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7-1 Chapter 7 Valuation Concepts Bond Values Stock Values Rates of Return Market Equilibrium Copyright © 2000 by Harcourt, Inc. All rights reserved. Requests for permission to make copies of any part of the work should be mailed to the following address: Permissions Department, Harcourt, Inc., 6277 Sea Harbor Drive, Orlando, Florida 328876777. Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-2 Basic Valuation From “The Time Value of Money” we realize that the value of anything is based on the present value of the cash flows the asset is expected to produce in the future. Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-3 Basic Valuation ^ ^ Asset CF CF 1 2 V 1 2 value 1 k 1 k N ^ CF 1 k t 1 ^ CF N 1 k N ^ CF = the cash flow expected to t t t be generated by the asset in period t k = the return investors consider appropriate for holding such an asset - usually referred to as the required return, based on riskiness and economic Copyright (C) 2000 by Harcourt, Inc. All rights conditions reserved. 7-4 Valuation of Financial Assets: Bonds - long term debt instruments Key Terms Principal Amount, Face Value, Maturity Value, Par Value: The amount of money the firm borrows and promises to repay at some future date, often at maturity. Coupon Payment: The specified number of dollars of interest paid each period, generally each six months, on a bond. Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-5 Key Terms Coupon Interest Rate: The stated annual rate of interest paid on a bond. Maturity Date: A specified date on which the par value of a bond must be repaid. Original Maturity: The number of years to maturity at the time the bond is issued. Call Provision: Gives the issuer right to pay off bonds prior to maturity. Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-6 The Basic Bond Valuation Model kd = required rate of return on a debt instrument N = number of years before the bond matures INT = dollars of interest paid each year (Coupon rate x Par value) M = par or face, value of the bond to be paid off at maturity Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-7 Bond Value V d INT INT 1 k d 1 1 k d 2 ... INT M N t 1 k 1 k d d t 1 INT(PVIFA k ,N d INT M 1 k d N 1 k d N ) M(PVIF k ,N d ) Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-8 Genesco 15%, 15year, $1,000 bonds valued at 15% required rate of return Numerical solution: Bond value 1 1 1 . 15 15 $ 150 0 . 15 1 $ 1, 000 1.15 15 Vd = $150 (5.8474) + $1,000 (0.1229) = $877.11 + $122.89 = $1,000 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-9 Genesco 15%, 15year, $1,000 bonds valued at 15% required rate of return Tabular solution: Look up the PVIF and PVIFA values in Tables A-1 and A-2 and insert them in the equation Vd = $150 (5.8474) + $1,000 (0.1229) = $877.11 + $122.89 = $1,000 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-10 Genesco 15%, 15year, $1,000 bonds valued at 15% required rate of return Financial calculator solution: INPUTS OUTPUT 15 N 15 I/YR PV - 1000 150 PMT 1000 FV Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-11 Changes in Bond Values Over Time If the market rate associated with a bond, kd, equals the coupon rate of interest, the bond will sell at its par value. If interest rates in the economy fall after the bonds are issued, kd is below the coupon rate. The interest payments and maturity payoff stay the same, but the PVIF and PVIFA values are based on the new kd increasing the bond value Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-12 Changes in Bond Values Over Time Current yield INT Vd Current yield is the annual interest payment on a bond divided by its current market value Beginning Ending Capital bond value bond value gains yield Beginning bond value V d, End V d, Begin V d, Begin Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-13 Changes in Bond Values Over Time Discount Bond A bond that sells below its par value, which occurs whenever the going rate of interest rises above the coupon rate Premium Bond A bond that sells above its par value, which occurs whenever the going rate of interest falls below the coupon rate Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-14 Changes in Bond Values Over Time An increase in interest rates will cause the price of an outstanding bond to fall A decrease in interest rates will cause the price to rise The market value of a bond will always approach its par value as its maturity date approaches, provided the firm does not go bankrupt Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-15 Time path of value of a 15% Coupon, $1000 par value bond Year k = 10% d when interest rates 0 $1,380.30 are 10%, 15%, 1 $1,368.33 2 $1,355.17 and 20% 3 4 5 6 7 8 9 10 11 12 13 14 15 $1,340.68 $1,324.75 $1,307.23 $1,287.95 $1,266.75 $1,243.42 $1,217.76 $1,189.54 $1,158.49 $1,124.34 $1,086.78 $1,045.45 $1,000.00 k d = 15% k d = 20% $1,000.00 $766.23 $1,000.00 $769.47 $1,000.00 $773.37 $1,000.00 $778.04 $1,000.00 $783.65 $1,000.00 $790.38 $1,000.00 $798.45 $1,000.00 $808.14 $1,000.00 $819.77 $1,000.00 $833.72 $1,000.00 $850.47 $1,000.00 $870.56 $1,000.00 $894.68 $1,000.00 $923.61 $1,000.00 $958.33 $1,000.00 $1,000.00 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-16 Changes in Bond Values Over Time Time path of value of a 15% Coupon, $1000 par value bond when interest rates are 10%, 15%, and 20% Bond Value $1,500 Kd < Coupon Rate $1,250 Kd = Coupon Rate $1,000 $750 Kd > Coupon Rate $500 $250 $0 1 3 5 7 9 11 13 15 Years Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-17 Finding the Interest Rate on a Bond: Yield to Maturity YTM is the average rate of return earned on a bond if it is held to maturity Annual Accrued interest capital gains Approximate yield to maturity Average value of bond (does not consider time value of money) M - Vd INT N 2 Vd M 3 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-18 Bond Values with Semiannual Compounding INT 2N Vd t 1 2 kd 1 2 t INT PVIFA 2 M kd 1 2 kd 2 ,2N 2N M PVIF kd 2 ,2N Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-19 Interest Rate Risk on a Bond Interest Rate Price Risk - the risk of changes in bond prices to which investors are exposed due to changing interest rates Interest Rate Reinvestment Rate Risk the risk that income from a bond portfolio will vary because cash flows have to be reinvested at current market rates Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-20 Value of Long and Short-Term 15% Annual Coupon Rate Bonds Value of Current Market Interest Rate, k 1-Year Bond 14-Y ear Bond d 5% $ 1,095.24 $ 1,989.86 10% 15% 20% 25% $ $ $ $ 1,045.45 1,000.00 958.33 920.00 $ $ $ $ 1,368.33 1,000.00 769.47 617.59 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-21 Value of Long and Short-Term 15% Annual Coupon Rate Bonds Bond Value ($) 2,000 14-Year Bond 1,500 1,000 1-Year Bond 500 0 5 10 15 20 25 Interest Rate, k d (%) Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-22 Bond Prices in Recent Years Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-23 Valuation of Financial Assets Equity (Stock) Common Stock Preferred Stock – hybrid • similar to bonds with fixed dividend amounts • similar to common stock as dividends are not required and have no fixed maturity date Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-24 Stock Valuation Models Terms: Expected Dividends Dˆ t dividend the stockholde r expects to recieve at the end of Year t D 0 is the most recent dividend Dˆ 1 is the next dividend and it will expected to be paid, be paid at the end of this year Dˆ 2 is the dividend All future dividends estimates already paid expected at the end of two years are expected values, so the may differ among investors Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-25 Stock Valuation Models Terms: Market Price P0 the price at which a stock sells in the market tod ay Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-26 Stock Valuation Models Terms: Intrinsic Value Pˆ 0 the value of an asset that , in the mind of an investor, is justified by the facts and may be different from the asset' s current market price, its book value , or both Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-27 Stock Valuation Models Terms: Expected Price Pˆ t the expected price of the stock at the end of each Year t Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-28 Stock Valuation Models Terms: Growth Rate g the expected in dividends rate of change per share Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-29 Stock Valuation Models Terms: Required Rate of Return k s the minimum rate of return on a common stock that stockholde consider acceptable given its riskiness and returns available other investment rs on s Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-30 Stock Valuation Models Terms: Dividend Yield ˆ D 1 P0 the expected dividend divided by the current price of a share of stock Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-31 Stock Valuation Models Terms: Capital Gain Yield P1 P0 the change in price (capital gain) P0 during a given year divided price at the beginning by its of the year Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-32 Stock Valuation Models Terms: Expected Rate of Return ˆk the rate of return on a common s stock that an individual investor expects to receive; equal to the expected dividend yield plus the expected capital gains yield Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-33 Stock Valuation Models Terms: Actual Rate of Return k s the rate of return on a common stock that actually an individual receives, investor after the equal to the dividend fact; yield plus the capital gains yield Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-34 Expected Dividends as the Basis for Stock Values If you hold a stock forever, all you receive is the dividend payments The value of the stock today is the present value of the future dividend payments Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-35 Expected Dividends as the Basis for Stock Values V s Pˆ 0 PV of expected future dividends Value of Stock ˆ D 1 1 k s 1 t 1 ˆ D 2 1 k s 2 ˆ D 1 ks ˆ D t 1 k s t Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-36 Stock Values with Zero Growth A Zero Growth Stock is a common stock whose future dividends are not expected to grow at all ˆ D ˆ ... D ˆ D g 0, and D 2 0 1 Pˆ 0 D 1 k s 1 D 1 k s 2 ... D 1 k s Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-37 Normal, or Constant, Growth Growth that is expected to continue into the foreseeable future at about the same rate as that of the economy as a whole g = a constant Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-38 Normal, or Constant, Growth (Gordon Model) D 0 1 g 1 Pˆ 0 1 1 k s D 0 1 g ks g D 0 1 g 2 1 2 ks D 0 1 g 1 ks ˆ D 1 ks g Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-39 Expected Rate of Return on a Constant Growth Stock Dividend yield Expected growth rate, or capital gains yield ˆk s ˆ D1 P0 g Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-40 Valuing Stocks with Nonconstant Growth Nonconstant Growth: The part of the life cycle of a firm in which its growth is either much faster or much slower than that of the economy as a whole Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-41 Valuing Stocks with Nonconstant Growth 1. Compute the value of the dividends that experience nonconstant growth, and then find the PV of these dividends 2. Find the price of the stock at the end of the nonconstant growth period, at which it has become a constant growth stock, and discount this price back to the present 3. Add these two components to find the intrinsic value of the stock, Pˆ . 0 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-42 Stock Market Equilibrium 1. The expected rate of return as seen by the marginal investor must equal the required rate of return, k ^ =k , x x 2. The actual market price of the stock must equal its intrinsic value as estimated by the marginal investor, P ^ P 0 = 0 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-43 Changes in Stock Prices Investors change the rates of return required to invest in stocks Expectations about the cash flows associated with stocks change Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-44 The Efficient Markets Hypothesis The weak form of the EMH states that all information contained in the past price movements is fully reflected in current market prices. The semistrong form states that current market prices reflect all publicly available information The strong form states that current market prices reflect all pertinent information, whether publicly available or privately held. Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-45 Valuation of Real (Tangible) Assets A company proposes to buy a machine so it can manufacture a new product. After five years the machine will be worthless, but during the five years it is used, the company will be able to increase its net cash flows by the following amounts: Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-46 Valuation of Real (Tangible) Assets Year 1 2 3 4 5 Expected Cash Flow, CF $120,000 $100,000 $150,000 $80,000 $50,000 To earn a 14% return on investments like this, what is the value of this machine? Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-47 Cash Flow Time Lines 0 14% 1 $120,000 2 3 4 5 $100,000 $150,000 $80,000 $50,000 PV of $120,000 PV of $100,000 PV of $150,000 PV of $80,000 PF of $50,000 Asset Value =V0 $ 120 , 000 1 . 14 1 $ 100 , 000 1 . 14 2 $ 150 , 000 1 . 14 3 $ 80 , 000 1 . 14 4 $ 50 , 000 1 . 14 5 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 7-48 End of Chapter 7 Valuation Concepts Copyright (C) 2000 by Harcourt, Inc. All rights reserved.