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Unformatted text preview: 61 P = $15; X = $15; t = 0.5; rRF = 0.06; 2 = 0.12; d1 = 0.24495; d2 = 0.0000; N(d1) = 0.59675; N(d2) = 0.500000; V = ? Using the BlackScholes option's value as: V = P[N(d1)] Option Pricing Model, you calculate the Xe rRF t [N(d2)] = $15(0.59675)  $15e(0.10)(0.5)(0.50000) = $8.95128  $15(0.9512)(0.50000) = $1.6729 $1.67. 142 a. 0 2 3 4 10% 1 8 4 4 4 4 NPV = $4.6795 million. b. Wait 2 years: 0 r = 10% 1   10% Prob. 0 0  90% Prob. 0  0 2  9  9 3  2.2  4.2 4  2.2  4.2 5  2.2  4.2 6  2.2  4.2 PV @ Yr. 2 $6.974 $13.313 Low CF scenario: NPV = (9 + 6.974)/(1.1)2 = $1.674 High CF scenario: NPV = (9 + 13.313)/(1.1)2 = $3.564 Expected NPV = .1(1.674) + .9(3.564) = 3.040 If the cash flows are only $2.2 million, the NPV of the project is negative and, thus, would not be undertaken. The value of the option of waiting two years is evaluated as 0.10($0) + 0.90($3.564) = $3.208 million. Since the NPV of waiting two years is less than going ahead and proceeding with the project today, it makes sense to drill today. 147 P = PV of all expected future cash flows if project is delayed. From Problem 142 we know that PV @ Year 2 of Low CF Scenario is $6.974 and PV @ Year 2 of High CF Scenario is $13.313. So the PV is: P = [0.1(6.974)+ 0.9(13.313] / 1.102 = $10.479. X = $9. t = 2. rRF = 0.06. 2 = 0.0111. r = 10% d1 = ln[10.479/9] + [0.06 + .5(.0111)](2) = 1.9010 (.0111)0.5 (2)0.5 d2 = 1.9010  (.0111)0.5 (2)0.5 = 1.7520 From Excel function NORMSDIST, or approximated from the table in Appendix A: N(d1) = 0.9713 N(d2) = 0.9601 Using the BlackScholes Option Pricing Model, you calculate the option's value as: V = P[N(d1)]  [N(d2)] = $10.479(0.9713) $9e(0.06)(2)(0.9601) = $10.178  $7.664 = $2.514 million. Mini Case: 13  2 ...
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 Winter '10
 Matthews
 Finance, Pricing

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