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 White Fox Media Company: White Fox 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, White Fox 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 White Fox's forecasted growth. One of White Fox'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 $5.00 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 $7.50 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 White Fox's desired growth in Brazil. In this case, the company expects to generate additional net advertising-related annual cash flows of only $2.50 million for the next five years. The project's expected cost of capital is 10.00%, and the risk-free rate is 4%. The project's WACC should be used to discount all cash flows. (Note: Given this information, the project's expected net present value (NPV) without the consideration of the growth option is Round all calculations to two decimal places.) $15.85 million $12.68 million $22.19 million $34.87 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, White Fox should consider investing $3.75 million to purchase an existing Brazilian marketing firm and creating a new subsidiary. The new subsidiary is expected to generate $3.00 million of additional annual cash flows in years 4 and year 5. However, if the Internet connectivity in Brazil is inadequate to support White Fox'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. (Note: Round all answers to two decimal places.) Value NPV of the project with growth option $16.51 million, $9.91 million, $26.42 million, or $29.01 million Growth option value $1.320 million, $0.66 million, $0.792 million, or $0.528 million 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 x N (di)) (X x e-Trf tx N (dz)) 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(d1) = estimates of the variance project's expected return X = the option's strike price, which is the cost of purchasing the Brazilian firm that will become the White Fox's subsidiary e = the mathematical constant equal to 2.718281828459045235360..., which can be truncated and rounded to 2.7183 PRF = 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 Value Project's cost of capital 10.00% $1.83 million, $2.19 million, $4.39 million, or $3.65 million Current value of the delayed investment (P) N(d), as estimated by Isabela N(dz), as estimated by Isabela 0.7573 0.7082 Delayed investment's strike price (X) $16.51 million, $5.00 million, 4.48 million, or $3.75 million According to Isabela, these variables should assume the following values: Variable Value Project's cost of capital 10.00% Current value of the delayed investment (P) N(di), as estimated by Isabela 0.7573 N(dz), as estimated by Isabela 0.7082 Delayed investment's strike price (X) Mathematical constant e 2.7183 Risk-free rate (rRF) 0.04 Time until the option expires (t) 6 years, 1 year, 2 years, or 3 years Given these values, the estimated value of White Fox's growth option using the Black-Scholes OPM (V) is (Note: Round all calculations to two decimal places.) $0.25 million, $0.41 million, $0.66 million, $0.53 million 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 White Fox Media Company: White Fox 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, White Fox 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 White Fox's forecasted growth. One of White Fox'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 $5.00 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 $7.50 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 White Fox's desired growth in Brazil. In this case, the company expects to generate additional net advertising-related annual cash flows of only $2.50 million for the next five years. The project's expected cost of capital is 10.00%, and the risk-free rate is 4%. The project's WACC should be used to discount all cash flows. (Note: Given this information, the project's expected net present value (NPV) without the consideration of the growth option is Round all calculations to two decimal places.) $15.85 million $12.68 million $22.19 million $34.87 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, White Fox should consider investing $3.75 million to purchase an existing Brazilian marketing firm and creating a new subsidiary. The new subsidiary is expected to generate $3.00 million of additional annual cash flows in years 4 and year 5. However, if the Internet connectivity in Brazil is inadequate to support White Fox'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. (Note: Round all answers to two decimal places.) Value NPV of the project with growth option $16.51 million, $9.91 million, $26.42 million, or $29.01 million Growth option value $1.320 million, $0.66 million, $0.792 million, or $0.528 million 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 x N (di)) (X x e-Trf tx N (dz)) 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(d1) = estimates of the variance project's expected return X = the option's strike price, which is the cost of purchasing the Brazilian firm that will become the White Fox's subsidiary e = the mathematical constant equal to 2.718281828459045235360..., which can be truncated and rounded to 2.7183 PRF = 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 Value Project's cost of capital 10.00% $1.83 million, $2.19 million, $4.39 million, or $3.65 million Current value of the delayed investment (P) N(d), as estimated by Isabela N(dz), as estimated by Isabela 0.7573 0.7082 Delayed investment's strike price (X) $16.51 million, $5.00 million, 4.48 million, or $3.75 million According to Isabela, these variables should assume the following values: Variable Value Project's cost of capital 10.00% Current value of the delayed investment (P) N(di), as estimated by Isabela 0.7573 N(dz), as estimated by Isabela 0.7082 Delayed investment's strike price (X) Mathematical constant e 2.7183 Risk-free rate (rRF) 0.04 Time until the option expires (t) 6 years, 1 year, 2 years, or 3 years Given these values, the estimated value of White Fox's growth option using the Black-Scholes OPM (V) is (Note: Round all calculations to two decimal places.) $0.25 million, $0.41 million, $0.66 million, $0.53 million