Chapter 18

# Chapter 18 - THE OPTION TO EXPAND Year 1 2 3 4 5 CF of...

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Unformatted text preview: THE OPTION TO EXPAND Year 1 2 3 4 5 CF of single machine-1000 220 300 400 200 150 Discount rate for machine cash flows 12% Riskless discount rate 6% 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 &lt;-- =B24 NPV of total project-63.48 &lt;-- =B8+B10*B11 Black-Scholes Option Pricing Formula S 932.52 PV of machine CFs X 1000.00 Exercise price = Machine cost r 6.00% Risk-free rate of interest T 1 Time to maturity of option (in years) Sigma 40% &lt;-- Volatility-0.9818 &lt;-- (LN(S/X)+(r+0.5*sigma^2)*T)/(sigma*SQRT(T))-0.9918 0.1631 0.1606 Option value = BS call price 0.80 Data Table -63.48 &lt;-- Table header: =B12 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 &lt;-- d 1 - sigma*SQRT(T) N(d 1 ) &lt;--- Uses formula NormSDist(d 1 ) N(d 2 ) &lt;--- Uses formula NormSDist(d 2 ) &lt;-- S*N(d 1 )-X*exp(-r*T)*N(d 2 ) 0% 10% 20% 30% 40% 50% 60% 70% 80% 100 200 300 400 500 600 700 Project Value as Function of Sigma Sigma A B C D 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 PRICING AN ABANDONMENT OPTION Market data State prices Expected market return 12% 0.3087 ### Sigma of market return 30% 0.6347 ### Risk-free rate 6% One-period &quot;up&quot; and &quot;down&quot; of market Up 1.521962 &lt;-- =EXP(B4+B5), note that a valid alternative is &quot;up&quot; = EXP(B5) Down 0.83527 &lt;-- =EXP(B4-B5), note that a valid alternative is &quot;down&quot; = EXP(-B5) Project cash flows State-dependent present value factors 150 0.0953 &lt;-- =E4^2 100 0.3087 80 0.1959 &lt;-- =E4*E5-50 1 80 0.1959 &lt;-- =E4*E5-50 0.6347-60 0.4028 &lt;-- =E5^2 State-by-state present value 14.2981 &lt;-- =E15*K15 30.8740 15.6755 &lt;-- =E17*K17-50 15.6755 &lt;-- =E19*K19-31.7328-24.1673 &lt;-- =E21*K21 Net present value-29.38 &lt;-- =SUM(A24:E30) Cash flows with abandonment Present value with abandonment 150 14.29808 100 30.87402 80 15.67551-50-50 Present value with abandonment 10.85 q u q d =C16*I16 A B C D E F G H I J K L M 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 46 PRICING AN ABANDONMENT OPTION Market data State prices Expected market return...
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## This note was uploaded on 02/02/2012 for the course BUSINESS 201 taught by Professor Acknan during the Spring '11 term at MIT.

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Chapter 18 - THE OPTION TO EXPAND Year 1 2 3 4 5 CF of...

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