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6. Valuing the growth option with the Black-Scholes option pricing model Real option analysis can be used to alter the timing, scale, or other aspects of an investment in response to market conditions Businesses face the dilemma of whether to invest in a project or abandon it if it does not add value to the firm. Real option analysis allow financial managers to determine the financial consequences of this flexibility and the value of the option. Consider the case of Fat Sheep Media Company Fat Sheep Media Company, a social networking company, has seen triple-digit growth in its website's registrations over the past two years. Most of the website's subscribers live outside the United States, and the company is seeing a significant increase in the number of users from Brazil. As a result, Fat Sheep is considering opening a marketing office in Brazil to expand its marketing efforts there. Management, however, is not sure if the Brazilian expansion via the opening of a subsidiary office will necessarily help the company grow and increase its value. Management's uncertainty is the result of the possibility that Brazil's Internet connectivity will be insufficient to support all of Fat Sheep's forecasted growth. One of Fat Sheep's employees, Isabela, who is originally from Brazil, conducted some preliminary market research and submitted the following details about the potential five-year project: . Opening the new marketing office in Brazil will require an initial investment of $4.00 million. * According to research on Brazil's mobile technology infrastructure, Isabela noted there is a 60% probability that the country's mobile connectivity will be sufficient to generate additional advertising cash flows of $6.00 million per year for the company for the next five years. * Alternatively, there is a 40% chance that Brazil's mobile Internet connectivity will be insufficient to support Fat Sheep's desired growth in Brazil. In this case, the company expects to generate additional net advertising-related annual cash flows of only $2.00 million for the next five years. * The project's expected cost of capital is 13.00%, and the risk-free rate is 4%. The project's weighted average cost of capital (WACC) should be used to discount all cash flows Given this information, the project's expected net present value (NPV) is $16.09 million After further research, Isabela added a few more details to her proposal: If Brazil's Internet connectivity is good, then at the end of Year 3, Fat Sheep should consider investing $3.00 million to purchase an existing Brazilan marketing firm and creating a new subsidiary The new subsidiary is expected to generate $2.40 million of additional annual cash flows in year 4 and year 5. However, if the Internet connectivity in Brazil is inadequate to support Fat Sheep's desired customer growth, then the company will not invest the additional funds in year 3 or earn the expected additional advertising-related cash flows Based on Isabela's additional information, use the decision tree analysis to calculate the NPV of the project including the growth option Then, calculate the value of the growth option by itself, and select the correct answers from the choices available in the following table. Remember to use the project's cost of capital to discount all cash flows Value NPV of the project with growth option h option value Lastly, Isabela wants to use the the Black-Scholes option pricing model (OPM) to determine the value of the growth option. To do this she has collected and computed the values for several additional variables, and has given you the Black-Scholes OPM equation for the valuation of an option (V): V = P[N(d 1)]-(Xe-(risk-free rate)(t)[N(d2)] where, P the current, or a proxy, price of the value of the underlying asset (P)-which equals the present value of the delayed project's forecasted future cash flows N(di) and N(destimates of the variance of the project's expected return X-the option's strike price, which is the cost of purchasing the Brazilian firm that will become the Fat Sheep's subsidiary e-the mathematical constant equal to 2.718281828459045235360, which can be truncated and rounded to 2.7183 RF the market's risk-free rate t-the time until the option expires, which, in this situation, is assumed to be the end of third year, when the potential purchase of the subsidiary would take place According to Isabela, these variables should assume the following values Variable Project's cost of capital Current value of the delayed investment (P) N(d1), as estimated by Isabela N(d2), as estimated by Isabela Delayed investment's strike price (X) Mathematical constant e Risk-free rate (rRF) Time until the option expires (t) Value 13.00% 0.7573 0.7082 2.7183 4.00% Given these values, the estimated value of Fat Sheep's growth option using the Black-Scholes OPM (V) is 6. Valuing the growth option with the Black-Scholes option pricing model Real option analysis can be used to alter the timing, scale, or other aspects of an investment in response to market conditions Businesses face the dilemma of whether to invest in a project or abandon it if it does not add value to the firm. Real option analysis allow financial managers to determine the financial consequences of this flexibility and the value of the option. Consider the case of Fat Sheep Media Company Fat Sheep Media Company, a social networking company, has seen triple-digit growth in its website's registrations over the past two years. Most of the website's subscribers live outside the United States, and the company is seeing a significant increase in the number of users from Brazil. As a result, Fat Sheep is considering opening a marketing office in Brazil to expand its marketing efforts there. Management, however, is not sure if the Brazilian expansion via the opening of a subsidiary office will necessarily help the company grow and increase its value. Management's uncertainty is the result of the possibility that Brazil's Internet connectivity will be insufficient to support all of Fat Sheep's forecasted growth. One of Fat Sheep's employees, Isabela, who is originally from Brazil, conducted some preliminary market research and submitted the following details about the potential five-year project: . Opening the new marketing office in Brazil will require an initial investment of $4.00 million. * According to research on Brazil's mobile technology infrastructure, Isabela noted there is a 60% probability that the country's mobile connectivity will be sufficient to generate additional advertising cash flows of $6.00 million per year for the company for the next five years. * Alternatively, there is a 40% chance that Brazil's mobile Internet connectivity will be insufficient to support Fat Sheep's desired growth in Brazil. In this case, the company expects to generate additional net advertising-related annual cash flows of only $2.00 million for the next five years. * The project's expected cost of capital is 13.00%, and the risk-free rate is 4%. The project's weighted average cost of capital (WACC) should be used to discount all cash flows Given this information, the project's expected net present value (NPV) is $16.09 million After further research, Isabela added a few more details to her proposal: If Brazil's Internet connectivity is good, then at the end of Year 3, Fat Sheep should consider investing $3.00 million to purchase an existing Brazilan marketing firm and creating a new subsidiary The new subsidiary is expected to generate $2.40 million of additional annual cash flows in year 4 and year 5. However, if the Internet connectivity in Brazil is inadequate to support Fat Sheep's desired customer growth, then the company will not invest the additional funds in year 3 or earn the expected additional advertising-related cash flows Based on Isabela's additional information, use the decision tree analysis to calculate the NPV of the project including the growth option Then, calculate the value of the growth option by itself, and select the correct answers from the choices available in the following table. Remember to use the project's cost of capital to discount all cash flows Value NPV of the project with growth option h option value Lastly, Isabela wants to use the the Black-Scholes option pricing model (OPM) to determine the value of the growth option. To do this she has collected and computed the values for several additional variables, and has given you the Black-Scholes OPM equation for the valuation of an option (V): V = P[N(d 1)]-(Xe-(risk-free rate)(t)[N(d2)] where, P the current, or a proxy, price of the value of the underlying asset (P)-which equals the present value of the delayed project's forecasted future cash flows N(di) and N(destimates of the variance of the project's expected return X-the option's strike price, which is the cost of purchasing the Brazilian firm that will become the Fat Sheep's subsidiary e-the mathematical constant equal to 2.718281828459045235360, which can be truncated and rounded to 2.7183 RF the market's risk-free rate t-the time until the option expires, which, in this situation, is assumed to be the end of third year, when the potential purchase of the subsidiary would take place According to Isabela, these variables should assume the following values Variable Project's cost of capital Current value of the delayed investment (P) N(d1), as estimated by Isabela N(d2), as estimated by Isabela Delayed investment's strike price (X) Mathematical constant e Risk-free rate (rRF) Time until the option expires (t) Value 13.00% 0.7573 0.7082 2.7183 4.00% Given these values, the estimated value of Fat Sheep's growth option using the Black-Scholes OPM (V) is