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fm3_chapter24 - A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17...

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THE OPTION TO EXPAND Year 0 1 2 CF of single machine -1000 220 300 Discount rate for machine cash flows (risk-adjusted) 12% Riskless discount rate 6% Present value of machine's future cash flows 932.52 ### NPV of single machine -67.48 ### Number of machines bought next year 5 Option value of single machine purchased in one more year 0.80 ### NPV of total project -63.48 ### Black-Scholes Option Pricing Formula S 932.52 PV of machine CFs X 1000.00 Exercise price = Machi r 6.00% Risk-free rate of interes T 1 Time to maturity of opt Sigma 40% <-- Volatility -0.9818 <-- (LN(S/X)+(r+0.5*sig -0.9918 0.1631 0.1606 Option value = BS call price 0.80 Data Table σ -63.48 ### 1% -63.48 10% -63.48 20% -63.48 30% -63.48 40% -63.48 50% -63.48 60% -63.48 70% -63.48 d 1 d 2 <-- d 1 - sigma*SQRT(T N(d 1 ) <--- Uses formula Norm N(d 2 ) <--- Uses formula Norm <-- S*N(d 1 )-X*exp(-r*T) -10% 0 100 200 300 400 500 600 700 A B C D 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
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3 4 5 400 200 150 ine cost st tion (in years) gma^2)*T)/(sigma*SQRT(T)) T) mSDist(d 1 ) mSDist(d 2 ) )*N(d 2 ) 0% 10% 20% 30% 40% 50% 60% 70% Project Value as Function of Sigma Sigma E F G H I J 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
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PRICING AN ABANDONMENT OPTIO Market data State prices Expected market return 12% 0.3087 ### Sigma of market return 30% 0.6347 ### Risk-free rate 6% One-period "up" and "down" of market Up 1.52 ### Down 0.84 ### Project cash flows State-dependent pres 150 100 80 -50 1 80 -50 -60 State-by-state present value 14.2981 ### 30.8740 15.6755 ### -50 15.6755 ### -31.73 -24.1673 ### Net present value -29.38 ### Cash flows with abandonment Present value with ab 150 100 80 -50 -50 0 0 0 Present value with ab q U q D =C15*I15 A B C D E F G H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
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ON sent value factors 0.0953 #MACRO? 0.3087 0.1959 #MACRO? 0.1959 #MACRO? 0.6347 0.4028 #MACRO? bandonment 14.2981 #MACRO? 30.8740 15.6755 #MACRO? 0 0 0 bandonment 10.85 #MACRO? I J K L 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
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PRICING AN ABANDONMENT OPTIO Market data State prices Expected market return 12% 0.3087 ### Sigma of market return 30% 0.6347 ### Risk-free rate 6% One-period "up" and "down" of market Up 1.52 ### Down 0.84 ### Project cash flows State-dependent pres 150 100 80 -50 1 80 -50 -60 State-by-state present value 14.2981 ### 30.8740 15.6755 ### -50 15.6755 ### -31.73 -24.1673 ### Net present value -29.38 ### Cash flows with abandonment Present value with ab 150 100 80 -50 -50 0 -10 0 Present value with ab q U q D =C15*I15 A B C D E F G H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
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ON sent value factors 0.0953 #MACRO?
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