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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, 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, Luana, 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, Luana 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 11.00%, and the risk-free rate is 4%. The project's WACC should be used to discount all cash flows. 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 Brazilian marketing firm and creating a new subsidiary. The new subsidiary is expected to generate $2.40 million of additional annual cash flows in years 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 Luana'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 Growth option value $20.40 million $12.75 million $7.65 million $22.37 million 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 Brazilian marketing firm and creating a new subsidiary. The new subsidiary is expected to generate $2.40 million of additional annual cash flows in years 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 Luana'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 Growth option value $0.48 million $0.576 million $0.960 million $0.384 million Lastly, Luana 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 x N(d)) - (X xerFlx N(d)) 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(d,) and NCC.)= estimates 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 TRF = 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 Variable Value Project's cost of capital 11.00% Current value of the delayed investment (P) N(d,), as estimated by Luana $2.80 million N(d), as estimated by Luana Delayed investment's strike price (X) $4.48 million Mathematical constant e $2.24 million Risk-free rate (rRF) $3.36 million Time until the option expires (t) Variable Value Project's cost of capital 11.00% Current value of the delayed investment (P) N(d,), as estimated by Luana 0.7573 N(d), as estimated by Luana 0.7082 Delayed investment's strike price (X) Mathematical constant e $2.40 million Risk-free rate (rRF) Time until the option expires (t) $ 6.00 million $4.00 million Given these values, the estimated value of Fat Sh lion using th $3.00 million final answer to three decimal places.) N(d.), as estimated by Luana 0.7082 $0.236 million Delayed investment's strike price (X) Mathematical constante 2.7183 $0.002 million Risk-free rate (PRF) 0.04% $0.378 million Time until the option expires (t) $0.189 million Given these values, the estimated value of Fat Sheep's growth option using the Black-Scholes OPM (V) is (Note: Round your final answer to three decimal places.) Variable Value Project's cost of capital 11.00% Current value of the delayed investment (P) 3 years N(d), as estimated by Luana N(d), as estimated by Luana 4 years Delayed investment's strike price (X) 5 years Mathematical constant e 2 years Risk-free rate (rRF) Time until the option expires (t) 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, 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, Luana, 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, Luana 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 11.00%, and the risk-free rate is 4%. The project's WACC should be used to discount all cash flows. 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 Brazilian marketing firm and creating a new subsidiary. The new subsidiary is expected to generate $2.40 million of additional annual cash flows in years 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 Luana'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 Growth option value $20.40 million $12.75 million $7.65 million $22.37 million 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 Brazilian marketing firm and creating a new subsidiary. The new subsidiary is expected to generate $2.40 million of additional annual cash flows in years 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 Luana'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 Growth option value $0.48 million $0.576 million $0.960 million $0.384 million Lastly, Luana 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 x N(d)) - (X xerFlx N(d)) 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(d,) and NCC.)= estimates 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 TRF = 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 Variable Value Project's cost of capital 11.00% Current value of the delayed investment (P) N(d,), as estimated by Luana $2.80 million N(d), as estimated by Luana Delayed investment's strike price (X) $4.48 million Mathematical constant e $2.24 million Risk-free rate (rRF) $3.36 million Time until the option expires (t) Variable Value Project's cost of capital 11.00% Current value of the delayed investment (P) N(d,), as estimated by Luana 0.7573 N(d), as estimated by Luana 0.7082 Delayed investment's strike price (X) Mathematical constant e $2.40 million Risk-free rate (rRF) Time until the option expires (t) $ 6.00 million $4.00 million Given these values, the estimated value of Fat Sh lion using th $3.00 million final answer to three decimal places.) N(d.), as estimated by Luana 0.7082 $0.236 million Delayed investment's strike price (X) Mathematical constante 2.7183 $0.002 million Risk-free rate (PRF) 0.04% $0.378 million Time until the option expires (t) $0.189 million Given these values, the estimated value of Fat Sheep's growth option using the Black-Scholes OPM (V) is (Note: Round your final answer to three decimal places.) Variable Value Project's cost of capital 11.00% Current value of the delayed investment (P) 3 years N(d), as estimated by Luana N(d), as estimated by Luana 4 years Delayed investment's strike price (X) 5 years Mathematical constant e 2 years Risk-free rate (rRF) Time until the option expires (t)
