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 Blue Gorilla Media Company:

Blue Gorilla Media Company, a social networking company, has seen triple-digit growth in its websites registrations over the past two years. Most of the websites subscribers live outside the United States, and the company is seeing a significant increase in the number of users from Brazil. As a result, Blue Gorilla 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. Managements uncertainty is the result of the possibility that Brazils Internet connectivity will be insufficient to support all of Blue Gorillas forecasted growth.

One of Blue Gorillas 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 $6.00 million.
	According to research on Brazils mobile technology infrastructure, Isabela noted there is a 60% probability that the countrys mobile connectivity will be sufficient to generate additional advertising cash flows of $9.00 million per year for the company for the next five years.
	Alternatively, there is a 40% chance that Brazils mobile Internet connectivity will be insufficient to support Blue Gorillas desired growth in Brazil. In this case, the company expects to generate additional net advertising-related annual cash flows of only $3.00 million for the next five years.
	The projects expected cost of capital is 14.00%, and the risk-free rate is 4%. The projects WACC should be used to discount all cash flows.

Given this information, the projects expected net present value (NPV) without the consideration of the growth option is . (Note: Round all calculations to two decimal places.)

After further research, Isabela added a few more details to her proposal:

	If Brazils Internet connectivity is good, then at the end of Year 3, Blue Gorilla should consider investing $4.50 million to purchase an existing Brazilian marketing firm and creating a new subsidiary.
	The new subsidiary is expected to generate $3.60 million of additional annual cash flows in years 4 and year 5.
	However, if the Internet connectivity in Brazil is inadequate to support Blue Gorillas 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 Isabelas 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 projects 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, Isabela wants to use the the BlackScholes 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(d1))(X erRFt N(d2))V=P Nd1X erRFt Nd2

where,

	P = the current, or a proxy, price of the value of the underlying asset (P)which equals the present value of the delayed projects forecasted future cash flows
	N(d) and N(d) = estimates of the variance of the projects expected return
	X = the options strike price, which is the cost of purchasing the Brazilian firm that will become the Blue Gorillas subsidiary
	e = the mathematical constant equal to 2.718281828459045235360..., which can be truncated and rounded to 2.7183
	rRFrRF= the markets 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
Projects cost of capital	14.00%
Current value of the delayed investment (P)
N(d), as estimated by Isabela	0.7573
N(d), as estimated by Isabela	0.7082
Delayed investments strike price (X)
Mathematical constant e	2.7183
Risk-free rate (rRFrRF)	0.04
Time until the option expires (t)

Given these values, the estimated value of Blue Gorillas growth option using the Black-Scholes OPM (V) is . (Note: Round all calculations to two decimal places.)