Assume that ABC is considering opening an ice cream shop in Amsterdam. The shop will cost 1.8 million Euros, and the present value of the expected cash flows from the store is 1.4 million Euros. Thus, by itself, the shop has a negative NPV of  €0.4 million. Assume, however, that by opening this shop, ABC acquires the option to expand into a much larger ice cream and dessert shop any time over the next 5 years. The cost of expansion will be €4 million, and it will be undertaken only if the present value of the expected cash flows exceeds €5 million. At the moment, the present value of the expected cash flows from the expansion is believed to be only €4 million. If it were not, ABC would have opened the larger shop right away. ABC  still does not know much about the market for its ice cream and desserts in the Netherlands, and there is considerable uncertainty about this estimate: the annual standard deviation of the returns on the larger shop is 0.3. The risk-free interest rate is 3% per year. 

a) Construct the five-year price tree for the larger shop using Dt = 1 year.

b) Since ABC can open the larger shop at any time, determine the nodes in the tree that you constructed in part a) at which it is optimal to open the shop (we are assuming that the decision to open the shop will be discussed at ABC only once per year). Modify the tree to reflect the early exercise of the option.

c) Determine the present value of the option of opening the larger store. Does it make sense for ABC to invest in the loss-making, smaller shop now?