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University of Guelph
ECON 2560
Nancy Bower

Chapter 1 Corporations are taxed twice Chapter 5 • There are two types of interest money can earn o Simple interest  Interest is earned only on the investment o compound interest  Interest is earned on the value of money that is in the account at the beginning of the period.  Interest earned on the investment from the previous period then has a chance to earn interest on top of that  FV = Value today * (1 + r)^t • E.g you invest $2000 today paying compound interest at the rate of 8% per year. How much will the account be worth in 5 years? o FV = 2000*(1+0.08)^5 o FV= 2938.66  PV = FV after t periods/(1 + r)^t • E.G You have been offered 1 million dollars five years from now. If the interest rate is expected to be 4% per year, how much is the prize worth to you today in dollars? • PV = 1 000 000/(1+0.04)^5 • PV = 821 927.11  Finding the interest rate • 680.58 = 1000 / (1 + r)^5 • 680.58*(1+r)^5 = 1000 • 1+r^5 = 1000/680.58 • R^5 = 1.4693-1 =.4693 • R= 5√.4693  Future value of multiple cash flows • You invest 1000 dollars today, 1200 dollars a year later and 1400 dollars the next year. If your bank offers you an 8% interest rate what is the future value after 3 years o FV= 1000*(1.08)+ 1200*(1.08)^2+ 1400*(1.08)^3 o FV= 4172 • Your car dealer offers you the option of paying 30000 today or 8000 now, 12 000 a year later and 12 000 a year after that. Which is the better deal? At a discount rate of 8% o 8000+ 12000/(1.08)+12000/(1.08)^2 = 29 399, take the second option o Level Cash Flows: perpetuities and annuities  Annuities • Cash flows of equal amount every period for a limited number of periods o E.g loan payments for automobiles, periodic earnings from the lottery • Present value: The present value of t period annuity with cash flow C and discount rate R is given by – o PV of t-period annuity = C*(1/r – 1/r[1+r]^t) o E.g you are purchasing a car. You are scheduled to make 3 annual installments of 12 000 per year with the first payment one year from now. Given a rate of interest of 6%, what is the price you are paying for the car? o PV = 12 000 * (1/.06 – 1/.06(1.06)^3 o PV = 32 076.14  Perpetuities • Cash flows of equal amount every period for an unlimited number of periods o E.g property tax payments, preferred stocks • Present value of perpetuity o PV = C/R o E.g in order to create an endowment that pays 150 000 per year for ever how much needs to be set aside today if the rate is 5% o PV = 150 000/0.05 o PV= 3 000 000 o E.g If the first perpetuity payment wont be received until four years from today, how much money needs to be set aside today? o PV = 3 000 000/(1.05)^3 o PV= 2 591 513 • Present value of a growing perpetuity o PV of growing P = C/R – G o PV of growing Annuity = C/r-g(1-[1+g/1+r]^t)  Inflation and the time value of money • Inflation: Rate at which prices as a whole are increasing • Nominal interest rate: Rate at which money invested grows • Real interest rate: Rate at which the purchasing power of an investment grows o 1+real rate = 1+nominal rate/1+inflation rate  Effective Annual Interest rates • Effective annual interest rate o Interest rate that is annualized using compound interest • Annual percentage rate o Interest rate that is annualized using simple interest • If m is the number of compounding periods per year, then o EAR= (1 + APR/m)^m – 1 • Summary of chapter 5 o Future value is the amount to which an investment will grow after earning interest o The present value of a future cash payment is the amount you would have to invest today to create that future cash payment o You can calculate the interest or discount rate and time periods as well o A level stream of payments which continue forever is called a perpetuity o A level stream of payments for a limited number of years is an annuity o You can use the FV and PV formulas to calculate their value o You need to distinguish between real and nominal cash flows that are affected by inflation o Effective Annual Rates annualize using compound interest Chapter 6 • Bonds and the bond market  Governments and corporations borrow money for the long time by issuing securities called bonds  The interest payment paid to the bond hold is called the coupon  The payment at the maturity of the bond is called the face value, principal or par value  The date on which the loan will be paid off is the maturity date  The coupon rate is the annual interest payment divided by the face value of the bond  The interest rate or discount rate is the rate at which the cash flows from the bond is discounted to determine its present value o Interest rates and bond prices  The price of a bond is the present value of its coupon payments plus the price of a bond • E.g calculate the current price of a 7.0% annual coupon bond, with a $1000 face value which matures in 3 years. Assume a required return of 5% o 1000 * .07 = $70 in year 1 and $70 in year 2 then 70$ + the price of the bond  70 + 70 + 70 + 1000 = 1210  When the coupon rate is equal to the required return the bond sells at face value or par  When the coupon rate is higher than the required return, the bond sells above face value (at a premium)  When the coupon rate is lower than the required return the bond sells below face value (At a discount)  Yield to maturity = interest rate for which the present value of the bonds payments equal the price • E.g a 3-year, 8% annual coupon bond, with face value of 1000 sells for 1053.46 o PV = 80/(1+.08)^1 + 80/(1.08)^2+80+1000/(1.08)^3  Rate of return is the earnings per period per dollar invested • You buy $1000 par, 3-year 8% annual coupon bond for 1053.46. one year later you sell it for 1100 o Rate of return = coupon income + price change / investment o Rate of return = 80 + 46.54 / 1053.46 o Rate of return = 0.1201 or 12.01% o The yield curve  Real return bond – the bonds with variable nominal coupon payments, determined by a fixed real coupon payment and the inflation rate  Fisher effect – the nominal interest rate is determined by the real interest rate and expected rate of inflation  Expectations theory – an explanatory theory that shows why there are different shapes of the yield curve o Corporate bonds and the risk of default  Interest rate risk is the risk in bond prices due to fluctuations in interest rates  Different bonds are affected differently by interest rate risks • Longer term bonds get hit harder than shorter term bonds and lower coupon rate bonds get hit harder than higher • Default risk or credit risk is the risk that a bond issuer defaults on its debts • The default premium or credit spread is the difference between the promised yield on a corporate bond and the promised yield on a government of Canada bond given the same coupon and maturity • The safety of a corporate bond can be judged from its bond rating • Bond ratings are provided by companies like o Dominion bond rating service (DBRS) o Moody’s o Standard and Poors • Bonds are BBB and above are called investment grade bonds • Bonds rated BB and below are called speculative grade, high yield, or junk bonds • Summary of Chapter 6 o Coupon rate is the bonds rate divided by its face value o Current yield is the bonds coupon rate divided by its current price o Yield to maturity measures the average return to an investor who purchases the bond and holds it until maturity o Bond prices and yield to maturity vary inversely o Bond prices vary in response to interest rates. The risk of price change is called interest rate risk  Long term bonds have greater interest rate risks than short term bonds o Investors use bond ratings to determine the risk of default on a bond o The additional return that investors demand for bearing credit risk is called the default premium Chapter 7 • Common stock : ownership shares in a publicly held company • Primary market: place where the sale of new stock first occurs • Initial public offering: first offering of stock to the general public • Seasoned issue: sale of new shares by a firm that has already been through its IPO • Secondary market: market in which already issued securities are traded by investors • P/E: price per share divided by earnings per share • Dividend: periodic cash distribution from the firm to its investors o Dividends represent that share of the firms profits that are redistributed • Retained Earnings: Profits that are retained in the firm and reinvested in operations • Liquidation value – net proceeds that would be realized by selling off the firms assets and paying off its creditors • Market value balance sheet: financial statement that uses market value of assets and liabilities • Expected return : the percentage yield that an investor forecasts from a specific investment over a set period of time o Expected return = Div1 / P0 + P1-P0/P0 or expected return = dividend yield + capital gains yield • Price and intrinsic value o The dividend discount model: share value equals the present value of all expected future dividends. If the discount rate is ‘r’ it can be written as  DDM = Div1/(1+r)^t + Div2/(1+r)^t+Div3/(1+r)^t o Simplifying the dividend discount model  Zero Growth Case • If the dividend paid by the company is not expected to change then the payment is treated as a perpetuity , the present value of all dividends is then P0 = Div1/r  Constant Growth Case • If the dividend paid by the stock is expected to grow at a constant rate, then the cash flows are treated like perpetual flows with a growth rate. In this case the PV of cash flows = Div1/r-g  Non-constant growth case • Many companies grow at rapid or irregular rates for many years before slowing down o Before the growth settles down each dividend must be calculated separately o When the growth rate does settle down, we can find the future stock price using the constant growth formula o At the end, we have to find the present values of all the dividends and the future stock price o Growth stocks and income stocks • The fraction of earnings retained by the firm is called the plowback ratio • The fraction of earnings a company pays out in dividends is called the pay out ratio • The growth rate for a company can be determined by multiplying the return on equity by the plowback ratio • G = ROE * Plowback ratio  Sustainable growth rate • Steady rate at which a firm can grow o G = Return on Equity * plowback ratio  Price earnings ratio • Stock price / earnings per share o Efficient market  A market where prices reflect all available information • Weak form efficiency o A market where prices rapidly reflect all information contained in the history of past prices and volumes • Semi strong form efficiency o A market where prices rapidly reflect all publicly available information • Strong form efficiency o A market where prices reflect all information that could be used to determine the real value of an asset • Summary chapter 7 o Valuing a common stock o PO = Div1/r Chapter 11 • Measuring rates of return o Percentage return = capital gain + dividend / initial share price o Capital gain yield = capital gain/initial share price o Dividend yield = dividend/initial share price o 1 + real rate = 1 + nominal rate/1+inflation rate • Investors receive a premium for risk o Therefore, rate of return on any security = rate of return on t-bills + market risk premium • Measuring risk o Volatility of returns is considered risk  Variance- the average value of squared deviations from the mean  Standard deviation – the square root of the variance o The risk-return trade off, T-bills have the lowest return and the lowest volatility. Conversely common stocks have the highest return and the highest volatility • Diversification and unique vs market risk o Diversification reduces risk through…  spreading ones portfolio over many investments  Since stocks do not increase or decrease in value in exact harmony when one stock is doing poorly the other is doing well  Reduction in risk of the portfolio also depends upon the correlation co- efficient • If you hold two stocks with a correlation coefficient that is less than one you can reduce the amount of risk by holding them together  possible because of unique risk and market risk  Market risk vs Unique risk • You cannot eliminate all risk from a portfolio by adding securities • Typically once you get to 15 stocks adding more stocks does very little to reduce the risk of a portfolio • The risk that cannot be diversified away is called market risk • For a reasonably well diversified portfolio only market risk matters • Unique risk is minimized by diversifying a portfolio • Market risks are macro risks o E.g changes in interest rates, industrial production, inflation • Summary of chapter 11 o Standard deviation and variance are measures of risk o Diversification reduces risk because stocks do not move in perfect contingency, poor performance by one stock can be offset by good performance by the other o Correlation coefficient is a measure of how two variable move with respect to one another o Risk which can be eliminated with diversification is called unique risk Chapter 12 o Is the sensitivity of a stocks return to the return on the market portfolio  Is a measure of risk o There are two ways of measuring beta  Beta of stock j = Bj = cov(Rj,Rm)/µ^2m  Where COV(j,m)= covariance of the stocks return with the markets return  µm= standard deviation of the market o portfolio beta  the weighted average of the betas of individual assets; with the weights being equal to the proportion of wealth invested in each asset  the beta of a portfolio with two assets st • portfolio beta = (fraction of portfolio in asset 1 * beta of 1 asset) + (fraction of portfolio in asset 2 * beta of 2 asset) o Capital Asset Pricing Model  The theory of the relationship between risk and return which states that expected risk premium on any security equals its beta times the market risk premium  According to the CAPM – E(Rj) = rf + Bj*(rm-rf)  Security Market Line • Graph showing the relationship between the market risk of the security and its expected return • According to the CAPM expected rates of return for all securities and portfolios fall on the SML Chapter 13 • WACC – Weighted Average Cost of Capital o The weighted average of returns on debt and equity, with weights depending on the relative market values of the two securities o WACC = [D/V *(1-Tc)r debt]+[E/V *r equity] o Three steps to calculating capital 1. Calculate the value of each security as a proportion of the firms market value 2. Determine the required rate of return on each security 3. Calculate the weighted average of these required returns  E.g executive fruit has issued debt, preferred stock and common stock. The market value of these securities are 4 mil, 6 mil and 2 mil. The required returns are 6%, 12% and 18% respectively  WACC = 4/12(1-.35)(.06)+6/12(.12)+2/12(.18) = 12.3% o When you can and cannot use the WACC  The WACC is the rate of return the firm must expect to earn on its average risk investments in order to compensate its investors • Thus WACC may be used to value assets that have the same risk as the old ones • Will support the same ratio of debt as the firm itself o Issues with using the WACC  Changing the capital structure might affect the required returns  Increasing debt might increase the cost of equity  Changing the capital structure might affect beta • Beta of the firm is the weighted average of the beta of its debt
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