McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 5-0 Corporate Finance Ross  Westerfield  Jaffe Seventh Edition 5 Chapter Five How to Value Bonds and Stocks

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 5-1 Chapter Outline 5.1Definition and Example of a Bond 5.2How to Value Bonds 5.3Bond Concepts 5.4The Present Value of Common Stocks 5.5Estimates of Parameters in the Dividend-Discount Model 5.6Growth Opportunities 5.7The Dividend Growth Model and the NPVGO Model (Advanced) 5.8Price Earnings Ratio 5.9 Stock Market Reporting

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 5-2 Valuation of Bonds and Stock First Principles: –Value of financial securities = PV of expected future cash flows To value bonds and stocks we need to: – Estimate future cash flows: Size (how much) and Timing (when) – Discount future cash flows at an appropriate rate: The rate should be appropriate to the risk presented by the security.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Definition and Example of a Bond A bond is a legally binding agreement between a borrower and a lender: –Specifies the principal amount of the loan. –Specifies the size and timing of the cash flows

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved How to Value Bonds Identify the size and timing of cash flows. Discount at the correct discount rate. –If you know the price of a bond and the size and timing of cash flows, the yield to maturity is the discount rate.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 5-5 Pure Discount Bonds Information needed for valuing pure discount bonds: –Time to maturity (T) = Maturity date - today’s date –Face value (F) –Discount rate (r) Present value of a pure discount bond at time 0:

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 5-6 Pure Discount Bonds: Example Find the value of a 30-year zero-coupon bond with a $1,000 par value and a YTM of 6%.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 5-7 Level-Coupon Bonds Information needed to value level-coupon bonds: –Coupon payment dates and time to maturity (T) –Coupon payment (C) per period and Face value (F) –Discount rate Value of a Level-coupon bond = PV of coupon payment annuity + PV of face value

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Bond Concepts 1.Bond prices and market interest rates move in opposite directions. 2.When coupon rate = YTM, price = par value. When coupon rate > YTM, price > par value (premium bond) When coupon rate < YTM, price < par value (discount bond) 3.A bond with longer maturity has higher relative (%) price change than one with shorter maturity when interest rate (YTM) changes. All other features are identical. 4. A lower coupon bond has a higher relative price change than a higher coupon bond when YTM changes. All other features are identical.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 5-9 YTM and Bond Value $ Discount Rate Bond Value 6 3/8 When the YTM < coupon, the bond trades at a premium. When the YTM = coupon, the bond trades at par. When the YTM > coupon, the bond trades at a discount.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Maturity and Bond Price Volatility C Consider two otherwise identical bonds. The long-maturity bond will have much more volatility with respect to changes in the discount rate Discount Rate Bond Value Par Short Maturity Bond Long Maturity Bond

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Coupon Rate and Bond Price Volatility Consider two otherwise identical bonds. The low-coupon bond will have much more volatility with respect to changes in the discount rate Discount Rate Bond Value High Coupon Bond Low Coupon Bond

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved The Present Value of Common Stocks Dividends versus Capital Gains Valuation of Different Types of Stocks –Zero Growth –Constant Growth –Differential Growth

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Case 1: Zero Growth Assume that dividends will remain at the same level forever  Since future cash flows are constant, the value of a zero growth stock is the present value of a perpetuity:

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Case 2: Constant Growth Since future cash flows grow at a constant rate forever, the value of a constant growth stock is the present value of a growing perpetuity: Assume that dividends will grow at a constant rate, g, forever. i.e....

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Case 3: Differential Growth Assume that dividends will grow at different rates in the foreseeable future and then will grow at a constant rate thereafter. To value a Differential Growth Stock, we need to: –Estimate future dividends in the foreseeable future. –Estimate the future stock price when the stock becomes a Constant Growth Stock (case 2). –Compute the total present value of the estimated future dividends and future stock price at the appropriate discount rate.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Estimates of Parameters in the Dividend-Discount Model The value of a firm depends upon its growth rate, g, and its discount rate, r. –Where does g come from? –Where does r come from?

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Where does g come from? g = Retention ratio * Return on retained earnings Net investment will be positive only if some earnings are retained.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Where does r come from? One of the methods: r = Div/P 0 + g The discount rate can be broken into two parts. –The dividend yield –The growth rate (in dividends) In practice, there is a great deal of estimation error involved in estimating r.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved A Healthy Sense of Skepticism –Estimate of g is based on a number of assumptions: return on reinvestment future retention ratio –Some financial economists suggest calculating the average r for an entire industry.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Two polar cases Case1: A firm paying no dividend, and going from no dividends to a positive number of dividends Case2: An analyst whose estimate of g for a particular firm is equal to or above r must have made a mistake.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Growth Opportunities Imagine a company with a level stream of earnings per share in perpetuity The company pays off these earnings out to stockholders as dividends. Hence. EPS = Div (Cash cow) It’s value equals EPS/r = Div/r

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Growth opportunities are opportunities to invest in positive NPV projects. Suppose the firm retains the entire dividend at date 1 in order to invest in a particular capital budgeting project Stock Price after Firm Commits to the New Project: EPS/r + NPVGO

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Two conditions must be met in order to increase value: –Earnings must be retained so that projects can be funded. –The projects must have positive net present value.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Example: EPS/r + NPVGO = 【〔 $1,000,000/1.1 〕 + 〔 $1,000,000/(1.1) 2 〕 +…+ 〔 $1,000,000/(1.1) n 〕】 + 【〔 -$1,000,000+($210,000/0.1) 〕 /1.1 】 = 〔 $1,000,000/0.1 〕 + 〔 -$1,000,000+ $2,100,000 〕 /1.1 = $10,000,000+$1,000,000 = $11,000,000 The price per share: $11,000,000/100,000 = $110

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Growth in Earnings and Dividends versus Growth Opportunities A policy of investing in projects with negative NPVs rather than paying out earnings as dividends will lead to growth in dividends and earnings, but will reduce value.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Dividends or Earnings: Which to discount? Dividends, or would ignore the investment that a firm must make today in order to generate future returns.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved The No-Dividend Firm A firm with many growth opportunities faces two choices: pays out dividends now, or forgoes dividends now and makes investments. The actual application of the dividend discount model is difficult for firms of this type.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved The Dividend Growth Model and the NPVGO Model (Advanced) A steady growth in dividends results from a continual investment in growth opportunities, not just in a single opportunity.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Example C has EPS of $10 at the end of the first year, a dividend-payout ratio of 40%, a discount rate of 16%, and a return on its retained earnings of 20%.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Solution The Dividend-Growth Model The NPVGO Model –Value Per Share of a Single Growth Opportunities -$6 + $1.20/0.16 = $1.5 –Value Per Share of All Opportunities NPVGO = $1.50/( )=$37.50 –Value Per Share if Firm Is a Cash Cow Div/r = $10/0.16 = $62.50 –Summation $ $62.5 = $100.0

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Price-Earnings Ratio (P/E ratio) P (Price per share) = EPS/r + NPVGO P/E = 1/r + NPVGO / EPS The market is merely pricing perceptions of the future, not the future itself. It implies that P/E ratio is a function of: growth opportunities, risk, and the choice of accounting methods.