Exercise 4-4 Investment decision making under uncertainty -

Decision tree analysis:flexible planning Close to a castle, possibly nominated for the list of the UNESCO World Heritage, an investor wants to build a leisure park. The listing would significantly increase the name recognition of the castle and therefore bring so many users into the leisure park as to assure its success. The investor has to decide to either build a huge park immediately or to wait until he could be sure of the development of demand. In this case, he would build only a small park with the option to expand after the first period. The immediate investment into a large-scale park is less expensive but also more risky than the split into two smaller investments. In case of an extension of the small investment in period 2, paybacks of the same amount as with a largescale investment are possible.

We look at a time horizon of two periods. The appropriate discount rate is 10 %. These are the cash outflows of the investment in MU, whereas the sum for the enlargement of the small facility in t! is the already discounted value to period to:

Point in time to Point in time t Large facility Small facility Enlargement of the small facility 140 -80 0 0 0 -80 The cash flows in each period depend on the development of the state of the economy. The following probabilities of occurrence are estimated for the state of the economy:
Period 1 p(h1) = 0.9;p(l,) = 0.1 Period 2 p(h2/h1) = 0.9;p(l2/h1) = 0.1 p(h2/l1) = 0.1;p(l2/l1) = 0.9 The estimated cash flows in each period will be as follows:
Present value cash flow in period 1 Present value cash flow in period 2 High demand Low demand High demand Low demand Small facility 50 30 50 30 Large facility 80 30 80 30

a) Diagram a decision tree to structure the decision management is facing.

b) Calculate the net present values for the outcome nodes in period 2.

c) State clearly whether the investor should start small and if appropriate enlarge the facility after period 1 or whether it is more attractive to start right away with a large facility.