In order to evaluate the NPV of the first-generation phone (project) ignoring the possibility of investing in the second-generation phone (project), we projected the free cash flows (FCF) of the first-generation phone through 2001 to 2006. The total FCF was calculated as EBIT plus deprecation and subtract any capital expenditures along with change in net working capital. With risk-free rate of 10%, comparable firms’ beta of 1.2, and market premium of 4%, the appropriate discount rate for the project was 14.8% using CAPM. Sum up each discounted cash flow, the NPV of the first-generation project was – $3,370,071. Since we got a negative NPV, we recommended that Penelope shouldn’t invest in the first-generation project alone. The option for Penelope to make the follow-on investments can be treated as a call option. Therefore, we evaluated the expected value of the second-generation project by using Black-Scholes.

If Penelope wanted to justify investing in the first-generation project by investing in the second-generation project, they would need the total APV equal or greater than zero, which means the sum of NPV of the first-generation project (- $3,370,071) and value of the call option to make the follow-on investment should be equal or greater than zero. The cost of second-generation project of $100 million was equivalent to the exercise price in Black-Scholes formula; its present value in 2001 was $68,301,346 (discounted at 10% risk-free rate). The value of the second-generation project was the asset price in Black-Scholes formula. Using solver function in excel, we calculated the value of the second-generation project by changing the value of the second-generation project to set APV equal to zero (or value of call option equal to $3,370,071). The current expected value of the second-generation project was $20,418,676 given the above assumption.

That is, if the current value of the second-generation project was equal or greater than $20,418,676, Penelope could expect generating profit from investing in both first- and second-generation project. The third scenario was ignoring the option to invest in the second-generation project and selling the equipment in year 2. We evaluated this option as a put option. First, we calculated the probabilities for going up and down based on the assumption of a risk neutral word. As a result, the probability of going upward is calculated as 0.3375 and downward probability is 0.6625. In order to determine the present value of all the sequence cash flow at the end of year 2, we calculated the upside change rate and downside change rate as 64.87% and -39.35%, respectfully.

The next step is to analyze the option value by using the “Binomial Tree” method. In order to determine the present value of all the subsequence cash flow at the end of year 2, we calculated the cash flow at each node on the tree, until 2006. We discounted all the cash flow at the risk free rate at 10%. The End of Year NPV of all the subsequence cash flow at Year 2 is calculated as $7,571,752, and the selling price of the equipment at end of 2 is $4,000,000, which is the salvage value. We found the NPV of selling the machine at end of Year 2 to be -$2,951,861 as of Year 0, which is negative. The APV of the project after adding the option turned out to be -$6,321,932. This negative APV suggest that the company should not undertake the project.