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. 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, Luana, who is originally from Brazil, conducted yome 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, Luana 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) $12.68 million $22 19 million After further research, Luann added a few more details to her proposal $3487 million 1 Brazil's Internet connectivity is good, then at the end of Year 3, White Fox should consider Investing $3.75 min 515.85 million 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 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. (Note: Round all answers to two decimal places.) Value NPV of the project with growth option Growth option value 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 additonal variables, and has given you the Black-Scholes OPM equation for the valuation of an option (V) V=(PxN()) - (XXe MIX 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 (du) and N (da) 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 White Fox's subsidiary e=the mathematical constant equal to 2.718261828459045235360..., which can be truncated and rounded to 2.7183 THF = 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 A Option 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 According to Luana, these variables should assume the following values: Value 10.00% 0.2573 Variable Project's cost of capital Current value of the delayed investment (P) Nd), as estimated by Luana N(d), as estimated by Luana Delayed investment's strike price (x) Mathematical constante Risk free rate (re) Time until the option expires (t) 0.7062 2.7183 0.04 (Note: Round al Given these values, the estimated value of White Fox's growth option using the Black-Scholes OPM (V) is calculations to two decimal places) 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. 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, Luana, who is originally from Brazil, conducted yome 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, Luana 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) $12.68 million $22 19 million After further research, Luann added a few more details to her proposal $3487 million 1 Brazil's Internet connectivity is good, then at the end of Year 3, White Fox should consider Investing $3.75 min 515.85 million 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 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. (Note: Round all answers to two decimal places.) Value NPV of the project with growth option Growth option value 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 additonal variables, and has given you the Black-Scholes OPM equation for the valuation of an option (V) V=(PxN()) - (XXe MIX 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 (du) and N (da) 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 White Fox's subsidiary e=the mathematical constant equal to 2.718261828459045235360..., which can be truncated and rounded to 2.7183 THF = 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 A Option 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 According to Luana, these variables should assume the following values: Value 10.00% 0.2573 Variable Project's cost of capital Current value of the delayed investment (P) Nd), as estimated by Luana N(d), as estimated by Luana Delayed investment's strike price (x) Mathematical constante Risk free rate (re) Time until the option expires (t) 0.7062 2.7183 0.04 (Note: Round al Given these values, the estimated value of White Fox's growth option using the Black-Scholes OPM (V) is calculations to two decimal places)