Now, we proceed to use the OPM: V = $56.06[N(d1)] - $75e-(0.06)(3)[N(d2)]. d1 = = -0.1085. d2 = d1 - (0.047)0.5(3)0.5 = -.1085 - 0.3755 = -0.4840. N(d1) = N(-0.1080) = 0.4568. N(d2) = N(-0.4835) = 0.3142. Therefore, V = $56.06(0.4568) - $75e-(0.06)(3)(0.3142) = $5.92. Total Value = NPV Of Project 1 + Value Of Growth Option =-$0.39 + $5.92 = $5.5 million j. What happens to the value of the growth option if the variance of the project’s return is 14.2 percent? What if it is 50 percent? How might this explain the high valuations of many dot.com companies? If risk, defined by then value of growth option goes up (see the file Answer: Ch26 σ2, goes up, for calculations): mini case.xls = 4.7%, option value = $5.92 σ2 = 14.2%, option value = $12.10 σ2 = 50%, option value = $24.09 σ2 If the future profitability of dot.com companies is very volatile (i.e., there is the potential for very high profits), then a company with a real option on those profits might have a very high value for its growth option.
Now, we proceed to use the OPM: V = $56.06[N(d1)] - $75e-(0.06)(3)[N(d2)]. d1 = = -0.1085. d2 = d1 - (0.047)0.5(3)0.5 = -.1085 - 0.3755 = -0.4840. N(d1) = N(-0.1080) = 0.4568. N(d2) = N(-0.4835) = 0.3142. Therefore, V = $56.06(0.4568) - $75e-(0.06)(3)(0.3142) = $5.92. Total Value = NPV Of Project 1 + Value Of Growth Option =-$0.39 + $5.92 = $5.5 million j. What happens to the value of the growth option if the variance of the project’s return is 14.2 percent? What if it is 50 percent? How might this explain the high valuations of many dot.com companies? Answer: If risk, defined by σ2, goes up, then value of growth option goes up (see the file Ch26 mini case.xls for calculations): σ2 = 4.7%, option value = $5.92 σ2 = 14.2%, option value = $12.10 σ2 = 50%, option value = $24.09 If the future profitability of dot.com companies is very volatile (i.e., there is the potential for very high profits), then a company with a real option on those profits might have a very high value for its growth option.
FM14e_SM_Ch26.docx