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Valuation Concepts Chapter 10 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 Basic Valuation Asset value V ^ CF 1 1 k 1 N t 1 ^ CF 2 1 k 2 ^ CF N N 1 k ^ CF t 1 k t ^t = the cash flow expected to be generated by CF the asset in period t Basic Valuation k = the return investors consider appropriate for holding such an asset usually referred to as the required return, based on riskiness and economic conditions Valuation of Financial Assets - Bonds Bond is a long term debt instrument Value is based on present value of: stream of interest payments principal repayment at maturity Valuation of Financial Assets - Bonds 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 Par value) M = par or face, value of the bond to be paid off at maturity Valuation of Financial Assets - Bonds Bond value Vd N INT INT 1 k d 1 1 k d 2 INT 1 k t 1 d t M 1 k d N INT M 1 k d N 1 k d N Valuation of Financial Assets - Bonds Genesco 15%, 15year, $1,000 bonds valued at 15% required rated of return Valuation of Financial Assets - Bonds Numerical solution: 1 15 1 1 . 15 Bond $150 0.15 value 1 $1,000 15 1.15 Vd = $150 (5.8474) + $1,000 (0.1229) = $877.11 + $122.89 = $1,000 Valuation of Financial Assets - Bonds Financial Calculator Solution: Inputs: N = 15; I = k = 15; PMT = INT = 150 M = FV = 1000; PV = ? Output: PV = -1,000 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 Changes in Bond Values over Time 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, causing the bond’s value to increase (investors demand lower returns, so they are willing to pay higher prices for bonds). Changes in Bond Values over Time Current yield is the annual interest payment on a bond divided by its current market value Current INT yield Vd Ending Beginning bond value bond value V Capital d, End Vd, Begin gains Vd,Begin Beginning bond value yield 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 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 Time path of value of a 15% Coupon, $1000 par value bond when interest Year k d = 10% k d = 15% k d = 20% rates are 10%,$1,000.00 15%, and 20% 0 $1,380.30 $766.23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 $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 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $769.47 $773.37 $778.04 $783.65 $790.38 $798.45 $808.14 $819.77 $833.72 $850.47 $870.56 $894.68 $923.61 $958.33 $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 $1,250 Kd < Coupon Rate Kd = Coupon Rate $1,000 $750 $500 Kd > Coupon Rate $250 $0 1 3 5 7 9 11 13 15 Years Yield to Maturity YTM is the average rate of return earned on a bond if it is held to maturity Approximate yield to maturity Annual Accrue d interest capital gains Average value of bond M - Vd INT N 2 Vd M 3 Bond Values with Semiannual Compounding INT 2N M 2 Vd t 2N t 1 kd kd 1 1 2 2 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 Value of Long and Short-Term 15% Annual Coupon Rate Bonds Current Market Interest Rate, k d 5% 10% 15% 20% 25% Value of 1-Year 14-Year Bond Bond $ 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 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 (%) 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 Stock Valuation Models Terms: Stock Valuation Models Terms: Expected Dividends D̂ t dividend the stockholde r expects to recieve at the end of Year t D 0 is the most recent dividend already paid D̂1 is the next dividend expected to be paid, and it will be paid at the end of this year D̂ 2 is the dividend expected at the end of two years All future dividends are expected values, so the estimates may differ among investors Stock Valuation Models Terms: Market Price P0 the price at which a stock sells in the market tod ay Stock Valuation Models Terms: Intrinsic Value P̂0 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 Stock Valuation Models Terms: Expected Price P̂t the expected price of the stock at the end of each Year t Stock Valuation Models Terms: Growth Rate g the expected rate of change in dividends per share Stock Valuation Models Terms: 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 Stock Valuation Models Terms: Dividend Yield D̂1 the expected dividend divided P0 by the current price of a share of stock Stock Valuation Models Terms: 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 Stock Valuation Models Terms: Expected Rate of Return k̂ s the rate of return on a common stock that an individual investor expects to receive expected dividend yield expected capital gains yield Stock Valuation Models Terms: Actual Rate of Return k s 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 Stock Valuation Models 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 Stock Valuation Models Expected Dividends as the Basis for Stock Values Value of Stock Vs Pˆ 0 PV of expected future dividends D̂1 D̂ 2 D̂ 1 2 1 k s 1 k s 1 k s D̂ t t t 1 1 k s Stock Valuation Models Stock Values with Zero Growth A zero growth stock is a common stock whose future dividends are not expected to grow at all D D D P̂0 1 2 1 k s 1 k s 1 k s D P̂0 ks D k̂ s P0 Stock Valuation Models 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 Stock Valuation Models Normal, or Constant, Growth (Gordon Model) D0 1 g D0 1 g D0 1 g P̂0 1 2 1 k s 1 k s 1 k s 1 D 0 1 g D̂1 ks g ks g 2 Expected Rate of Return on a Constant Growth Stock k̂ s D̂1 P0 g Dividend yield Capital gain 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 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 becomes 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, P̂. 0 Changes in Stock Prices Investors change the rates of return required to invest in stocks Expectations about the cash flows associated with stocks change Valuation of Real (Tangible) Assets Valuation is still based on expected cash flows of the asset 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? Cash Flow Time Lines 0 14% 1 2 3 4 5 $120,000 $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 $356,790 $120,000 $100,000 $150,000 $80,000 $50,000 1 2 3 4 1.14 1.14 1.14 1.14 1.145 End of Chapter 10 Valuation Concepts