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Chapter 5 Valuation Concepts 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. 2 Basic Valuation The Value of the Asset = the sum of the discounted cash flows the asset is expected to generate over time Required return = the rate you use to discount the cash flows back. = the rate of return investors consider appropriate for holding such an asset = based on riskiness and economic conditions 3 Key Terms for Bonds Principal Amount = Face Value = Maturity Value,= Par Value: The amount of money borrowed Coupon Payment: The specified number of dollars of interest paid each period, generally each six months, on a bond. 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 the right to pay off bonds prior to maturity. 4 Task: Find the present Value of Genesco’s 15%, 15-year, $1,000 bonds valued at 15% required rate of return 5 Task: Find the present Value of Genesco’s 15%, 15-year, $1,000 bonds valued at 15% required rate of return Financial calculator solution: INPUTS OUTPUT 15 N 15 I/YR ? 150 PV PMT -1000 1000 FV 6 Changes in Bond Values Over Time Par Value Bond Discount Bond Premium Bond 7 Par Value Bonds Par Value Bond: When the going interest rate = the bond’s coupon interest rate The market value of a bond will always approach its par value as its maturity date approaches, provided the firm does not go bankrupt. 8 Discount Bonds An increase in interest rates in the economy causes the price to fall Discount Bond = when a bond sells below its par value occurs whenever the going rate of interest rises above the coupon rate The bond value decreases so that the rate of return investors earn equates to the higher kd. 9 Premium Bonds A decrease in interest rates in the economy causes the bond price to rise Premium = when a bond sells above its par value occurs whenever the going rate of interest falls below the coupon rate The bond value increases so that the rate of return investors earn equates to the lower kd. 10 Calculating a Bond’s Current Yield Current yield = the annual interest payment on a bond divided by its current market value Current yield INT Vd 11 Time path of value of a 15% Coupon, $1000 par value bond when interest rates are 10%, 15%, and 20% Year 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 k d = 10% $1,380.30 $1,368.33 $1,355.17 $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 12 $1,000.00 $1,000.00 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 13 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. Financial calculator solution: INPUTS OUTPUT 15 N ? -950 I/YR PV 15.89 150 PMT 1000 FV 14 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 (presumably lower) market rates. 15 Value of Long and Short-Term 15% Annual Coupon Rate Bonds Value of Current Market 1-Year Bond 14-Year Bond Interest Rate, k d 5% 10% 15% 20% 25% $ $ $ $ $ 1,095.24 1,045.45 1,000.00 958.33 920.00 $ $ $ $ $ 1,989.86 1,368.33 1,000.00 769.47 617.59 16 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 17 Stock Valuation Models Term: Expected Dividends D̂ t dividendthe stockholder expects to receive at the end of Year t D0 is the most recent dividendalready paid D̂1 is the next dividendexpected to be paid, and it willbe paid at the end of this year D̂ 2 is the dividendexpected at the end of two years All future dividendsare expected values,so the estimates may differ among investors. 18 Stock Valuation Models Term: Market Price P0 the price at which a stock sells in the market tod ay. 19 Stock Valuation Models Term: Intrinsic Value P̂0 the value of an asset that , in the mind of an investor, is justified by the facts; may differ from the asset' s current market price, its book value , or both. 20 Stock Valuation Models Term: Expected Price P̂t the expected price of the stock at the end of each Year t. 21 Stock Valuation Models Term: Growth Rate g the expected rate of change in dividendsper share 22 Stock Valuation Models Term: Required Rate of Return k s the minimum rate of return on a common stock that stockholde rs consider acceptable given its riskiness and returns available on other investment s. 23 Stock Valuation Models Term: Dividend Yield D̂1 the expected dividend divided P0 by the current price of a share of stock 24 Stock Valuation Models Term: Capital Gain Yield P1 P0 the change in price (capital gain) P0 during a given year divided by its price at the beginning of the year 25 Stock Valuation Models Term: Expected Rate of Return = Expected dividend yield + capital gains yield k̂ s the rate of return on a common stock that an individual investor expects to receive D̂1 P1 P0 P0 P0 26 Stock Valuation Models Term: Actual Rate of Return ks the rate of return on a common stock that an individual investor actually receives, after the fact; equal to the dividend yield plus the capital gains yield. 27 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. 28 Stock Values with Zero Growth A Zero Growth Stock is a common stock whose future dividends are not expected to grow at all = A PERPETUITY g 0, and D̂ 1 D̂ 2 D̂ D 0 D P̂0 ks 29 Normal, or Constant, Growth Normal Growth is 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 30 Normal, or Constant, Growth (Gordon Growth Model) A Constant Growth Stock is a common stock whose future dividends are expected to grow at a constant rate = A GROWING PERPETUITY P̂0 Div1 ks g 31 Expected Rate of Return on a Constant Growth Stock Rearrange the formula for the price to get Dividend Yield k̂ s D̂1 g P0 32 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. 33 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 time 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 P0. 34 Stock Market Equilibrium 1. The expected rate of return as seen by the marginal investor must equal the required ^ =k . rate of return, 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. 35 Changes in Stock Prices Investors change the rates of return required to invest in stocks. Expectations change about the cash flows associated with particular stocks. 36 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, 37 whether publicly available or privately held. 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: 38 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? 39 Calculator Solution: In “CF” register: Type: 2nd, CE/C to clear information stored CF0 = 0 C01 = 120,000 F01 = 1 C02 = 100,000 F02 = 1 C03 = 120,000 F03 = 1 C04 = 80,000 F04 = 1 C05 = 50,000 F05 = 1 In “NPV” Register: Type: I = 14, enter, down arrow See: NPV = (varies) Type: CPT See: NPV = 356,790.50 40 For Next Class Review Chapter 5 materials Do Chapter 5 homework Prepare for Quiz on Chapter 5 Read Chapter 6 (Capital Budgeting) 41