4. Investment timing option - Decision tree and the Black-Scholes valuation

Suppose a technical glitch in the trading systems in the stock markets led to several erroneous trades.

Soon after, Lesnor Co., a professional training company, came up with the idea of developing a new division that would teach securities traders to communicate by using an old style of hand language on the trading floor, which would help revive that dying language.

A young product development employee, Ryan, proposed this idea and also submitted the following details about the project:

	The division would need an initial investment of $4.0 million.
	Ryan expects that this division will bring in an additional $3.5 million at the end of each of the next five years.
	The projects cost of capital is 9%, and the risk-free rate is 4%. The WACC is used to discount all cash flows.

Based on the given information, what is the projects expected net present value (NPV)? (Note: Do not round intermediate calculations.)

$7.69 million

$10.57 million

$9.61 million

$14.42 million

After further research, Ryan added a few more details about the project to the proposal. When Ryan submitted the proposal, he again included the probability of the projects success based on whether a financial services tax would be imposed on the revenues from the project for stock broker training.

Based on discussions with lawyers, there is a 60% chance that the tax would not be imposed, in which case the project would generate a cash flow of $5.3 million. If a financial services tax is imposed, the project would generate a cash flow of $0.8 million. Lesnor Co. now has the option of knowing about the tax situation before it commits to the project.

Lesnors management decides to wait for a year before they make a decision on launching the project. However, Ryan mentions that the cash flow estimations for the project will remain valid only for the next five years. (For valuation purposes, the project has the same end date even with the option of waiting.) In the meantime, the managers decide to invest $4.0 million in securities for one year, which is expected to generate a rate of return equal to the projects cost of capital.

Based on the information that Ryan submitted in his report, calculate the values in the following table. Use the WACC to discount all cash flows. (Note: Do not round intermediate calculations.)

	Value
NPV of the project after one year
Option value of waiting

Using the BlackScholes option pricing model (OPM), Ryan takes his research a step further and calculates more variables to find the value of the option of waiting for one year to accept or reject the project. He uses N(d) = 0.8544, N(d) = 0.8425, and 2.7183 as the approximate value of e. If Ryan uses the BlackScholes OPM, what will be the value of the option of waiting for one year? (Note: Do not round intermediate calculations.)

$5.65 million

$6.78 million

$3.96 million

$7.35 million