VIEWS: 27 PAGES: 37 POSTED ON: 2/14/2011
Business Valuation PREPARED BY KELDON BAUER, PHD FOR FIL 240 Introduction The valuation of all financial securities is based on the expected PV of future cash flows. E CF 1 E CF 2 E CF n P0 E CF0 1 k 1 k 2 1 k n n E CF t 1 k t 0 t Introduction n E CFt P0 1 k t 0 t E[CFt] = Expected cash flow at time t. k = The required return (based on economic conditions & riskiness). Value increases as cash flow increases or k decreases. Bond Valuation Two major components Interest payments (an annuity). Principal (future lump-sum). n 1 k 1 k Interest Par ValueB t n t 1 B B = PV of Annuity + PV of Par Value Bond Valuation - Example 1 The value of a 15 year $10,000 bond, paying semi-annual payments of $500, when market rate is 10%. VB PV of Annuity + PV of Par Value 1 1- 1+ 0.05 30 = 500 10,000 1 30 0.05 1 0.05 7,686.23 2,313.77 10,000 Bond Valuation - Example 2 The value of a 7 year $10,000 bond, paying semi-annual payments of $500, when market rate is 10%. VB PV of Annuity + PV of Par Value 1 1- 1+ 0.05 14 = 500 10,000 1 14 0.05 1 0.05 4,949.32 5,050.68 10,000 - Same as before! Bond Valuation - Example 3 The value of a 7 year $10,000 bond, paying semi-annual payments of $500, when market rate is 8%. VB PV of Annuity + PV of Par Value 1 1- 1+ 0.04 14 = 500 10,000 1 14 0.04 1 0.04 5,28156 5,774.75 11,056.31 - More than before! . Bond Valuation - Example 4 The value of a 7 year $10,000 bond, paying semi-annual payments of $500, when market rate is 12%. VB PV of Annuity + PV of Par Value 1 1- 1+ 0.06 14 = 500 10,000 1 14 0.06 1 0.06 9,070.50 4,647.49 9,070.50 - Less than before! Some Conclusions Return or loss on bonds comes from two components. Interest Payment (Current Yield) = (Interest Payment)/VB Change in Face Value (Capital Gain) = (VEnding - VBeginning)/VBeginning Current Yield - Example The value of a 7 year $10,000 bond, paying semi-annual payments of $500, when market rate is 8%. Interest Payment Current Yield = # of Payments per year Value of Bond t 500 2 9.04% 11,056.31 Capital Gains Yield - Example The value of a 7 year $10,000 bond, paying semi-annual payments of $500, when market rate is 8%. Value t+1 Value t Capital Gains Yield = # of Payments per year Value t 10,948.56 11,056.31 2 104% . 11,056.31 Total Yield - Example The value of a 7 year $10,000 bond, paying semi-annual payments of $500, when market rate is 8%. Total Yield = Current Yield + Capital Gains Yield 9.04% 104% 8.00% market rate . Some Conclusions When market rate = kB the bond sells at par or face value. When market rate < kB the bond sells at a premium. When interest rates go down, bond prices go up. When market rate > kB the bond sells at a discount. Some Conclusions As time to maturity approaches zero, market value approaches face value. If a 15 year, 10% coupon bond at 5% 10% and 15% market rates were sold on the market, the values of the bond would be as shown in the following graph. Value of a 10% Coupon Bond 1,600 Market Rate =5% 1,400 1,200 Market Value Market Rate =10% 1,000 800 Market Rate =15% 600 400 200 0 -1 1 3 5 7 9 11 13 15 Time Some Conclusions As time to maturity approaches zero, market value approaches the face value of the bond. Yield to Maturity (YTM) Yield to Maturity (YTM): The effective interest rate earned on the bond. Your calculator can calculate it directly. Input the n, PV (Market Value), PMT (semi-annual payments), FV (Par Value), and have it compute i (then adjust). YTM - Example What is the yield-to-maturity of a bond with current market value of $950.51, a par value of $1,000 (which is returned in seven years), making a coupon payment of $45 every six months? Answer: 10.00% Bond Values If one knows the market interest rate, the maturity, the coupon payments, and the par value, one can calculate the bond’s value by using one’s calculator! Bond Values - Example What is the market value of a bond with current market rate of 10%, a par value of $1,000 (which is returned in seven years), making a coupon payment of $54 every six months? Answer: $1,039.59 Interest Rate Risk Two types of interest rate risk associated with bond value. Price Risk Reinvestment Risk Price Risk: The risk of change in price give change in interest. As interest increases, value decreases. Price Risk - Effect of Maturity Value of 10% Coupon Bond 1,600 1,400 1,200 Bond Value 1,000 1-Year Bond 800 600 400 14-Year Bond 200 0 0% 5% 10% 15% 20% 25% 30% Market Rate Interest Rate Risk Reinvestment Risk: The risk of worse reinvestment opportunities when repaid. When interest rates increase reinvestment opportunities improve. Note: Price and Reinvestment Risks go in opposite directions. Price Risk - Effect of Payment 14 Year Debt Instrument - 10% Contract Rate 2,500 2,000 Bond Value 1,500 Coupon Bond Zero Coupon 1,000 Monthly Loan 500 0 0% 5% 10% 15% 20% 25% 30% Market Rate Equity Valuation - Dividend Based Models The first economic based valuation models assessed the present value of expected dividends. Myron Gordon applied the previous equation to expected dividends, assuming a constant growth rate. Since stocks never mature, n must be allowed to approach infinity. Dividend Based Models The Gordon Constant Growth Model: D0 1 g D0 1 g D0 1 g 2 [1] P0 1 k s 1 k s 2 1 k s multiplyin g both sides by 1 g 1 k s [2] 1 g P D0 1 g 2 D0 1 g 3 D0 1 g 1 k s 0 1 k s 2 1 k s 3 1 k s Gordon Constant Growth Model Subtracting [2] from [1]: P0 1 g P D0 1 g 1 k s 0 1 k s 1 k s 1 g D0 1 g 1 k 1 k 1 k P0 s s s k s g D0 1 g 1 k 1 k P0 s s Gordon Constant Growth Model Solving for PV: k s g 1 k s D0 1 g 1 k s P0 1 k k g 1 k k g s s s s D0 1 g ˆ D1 P0 ks g ks g Free Cash Flow Models Many stocks do not offer a dividend. If the same assumptions are made, except that free cash flow, not dividends are being valued, the same process can be used to derive another valuation model: FCF0 1 g P0 k s g What Affects Stock Prices? FCF0 1 g P0 k s g Stock prices should therefore depend on: Expected cash flow. Growth rate. The company’s required return. What Affects Stock Prices? Required return is a function of the Capital Asset Pricing Model (CAPM): k s RF km RF s Therefore ks depends on: Interest rates. Systematic risk of the firm. Market risk aversion. Non-Constant Growth Valuation Since constant growth is unlikely, we will now consider how to value stock under non-constant growth. First, project dividends (or free cash flows) as far as practical. From there estimate a constant growth rate. Then take the PV as we discussed in an earlier chapter. Non-Constant Growth - Example If Buford’s Bulldozer is expected to pay the following dividends, and then grow indefinitely at 4.5% (assuming a discount rate of 14.50%), what would its stock value be? T im e Div idends 1 1 .25 2 2.7 5 3 1 .50 4 2.80 5 3.20 Non-Constant Growth - Example First we consider the price of the stock at time five. 3.20(1 0.045) 3.344 D5 1 g P5 $33.44 k g 0145 0.045 010 s . . Non-Constant Growth - Example Next we sum all period cash flows. T im e Div idends Stock Value T otal 1 1 .25 1 .25 2 2.7 5 2.7 5 3 1 .50 1 .50 4 2.80 2.80 5 3.20 33.44 36.64 Non-Constant Growth - Example 0 1 2 3 4 5 14.5% $1.25 $2.75 $1.50 $2.80 $36.64 $ 1.09 $ 2.10 $ 1.00 $ 1.63 $18.62 $24.44 = Present Value Other Valuation Methods Book Value Method. Liquidation Value Method. Price/Earnings (P/E) Multiples.