and not CFs EXAMPLE
EXAMPLE -­‐ SOLUTION
EXAMPLE – SOLUTION CONTINUED
What-­‐If Analysis
•  Sensi1vity Analysis: examines effect on NPV when one variable is changed AssumpAon: individual variables are independent of each other •  Scenario Analysis: effect of combinaAon of variables (one scenario) on NPV Variables are interdependent •  NPV Break Even Analysis: determines level of variable that generates NPV = 0 For example, IRR à NPV Risk and Return
•  Risk-­‐return trade off: higher risk à higher returns •  Normal distribuAon and return on poruolio of large stocks Risk and Return Continued
•  Expected Value: average value we would obtain for a random variable Where: x is possible outcome of X p(x) is probability of x •  Variance: measures spread •  Standard Devia1on is square root of variance Risk and Return Continued
•  Covariance: measures degree to which 2 random variables move together •  Correla1on Coefficient: is normalizaAon of covariance •  à Takes values from -­‐1 to 1 Risk and Return Continued
•  Func1ons of Random Variables: Involving constant ‘a’ Involving constant ‘a’ & ‘b’ •  For every addiAonal variable: add one variance and covariance for every pair of random variables Risk and Return Continued
•  Risk aversion: Assume investors are risk averse •  Mean Variance Criterion: Assume at least one is true 1.  Returns of risky assets à normal distribuAon 2.  Investors have quadraAc uAlity funcAon à Only mean and variance maxer Says that if 2 investments have the same expected rate of return, investors will prefer the one with lower variance of realized returns Like à E(r), Dislike à Variance of returns High risk is compensated with risk premium DiversiVication
•  Diversifica1on: is reducing variance How? Adding more than one security to the poruolio LOWER AN ASSET’S COVARIANCE (CORRELATION) à GREATER DIVERSIFICATION BENEFITS NOTE: CORRELATION NEED NOT BE NEGATIVE FOR IT TO BE EFFECTIVE DiversiVication Continued
•  DiversificaAon: Generally about 30 are needed to benefit DiversiVication Continued
•  LimitaAons: 1.  Some risk always remains (SD is not equal to zero) 2.  SystemaAc / Market Risk remains •  High risk à high returns (risk premium) Investors are rewarded for bearing the assets risk ALWAYS REMEMBER COVARIANCE IS IMPORTANT ONE VARIANCE VS ‘N’ COVARIANCES EXAMPLE
EXAMPLE -­‐ SOLUTION
EXAMPLE – SOLUTION CONTINUED
CAPM
CAPM CONTINUED
•  Efficient PorZolio: 2 condiAons 1.  Higher expected returns for equal or lower variance 2.  Equal expected return for lower variance •  Efficient Fron1er: subset of minimum variance poruolios that are efficient It is the top half of Maximum variance poruolio Efficient FronAer CAPM CONTINUED
•  Riskless Asset: same realized and expected returns i.e. Risk free rate of return rf CAPM CONTINUED
•  Capital Market Line (CML): 1.  Originates from rf 2.  represents new risk-­‐return combinaAons available to investors 3.  Tangent to efficient fronAer 4.  Point of tangency (m) à Market Poruolio To the lez of m à investor invests some money in m (mkt poruolio) and lends the rest To the right of m à invests all money in m and borrows addiAonal money to invest CAPM CONTINUED
•  New efficient fron1er = CML •  Move towards upper lez corner to choose efficient poruolios •  Only efficient poruolios are a combinaAon of m and riskless borrowing or lending •  Only risky poruolio that is part of all efficient poruolios is market poruolio (m) CAPM CONTINUED
•  Let wm be the weight on market poruolio and (1-­‐wm) is the weight on risk free asset, then expected return is: Rearranging; •  Since rf is a constant, variance is 0 and covariance is 0 •  CML à draw any combinaAons of m and riskless asset as a straight line CAPM CONTINUED
•  Investor can obtain any of the previous poruolios plus all risk-­‐return combinaAons represented by CML •  Only poruolios on the CML are efficient •  RaAonal investors hold some amount of m and some amount of borrowing or lending at risk free rate Low risk aversion à higher weight on m (more risk) High risk aversion à lower weight on m (less risk) All investors are risk averse à risk aversion is rela1ve CAPM CONTINUED
•  Individual Assets – investors are compensated for systemaAc risk •  All risky assets are priced such that they are a part of the market poruolio •  Pricing formula for individual risky assets: CAPM CONTINUED
•  Security Market Line (SML) Beta is given by: Hence, individual asset’s expected return in equilibrium becomes: This is known as the SML CAPM CONTINUED
•  Security Market Line (SML) •  Beta measures an asset’s systemaAc risk •  is the risk premium for each unit of beta risk •  SML plots expected returns versus beta CAPM CONTINUED
CAPM CONTINUED
•  Beta of market is always 1 •  Beta of riskless asset is 0 (expected return is constant) •  Beta is the sensiAvity of a stock’s return to fluctuaAons in market poruolio returns •  Beta is the slope of the regression line of individual stock returns on market poruolio returns and hence CML VS SML
•  CML Ø  Plots expected return vs standard devia1on Ø  Tells us what investors will choose to hold (efficient porZolio) Ø  Helps us determine the loca1on of the market porZolio Ø  Does not help price individual assets •  SML Ø  Plots expected return vs beta Ø  Shows relaAonship between systema1c risk and expected return Ø  Does not help determine locaAon of mkt poruolio Ø  Helps price individual assets EXAMPLE
EXAMPLE -­‐ SOLUTION
EXAMPLE -­‐ SOLUTION
ANOTHER EXAMPLE
ANOTHER EXAMPLE -­‐ SOLUTION
MISPRICED SECURITIES
•  A security is mispriced if it does not plot on the SML •  A stock located below SML is overpriced i.e. expected return is too low relaAve to its beta •  A stock located above SML is underpriced i.e. expected return is too high relaAve to its beta •  In equilibrium price is on SML PORTFOLIO BETA
•  Is the weighted average of the betas of the individual stocks of the poruolio COST OF CAPITAL
•  Cost of capital associated with an investment depends upon the risk of that investment •  Firm’s financial policy is about choosing the right mix of debt and equity…its capital structure •  A firm’s cost of capital reflects the required return on the firm’s assets as a whole COST OF CAPITAL OF AN ALL EQUITY FIRM
Owning the firm = Owning the equity Value of firm = value of equity Risk of firm = risk of equity Rate of return from firm = rate of return on equity Firm’s cost of capital = Investor’s required rate of return on equity COST OF EQUITY – SML APPROACH
The SML approach Advantages •  Explicitly adjusts for risk •  Applicable to companies other than those with steady dividend growth Disadvantages •  Results rely heavily on market risk premium and beta esAmates •  Uses historical data to predict future returns COST OF CAPITAL OF LEVERAGED FIRM
Owning the firm = Owning both the debt and equity Value of firm = value of debt + value of equity Rate of return from firm = rate of return on a poruolio of debt and equity securiAes Expected poruolio return is a weighted average of the returns on the securiAes in the poruolio. Therefore, Firm’s cost of capital = Weighted average of debt and equity returns This is known as WACC COST OF CAPITAL OF DEBT+EQUITY FIRM
•  WACC is weighted average cost of capital V = D + E ….combined market value of debt and equity •  Cost of debt is return required by lenders •  It is the YTM on the firm’s bonds O/S •  AlternaAvely, if we know the bond raAng, we can use the interest rate on newly issued bonds with the same raAng •  Coupon rate is NOT the cost of debt COST OF CAPITAL OF DEBT+EQUITY (P & C) FIRM
•  WACC is weighted average cost of capital V = D + P + E ….combined market value of debt, preferred equity & common equity •  Rp is cost of preferred stock (perpetuity with fixed dividend) CALCULATING WACC: Summary
•  Measure the capital structure of the firms. Use market values, not book values •  Determine the required rates of return on securiAes: Ø  Use SML from the CAPM for common equity Ø  Use dividend yield on preference shares Ø  Use the YTM for bonds •  Compute WACC using the weighted average formula •  WACC can be used as a discount rate when evaluaAng investment projects with risk characterisAcs similar to the firm’s exisAng assets WACC EXAMPLE
WACC EXAMPLE -­‐ SOLUTION
THANK YOU!!
•  Abhishek Makhijani [email protected] •  +604 (773) 6915