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 finandal 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 Brazi. 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 ite 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, Lsabela, 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 fracil's moblle tectinology infrastructure, Isabela noted there is a 6096 probability that the country's moble connectivity will be sufficient to oenerate additional advertising cash flows of $6.00 million per year for the company for the next five years. - Atternatively, there is a 405 , chance that Braal's mobile Internet connectivity will be insufficient to sopport White Fox's desired growth in Brazll. In this case, the company expects to qenerate additional net advertising-related annual cach flows of only 52.00 million for the next five yeart. - The project's expected coit of capital is 11.005, and the risk-tree rate is 4%. The project's wacc should be wsed to discount all cash Hows. Given this information, the projects expected net present valje (NPV) without the consideration of the oronth option it (Note: flound all calculations to two decimal places.) Ateen further research, fabela added a few more detalls to her proposal: - If Brazil's Internet connectivity is good, then at the end of Year 3, White Fox should consider investing $3.00 million to purchase an existing Braxilian 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 Brazi is inadequate to support White Fox's desired aistomer arowth, 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 analyss to calculate the woy of the project including the growth option. Then. alculate the value of the growth option by itseif, and select the correct answers from the choicar available in the following table. Remember to uset he projects cost of capltal to discount ail cash flows. (Note: Round all answers to two decimal Dlyces.) V=(PN(d1))(XetztN(d2)), 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(d1) and N(d2) = 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 2.718281828459045235360 which can be truncated and rounded to 2.7183 Tay - 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: Glven these values, the estimated value of White Fox's growth option using the Black-schiles opM (V) is (Note: Round all calculations to two decimal places.)