VIEWS: 0 PAGES: 35 POSTED ON: 10/21/2011 Public Domain
Part Three Valuation Outline of Valuation Discounted Cash Flow Analysis Valuation Model Risk and Return Type of Cash Flow A lump sum $0 $0 $100 $0 An annuity of $100: $0 $100 $100 $100 An uneven cash flow stream ($50) $100 $75 $50 Future Value Find the FV of $100 left for 3 years in an account paying 10 percent annual interest: FV = PV(1 + k)" = PV(FVIFk n) = $100(1.10)3 = $100(1.3310) = $133.10. Present Value Find the PV of $100 to be received in 3 years if the appropriate interest rate is 10 percent: n PV = FVn/(1 + k) = $100(1/1.10)3 =$100(0.7513) = $75.13. Annuities Ordinary Annuity: PV $100 $100 $100 FV Annuity Due $100 $100 $100 FV PV Future Value of an Annuity (Time Line Approach) 0 $100 $100 $100 $110 10% $121 $331 Future Value of an Annuity (Formula Approach) FVAn = PMT(FVIFA) = $100(3.3100) = $331. If the annuity is an annuity due, then : FVAn(Annuity due) = FVAn(1 + k) =$331(1.10)= $364.10 Present Value of an Annuity (Time Line Approach) 0 $100 $100 $100 10% $ 90.91 82.64 —————— 75.13————————— $248.68 Present Value of an Annuity (Formula Approach) PVA= PMT(PVIFA k,n) = $100(2.4869) = $248.69. The present value of an annuity due is PVA(Annuity due) = PVA(1 + k) = $248.69(1.10) = $273.56. Uneven Cash Flow Stream 0 $100 $300 $300 $(50) 10% 90.91 247.93 225.39 (34.15) $530.08 Finding the Interest Rate $100(1 + x)3 = $125.97 $100(FVIF k,3) = $125.97 FVIF k,3 = 1.2597 Look at Table of Future Value for K. The 1.2597 is at Row 3 in the 8% column. Therefore, k = 8%. General Valuation Model The value of any asset can be found as the present value of its expected future cash flows, CFi, discounted at the rate k: V= CF 1 + CF2 + CF3 (1 +k)1 (1 +k)2 (1 +k)n• Bond Valuation V=l(PVIFA + M(PVIF k,n) k,n) =$100(PVIFA 10%,10) + $1,000(PVIF 10%,10) =$614.46 + $385.54 =$1,000. Yield to Maturity of Bond Par value = $1,000 Current price = $887 Annual coupon = $100 Term to maturity = 10 years 0 1 2 ……… 9 10 -$887 $100 $100 $100 $100 $1,000 $887 = $1oo(PVIFA ytm,10) + $1,ooo(PVIFytm, 10) YTM = 12%. Current Yield of Bond Annual coupon payment Current yield = Current price General Stock Valuation Model D1 P0 = ks – g D0(1+g) = kg - g Value of Perpetuity PMT V = k $2 = = $12.50. 0.16 Supernormal Growth $2.000 $2.600 $3.380 $4.394 $4.658 g = 30% g = 30% g = 30% g = 6% g = 6% PV of Supernormal Dividends PV D1 = $2.600/(1.16)1 = $2.241 PV Ds2= $3.380/(1.16)2 = $2.512 PV D3 = $4.394/(1.16)3 = $2.815 $7.568 Stock Price at t = 3 p = D4 = $4.658 = $4.658 = $46.58 ks - g 0.16-0.06 0.10 PV of P3 $46.58 / (1.16) = $29.84 Value of Stock Po = $7.57 + $29.84 = $37.41. Concept of Risk Risk refers to the possibility that some unfavorable event will occur Investment risk is associated with the probability of low or negative returns on an investment. Probability Distribution (payoff Matrix) Rate of Return Demand Comapany Company for the Probability A B products Strong 0.3 100 20 Normal 0.4 15 15 Weak 0.3 -70 10 Probability of Distribution Probability of Probability of Co.B Co.A -70 100 Rate of Return 10 15 20 15 Probability Density Expected Rate of Return Expected rate of return n ˆ k i 1 pi ki = .3(100%)+.4(15%)+.3(-70) = 15% ˆ Deviation kj k Variance and Standard Deviation n Variance 2 ( Ki K ) Pi 2 i 1 n Std Deviation (K i 1 i K ) Pi 2 The smaller the standard deviation, the lower the risk associated with the event. Coefficient of Variation The coefficient of variation shows the risk per unit of return and a better measure for evaluation risk in situation where investments have substantially different expected returns. Coefficien of Deviation CV t ˆ K Portfolio Return ˆp Portfolio Re turn K ˆ ˆ ˆ W K ....... W K W1 K1 2 2 n n n Wi K i ˆ i 1 Portfolio Risk The risk of a portfolio depends not only on the standard deviation of the individual stocks, but also on the correlation between the stocks. Portfolio Risk m n W W j 1 k 1 j k jk j , k rj , kjk When R = -1 Year stock A % Stock B % Portfolio AB % 1992 40 -10 15 1993 -10 40 15 1994 35 -5 15 1995 -5 35 15 1996 15 15 15 Average 15 15 15 return standard 22.6 22.6 0 deviation When r = +1 Year stock A % Stock B % Portfolio AB % 1992 -10 -10 -10 1993 40 40 40 1994 -5 -5 -5 1995 35 35 35 1996 15 15 15 Average 15 15 15 return standard 22.6 22.6 22.6 deviation When +1 > r > -1 Year stock A % Stock B % Portfolio AB % 1992 40 28 34 1993 -10 20 5 1994 35 41 38 1995 -5 -17 -11 1996 15 3 9 Average 15 15 15 return standard 22.6 22.6 20.6 deviation Classification of Risk Total risk can be separated into two parts: Market risk Company-specific risk Effects of Portfolio Size on Risk