The cost of capital

The cost of capital The application of the portfolio theory and CAPM FIN351: lecture 6 Today’s plan   What have we accomplished in the last lecture? Cost of capital • Capital structure and WACC • Calculate WACC without tax • Calculate WACC with tax  The market efficiency concept FIN351: lecture 6 What have we learned in the last lecture? Beta (β): Measuring market risk or systematic risk of a security • Which is defined as the contribution • of a security to the risk on the market portfolio, Mathematically, ~ Cov(~ , Rm ) ri i  ~ Var ( Rm ) • How to understand β intuitively? FIN351: lecture 6 What have we learned in the last lecture? (1) Portfolio standard deviation Unique risk Market risk 0 5 10 15 Number of Securities FIN351: lecture 6 What have we learned in the last lecture? (2)  The beta of a portfolio • The beta of a portfolio will be an weighted average of the betas of the securities in the portfolio.  The expected return of a portfolio • The expected return of a portfolio will be an weighted average of the expected returns of the securities in the portfolio. FIN351: lecture 6 What have we learned in the last lecture? (3)  CAPM (Capital Asset Pricing Model) • The risk premium on each security is • proportional to the market risk premium and the beta of the security. That is, ri  r f  i ( Rm  r f ) ri  r f  risk premium for sec urity i Rm  r f  risk premium for the market portfolio FIN351: lecture 6 What have we learned in the last lecture? (4)  The graphic representation of CAPM in the expected return and Beta plane 16 14 Security Market Line Expected Return (%) . 12 10 8 6 4 2 0 0 Rm rf 0.2 0.4 0.6 Beta FIN351: lecture 6 0.8 1 1.2 What have we learned in the last lecture? (5)  We can use the Beta of the project cash flows to measure the risk of the project and use CAPM to get the discount rate or the expected return required by investors • rproject  r f   project ( Rm  r f ) FIN351: lecture 6 What have we learned in the last lecture? (6)  Some results • The Beta of the market portfolio is 1. • The Beta of the risk-free asset is 0. • The portfolio weights can be negative, but their sum must be 1. FIN351: lecture 6 Example 1   You have $1 million of your own money to invest in stock A and B. You short-sell $1 million stock A and then invest in stock B. The expected returns for stock A and B are 17% and 21%, respectively. The risk-free rate is 5%. Stock A has a beta of 1.5 and stock B has a beta of 2.0.The expected rate of return for the market portfolio is 13%. Please use two approaches to calculate the expected rate of return on your portfolio? FIN351: lecture 6 Solution First, calculate the portfolio weight as follows: x A  1; xB  2 (1) The expected rate of return of a portfolio is the weighted average of the rates of return of the securities in the portfolio. R p  1* 0.15  2 * 0.2  25% (2) The beta of a portfolio is the weighted average of the betas of the securities in the portfolio. Then use CAPM to calculate the expected return  p  1*1.5  2 * 2  2.5 R p  5%  2.5 * 8%  25% FIN351: lecture 6 The cost of capital Cost of Capital • The expected return the firm’s investors require if they invest in securities or projects with comparable degrees of risk. FIN351: lecture 6 The cost of capital for the bond  The cost of capital for the bond • It is the YTM, the expected return required • the investors. That is Pbond  cpn cpn cpn  principal   1  rd 1  rd 2 1  rd t by • The expected return on a bond can also be calculated by using CAPM rd  r f  d ( Rm  r f ) FIN351: lecture 6 Example 2  A bond with a face value of $2000 matures in 5 years. The coupon rate is 8%. If the market price for this bond is $1600. (a) What is the expected return on this bond or what is the cost of debt or interest rate for this bond? (b) Suppose that the YTM is 9%, what is the market value of this bond? FIN351: lecture 6 Solution (a)  1  1 2000  1600  160   YTM YTM (1  YTM )5  (1  YTM )5   YTM  13.8% (b) 1  1  2000 Pbond  160     $1,922 5  5  0.09 0.09 *1.09  1.09 FIN351: lecture 6 The cost of capital for a stock  The cost of capital for a stock is calculated by using • CAPM re = rf + i (R m - rf ) • Dividend growth model DIV1 DIV1 P0   re  g re  g P0 FIN351: lecture 6 Example 3  Sock A now pays a dividend of $1.5 per share annually, It is expected that dividend is going to grow at a constant rate of 2%. The current price for stock A is $25 per share. What is the expected return or the cost of capital by investing in this stock? FIN351: lecture 6 Solution Using the dividend discount model, we have 1.5 *1.02 25   r  8.12% r  0.02 FIN351: lecture 6 Capital structure  Capital Structure • The firm’s mix of debt financing and equity • • • financing. If we use D , E and V to denote the values of debt, equity and firm (asset), respectively. Then V=D+E The ratio of D/V or D/E can be used to measure the capital structure of the firm. FIN351: lecture 6 Weighted Average Cost of Capital (WACC)     If you invest in a stock, you require a an expected rate of return, or the cost of capital for the stock If you invest in a bond, you require a an expected rate of return, or the cost of capital for the bond Then, if you invest in a a portfolio of all the firm’s securities (debt and stock), what is the expected rate of return you require? The expected rate of return on a portfolio of all the firm’s securities is called the weighted average cost of capital (WACC). It is also called the expected return on the asset of the firm. FIN351: lecture 6 WACC (continues)   According to portfolio theory, we know the expected return on a portfolio is the weighted average of the expected returns on the securities of the portfolio. Thus, WACC for a firm with debt and equity is E D WACC  V re  V rd where V  D  E FIN351: lecture 6 WACC (continue)    In calculating WACC, we have to use market values of debt and equity. Even if you are given the book value of debt, you may convert this book value to market debt value to calculate WACC Why do we use market values of debt and equity, but not book values of debt and equity, in calculating WACC? FIN351: lecture 6 Example 4  Geothermal Inc. has two securities: debt and stocks. The market debt value is $194 million, but the firm’s market value is $647 million. Given that geothermal pays 8% for debt and 14% for equity, what is the Company Cost of Capital? FIN351: lecture 6 Solution 194 453 WACC  * 0.08  * 0.14  12.2% 647 647 FIN351: lecture 6 Example 5  Executive Fruit has issued debt, preferred stock and common stock. The market value of these securities are $4mil, $2mil, and $6mil, respectively. The required returns are 6%, 12%, and 18%, respectively. • What is the WACC for Executive Fruit, Inc.? FIN351: lecture 6 Solution V  4  2  6  12 4 2 6 WACC  * 0.06  * 0.12  * 0.18 12 12 12  13 % FIN351: lecture 6 Summary of WACC calculation  Three steps in calculating WACC • First step: Calculate the portfolio weight using • • the market value. Second step: Determine the required rate of return on each security in the portfolio. Third step: Calculate a weighted average of these returns, or the expected return on the protfolio. FIN351: lecture 6 The impact of tax on WACC  Taxes are an important consideration in the company cost of capital because interest payments are deducted from income before tax is calculated. After - tax cost of debt = (pretax cost of debt) times (1 - tax rate) = rd (1 - Tc) FIN351: lecture 6 WACC with tax Weighted -average cost of capital= D E WACC = V (1 - Tc)rd + V re FIN351: lecture 6 A summary example  John Cox, a recent MBA student of SFSU, was asked by his boss in Geothermal to decide whether the firm should take an expansion project: the cost of the project is $30 million, and the project is expected to generate a perpetual incremental cash flow of $4.5 million. Currently, Geothermal has 20 million shares of common stocks outstanding, with a market price of $22.65 per share. The Beta of the firm’s equity is 1.1. The risk free rate is 4% and the market risk premium is 5.6%. The firm also has long-term debt, with the YTM of 9%. John also got the following information from the firm’s balance sheet: • • Debt (12 years maturity, 8% coupon): $200 million Common stocks:$110 million  If the tax rate is 35%, should John suggest to his boss to take the project or not? FIN351: lecture 6 Solution rd  9% re  4%  1.1* 5.6%  10.16% E  20 * 22.65  453 1 1 200 D  16 * (  )  185.7 12 12 0.09 0.09 *1.09 1.09 D E WACC  (1  t )rd  re  8.9% DE DE FIN351: lecture 6 Investment vs. Financing Asset V Liabilities and equity Debt: D Equity: E   Investment decisions or capital budgeting is about how to take projects to maximize V. Financing decisions are about how to raise capital (E or D) to finance the projects to be taken FIN351: lecture 6 Financing and market Efficiency Market Efficiency Market efficiency is concerned about whether capital markets have all information about the cash flows and risk of projects. FIN351: lecture 6 Efficient capital markets Efficient Capital Markets – If capital markets are efficient, then security prices reflect all relevant information about asset values ( cash flows and risk) FIN351: lecture 6 Market efficiency and random walk   Market efficiency concepts are very abstract. How can we use a simple way to check whether the stock market (one of the capital markets) is efficient or not? the stock market is efficient. • If the stock price follows a random walk, then FIN351: lecture 6 What is a random walk of stock prices?   The movement of stock prices from day to day DO NOT reflect any pattern. Statistically speaking, the movement of stock prices is random. FIN351: lecture 6 A Random Walk example Heads Heads $106.09 $103.00 Tails $100.43 $100.00 Heads $100.43 Tails $97.50 Tails $95.06 Coin Toss Game FIN351: lecture 6 Three forms of market efficiency   The random walk concept is still abstract Financial economists have used three more specific forms to characterize or judge market efficiency. • Weak-form • Semi-strong form • Strong form FIN351: lecture 6 Weak-form of market efficiency Weak Form Efficiency - Market prices reflect all information contained in the history of past prices, or you cannot use past stock prices to predict future prices Technical Analysts - Investors who attempt to identify over- or undervalued stocks by searching for patterns in past prices. FIN351: lecture 6 Efficient Market Theory $90 EI’s Stock Price 70 50 Cycles disappear once identified Last Month FIN351: lecture 6 This Month Next Month Semi-strong form of market efficiency  Semi-Strong Form Efficiency - Market prices reflect all publicly available information such as earnings, price-to-earnings ratios,etc. Fundamental Analysts - Analysts who attempt to fund under- or overvalued securities by analyzing fundamental information, such as earnings, asset values, and business prospects. FIN351: lecture 6 Efficient Market Theory 39 34 29 24 19 14 9 4 -1 -6 -11 -16 Cumulative Abnormal Return (%) Announcement Date Days Relative to annoncement date FIN351: lecture 6 Market Efficiency Fama & French Return vs. Book-Market 25 Average return, percent 20 15 10 5 0 Highest FIN351: lecture 6 Book-Market Ratio Strong form of market efficiency Strong Form Efficiency - Market prices reflect all information that could in principle be used to determine true value.  Inside trading • Investors use private information to predict future price movements FIN351: lecture 6 Efficient Market Theory Date Announcement 39 34 29 24 19 14 9 4 -1 -6 -11 -16 Days Relative to annoncement date Cumulative Abnormal Return (%) FIN351: lecture 6 Some exercises 1. 2. If stock markets are efficient, what should the correlation between stock returns for two non-overlapping periods? Which is the most likely to contradict the weak-form of efficiency a. Over 25% of mutual funds outperform the market on b. c. average Insiders can make abnormal profits Every January, the stock market earns abnormal return FIN351: lecture 6 Several types of securities  Three types of securities • Common Stock • Preferred stock • Corporate debt FIN351: lecture 6 Common Stock  Common stocks have the following forms: • Treasury stock • Issued shares • Outstanding shares • Authorized share capital • Par value  Ownership of the corporation FIN351: lecture 6 Corporate debt  Corporate bonds • Primary rate • Funded debt • Sink fund • Callable bond • Subordinate debt • Secure debt FIN351: lecture 6 Preferred stock  Preferred stock and common stock • Priority and voting rights  Preferred stock and bond • Obligation and bankruptcy FIN351: lecture 6